Analyses of Linear Encoder Application (Glass Scale) on Quality of Machining Centre by Santiago M....

Politechnika

WROCŁAWSKA

WYDZIAŁ

MECHANICZNY

PRACA DYPLOMOWA MAGISTERSKA

TEMAT:

Analyses of linear encoder application (glass scale) on quality of machining centre

Promotor: Realized by:

Dr inż. Zbigniew Kowal Santiago Manuel Vilar Blanco

WROCLAW, Poland July 2010

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Index

1. Introduction……………………………………………………………………………………………………………..3

2. Aim and range of necessary analyses of linear encoder application (glass scale) on

quality of machining centre………………………………………………………………………………………….3

3. Define by drawing a dependency diagram quality of machining centre……………………5

3.1 Issues needed to obtain quality of machining centre………..……………………………..17

4. Design of geometric models for simulation of machining centre in FEM method

4.1 Geometrical model of the machine tool with ball screw…………………………...….…19

4.1.1 How to design geometrical model………………………………………………………….20

4.1.2 Assembly the geometrical model…………………………………………………………..26

4.2 Geometrical model of the machine tool with glass scale…………………………………28

5. Boundary conditions for finite elements thermal models……………………………………...37

5.1 Analysis of Power Losses………………………………………………………………………………...37

5.1.1 Power Losses in ball screws…………………………………………………………………..37

5.1.2 Power losses in motors………………………………………………………………………….41

5.1.3 Power losses in bearings……………………………………………………………………….43

5.2 Analysis of forced and natural convection………………………………………………………45

5.3 Machine tool model for analyze temperature with SimDesigner R2……………….48

6. Machine Tool Model for analyze deformation with CATIA V5R17………………………...58

6.1 Boundary conditions for finite elements deformation models……………….……….58

6.1.1 Define connection property to assembly constrains……………………………..59

6.1.2 Load data of temperature distribution obtained by SimDesigner

R2……………………………………………………………………..………………………………….66

6.1.3 Define local sensors to measure deformations……………………………………..67

7. Design plan of computing……………………………………………………………………………………..70

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7.1 Operating conditions and positions………………………………………………….………........70

7.2 Design of working cycle…………………………………………………………………….……………..72

7.3 Selected data for analyses…………………………………………………………….………………...75

8. Results of computing and conclusions……………………………………………………………………75

8.1 Analyses of displacements at position BEH……………………………………………………..77

8.1.1 Analyses of work cycle with initial temperature 293K at BEH………………..77



8.1.4 Conclusions at position BEH with different initial temperatures……………83

8.2 Analyses of displacements at position CFG……………………………………………………..85

8.2.1 Analyses of work cycle with initial temperature 293K at CFG…….............85



8.2.4 Conclusions at position CFG with different initial temperatures……………90

8.3 Conclusions drawn from computing analysis…………………………………………………..91

9. Conclusions leading to improve of machining centre design………………………………….93

10. Attachments……………………………………………………………………………………………………..…94

11. References………………………………………………………………………………………………………...132

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1. Introduction

Thermal deformation at machining centre induces errors that reduce the accuracy in

precision machining. This thermal deformation is caused by high speed spindles

rotation and environment changes. There are a lot of studies in order to reduce these

errors and increase accuracy of machining centre, which information was taking as a

knowledge base for this project. Some of these papers are Particular behavior of

spindle thermal deformation by thermal bending by Tae Jo Ko, Tae-‐weon Gim and Jae-‐

yong Ha; Thermal behavior of a machine tool equipped with linear motors by Jong-‐Jin

Kim, Young Hun Jeong and Dong-‐Woo Cho; Thermal Error Measurement and Real Time

Compensation System for the CNC Machine Tools Incorporating the Spindle Thermal

Error and the Feed Axis Thermal Error by H.J. Pahk and S.W. Lee. The solution proposed

in this project to reduce the errors caused by thermal deformation in the way to

increase accuracy precision machining is to use linear encoders, glass scale, to

determine position of headstock and work piece by reading heads to these linear

encoders.

2. Aim and range of necessary analyses of linear encoder application (glass scale) on

quality of machining centre

The main aim of this project will be to recognize, in operational conditions, influence of

machining centre thermal behavior on machining error for circular encoder where

position of headstock and work piece is determine by number of rotations of the ball

screw and linear encoder where this position is determine by reading head at the glass

scale. This aim involves the following range of project:

§ Working out geometric model suitable for simulation of machining centre in

FEM method.

§ Preparing such data as material constants, bearings preload and tolerances,

lubrication, operating conditions, cooling system and data related to

distribution of power losses.

§ Working out FEM model for simulation of temperature distribution.

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§ Working out FEM model for simulation of deformation.

§ Determine factors influence on values of machining error for milling machine.

§ Working out the plan of computing in chosen operating conditions and

positions.

§ Working out the result of computing.

§ Creating a conclusion leading to improving of machining centre design by

proper application of measuring system base on linear encoder.

Once we know the aim and the range of the project we have to say that the most

obvious characteristic of the design problem is that it is complex because there are so

many aspects like power losses, ambient temperature, materials thermal conduction

and expansion coefficients, forced and natural convection, etc to our design problem.

It is impossible to deal with all the aspects at once. Design problem have to be broken

down into easy sub problems like build different models one for analyze temperature

distribution and one for analyze deformation, which can be analyzed separately. The

design process is open in the sense that the boundaries of the process are not limited.

There are the undetermined goals, the means to achieve them, the issues and options

to be considered, time and money and so on. These means that there is not a

prescribed set of solutions, in other words, design calls for creativity and ingenuity.

We are going to design a dependency diagram from idea of expert system creation as

an assessment guideline for this project. An expert system is a collection normally

composed of a knowledge base, the analysis of this knowledge and the end users

interface. Knowledge acquisition for expert systems is a practical problem to be solved

by experiments (in this project by computer simulation with CATIA V5R17 and

SimDesigner R2 software). The knowledge that the expert provides varies with the

context and gets its validity from its ability to explain data and justify the expert

judgment.

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3. Define by drawing a dependency diagram quality of machining centre

A dependency diagram is a visual representation of the factors that affects to our

project and the relationship of those factors. The dependency diagram is an essential

tool for representing information and makes easy the rule creation process. The

diagram consists of multiple nodes, rectangles, each of which represent an important

factor to the problem. Nodes are connected by arrows that portray the dependencies

which exist among the data variables. Variables which make a direct interference to

the goal variable are referred to as first-‐level concept variables. Bottom-‐level concept

variables are affected by raw data input variables. Raw data input variables directly

accept input data from the expert system.

GOAL

values

First LevelConcept variable

values

First LevelConcept variable

values

SecondLevelConcept variable

values

SecondLevelConcept variable

values

Bottom LevelConcept variable

values

Bottom LevelConcept variable

values

Raw input data variable

values


values


values


values

Fig 3.1 Dependency diagram format [9]

Depending on the problem that we want to solve there are three possible approaches:

goal-‐driven, relationship-‐driven and data-‐driven. In most of the cases it is enough to

construct the dependency diagram by using only one of these approaches, but it could

be possible also in some cases to use a combination of all three to achieve the final

diagram. To use the goal-‐driven approach, specify the goal first and then ask the

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question “what information does the expert system need to consider in order to make

a decision about the goal?” In this approach first specify top of the diagram (the goal

variable) and work down toward the raw data input. The data-‐driven approach is used

to construct a dependency diagram beginning by making a list of all know input data

and information important to the problem domain. This method of drawing the

dependency diagram uses a bottom-‐up approach. First specify the bottom level and

work up toward specifying the goal variable. The relationship-‐driven approach is used

to describe problems by outlining existing relationships which directly affect the

outcome of a decision. With this approach, establish separate relationships by

grouping them as intermediate, first and bottom-‐level concepts that eventually direct

you to the goal variable and data input. Attending to the aim of this project, analysis

on quality of a machine centre using a glass scale as a linear encoder, it is easy to

choose the appropriate approach thinking that our goal is the main aim of this project.

That is why we use the goal-‐driven approach to design our dependency diagram.

First step to design the dependency diagram using the goal-‐driven approach is to

identify the goal. In this project the goal is Analyses of application linear encoder (glass

scale) on quality of machining centre. The variable used to represent this goal is called

quality of machine tool. Bellow this variable there is a list of kind of values that the

variable can accept as in figure 3.2

Fig 3.2 Identifying the goal variable

Step two is to make a list of the items that need to be considered by the expert system

to determine a value for the goal. These are the factors that determine how much

quality of the machine tool is. It is a very important step in this project: To define in a

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correctly way these factors to design the best possible dependency diagram, because

this diagram is going to be the roadmap of the project.

To know which factors have influence on machine tool quality it is necessary to start

analyzing all the different possible factors and then choose the ones that really have a

direct influence on the goal.

In general terms referring to the accuracy of work pieces, the errors making on

accurate length or circle and in testing these, should be no greater than 1.0-‐0.3 µm.

The base guide of precision surface-‐grinding machine should be made so that the

deviations from linearity should be no greater than 1-‐2 µm in 500 mm. The measuring

errors in testing the linearity and flatness of precision guides should be no greater than

±0.0005 mm. The accuracy of the machines and tools depends on the accuracy of the

measuring systems built into them. About the measuring systems we have to consider

the errors in the measuring system itself (the difference of the nominal and actual

value of the total length of the measuring system or the length of its scale divisions)

and also the errors in testing this measuring system. A major proportion of the errors

in measuring systems depend on the total length of the measuring system according to

the All-‐Union State Standard 12069-‐66, should be expressed in the form:

∆= ! + !"

Where a is the constant part and bl is the component of error depending on the length

of the measuring system (temperature errors, misalignment of the measuring system,

etc).

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Fig 3.3 List of the formulas for linear displacements in different machines and also the

classes of accuracy of graduated measuring systems which, according to the All-‐Union

State Standard 12069-‐661, may be used as scales for these machines [6].

The temperature has also a big influence on the quality of a machine tool. The effects

of the temperature must be analyzed to reduce thermal induced deformations in

machine tools to avoid displacements between tool and work-‐ piece. To solve this

problem we need to do an analysis of different heat sources and how their

deformations are. Failures on geometric of the work-‐piece can be produced by

deformations on the machine tools, causes by internal and external heat sources.

1 The new standards for plane-‐parallel end-‐type length measuring systems in general correspond to the international norms indicated in the recommendations of the Comecon organization and also to the 1973 recommendation of the International Organization for the Unification of Measurements MOZM No. 30.

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Fig 3.4 Illustrates different heat sources and different ways of heat transfer over the

machine structure causing size and geometric errors in the measuring system, the

machine structure and finally in the work-‐piece. [5]

Heat sources can be classified as internal and external. Internal sources are basically

heat produced by running the machine and the process of machining. External sources

are changes in environment e.g. solar radiation, lightning etc. Referring to external

heat sources, variation of the ambient temperature causes temperature vertical and

horizontal gradients that cause thermo-‐elastic deformations of the machine tools.

Figure 3.5 shows the solar energy radiation over a 12 month period for Frankfurt and

the temperature range over the same time. Also shows the variation of the

temperature in a machine shop. So the amplitude of the temperature will vary with

geographical location, the season and the thermal characteristics of the machine shop.

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Fig 3.5 Shows a not unusual variation of 5 oC during the winter and 15 oC during the

summer time. [5]

On figure 3.6 is illustrated how a rapid ambient temperature of 10 oC causes radial

displacements on a lathe. During the first three hours after the temperature rise the

distance between tool and spindle reduces quickly by 40 µm followed by a low

increase during the next 8 hours. This means that the machine has large time

constants in reacting to ambient temperature changes.

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Fig 3.6. Machine reaction to ambient temperature changes. [5]

Thermal deformation also depends on the geometry of the machine. It is good to make

equal the time constants for different components of the machine to reduce thermal

deformations caused by external heat sources. Figure 3.7 shows this effect for a portal

of a milling machine. Because of different wall thicknesses of the front and back of the

column, the back gets warm up faster in the morning when the hall temperature rises

and cools down more quickly in the afternoon than the front wall. This results also on a

deformation of the machine. To avoid this effect, it is possible to insulate the thin wall

with polystyrene, so the time constants can be more equal and the deformation cause

by temperature changes were substantially reduced.

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Fig 3.7 Shows thermal deformations caused by external heat sources on a milling

machine. [5]

Referring to internal heat sources, these ones directly conduct the heat into the

machine structure and causes thermal deformation. One of the most important heat

sources is the spindle system and its bearing. Depending on the bearing type and on

the diameter of the spindle the power losses can be up 100W for a 100mm ball bearing

running at 10000rpm and up to 1kW for a hydrostatic bearing of the same size and

speed rotation. The roller bearings, the ball-‐screw and its nut must take in

consideration. Due to a study of Schulz and Schmitt the main heat source is the ball

screw and its nut. Another internal heat source is the cutting process itself, which

warm ups the tool, tool-‐holder, work-‐piece and clamping device. In the same way the

table, machine and other components can also be heated up indirectly by hot chips.

Making an analysis of all these information it is possible now to define the factor that

have a direct influence on the quality of machine tool (goal). This quality depends on

one side by the design conditions of the work piece; this is the accuracy of the work

piece. On the other side, quality of machine tool also depends on the error that the

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machine makes at the production of the work piece caused by the different heat

sources and ambient temperature variations. These variables are referred to first level

concept variables. Variable names are going to be accuracy of work piece and

machining error. In this case the values that these variables can accept are going to be

the same in the two cases, µm, as in figure 3.8. If value of machining error is X µm and

value of accuracy of work piece is Y µm with X<Y then value of quality of machine tool

is good. If value of machining error is X µm and value of work piece is Y µm with X>Y

then value of quality of machine tool is poor.

Fig 3.8 Representing first level concept variables.

Step three on designing dependency diagram is to list the items that need to be

considered by the expert system to make a decision about each first level concept

variable listed in step two. This step is basically the same than step two but now

referring to the first level concept variables, accuracy of work piece and machining

error, instead to the goal variable (quality of machine tool).

There are three main factors that have influence on the accuracy of work piece. First

one is the final work piece finish. In this case this variable is going to be called as

roughness. The values that can be accepted by this variable are going to be also µm.

Second one is the range of values where dimensions of work piece must be to be

considered as valid. This variable is going to be called tolerance. There values that can

be accepted by tolerance are going to be standard tolerances that are common in work

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pieces for this machine centre, H/h 7,6,5. As we see on figure 3.9, table shows that

there is a relation between tolerance and dimension of work piece; that is why

dimension of work piece is going to be another factor with influence on the accuracy

of work piece.

Fig 3.9 Tolerance table. As we can see there is a relation between the tolerances and

dimension of work piece.

Referring to the other first level variable, machining error, there are two main factors

that have influence on it. In one hand we have errors on the work piece because

displacement of the tool. The tool of the machine centre has direct dependency with

the spindle, if the spindle varies the position the tool will move also. This variable is

going to be called end of spindle displacement. On the other hand there are errors at

the work piece because the work piece itself is no located at the exactly position. This

variable is going to be called as displacement of work piece. As we can see on figure

3.10 there is now defined the second level concept variables.

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Fig 3.10 Representing the second level concept variables.

Next step is to define the factors that have influence in the second level concept

variables. In this case there is only necessary to define third level concept variables for

end of spindle displacement and displacement of work piece because these second

level variables have dependency on many other factors. In case of roughness,

dimension of work piece and tolerance of work piece there is no necessary to define

third level concept variables because there data and have no dependency on any other

factors. End of spindle displacement and displacement of work piece have their

dependency on the same factors because both of them are displacements at the end.

Depending on the configuration of the machine centre, with or without glass scale, the

displacement at these two points should be different as different should be the

behavior of the machine centre during thermal deformation for these two different

configurations. This third level concept variable is called as equipment and as we said

the values that can be accepted by this variable are ball screw, referring to machine

centre without glass scale, and glass scale for the machine centre with this linear

encoder. There are also two more factors that have influence on end of spindle

displacement and displacement of work piece. These are in one hand the position

where the machine centre is working and where it is going to work, in other words, the

direction and position of work. On the other hand the displacements depend also on

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the state before and during the working conditions of the machine centre. This factor

is called as time. We can see third level concept variables in the next picture.

Fig 3.11 Representing the third level concept variables.

Next step is to define the factors that have influence in the third level concept variables, direction & position and time. For the first one the factors are as it said direction of machining and position of machining. For the variable time, this depends on the cycle of machining and also on ambient temperature. All these four level concept variables there have no dependency on any other factors, there are data, that is why these four level concept variables are bottom level variables and that means that the dependency diagram is finally designed as we can see on the next picture.

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Quality of Machine Tool

Accuracy of work piece

Machining Error

µm

µm

GoodPoor

Roughness

Dimension of work piece

Tolerance of work pieceH7H5H6

End of spindle displacement

Displacement of work piece

Equipment

Direction and

Position

Time

Ball ScrewGlass Scale

Direction of machining

Position of machining

Cycle of Machining

Ambient Temperature

XYZ

Xa Ya ZaXb Yb ZbXc Yc Zc

X Y Z

A

B

C

rpm

h

Fig 3.12 Dependency diagram for analyses of linear encoder application (glass scale) on quality of machining centre

3.1 Issues needed to obtain quality of machining centre

The dependency diagram shows us now what issues must take in account to obtain

good or poor quality of machine tool. In one hand we must attend the design

conditions of the work piece, the characteristics that we want the work piece to own,

like the roughness and the tolerances. In the other hand there are the errors we made

during the process. These errors at the end depend on the equipment, direction of

machining, position of machining, cycle of machining and ambient temperature. The

main aim of this project is to analyze all this factors and how do they affect together to

the quality of machine tool. We will see how errors changes if also changes ambient

temperature. Also there is important to analyze the cycle of machining, if different

spindle speed rotations has or no influence on quality of machine tool or if for the

same spindle speed rotations we have or not errors depending on cycle position. As we

see on figure 3.1.1, work cycle for this project, point A and point B have the same

spindle speed rotation but the thermal conditions and deformations may not be the

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same there are at different positions in the cycle. We will also analyze this in order to

check if this difference has influence on quality of machine tool.

Fig 3.1.1 Point A and Point B have same spindle speed rotation but different position in

the work cycle.

Also it is important to analyze how direction of machining has influence or not on

quality of machine tool as well as the position of the table and headstock of the

machine centre. Figure 3.1.2, illustrates the three direction of movement each one

with a ball screw. Every ball screws as is fixed by one side with the motor and slides at

the other side. When machine starts working the thermal deformation will affect to

these ball screws and displacement also will depend if the headstock or table is near

the fixed point or not in order to the equation:

∆! = !"∆!

Where ∆L is the total displacement of the ball screw, β is the expansion coefficient, L is

the length between the nut and the fixed point of the ball screw and ∆T is the increase

of temperature of the ball screw.

Point B Point A

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Fig 3.1.2 Directions of movement of headstock and table of the machine centre.

4. Design of Geometric Models for simulation of machining centre in FEM method

4.1 Geometrical Model of the Machine Tool with Ball Screw

It is necessary to design a simple model of the machine tool in order to analyze it in the

computer system. If we simplify the machine tool we will obtain short times of

calculation.

Simplify the machine tool means to delete all the parts that do not have influence on

thermal behavior of the machine centre and also delete screws, shapes, pockets,

chamfers, draft angles etc, because there are an unnecessary number of objects that

are not necessary to be analyzed to compute displacements or Von Mises stress,

because they have not a direct influence on the behavior of the machine tool.

Figure 4.1.1 shows the production model of the machine tool while Figure 4.1.2 shows

the geometrical model of the machine tool with ball screw, the one we are looking for.

Direction X

Direction Z

Direction Y

Position of work piece

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Fig 4.1.1 Production model Fig 4.1.2 Geometrical model

4.1.1 How to design model

The first step to obtain a geometrical model of the machine tool suitable to analyze it

on CATIA is to delete all this aforementioned issues of the original machine tool model.

The best way to do this is to start simplifying part by part. As we see on Figure 4.1.1

there are many parts and shapes that may be susceptible to delete, e.g. the holes of

the base, the servomotors or the different chamfers.

Figure 4.1.1.1 illustrates all the parts that have been deleted from the production

model of machine tool:

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Fig 4.1.1.1 illustrates all the parts that have been deleted from the production model of machine tool.

Second step is to simplifly all the non-‐deleted parts in order to obtain short time of computation. In some cases there is only necessary to delete holes, pockets and chamfers, but in other cases is also necessary to change the shape of the part so we can obtain a simple design.

Figure 4.1.1.2 illustrates all the parts that have been modified from the production model:

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Fig 4.1.1.2 illustrates all the parts that have been simplify from the production model.

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Once we have simplified all the parts, we need to fix them in their correct position by using the assembly constrains. After we have totally assembly the machine tool we can analyze it with SimDesigner and create a thermal model for determine temperature. This model is also the start point for create a second model for determine deformation by CATIA.

4.1.2 Assembly the geometrical model

To obtain the machine tool model fully assembled, CATIA allow us to use a group of

different assembly constrains. In this case it is enough to use only two of them to have

assembly the machine tool. These are the contact constrain and the offset constrain.

Contact Constrain Offset Constrain

Fig 4.1.2.1 Offset Constrain

There are some cases where it is important to make sure the contact constrain makes

contact between two parts along all the contact surface instead of making the contact

only along a line. These are the cases of the screws with the house bearings as we see

on figure 4.1.2.2. To obtain the correct contact between these two parts it is necessary

that both of them have the same diameter. If not, there are going to be in contact

after using the assembly constrain but the contact between them is going to be only

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along a line. From the point of view of the assembly model this type of contact does

not represent a problem, but it is from the point of view of the temperature model and

deformation model, both of them created from this first assembly model.

Fig 4.1.2.2 contact between the screw and the house bearings

To make sure that the assembly of the machine tool is done correctly it is necessary to

explode the machine tool as we see on figure 4.1.2.3 and then do an update and check

that all the parts are fixed in their correct positions.

Fig 4.1.2.3 final aspect of geometrical model with assembly constrains in green.

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4.2 Geometrical Model of the Machine Tool with Glass Scale

This is a modification of the model with ball screw. To build this model it is necessary

to design new parts and later assembly them to the machine model with ball screw.

These new parts fixed together forms the glass scale. The glass scale is a linear encoder

that measures the position of linear axes without additional mechanical transfer

elements. With this linear encoder we eliminate positioning error due to thermal

behavior of the ball screw.

Optical encoders are normally used for high accuracy position measure system. In

order to determine the position, the optical encoders generate two electrical signals

that are combined using the arctangent algorithm [2].

In the case of this project these linear encoders are made up with an aluminum body

that has inside the scale, the scanning unit and the guide way. The scanning unit is

connected with the external mounting block as we see on figure 4.2.1. This encoders

incorporates measuring standards made of periodic structures know as graduations.

These graduations are applied to the glass so the absolute position information is read

from the scale graduation as we see on figure 4.2.2

Fig 4.2.1 Simplified representation of the LS 186 Sealed linear encoder [1]

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Fig 4.2.2 Graduations of absolute linear encoders and absolute code structure [1]

This linear encoder operates on the principle of photoelectric scanning. As we see on

figure 4.2.3, if the gaps between the scanning reticle and the measuring standard are

aligned, light passes through. If the lines of one grating coincide with the gaps of the

other, no light passes through. Photocell converts these variations on light intensity

into sinusoidal electrical signals.

Fig 4.2.3 Scanning principle [1]

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There are a number of situations, optical, mechanical and electronic that affects these

signals and produces an error in the position measurement. This error is important not

only for metrological purposes. In this case the encoder is used for the position

feedback and additionally the control electronics normally uses the measured data in

order to get the speed of the movement. Then the positional error is translated into

the speed calculation with the result of possible modifications on the dynamics of the

machine. With the two sinusoidal electrical signals, the relative displacement between

the scale and the reading head can be determined using the arctangent algorithm in

this way

!!"#$!% =!!!arctan (!!

!!) [2]

where !!"#$!% is the value of the displacement when it is calculated by the arctangent

algorithm. The two electrical signals can be described in this way

!! = !!!!(2!!!+ ∅!)+ !! [2]

!! = !!!! 2! !!+ ∅! + !! [2]

where !! and !! are the amplitudes, !! and !! are the background levels, ∅! and ∅!

are the phases of the signals and !! and !! are the functions that describe the shape of

the signals with min(Fα) = -‐1 and max(Fα) = 1. For the ideal case the parameters of the

equation are A1=A2=A, B1=B2=0, the phase between signals ∅! -‐ ∅! = ! /2 and the two

signals are sinusoidal F1 = F2 = sin. With non ideal electrical signals, the relative

displacement obtained using the arctangent algorithm is calculated by

!""#" ! = ! !"# ! − !!"#$!% [2]

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where mod id the modulus after division function. Then the linear term of the series

expansion with respect to the nominal values will produce an error that is described as

! ! = !"##$#(!)!" !!

∆! [2]

where g is any of the parameters of the electrical signals that may change from its

nominal value go to go + ∆g.

Fig 4.2.4 Experimental SA and SB sinusoidal signals. Theoretical signals are also shown.

They perfectly fit the experimental data. [2]

Fig 4.2.5. Experimental error in the position measurement obtained when the

measurement of the optical encoder is compared with an interferometer. Theoretical

error obtained for the arctangent algorithm and for linear series expansion. [2]

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In conclusion we can say that the accuracy of the linear measurement is determined by

the quality of the graduation, the quality of scanning, quality of the signal processing

electronics and the error from the scale guide way over the scanning unit, whereas this

error con be reduced by using the arctangent algorithm.

Deformations of the glass of the linear encoder can be caused by inappropriate

assembly or as a consequence of modification by the structure of the machine tool in

which the encoder is incorporated during working conditions.

Glass scale is normally fixe to the machine tool in the middle and both sides and more

if it is precisely. To make sure that the reading head is going to measure with the

correct accuracy it is necessary to assembly the linear encoder with deviations less

than 0,1 mm respect the measured direction.

Fig 4.2.6 Different deformations of glass scale on linear encoder. [3]

There are two most common cases of deformation of the glass scale (figure 4.2.6). The

deformation at the left side can be produced by two causes. First one because the

surface to be fixed the reading head it is not flat enough. Second one because of

changes on the geometry of the machine tool caused by changes on ambient

temperature or forces on the machine. Figure 4.2.7 shows the lost of accuracy of a

glass scale of 1 meter of length. In this graphic we can see that for each tenth of

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elevation on the middle of the glass scale, the linear encoder will have an error of 1,1

µm.

Fig 4.2.7 Precision of a glass scale fixed on the bottom (with two different widths) to

the machine tool. [3]

In second case (figure 4.2.6, right side), this kind of deformation makes variations

between the distances of the graduations of the glass scale (figure 4.2.2). This situation

is typical of a glass scale only fixed to the body of the machine tool by right and left

side. The weight of the glass scale makes this deformation (figure 4.2.8). In this case

the deformation is up to 3,2 µm for each tenth of deformation.

Fig 4.2.8 Precision of a glass scale fixed by right and left side to the machine tool. [3]

34

The just mentioned errors are the ones that owns to a glass scale but in case of this

project the errors we want to recognize and remove are the displacements produced

by thermal deformation caused by power losses. In case of model with ball screw

these displacements, ∆L, are calculated as the equation

∆! = !"∆!

where β is the thermal expansion coefficient of the ball screw, ∆T is the temperature

variation in the ball screw and L is calculated as

! = ! ∗ !!

where n are the number of rotations at the motor and lD is the lead of the screw.

For machine tool with glass scale the displacements, ∆L, are going to be calculated in

the same form

∆! = !"∆!

but in this case β is the thermal expansion coefficient of the glass, ∆T is the

temperature variation of the glass scale and L is the length from the fixed point of the

glass scale (middle point of the glass case in our case) and the reading head.

To obtain the geometrical model of the machine tool with glass scale, it is necessary to

design by CATIA V5R17 the linear encoder. This linear encoder is going to be

represented three new parts, the aluminum body (figure 4.2.9), the glass scale (figure

4.2.10) and the reading head (figure 4.2.11).

Fig 4.2.9 Aluminum body of linear encoder Fig 4.2.10 Glass Scale

35

Fig. 4.2.11 Reading head

It is necessary also to do specific shapes to the body of the machine tool where we

want to fix the linear encoder.

Fig 4.2.12 New shapes at the base of the table for supporting the glass scale.

Attending to the three directions of movement of the machine tool (figure 4.2.13),

there are a total number of seven possible combinations, glass scale on direction X

only, direction Y only, direction Z only, directions XY, directions XZ, directions YZ and

directions XYZ.

36

Fig 4.2.13 Shows glass scale X, Y and Z directions and new shapes to fix the aluminum

body and reading head.

The way to simulate a real glass scale with these three new parts is to fix together the

reading head and the glass. We do this because in a real linear encoder, the reading

head measures the position of the moving part in the glass and send this information

another time as feedback to the motors at the screws to correct the position with the

new information. If we fix the reading head to the glass we are simulating the real

behavior of the glass scale, because this fixed point makes a dependency between the

glass and the reading head like the feedback do. Also it is necessary to assembly the

aluminum body of the glass scale to the body of the machine centre in a proper way.

The middle point of the aluminum body must be fixed together with the body of the

machine centre and also the aluminum body must by fixed at both side but in a way it

will be possible to slide in that two points because of thermal deformation as we see

on figure 4.2.14

37

Fig 4.2.14 In reality the reading head at the glass scale send feedback to the motors.

This is simulated in our model by fixing the reading head to the glass. Also are

illustrated the three points where the aluminum body is fixed to the machine body.

5. Boundary conditions for finite elements thermal models

5.1 Analysis of Power Losses

There are different power losses while the machine centre is working. These are the

power losses in the ball screws, in the bearings and in the motor. Power losses induce

heat flux that produces thermal deformation on the machine centre.

The value of some of the parameters needed to calculate power losses in ball screws

are typical values from real working conditions. It is not necessary in this project to use

the exact data for this machine centre to calculate power losses because the main

object of the project is to compare the behavior of the machine with and without glass

scale. This means that, using the same data to both different configurations of the

machine centre, it will be possible to compare results in a proper way.

5.1.1 Power Losses in ball screw

This kind of power losses are calculated according to the SKF formulas. First step is to

calculate the theoretical efficiency

Reading head is fixed to the glass

feedback

Slider point Slider point

Fixed point

38

! =1

1+ !×!!!!

where the constant K is 0.018 for this type of ball screw according to SKF catalog, d0 is

47mm and the lead of the screw is 10mm. With these values η is 0,992. Second step is

to calculate the practical efficiency

!! = !×0,9

where ηp is 0,8298. Third step is to calculate the input torque in a steady state (Nm) by

the way

! =!×!!

2000×!×!!

where F is the maximum load of the cycle (N) and according to normal values of

working conditions is 800 N. With these values T is 0,1574Nm. Next step is necessary

to calculate the power required in steady state, P

! =!×!×!!60000×!!

where n are the rpm and in this case is 120 rpm according to normal values of working

conditions. With these values P is 19,28W. With this result it is necessary to calculate

the preloaded torque (Nm) according to the formula

!!" =!!"×!!1000×!

1!!− 1

39

where Fpr is the preloaded force between a nut and the shaft (N) and in this case is

1019N according to normal values of working conditions. With these values Tpr is

0,6656Nm. Now it is possible to calculate the power preloaded (W) using the equation

!!"# =!×!×!!"

30

where n and Tpr are the same above so Ppre is 8,36W. It is possible to define the power

losses, ∆P, as the difference between the electric power of the motor, Pelec, and the

power that we have on the work piece, Pwork. This definition is represented by the

equation

∆! = !!"!# − !!"#$

and also in this way it is possible to define the Pwork as

!!"#$ = !!"!#$×!!

so power losses are

∆! =!!"#$!!

− !!"#$ = !!"#$1!!− 1

At this point it is necessary to define what Pwork means. It is possible to define it like the

sum of power preloaded, the power required in steady state and the power of inertia.

The power of inertia is caused by the masses of the work piece and table but in this

case power of inertia is going to be considered as cero, so Pwork can be calculated using

the equation

!!"#$ = !!"# + !

40

Considering last equation power losses can finally be define by the equation

∆! = !!"# + !1!!− 1

Attending to these equations it is possible to calculate power losses for different

preloaded force between nut and shaft, Fpr , as it is illustrated un the graphic

Fig 5.1.1.1 variation of power losses with rpm between nut and shaft

To introduce these power losses to the model it is necessary to put them in the way

W/m2, so they can be analyzed by SimDesigner as heat flux. To do that it is necessary

to know the surface where the power losses are, so the heat flux will be the power

losses divided by this area.

0 1 2 3 4 5 6 7 8

700 1019 1500 1800

power losses [W

]

preload [N]

power losses in ball screw

41

Fig 5.1.1.2 Illustrates the power losses in the ball screw X.

5.1.2 Power losses in motors

According to Bernd Bossmanns research, “A Power flow model for high speed

motorized spindle” power losses in motors can be calculated by the equations

!!"#"$ = !!"#"$ !"#×!!"#$ !"##$×!!"#$ !"#$

where ηmotor max can be calculated from engineering handbook Avallone and

Baumeister and ηspec speed and ηspec load are dimensionless values related to efficiency

related to loads and speeds. The ηspec speed can be calculated from experimental data as

!!"#$ !"##$ = 0,92+ !!"#"$ !"#×0,80

and the ηspec load can be interpolated from the following table

42

These two dimensionless values are function of two dimensionless speed and load

variables respectively

!!"#"$ !"# =!!"#"$

!!"#"$ !"# !"#$!"#"$ !"# =

! !"#"$!!"#"$ !"#

Once the ηmotor is calculated it is possible to calculate the power losses in the motor,

Qmotor (W), by the equation

!!"#"$ = 2!×!!"#"$×!!"#"$×1− !!"#"$!!"#"$

In the case of this project, calculate of power losses in the motors it is not necessary

because the Company provide us with data from the ACE Series VMD 450 (Machining

centre of this project), where the total values represents the power losses in the

motor.

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 rpms tator 127 246 350 572 776 1090 1423 1796 2250 2701 Wrotor 1 3 9 7 8 14 27 32 33 35 Wtotal 128 249 359 579 784 1104 1450 1828 2283 2736 W

Power losses distribution for motor idle runDelivered by Factory

43

Fig 5.1.2.1 motor power losses as a function of spindle speed

It is necessary to convert these power losses from W to W/m2 so that they can be

introduced to the model to analyze it with SimDesigner. The heat flux will be each of

the power losses divided by the area where each of the power losses has influence.

Fig 5.1.2.2 Values of power losses at the motor expressed in [w] and [w/m2] for

different spindle speed.

5.1.3 Power losses in bearings

More over there are another additional heat sources in mechanism elements like ball

bearings that we must take in accounts. Spindle of this machine centre has five ball

Power losses in 20000rpm spindleload 0 kW

0

500

1000

1500

2000

2500

3000

0 5000 10000 15000 20000speed rotational [rpm]

pow

er lo

sses

[W]

statorrotortotal

rpm Power Losses [W] Heat Flux [W/m2]2000 128 5254000 249 10206000 359 14718000 579 237310000 784 321312000 1104 452514000 1450 594316000 1828 749218000 2283 935720000 2736 11213

44

bearings, four of them at the front and the last one at the rear side (figure 5.1.3.1)

Fig 5.1.3.1 headstock section of the machine centre with the components that

generates heat during the working conditions and also the cooling system.

The factory also provides data of power losses at the bearings for different loads:

Fig 5.1.3.2 Power losses at the bearings as function of spindle speed for load 0KW.

It is also necessary again to divide these values of power losses by the area of each of

the bearings in the way to have power losses expressed as W/m2 so they can be

introduced to the SimDesigner model.

0

10

20

30

40

50

60

0 5000 10000 15000 20000

Pow

er lo

sses

[W]

Spindle speed [rpm]

Power losses in bearings as a function of spindle speed for load 0kW clearance W1= +10um, W2= -10um

bearing 1

bearing 2

bearing 3

bearing 4

bearing rear

45

Fig 5.1.3.3 Values for power losses at bearings expressed in [W] and [W/m2] for

different spindle speed and load 0KW.

5.2 Analysis of forced and natural convection

In terms of surface convection it is necessary to define two kind of surface. First one is

the surface exposed to natural convection. These surfaces are all ones of the machine

centre in contact with ambient, called natural convection. Second kind is the one

exposed to cooling systems or forced convection. In case of this project, the machine

centre has a cooling system for the motor and bearings that affect to the surface of the

headstock. These two different kinds of convection translate in two different values of

α coefficient [W/Km2].

Fig 5.2.1 The sketch represents the pockets for the oil of the cooling system for motor

and bearings (see figure 5.1.3.1)

It is necessary to calculate α coefficient in case of forced convection. As it is illustrated

on figure 5.2.1, the sketch represents the ways for the cooling liquid around the stator

and the bearings. The value of α coefficient it is determinate by Reynolds number and

load 0KWpower losses [w] heat flux [W/m2]

rpm bearing 1 bearing 2 bearing 3 bearing 4 rear bearing bearing 1 bearing 2 bearing 3 bearing 4 rear bearing2000 7,6 7,6 7,6 7,6 2,8 190 190 190 190 1753000 12 12 12 12 4,6 300 300 300 300 287,58000 19 19 18 19 14,8 475 475 450 475 92512000 30,1 31 28 30,1 22,6 752,5 775 700 752,5 1412,520000 54 55,6 48,6 53,6 35,9 1350 1390 1215 1340 2243,75

46

Re*Pr*dhb/l where Pr is the Prandtl number. According to this there are three possible

α coefficient

§ If Re*Pr*dhb/l < 4,5 and Re < Recrit (laminar flow) then:

! = !×0,5×!"×!"×!ℎ!/!×!"#$%"/!ℎ!

§ If Re*Pr*dhb/l > 4,5 and Re < Recrit (laminar flow) then:

! = !×1,86× !"×!"×!ℎ!/! !,!!×!"#$%"/!ℎ!

§ If Re > Recrit (turbulence flow) then:

! = !×0,023×!"!,!×!"!,!×!"#$%"/!ℎ!

where dhb is hydraulic diameter

!ℎ! = !×ℎ× !!!!

the constant k is calculated by the way

! = 1+ 1,77×2×!ℎ!!

There is data of α coefficient for stator, rear and front bearings. As it is illustrated

forward, the value of α coefficient depend on the quantity of cooling liquid, in this case

oil. The values of α coefficient used for compute with SimDesigner there are the ones

for 20 l/min of oil quantity.

For surface without forced convection, the ones in contact with ambient, α coefficient

has always the same value, 10 W/Km2, that it is a typical value from real working

conditions.

47

Fig 5.2.2 Variation of α coefficient and power losses with cooling liquid in stator.

Fig 5.2.3. Variation of α coefficient and power losses with cooling liquid in front

bearings.

Fig 5.2.4 Variation of α coefficient and power losses with cooling liquid in rear bearing.

0

200

400

600

5 10 15 20 25 30 35 40

alfa

[W/m

K]

pow

er lo

sses

[W]

oil quantity [l/min]

stator cooller - oil cooling Convection coef.

0

100

200

300

400

500

5 10 15 20 25 30

alfa

[W/m

K]

pow

er lo

sses

[W]


front bearings cooler

Convection coef.

0

100

200

300

400

500

600

700

5 10 15 20 25 30

alfa

[W/m

K]

pow

er lo

sses

[W]


rear bearings cooler

alfa

48

5.3 Machine Tool Model for analyze temperature with SimDesigner R2

The start point of this model is the Geometrical Model of Machine Tool with Glass

Scale. The aim of this part of the project is to obtain the temperature distribution of

heat flows along the machine tool produced by the power losses, natural and forced

convection. The election of the geometrical model with glass scale against the model

with ball screw it is because it is necessary to determine data of this distribution of all

the parts of the machine centre. Geometrical model of machine tool with glass scale is

the same model than the ones with ball screw but with extra parts, the ones that

represents the glass scale. Data for temperature distribution for geometrical model of

machine tool with glass scale it would be suitable also for model with ball screw as

long as both model have their moving parts in the same position.

This analysis was do it with SimDesigner R2 compatible with CATIA V5R17.

Fig 5.3.1 Temperature distribution computed by SimDesigner R2 along the machine

tool produce by power losses and natural and forced convection.

49

The process of designing this model starts by defining thermal properties of all

materials of the machine centre. It is necessary to define up to three properties,

thermal conductivity, specific heat and emissivity. In case of thermal conductivity the

value for all materials of the machine centre is going to be 40 W/mK that it is a normal

value from real experimental data. In case of specific heat also there is going to be one

value for all materials, 0,5 KJ/kgK, and it is also a normal value for real working

conditions. In case of the emissivity all materials are going to have also the same value,

cero.

Fig 5.3.2 Thermal properties of materials: Thermal conductivity, Specific heat and

emissivity.

Next step is to define the boundary conditions. In case of this project the boundary

conditions are the initial temperature . Initial temperature is a parameter that

affects the reaction of the machine tool against the power losses, so it is an important

parameter and also it is a parameter as we can see along this project susceptible to

select different values to study different behaviors. In first case value for initial

temperature is normal ambient temperature, 293 K for all the parts of the machine

centre.

50

Fig 5.3.3 Value for initial temperature for all parts of machine tool. In first case this

value is ambient temperature. This initial temperature is the boundary conditions of

thermal model.

After defining the boundary conditions it is necessary to define thermal loads. These

are going to be the all the heat flows and different type of convections the machine

tool is affected. In case of this machine tool as it is define on this project, is going to be

affected by power losses, forced and natural convection. Power losses are heat flows

and CATIA V5R17 gives us the possibility to introduce heat flows by two different ways.

In our case the proper way to do this is selecting Heat Flux , because there are in

the form [W/m2]. This is the correct way to introduce power losses [W] to the model, if

we know the area [m2] where the power losses are, finally we will know power losses

as heat flux. As we seen on figure 5.3.4 read arrows indicates power losses as heat flux

through the selected surface. For power losses in the ball screw the selected area for

the heat flux are the spindles, because the ball screw moves along the spindle so the

power losses affect along this surface. In this machine tool there are going to be power

losses in the three different ball screws and also power losses in the motor. It is

important to define as much heat flux as power losses are in the way to be able to

select different values of heat flux for each different power losses.

51

Fig 5.3.4 Indicates heat flux by red arrows in the ball screw X.

There are also, apart from power losses in the three ball screws, power losses in the

motor. These power losses are the ones at the stator and the ones at the bearings. In

case of the motor of this machine tool we have five different bearings, four front

bearings and one rear bearing. This makes a total of six different heat fluxes to

represent the power losses in the motor, the ones at the stator and the ones at the

five different bearings. To introduce these power losses the area selected is the

interior of the heat stock as we see on figure 5.3.5 for all the six different heat fluxes

that represents power losses in the motor and bearings.

52

Fig 5.3.5 Power losses in the motor represented by red arrows as heat flux through the

heat stock.

Once all of the different power losses are introduced as different heat fluxes to our

model it is necessary to define the different convections the model is affected by.

This model has two different types on convection, natural and forced. All natural

convections are marked with blue cones along the selected surface as we can see on

figure 5.3.5. There is natural convection in all the surfaces in contact with ambient and

it is not necessary to define as much convection loads as surface in contact with

ambient for natural convection because for all of them the properties are the same, 10

W/Km2 for convection film coefficient and 293 K for reference sink temperature. The

values for these convection properties are normal values from typical working

conditions.

53

Fig 5.3.6 Typical values from working conditions for natural convection properties.

There is forced convection in the motor, particularly in the stator and in the five

different bearings. This means that we need to define up to six different forced

convections. As we did with power losses in the motor, the selected area to introduce

these six convections is the interior of the head stock.

Fig 5.3.7 Shows forced convection in the stator. It is represented by the blue cones inside the head stock.

54

To make sure that the machine tool for analyze temperature with SimDesigner is

proper done, this means, that the different heats flows perfect with no interruption

along all the surface of the machine tool it is necessary in some parts of the machine

tool to select the proper mesh in order to obtain this correct flow of the heat. This

means that in some parts of the machine tool because of the difference between the

size of the mesh of two parts in contact, if this difference is too big, could happened

that the heat do not flows in the correct way along the two surface in contact. Better

solution to solve this problem is to define local mesh in one of the surface in contact to

make more similar to the other surface so in this way there will be no problems of bad

connection between nodes. To do this it is necessary to add to the mess of the part

where we want to change the mesh at the surface, a local size and local sag and define

the supported surface and the values for local mesh sag and local mesh size as we see

on figure 5.3.8. The advantage of changing only the mesh of the surface instead the

mesh of all one part it is that compute time is going to be shorter.

Fig 5.3.8. Definition of local mesh

55

Fig 5.3.9 Shows local mesh at the base of the machine tool next to the house bearing

and also local mesh at the house bearing next to the end of spindle in order to have

good contact between nodes.

To prove that the contact between local mesh as we see on figure 5.3.9 is correct is

possible to choose a value for, in this case heat flux at the ball screw X, big enough to

see if the heat flows in a correct way from one part to the other. This is illustrated on

figure 5.3.10, as we can see the temperature values is not important in this case but it

is the fact that there is a flow of heat from the spindle to the house bearing and from

this to the base of the machine tool. That means that there is a correct contact

between parts because of the new local mesh.

Correct contact between different mesh

56

Fig 5.3.10. Shows how heat flows in a correct way from the spindle to the house

bearing and from this one to the base of the machine tool.

Once the model is ready is possible to compute and generate image

to obtain the temperature field fringe and after it will be possible to export data as a

text file to use it as temperature field and analyze deformation of machine tool with

CATIA V5R17.

57

Fig 5.3.11 Shows how to select temperature field fringe and save it as data on to a text

file to analyze it later with CATIA V5R17.

Fig 5.3.12 Machine tool model with glass scale temperature distribution at positions BEH (left) and CFG (right) with initial temperature 293K.

58

6. Machine Tool Model for analyze deformation with CATIA V5R17

6.1 Boundary conditions for finite elements deformation models

The aim of this part of the project is to obtain two different models, one for ball screw

configuration and other for glass scale, ready to analyze them with CATIA V5R17 and

obtain the deformation produced by power losses and natural and forced convection

on the machine centre. The starting point is going to be the geometrical model of

machine tool, one for each configuration. Basically we need to do three steps to obtain

each model. First step is to add to every assembly constrain a proper connection

property so the relative move between the parts in contact will be the one in the

correct direction. Second step is to load the data of temperature distribution obtained

by SimDesigner R2 in a proper way. This data represents the temperature distribution

of heat flow caused by power losses and natural and forced convection. Third and final

step is to create as much as local sensors needed to measure the deformation of the

machine centre in a correct way so we can compare results for both model in the way

to decide which model has more accuracy for which working condition.

Fig 1. Shows deformation computed by CATIA VR517 produced by power losses and

forced and natural convection of the machine tool.

59

6.1.1 Define connection property to assembly constrains

The process of designing this model begins with the necessity of using one restraint,

the clamp , and it is necessary to add it to the base on the machine tool in order to

simulate that it is fixed to the ground as it is illustrates in figure 6.1.1.1

Fig 6.1.1.1 Illustrates the clamp at the base of the machine tool. The clamp fixes the

machine tool to the ground.

To add properties to the assembly constraints in case of this machine tool it is only

necessary to use two types of connection property. These connection properties are

the slider connection property and the fastened connection property . With

the first one, slider connection property, the bodies in contact by the assembly

constrain, will move one through the other during the deformation but always keeping

the contact between them. As we will see later it will be important to define the

direction where we want to move the parts when we use the slider connection

property. With the fastened connection property the bodies in contact by the

assembly constrain will keep the same relative position between them during the

deformation. There is only one way of thinking at the time to choose between slider

and fastened connection property. This means that all part that is fixed to another part

by right and left side it is going to deform by the two sides, so in one side should be

fixed to the other body as fastened connection property and on the other side should

be fixed as slider connection property in order to avoid that the part breaks during the

deformation as we can see on figure 6.1.1.2

60

Fig 6.1.1.2 The house bearing is fixed to the base of the machine tool on the right side

by fastened connection and on the left side by slider connection property in order to

avoid that the part breaks during the deformation of machine tool.

This approach must be for all the parts in the same situation. In case of screws the way

of thinking is the same but the slider connection property must be at the side of the

bearing and it must be also fastened at the side of the motor. This is because the

fastened connection property simulates that the motor moves the screw and only the

screw can deforms in the side of the bearing.

Fig 6.1.1.3 Illustrates how the screw is fixed as fastened on the right side where it is the

motor (not illustrated) and also fixed as slider connection on the left side where it is

the house bearing

fixed moves

fixed

moves

61

In case of the blocks, first it is necessary to define the behavior against the rail. The

block must slide by the rail in all the surfaces where there is contact between the two

parts as we see on figure 6.1.1.4

Fig 6.1.1.4 Shows the relative move of a block against the rail. It must be slider in all

surface where there is contact between block and rail.

Second it is necessary to define the behavior of the blocks against the table, headstock

and body of the machine tool. In all cases the approach is the same than in the other

cases. Blocks of one side must be fixed to the part as fastened and blocks from the

other side must be fixed as slider connection property. It is important as we said to

define the direction where we want to make the blocks slides through. In case of the

blocks of the table the ones at the right side are fixed as fastened connection property

to the table as we can see on figure 6.1.1.5 The ones at the left side must slide in Y

direction. To force the blocks from the left side to move in the correct direction during

the deformation it was necessary to design a special shape to the bottom side of the

table as we can see on figure 6.1.1.6. To make this apart from the special shape we

need to add slider connection property to the assembly constrain between the left side

blocks and the new shape.

moves

moves

62

Fig 6.1.1.5 Shows the blocks that must be fixed in their position and the ones that must

slide through the correct direction in order to avoid that the guide breaks during the

deformation.

Fig 6.1.1.6 Shows how the blocks at the left side of the table slide through the new

shape in the correct direction.

fixed

fixed

moves

moves

moves

moves

63

These special shapes are also necessary on the headstock and on the other moving

part.

Fig 6.1.1.7 Shows the direction of movement of the blocks through the new shapes at

the backside of the headstock.

Fig 6.1.1.8 Shows the direction of movement of the blocks through the new shapes at

the backside of this moving part.

moves

moves

moves moves

fixed

fixed

fixed fixed

64

Once all the assembly constrains have their own connection property it is important at

this point to make a difference between the configuration of model with glass scale

and the one without glass scale (ball screw model). For model of machine tool with ball

screw the property associated to the assembly constrain between the ball screw and

the spindle itself must be fastened connection property so that the ball screw moves

together with the spindle during the deformation as we see on figure 6.1.1.9. This

approach must be the same for the rest of the ball screws and spindles in case of

machine tool with ball screw configuration.

Fig 6.1.1.9 Illustrates the fastened connection property for the assembly constrain

between the ball screw and the spindle in the machine tool model with ball screw.

In case of model of machine tool with glass scale, the connection property associated

to the assembly constrain between the ball screw and the spindle must be slider

connection, but at the same time, the connection property of the assembly constrain

between the reading head and the glass scale must be fastened connection, as we see

on figure 6.1.1.10. Doing this, we are simulating the effect that the reading head has

on the machine tool. This means that if we fastened the reading head to the glass scale

itself, we are simulating the feedback that the reading head sends to the motors to act

through the position of the ball screw. This approach must be the same for the rest of

ball screws and reading heads in case of machine tool with glass scale model.

fixed

65

Fig 6.1.1.10 Shows the reading head fastened to the glass scale while the ball screw is

slider through the spindle for the machine tool with glass scale model.

Continue with model of machine tool with glass scale it is necessary to define how they

are the connection properties of the assembly constrains of the glass scale. For all of

the tree glass scale that the machine tool is up to be equipped, the connection

properties for the assembly constrains are always the same. The glass scale it is formed

by two parts, the aluminum body and the glass itself. The aluminum body is the one

fixed to the body of the machine tool. This part must be fastened in the middle point

and slider at left and right side. The glass must be fixed, normally in the middle point,

to the aluminum body by fastened connection property as we can see on figure

6.1.1.11

moves

fixed

66

Fig 6.1.1.11 Shows how connection properties of assembly constrain of glass scale

must be.

6.1.2 Load data of temperature distribution obtained by SimDesigner R2

At this point, where all the assembly constrains have their own proper connection

property for both models, one with ball screw and other with glass scale, it is

necessary to load the data with temperature distribution that we obtain from the

computing of SimDesigner R2. To do this, first is necessary to modify this data in the

correct way to make it compatible for CATIA V5R17. As we see on figure 6.1.2.1, it will

be necessary to delete the marked lines to make it compatible with CATIA V5R17

before load it.

Fig 6.1.2.1 Shows data with temperature distribution computed by SimDesigner R2. It

is necessary to delete the marked parts to make it compatible with CATIA V5R17.

moves

moves

fixed

67

Once this data is ready we can load it to our model for analyze deformation with CATIA

V5R17 as temperature field . As we can see on figure 6.1.2.2 the correct way to

load this data is by selecting 1 Kdeg the temperature. Doing this CATIA V5R17

multiplies the values from the data with the value on Temperature. If we select as

Temperature 1 kdeg we will have the same values from the data on our model at

CATIA V5R17.

Fig 6.1.2.2 Shows how to load the data from SimDesigner R2 to CATIA V5R17 in the

correct way.

6.1.3 Define local sensors to measure deformations

At this point it is now possible to add local sensors to both models to measure the

deformation produce by the power losses and natural and forced convection. It is only

necessary to add the sensor we think they will give us useful data. The sensors are

going to be in the same points for both models, with and without glass scale, in order

to compare results. There are going to be three sensors per selected point so we can

measure the displacement on the three directions. The selected points are going to be

the end of spindles, one corner of the table and also the middle point of the head

stock. This makes a total of 15 sensors per model. In case of the sensors of the middle

point of the headstock it is necessary to design a new shape at the end of the

headstock so we can select the middle point. Figure 6.1.3.1 illustrates the new shape

at the end of the head stock and the values of the sensors. It was chosen this point to

68

simulate the measure at the tools so we can obtain their displacements during the

deformation.

Fig 6.1.3.1 Shows the new shape at the end of the headstock and the value of sensors

at the middle point.

There are two kind of sensors that measures displacement as we can see on figure

6.1.3.2. These are the Displacement Magnitude and the Displacement Vector.

Fig 6.1.3.2 Illustrates the two types of sensor that CATIA V5R17 allows to choose to

measure displacement.

69

To choose between these two kinds of sensors in our case we want to measure the

displacement in the three directions of each point. As we see on figure 6.1.3.3, the

displacement could be different (black arrows) at the time that the magnitude vector

(red arrows) could be the same. Attending to this, in our case we must choose

displacement vectors.

Fig 6.1.3.3 Shows the difference between displacement and magnitude vectors. In our

case we need to choose sensors as Displacement vector in order to measure the

displacement of the point in the tree axis.

Now it is possible to compute, , and generate image, , of the

deformed mesh to have final model for analyze deformation with CATIA V5R17 as it is

illustrated on figure 6.1.3.4.

Fig 6.1.3.4 Shows deformed mesh of geometrical model with glass scale. The values

marked as red indicates position and measure by the local displacement sensors.

70

7. Design plan of computing

Before starts work cycle there are no power losses in bearings/motor and spindle

speed rotation equals to zero so there will be no thermal displacements. Working

conditions starts with initial temperature equals to ambient. These conditions changes

gradually with time due to machine working cycle, because of different spindle speed

rotations, variations in ambient temperature, different headstock and table positions.

All these phenomena are the sources of different power losses and different

displacements causes by thermal deformation.

As we see on the dependency diagram we focus on the factors that we consider have

influence on quality of machine tool. But there is impossible to study the influence of

these factors all at the same time. It is necessary to separate analyses for different

working conditions in order to obtain relations between these working conditions and

displacements so we can define behavior of machining centre.

7.1 Operating positions and conditions

The proposed studies are analyzing changing of displacements in chosen points during

work cycle with three different Ambient Temperatures (293K, 295K and 298K) and two

different headstock/table positions, position BEH and position CFG, as we see on figure

7.1.1. These studies were done with software CATIA V5R17, for analyze thermal

deformation, and SimDesigner R2 for analyze temperature distributions. Positions are

defined in picture 7.1.1. The positions are not random positions, there are in the

middle and in both sides of glass scale. Machine centre has one glass scale for each

direction X, Y and Z. We select three points per glass scale, one in the middle and two

at both sides. Also there are not random points. The ones at the middle of the glass

scale it were chosen because we suppose it is the point where glass scale makes

smaller error because glass scale is fixed in the middle as fastened connection property

so in this point L≈0 so the displacement should be the smallest in order to

∆! = !"∆!

71

If we select three points per glass scale, this makes a total of 27 possible combinations

of different headstock/table positions. The two selected, BEH and CFG were selected

to analyze behavior of machine centre in two different positions. First one, position

BEH, was chosen because it is the one in the middle of the three glass scales. Second

position, CFG, was chosen in order to analyze other position different to the first one.

In this case no one of the reading heads are in the middle of the glass scales. Ball screw

X and ball screw Z are at the opposite side of the motor and ball screw Y is close to the

motor. This should means that for ball screw X and ball screw Z must be L=Lmax so

displacement should be maximum in order to

∆! = !"∆!

but for ball screw Y must be L≈0 so the displacement should be minimum according to

the same equation.

Fig 7.1.1 Shows the two selected positions of the headstock and table, BEF and CFG,

for our studies.

A B C

D

E

F

G H I

C

F

G

72

7.2 Design of working cycle

To reach proposed studies it is necessary to design a work cycle that imitates real

machine working conditions. Once we have designed this cycle, we can compute

temperature distribution and thermal deformation for defined FEM models. The work

cycle must have some requirements such as representative spindle speed rotation

along all speed range; realistic machining times in order to observe real machine tool

displacements and enough time steps to extract as much data as necessary. In figure

7.2.1 we can observe the work cycle that is going to be used for our studies. In this

work cycle machine centre starts working 8000 r.p.m. during first hour. This value of

spindle speed rotation was chosen in order to analyze behavior of machine centre

working nearly the middle range of r.p.m. During the second hour the machine centre

stops working so we will analyze what happens with thermal deformation during a

time without heat sources and after that stars working at maximum spindle speed

rotation, 20000 r.p.m. during another hour. After the third hour continues working at

8000 r.p.m. for another hour and finish the work cycle.

Fig 7.2.1 Work cycle used in the different analyses of this project.

73

Attending to the work cycle it is necessary to introduce the power losses not as

constant but as transient values to machine tool model for analyze temperature with

SimDesigner R2 as we see on figure 7.2.2 and figure 7.2.3

Fig 7.2.2 Shows how to introduce power losses as a transient value to SimDesigner

model.

Fig 7.2.3 Illustrates how to introduce, in this case for stator, transient power losses and

transient forced convection according to our work cycle.

74

Fig 7.2.4 Power losses as heat flux in stator during work cycle. The graphic has the

same form than the work cycle.

Fig 7.2.5 Forced convection at stator. This graphic do not have the same form that the

work cycle because forced convection does not depends on spindle speed rotation,

depends of quantity of oil cooling flow.

75

7.3 Selected data for analyses

§ Power losses at the motor

§ Power losses at the bearings

§ Constant ball screw (X, Y and Z) power losses: 64,04 W/m2

§ Oil cooling flow: 20 L/min

§ Free film convection value: 10 W/Km2

8. Results of computing and conclusions

All the results and graphics of the project are shown in the attachment. In this section

there are shown only the ones which can give us information about behavior of

machine centre.

Fig 8.1Machine tool model with glass scale temperature distribution at position BEH

with initial temperature 293K.

rpm Power Losses [W] Heat Flux [W/m2]8000 579 237320000 2736 11213

power losses [w] heat flux [W/m2]rpm bearing 1 bearing 2 bearing 3 bearing 4 rear bearing bearing 1 bearing 2 bearing 3 bearing 4 rear bearing8000 19 19 18 19 14,8 475 475 450 475 92520000 54 55,6 48,6 53,6 35,9 1350 1390 1215 1340 2243,75

76

Fig 8.2 Machine tool model with glass scale deformation at position BEH with initial

temperature 293K.

Fig 8.3 Machine tool model with glass scale temperature distribution at position CFG

with initial temperature 293K.

77

Fig 8.4 Machine tool model deformation at position CFG with initial temperature 293K.

8.1 Analyses of displacements at position BEH

8.1.1 Analyses of work cycle with initial temperature 293K at BEH

Result for displacements (mm) during work cycle with initial temperature 293K at

position BEH:

GLASS SCALE T=293K Position BEH

time (s)sensor displacement direction 0 3600 7200 10800 14400

dispacement (mm) ball screw X X 0 0,0120 0,0170 0,0190 0,0200Y 0 0,0003 0,0005 0,0005 0,0005Z 0 0,0009 0,0009 0,0008 0,0008

ball screw Y X 0 0,0009 0,0010 0,0010 0,0010Y 0 0,0300 0,0480 0,0600 0,0700Z 0 0,0020 0,0010 0,0001 -0,0006

ball screw Z X 0 0,0020 0,0030 0,0080 0,0110Y 0 0,0040 0,0040 0,0090 0,0090Z 0 0,0210 0,0290 0,0470 0,0500

tool X 0 0,0030 0,0110 0,0240 0,0500Y 0 0,0170 0,0110 0,0630 0,0260Z 0 0,0370 0,0250 0,1270 0,0530

table X 0 -0,0010 -0,0009 -0,0008 -0,0007Y 0 0,0006 0,0005 0,0004 0,0003Z 0 0,0010 0,0010 0,0010 0,0010

78

Attending to these results we can observe that:

§ Displacement of ball screw X (ball screw in X direction) of course is the same for

ball screw configuration (without glass scale) and with glass scale in the three X,

Y and Z directions because glass scale has no influence at the end of the ball

screws. This is useful to probe that both models, with and without glass scale,

are well done.

Conclusion: Glass scale does not improve ball screw X displacement in X, Y and

Z directions.

§ Displacement of ball screw Y (ball screw in Y direction) is of course the same for

ball screw and for glass scale in X, Y and Z directions.

Conclusion: Glass scale does not improve ball screw Y displacement in X, Y and

Z directions.

§ Displacement of ball screw Z (ball screw in Z direction) is practically the same

for ball screw and for glass scale in X and Z direction but not in Y direction

where there is displacement for ball screw bigger than the one for glass scale of

0,01 mm at the first hour, 0,016 mm at the second hour, 0,019 mm at the third

hour and 0,024 mm at the fourth hour.

BALL SCREW T=293K Position BEH



ball screw Y X 0 0,0009 0,0010 0,0010 0,0010Y 0 0,0300 0,0470 0,0600 0,0700Z 0 0,0020 0,0009 0,0003 -0,0008

ball screw Z X 0 0,0010 0,0030 0,0070 0,0110Y 0 0,0140 0,0200 0,0280 0,0330Z 0 0,0200 0,0270 0,0450 0,0490

tool X 0 0,0040 0,0110 0,0260 0,0510Y 0 0,0280 0,0280 0,0830 0,0510Z 0 0,0450 0,0380 0,1500 0,0810

table X 0 0,0080 0,0130 0,0150 0,0160Y 0 0,0006 0,0005 0,0004 0,0003Z 0 0,0010 0,0010 0,0010 0,0010

79

Conclusion: Glass scale does not improve ball screw Z displacement in X and Z

directions but it has nearly 0,020 mm less displacement than ball screw in Y

direction.

§ Displacement of Tool (end of spindle displacement) of course is the same for

ball screw and for glass scale in X direction because glass scale has no influence

in this direction, but not in Y and Z. Displacement for ball screw is bigger than

for glass scale in 0,011 mm to 0,025 mm when spindle speed increase from

8000 r.p.m. to 20000 r.p.m. respectively for Y and Z directions.

0,00000

0,00500

0,01000

0,01500

0,02000

0,02500

0,03000

0,03500

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Z, displacement in Y during work cycle with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

0,00000 0,01000 0,02000 0,03000 0,04000 0,05000 0,06000 0,07000 0,08000 0,09000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in Y during work cycle with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

80

Conclusion: Glass scale does not improve end of spindle displacement in X

direction but has nearly 0,020 mm less displacement than ball screw in Y and Z

direction. This displacement increase when we raise spindle speed rotation.

§ Displacement for Table is the same for ball screw and glass scale in Y and Z

directions. In X direction displacement for glass scale is practically zero but

there is a big displacement for ball screw from 0,013 mm second hour, 0,015

mm third hour and 0,016 mm forth hour.

Conclusion: Glass scale does not improve Table displacement in Y and Z

directions but it does in X direction.

0,00000

0,02000

0,04000

0,06000

0,08000

0,10000

0,12000

0,14000

0,16000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in Z during work cycle with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

-‐0,005

0

0,005

0,01

0,015

0,02

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Table, displacement in X during work cycle with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

81



position BEH:

§ Displacement of ball screw X: Same case than for 293K but displacements

increase with temperature.

§ Displacement of ball screw Y: Same case than for 293K.

§ Displacement of ball screw Z: Same case than for 293K. The difference between

displacement of ball screw and glass scale in Y direction continues being 0,020

mm but level of displacement increase with temperature.



dispacement (mm) ball screw X X 0 0,0230 0,0280 0,0310 0,0320Y 0 0,0020 0,0020 0,0020 0,0020Z 0 -0,0100 -0,0100 -0,0100 -0,0090

ball screw Y X 0 -0,0070 -0,0070 -0,0060 -0,0060Y 0 0,0260 0,0430 0,0550 0,0650Z 0 -0,0510 -0,0510 -0,0510 -0,0500

ball screw Z X 0 0,0020 0,0030 0,0080 0,0100Y 0 -0,0100 -0,0100 -0,0060 -0,0060Z 0 -0,0190 -0,0110 0,0070 0,0110

tool X 0 0,0100 0,0160 0,0280 0,0530Y 0 0,0020 -0,0040 0,0470 0,0100Z 0 -0,0090 -0,0180 0,0830 0,0100

table X 0 0,0120 0,0120 0,0120 0,0120Y 0 -0,0080 -0,0080 -0,0080 -0,0080Z 0 -0,0130 -0,0130 -0,0130 -0,0120




ball screw Y X 0 -0,0070 -0,0070 -0,0060 -0,0060Y 0 0,0260 0,0420 0,0540 0,0640Z 0 -0,0510 -0,0510 -0,0510 -0,0500

ball screw Z X 0 0,0020 0,0030 0,0070 0,0100Y 0 0,0020 0,0080 0,0160 0,0210Z 0 -0,0210 -0,0130 0,0050 0,0100

tool X 0 0,0100 0,0160 0,0300 0,0540Y 0 0,0150 0,0150 0,0700 0,0370Z 0 -0,0008 -0,0060 0,1050 0,0370

table X 0 0,0220 0,0260 0,0280 0,0290Y 0 -0,0080 -0,0080 -0,0080 -0,0080Z 0 -0,0130 -0,0130 -0,0130 -0,0120

82

§ Displacement of Tool: Same case than 293K. The difference between

displacement of ball screw and glass scale in Y and Z directions continues being

0,020 mm.

§ Displacement of Table: Same case than for 293K but now, even if the

difference between glass scale and ball screw is the same, displacement for

glass scale is medium value of 0,012 mm in X direction.



position BEH:

0,0000

0,0050

0,0100

0,0150

0,0200

0,0250

0,0300

0,0350

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO




ball screw Y X 0 -0,0180 -0,0180 -0,0180 -0,0180Y 0 0,0200 0,0350 0,0470 0,0560Z 0 -0,1310 -0,1300 -0,1270 -0,1240

ball screw Z X 0 0,0030 0,0040 0,0080 0,0100Y 0 -0,0310 -0,0320 -0,0280 -0,0280Z 0 -0,0800 -0,0710 -0,0520 -0,0460

tool X 0 0,0190 0,0240 0,0340 0,0570Y 0 -0,0210 -0,0270 0,0220 -0,0150Z 0 -0,0780 -0,0830 0,0160 -0,0540

table X 0 0,0310 0,0310 0,0300 0,0300Y 0 -0,0210 -0,0210 -0,0210 -0,0210Z 0 -0,0360 -0,0350 -0,0340 -0,0330

83

§ Displacement of ball screw X: Same case than for 293K and 295K but

displacements increase with temperature.

§ Displacement of ball screw Y: Same case than for 293K and 295K.

§ Displacement of ball screw Z: Same case than for 293K and 295K. The

difference between displacement of ball screw and glass scale in Y direction

continues being 0,020 mm but level of displacement increase with

temperature.

§ Displacement of Tool: Same case than for 293K and 295K. The difference

between displacement of ball screw and glass scale in Y and Z directions

continues being 0,020 mm.

§ Displacement of Table: Same case than for 293K and 295K but 293K but now,

even if the difference between glass scale and ball screw is the same,

displacement for glass scale is medium value of 0,031 mm in X direction.

8.1.4 Conclusions at position BEH with different initial temperatures

We can say as general conclusions at position BEH that:

§ For ball screw X glass scale does not improves displacements in any direction

and these displacements increase with initial temperature in all directions.




ball screw Y X 0 -0,0180 -0,0180 -0,0180 -0,0180Y 0 0,0200 0,0350 0,0470 0,0550Z 0 -0,1310 -0,1300 -0,1270 -0,1240

ball screw Z X 0 0,0030 0,0040 0,0080 0,0100Y 0 -0,0160 -0,0100 -0,0020 0,0020Z 0 -0,0810 -0,0720 -0,0530 -0,0470

tool X 0 0,0190 0,0240 0,0350 0,0580Y 0 -0,0050 -0,0040 0,0490 0,0160Z 0 -0,0690 -0,0710 0,0380 -0,0280

table X 0 0,0420 0,0470 0,0490 0,0490Y 0 -0,0210 -0,0210 -0,0210 -0,0210Z 0 -0,0350 -0,0340 -0,0330 -0,0330

84

§ For ball screw Y: glass scale does not improve displacement in any direction.

§ For ball screw Z: glass scale improves displacement between glass scale in

0,020 mm in Y direction but level of displacement increase with initial

temperature

§ For Tool: glass scale improves displacements in 0,020 mm in Y and Z directions

with dependency of spindle speed rotation.

§ For Table: glass scale improves displacement in X direction but this

displacement increase with initial temperature.

-‐0,04000

-‐0,03000

-‐0,02000

-‐0,01000

0,00000

0,01000

0,02000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Z, displacement in Y during work cycle with different iniaal temperatures at posiaon BEH

glass scale YES 293K



-‐0,005

0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Table, displacement in X during work cycle with different iniaal temperatures at posiaon BEH




85

8.2 Analyses of displacements at position CFG

8.2.1 Analyses of work cycle with initial temperature 293K at CFG


position CFG:

§ Displacement of ball screw X: is practically the same for ball screw and for glass

scale in X, Y and Z directions.

GLASS SCALE T=293K Position CFG



ball screw Y X 0 0,0009 0,0010 0,0010 0,0010Y 0 0,0400 0,0690 0,0920 0,1100Z 0 0,0020 -0,0004 -0,0020 -0,0030

ball screw Z X 0 0,0020 0,0030 0,0090 0,0120Y 0 0,0040 0,0050 0,0100 0,0100Z 0 0,0230 0,0330 0,0490 0,0530

tool X 0 0,0020 0,0100 0,0200 0,0490Y 0 0,0140 0,0090 0,0520 0,0180Z 0 0,0310 0,0230 0,1130 0,0520

table X 0 -0,0010 -0,0010 -0,0010 -0,0010Y 0 0,0006 0,0004 0,0003 0,0003Z 0 0,0010 0,0010 0,0010 0,0010

BALL SCREW T=293K Position CFG



ball screw Y X 0 0,0009 0,0010 0,0010 0,0010Y 0 0,0390 0,0680 0,0910 0,1100Z 0 0,0020 -0,0004 -0,0020 -0,0030

ball screw Z X 0 0,0020 0,0030 0,0100 0,0120Y 0 0,0050 0,0060 0,0120 0,0130Z 0 0,0230 0,0330 0,0520 0,0540

tool X 0 0,0020 0,0100 0,0210 0,0500Y 0 0,0160 0,0110 0,0550 0,0230Z 0 0,0500 0,0510 0,1630 0,1010

table X 0 0,0200 0,0320 0,0400 0,0440Y 0 0,0006 0,0004 0,0004 0,0003Z 0 0,0010 0,0010 0,0010 0,0010

86

Conclusion: Glass scale does not improve ball screw X displacement in X, Y and

Z directions.

§ Displacement of ball screw Y: is practically the same for ball screw and for glass



Z directions.

§ Displacement of ball screw Z: is practically the same for ball screw and for glass



Z directions

§ Displacement of Tool: is practically the same for ball screw and for glass scale in

X and Y direction but not in Z. Displacement for ball screw is bigger than for

glass scale in practically a value of 0,02 mm to 0,05 mm when spindle speed

increase from 8000 r.p.m. to 20000 r.p.m. respectively for Z direction.

Conclusion: Glass scale does not improve end of spindle displacement in X and

Y directions but has nearly 0,020 mm less displacement than ball screw in Z

direction. This displacement increase to 0,05 mm when we raise spindle speed

rotation.

-‐0,0200

0,0000

0,0200

0,0400

0,0600

0,0800

0,1000

0,1200

0,1400

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in Z during work cycle with iniaal temperature 295K at posiaon CFG

glass scale YES

glass scale NO

87

§ Displacement of Table: is the same for ball screw and glass scale in Y and Z

directions. In X direction displacement for glass scale is practically cero but

there is a big displacement for ball screw from 0,02 mm first hour, 0,032 mm

second hour, 0,040 mm third hour and 0,044 mm fourth hour.

Conclusion: Glass scale does not improve Table displacements in Y and Z

directions but it does in X direction.



position CFG:

-‐0,0050 0,0000 0,0050 0,0100 0,0150 0,0200 0,0250 0,0300 0,0350 0,0400 0,0450 0,0500

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Table, displacement in X during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO




ball screw Y X 0 -0,0070 -0,0060 -0,0060 -0,0060Y 0 0,0360 0,0640 0,0870 0,1050Z 0 -0,0520 -0,0530 -0,0530 -0,0530

ball screw Z X 0 0,0020 0,0030 0,0090 0,0120Y 0 -0,0150 -0,0150 -0,0100 -0,0100Z 0 -0,0110 -0,0004 0,0160 0,0210

tool X 0 0,0100 0,0160 0,0250 0,0530Y 0 -0,0030 -0,0080 0,0350 0,0009Z 0 -0,0050 -0,0110 0,0790 0,0190

table X 0 0,0170 0,0170 0,0170 0,0160Y 0 -0,0080 -0,0080 -0,0080 -0,0080Z 0 -0,0100 -0,0090 -0,0090 -0,0080

88

§ Displacement of ball screw X: same case than for 293K.

§ Displacement of ball screw Y: same case than for 293K.

§ Displacement of ball screw Z: same case than for 293K.

§ Displacement of Tool: Same case than for 293K. The difference between

displacement of ball screw and glass scale in Z direction continues being 0,020

mm and increase to 0,05 mm when we raise spindle speed rotation.

§ Displacement of Table: Same case than for 293K, but now, even if the






ball screw Y X 0 -0,0070 -0,0060 -0,0060 -0,0060Y 0 0,0350 0,0640 0,0860 0,1050Z 0 -0,0520 -0,0530 -0,0530 -0,0530

ball screw Z X 0 0,0020 0,0030 0,0090 0,0120Y 0 -0,0150 -0,0140 -0,0080 -0,0070Z 0 -0,0110 -0,0006 0,0190 0,0220

tool X 0 0,0100 0,0160 0,0250 0,0530Y 0 -0,0020 -0,0050 0,0380 0,0060

0 0,0150 0,0180 0,1280 0,0660table X 0 0,0410 0,0530 0,0610 0,0650

Y 0 -0,0080 -0,0080 -0,0080 -0,0080Z 0 -0,0100 -0,0090 -0,0090 -0,0090

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

0,0700

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

89



position CFG:

§ Displacement of ball screw X: Displacement of ball screw X: same case than for

293K and 295K.

§ Displacement of ball screw Y: same case than for 293K and 295K.

§ Displacement of ball screw Z: Displacement of ball screw Z: same case than for

293K and 295K.

GLASS SCALE T=298K Positions CFG



ball screw Y X 0 -0,0180 -0,0180 -0,0180 -0,0180Y 0 0,0290 0,0570 0,0790 0,0970Z 0 -0,1320 -0,1310 -0,1290 -0,1270

ball screw Z X 0 0,0020 0,0030 0,0080 0,0100Y 0 -0,0440 -0,0440 -0,0390 -0,0390Z 0 -0,0620 -0,0500 -0,0330 -0,0270

tool X 0 0,0210 0,0250 0,0320 0,0570Y 0 -0,0280 -0,0320 0,0090 -0,0240Z 0 -0,0580 -0,0600 0,0280 -0,0310

table X 0 0,0440 0,0440 0,0430 0,0430Y 0 -0,0210 -0,0210 -0,0210 -0,0200Z 0 -0,0260 -0,0240 -0,0240 -0,0230




ball screw Y X 0 -0,0180 -0,0180 -0,0180 -0,0180Y 0 0,0290 0,0570 0,0790 0,0970Z 0 -0,1320 -0,1310 -0,1290 -0,1270

ball screw Z X 0 0,0020 0,0030 0,0080 0,0100Y 0 -0,0450 -0,0440 -0,0380 -0,0360Z 0 -0,0620 -0,0500 -0,0310 -0,0260

tool X 0 0,0210 0,0250 0,0320 0,0580Y 0 -0,0280 -0,0300 0,0120 -0,0200Z 0 -0,0380 -0,0320 0,0760 0,0150

table X 0 0,0730 0,0850 0,0930 0,0970Y 0 -0,0210 -0,0210 -0,0210 -0,0200Z 0 -0,0260 -0,0240 -0,0240 -0,0230

90

§ Displacement of Tool: Same case than for 293K and 295K. The difference

between displacement of ball screw and glass scale in Z direction continues

being 0,020 mm and increase to 0,05 mm when we raise spindle speed

rotation.

§ Displacement of Table: Same case than for 293K and 295K, but now, even if the



8.2.4 Conclusions at position CFG with different initial temperatures

We can say as general conclusions at position BEH that:

§ For ball screw X glass scale does not improve displacements in any direction

and these displacements increase with initial temperature in all directions.

§ For ball screw Y: glass scale does not improve displacement in any direction.

§ For ball screw Z: glass scale improves displacement between glass scale in

0,020 mm in Y direction but level of this displacement increase with initial

temperature.

§ For Tool: glass scale improves displacements in 0,020 mm in Z direction with

dependency of spindle speed rotation.

-‐0,0500

-‐0,0400

-‐0,0300

-‐0,0200

-‐0,0100

0,0000

0,0100

0,0200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Z, displacement in Y during work cycle with different iniaal temperatures at posiaon CFG




91

§ For Table: glass scale improves displacement in X direction but this

displacement increase with initial temperature.

8.3 Conclusions drawn from computing analysis

Attending to conclusions draw from position BEH and position CFG we are looking in

this section for common or different aspects of behavior of machine centre in function

of position of headstock and table.

§ For ball screw X: glass scale of course does not improve displacements in any

direction. This is useful to probe that both models, with and without glass scale,

are well done. These displacements increase with initial temperature in all

directions. If ball screw X is in point G, then LG=Lmax (where Lmax is measured

from the motor to the nut) and in order to

∆! = !"∆!

end of spindle displacements in X direction are maximum and double than in

point H because LH=LG/2

§ For ball screw Y: glass scale of course does not improve displacements in any

directions and has no dependency on position. Is important here to notice that

displacements in Y direction there are for each point in the range of 0,030 mm

to 0,110 mm. These are quite big displacements that did not been reduced with

the glass scale.

-‐0,0100

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Table, displacement in X during work cycle with different iniaal temperatures at posiaon CFG




92

§ For ball screw Z: glass scale improves displacement in 0,020 mm in Y direction

but level of displacement increase with initial temperature and has no

dependency of position but increase in a constant value of 0,020 mm from

293K to 295K and 0,020 mm from 295K to 298K so it is possible to correct these

displacements.

§ For Tool: glass scale improves displacement depending on position and spindle

speed rotation. For position BEH glass scale improves displacement in Y and Z

direction but for position CFG only improves in Z direction. This means that in

positions at middle point of glass scale, L≈0 (in case of glass scale we measure L

from the middle point to the reading head) displacements are smaller in order

to

∆! = !"∆!

§ For Table: glass scale improves displacement only in X direction and with

dependency on ambient temperature which makes level of displacement

increase in constant values so it is possible to correct these displacements.

In general terms, a glass scale at X direction (the one with the reading head fix to the

table) improves displacements of the table in X direction and although level of these

displacements increase with initial temperature, it is possible to compensate them

because increases in constant values.

There is a big displacement in the range of 0,030 mm to 0,110 mm for ball screw Y in Y

direction with or without glass scale with any dependency of position.

Glass scale at the headstock improves displacement of headstock always in Z direction

with dependency of spindle speed rotation and in Y direction only when headstock is

at the middle of glass scale.

93

9. Conclusions leading to improve of machining centre design

In order to conclusions on section 8.3 we know that glass scale improves displacements when heat fluxes do not increase too much temperature of the glass scale. This happens with the glass scale on X direction, the one in the base of the machine centre and with the reading head fixed to the table. This glass scale is only influenced by power losses of ball screw X. This power losses are not too big so the thermal deformation of the glass scale is small, in other words, glass scale at the table does not increase its own temperature too much. When this happens glass scale improves displacements like glass scale at the table with table displacements in X direction.

According to this, we know that it is important that glass scale do not increase it own temperature during thermal deformation. Power losses at the headstock are big and produces hit fluxes that increase temperature of glass scale on Z direction. One solution to avoid this problem is to isolate the glass scale at the head stock. This can be made by using low thermal conductivity materials between the aluminum body of the linear encoder and the special shapes to fix it to the body of the machine tool. Doing this, heat fluxes from power losses at the headstock will increase temperature of glass scale in Z direction but not too much so thermal deformation of the glass scale will be smaller.

Position of glass scale is also important. As we see after computation, when reading head is at middle point of glass scale (the point that is fixed as fastened connection property) displacements are smaller. If we change position of glass scale so the fixed point will be closer to end of spindle, displacements at this point will be better, but it will be worst in the middle and in the other side of the spindle. Better solution is to keep glass scale positions as in our models so displacements will be smaller when table and headstocks are at position BEH.

94

10. Attachments

Here are shown all the results of computation.




ball screw Y X 0 0,0009 0,0010 0,0010 0,0010Y 0 0,0300 0,0480 0,0600 0,0700Z 0 0,0020 0,0010 0,0001 -0,0006

ball screw Z X 0 0,0020 0,0030 0,0080 0,0110Y 0 0,0040 0,0040 0,0090 0,0090Z 0 0,0210 0,0290 0,0470 0,0500

tool X 0 0,0030 0,0110 0,0240 0,0500Y 0 0,0170 0,0110 0,0630 0,0260Z 0 0,0370 0,0250 0,1270 0,0530

table X 0 -0,0010 -0,0009 -0,0008 -0,0007Y 0 0,0006 0,0005 0,0004 0,0003Z 0 0,0010 0,0010 0,0010 0,0010




ball screw Y X 0 -0,0070 -0,0070 -0,0060 -0,0060Y 0 0,0260 0,0430 0,0550 0,0650Z 0 -0,0510 -0,0510 -0,0510 -0,0500

ball screw Z X 0 0,0020 0,0030 0,0080 0,0100Y 0 -0,0100 -0,0100 -0,0060 -0,0060Z 0 -0,0190 -0,0110 0,0070 0,0110

tool X 0 0,0100 0,0160 0,0280 0,0530Y 0 0,0020 -0,0040 0,0470 0,0100Z 0 -0,0090 -0,0180 0,0830 0,0100

table X 0 0,0120 0,0120 0,0120 0,0120Y 0 -0,0080 -0,0080 -0,0080 -0,0080Z 0 -0,0130 -0,0130 -0,0130 -0,0120

95




ball screw Y X 0 -0,0180 -0,0180 -0,0180 -0,0180Y 0 0,0200 0,0350 0,0470 0,0560Z 0 -0,1310 -0,1300 -0,1270 -0,1240

ball screw Z X 0 0,0030 0,0040 0,0080 0,0100Y 0 -0,0310 -0,0320 -0,0280 -0,0280Z 0 -0,0800 -0,0710 -0,0520 -0,0460

tool X 0 0,0190 0,0240 0,0340 0,0570Y 0 -0,0210 -0,0270 0,0220 -0,0150Z 0 -0,0780 -0,0830 0,0160 -0,0540

table X 0 0,0310 0,0310 0,0300 0,0300Y 0 -0,0210 -0,0210 -0,0210 -0,0210Z 0 -0,0360 -0,0350 -0,0340 -0,0330




ball screw Y X 0 0,0009 0,0010 0,0010 0,0010Y 0 0,0400 0,0690 0,0920 0,1100Z 0 0,0020 -0,0004 -0,0020 -0,0030

ball screw Z X 0 0,0020 0,0030 0,0090 0,0120Y 0 0,0040 0,0050 0,0100 0,0100Z 0 0,0230 0,0330 0,0490 0,0530

tool X 0 0,0020 0,0100 0,0200 0,0490Y 0 0,0140 0,0090 0,0520 0,0180Z 0 0,0310 0,0230 0,1130 0,0520

table X 0 -0,0010 -0,0010 -0,0010 -0,0010Y 0 0,0006 0,0004 0,0003 0,0003Z 0 0,0010 0,0010 0,0010 0,0010




ball screw Y X 0 -0,0070 -0,0060 -0,0060 -0,0060Y 0 0,0360 0,0640 0,0870 0,1050Z 0 -0,0520 -0,0530 -0,0530 -0,0530

ball screw Z X 0 0,0020 0,0030 0,0090 0,0120Y 0 -0,0150 -0,0150 -0,0100 -0,0100Z 0 -0,0110 -0,0004 0,0160 0,0210

tool X 0 0,0100 0,0160 0,0250 0,0530Y 0 -0,0030 -0,0080 0,0350 0,0009Z 0 -0,0050 -0,0110 0,0790 0,0190

table X 0 0,0170 0,0170 0,0170 0,0160Y 0 -0,0080 -0,0080 -0,0080 -0,0080Z 0 -0,0100 -0,0090 -0,0090 -0,0080

96

GLASS SCALE T=298K Positions CFG



ball screw Y X 0 -0,0180 -0,0180 -0,0180 -0,0180Y 0 0,0290 0,0570 0,0790 0,0970Z 0 -0,1320 -0,1310 -0,1290 -0,1270

ball screw Z X 0 0,0020 0,0030 0,0080 0,0100Y 0 -0,0440 -0,0440 -0,0390 -0,0390Z 0 -0,0620 -0,0500 -0,0330 -0,0270

tool X 0 0,0210 0,0250 0,0320 0,0570Y 0 -0,0280 -0,0320 0,0090 -0,0240Z 0 -0,0580 -0,0600 0,0280 -0,0310

table X 0 0,0440 0,0440 0,0430 0,0430Y 0 -0,0210 -0,0210 -0,0210 -0,0200Z 0 -0,0260 -0,0240 -0,0240 -0,0230




ball screw Y X 0 0,0009 0,0010 0,0010 0,0010Y 0 0,0300 0,0470 0,0600 0,0700Z 0 0,0020 0,0009 0,0003 -0,0008

ball screw Z X 0 0,0010 0,0030 0,0070 0,0110Y 0 0,0140 0,0200 0,0280 0,0330Z 0 0,0200 0,0270 0,0450 0,0490

tool X 0 0,0040 0,0110 0,0260 0,0510Y 0 0,0280 0,0280 0,0830 0,0510Z 0 0,0450 0,0380 0,1500 0,0810

table X 0 0,0080 0,0130 0,0150 0,0160Y 0 0,0006 0,0005 0,0004 0,0003Z 0 0,0010 0,0010 0,0010 0,0010




ball screw Y X 0 -0,0070 -0,0070 -0,0060 -0,0060Y 0 0,0260 0,0420 0,0540 0,0640Z 0 -0,0510 -0,0510 -0,0510 -0,0500

ball screw Z X 0 0,0020 0,0030 0,0070 0,0100Y 0 0,0020 0,0080 0,0160 0,0210Z 0 -0,0210 -0,0130 0,0050 0,0100

tool X 0 0,0100 0,0160 0,0300 0,0540Y 0 0,0150 0,0150 0,0700 0,0370Z 0 -0,0008 -0,0060 0,1050 0,0370

table X 0 0,0220 0,0260 0,0280 0,0290Y 0 -0,0080 -0,0080 -0,0080 -0,0080Z 0 -0,0130 -0,0130 -0,0130 -0,0120

97




ball screw Y X 0 -0,0180 -0,0180 -0,0180 -0,0180Y 0 0,0200 0,0350 0,0470 0,0550Z 0 -0,1310 -0,1300 -0,1270 -0,1240

ball screw Z X 0 0,0030 0,0040 0,0080 0,0100Y 0 -0,0160 -0,0100 -0,0020 0,0020Z 0 -0,0810 -0,0720 -0,0530 -0,0470

tool X 0 0,0190 0,0240 0,0350 0,0580Y 0 -0,0050 -0,0040 0,0490 0,0160Z 0 -0,0690 -0,0710 0,0380 -0,0280

table X 0 0,0420 0,0470 0,0490 0,0490Y 0 -0,0210 -0,0210 -0,0210 -0,0210Z 0 -0,0350 -0,0340 -0,0330 -0,0330




ball screw Y X 0 0,0009 0,0010 0,0010 0,0010Y 0 0,0390 0,0680 0,0910 0,1100Z 0 0,0020 -0,0004 -0,0020 -0,0030

ball screw Z X 0 0,0020 0,0030 0,0100 0,0120Y 0 0,0050 0,0060 0,0120 0,0130Z 0 0,0230 0,0330 0,0520 0,0540

tool X 0 0,0020 0,0100 0,0210 0,0500Y 0 0,0160 0,0110 0,0550 0,0230Z 0 0,0500 0,0510 0,1630 0,1010

table X 0 0,0200 0,0320 0,0400 0,0440Y 0 0,0006 0,0004 0,0004 0,0003Z 0 0,0010 0,0010 0,0010 0,0010




ball screw Y X 0 -0,0070 -0,0060 -0,0060 -0,0060Y 0 0,0350 0,0640 0,0860 0,1050Z 0 -0,0520 -0,0530 -0,0530 -0,0530

ball screw Z X 0 0,0020 0,0030 0,0090 0,0120Y 0 -0,0150 -0,0140 -0,0080 -0,0070Z 0 -0,0110 -0,0006 0,0190 0,0220

tool X 0 0,0100 0,0160 0,0250 0,0530Y 0 -0,0020 -0,0050 0,0380 0,0060

0 0,0150 0,0180 0,1280 0,0660table X 0 0,0410 0,0530 0,0610 0,0650

Y 0 -0,0080 -0,0080 -0,0080 -0,0080Z 0 -0,0100 -0,0090 -0,0090 -0,0090

98




ball screw Y X 0 -0,0180 -0,0180 -0,0180 -0,0180Y 0 0,0290 0,0570 0,0790 0,0970Z 0 -0,1320 -0,1310 -0,1290 -0,1270

ball screw Z X 0 0,0020 0,0030 0,0080 0,0100Y 0 -0,0450 -0,0440 -0,0380 -0,0360Z 0 -0,0620 -0,0500 -0,0310 -0,0260

tool X 0 0,0210 0,0250 0,0320 0,0580Y 0 -0,0280 -0,0300 0,0120 -0,0200Z 0 -0,0380 -0,0320 0,0760 0,0150

table X 0 0,0730 0,0850 0,0930 0,0970Y 0 -0,0210 -0,0210 -0,0210 -0,0200Z 0 -0,0260 -0,0240 -0,0240 -0,0230

99

0,0000 0,0050 0,0100 0,0150 0,0200 0,0250 0,0300 0,0350

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw X, displacement in X during work cycle with iniaal temperature 295K at posiaon BEH

glass scale YES

glass scale NO

0,0000

0,0005

0,0010

0,0015

0,0020

0,0025

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw X, displacement in Y during work cycle with iniaal temperature 295K at posiaon BEH

glass scale YES

glass scale NO

100

-‐0,0105

-‐0,0100

-‐0,0095

-‐0,0090

-‐0,0085 3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw X, displacement in Z during work cycle with iniaal temperature 295K at posiaon BEH

glass scale YES

glass scale NO

0,0360 0,0380 0,0400 0,0420 0,0440 0,0460 0,0480 0,0500

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw X, displacement in X during work cycle with iniaal temperature 298K at posiaon BEH

glass scale YES

glass scale NO

0,0000

0,0010

0,0020

0,0030

0,0040

0,0050

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw X, displacement in Y during work cycle with iniaal temperature 298K at posiaon BEH

glass scale YES

glass scale NO

101

-‐0,0265

-‐0,0260

-‐0,0255

-‐0,0250

-‐0,0245

-‐0,0240

-‐0,0235

-‐0,0230 3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw X, displacement in Z during work cycle with iniaal temperature 298K at posiaon BEH

glass scale YES

glass scale NO

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw X, displacement in X during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

0,0000

0,0001

0,0002

0,0003

0,0004

0,0005

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw X, displacement in Y during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

102

0,0000

0,0002

0,0004

0,0006

0,0008

0,0010

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw X, displacement in Z during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000

0,0005

0,0010

0,0015

0,0020

0,0025

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

103

-‐0,0120

-‐0,0100

-‐0,0080

-‐0,0060

-‐0,0040

-‐0,0020

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000 0,0100 0,0200 0,0300 0,0400 0,0500 0,0600 0,0700 0,0800

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000 0,0005 0,0010 0,0015 0,0020 0,0025 0,0030 0,0035

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

104

-‐0,0275

-‐0,0270

-‐0,0265

-‐0,0260

-‐0,0255

-‐0,0250

-‐0,0245

-‐0,0240 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0009 0,0009 0,0009 0,0009 0,0010 0,0010 0,0010 0,0010

3600 7200 10800 14400

displacemen

t (mm)

ame(s)

ball screw Y, displacement in X during work cycle with iniaal temperature 293K at posiaon BEH

ball screw YES

ball screw NO

0,0000 0,0100 0,0200 0,0300 0,0400 0,0500 0,0600 0,0700 0,0800

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Y, displacement in Y during work cycle with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

105

-‐0,0010

-‐0,0005

0,0000

0,0005

0,0010

0,0015

0,0020

0,0025

3600 7200 10800 14400 displacemen

t (mm)

ame (s)

ball screw Y, displacement in Z during work cylce with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

-‐0,0072 -‐0,0070 -‐0,0068 -‐0,0066 -‐0,0064 -‐0,0062 -‐0,0060 -‐0,0058 -‐0,0056 -‐0,0054

3600 7200 10800 14400

displacemen

t (mm)

ame(s)


glass scale YES

glass scale NO

0,0000 0,0100 0,0200 0,0300 0,0400 0,0500 0,0600 0,0700

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

106

-‐0,0512 -‐0,0510 -‐0,0508 -‐0,0506 -‐0,0504 -‐0,0502 -‐0,0500 -‐0,0498 -‐0,0496 -‐0,0494

3600 7200 10800 14400 displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0200

-‐0,0150

-‐0,0100

-‐0,0050

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame(s)


glass scale YES

glass scale NO

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

107

-‐0,1320

-‐0,1300

-‐0,1280

-‐0,1260

-‐0,1240

-‐0,1220

-‐0,1200 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0008

0,0009

0,0009

0,0010

0,0010

0,0011

3600 7200 10800 14400

displacemen

t (mm)

ame(s)

ball screw Y, displacement in X during work cycle with iniaal temperature 293K at posiaon CFG

ball screw YES

ball screw NO

0,0000

0,0200

0,0400

0,0600

0,0800

0,1000

0,1200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Y, displacement in Y during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

108

-‐0,0040

-‐0,0030

-‐0,0020

-‐0,0010

0,0000

0,0010

0,0020

0,0030

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Y, displacement in Z during work cylce with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

-‐0,0072 -‐0,0070 -‐0,0068 -‐0,0066 -‐0,0064 -‐0,0062 -‐0,0060 -‐0,0058 -‐0,0056 -‐0,0054

3600 7200 10800 14400

displacemen

t (mm)

ame(s)


glass scale YES

glass scale NO

0,0000

0,0200

0,0400

0,0600

0,0800

0,1000

0,1200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

109

-‐0,0532 -‐0,0530 -‐0,0528 -‐0,0526 -‐0,0524 -‐0,0522 -‐0,0520 -‐0,0518 -‐0,0516 -‐0,0514

3600 7200 10800 14400 displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0200

-‐0,0150

-‐0,0100

-‐0,0050

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame(s)


glass scale YES

glass scale NO

0,0000

0,0200

0,0400

0,0600

0,0800

0,1000

0,1200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

110

-‐0,1330 -‐0,1320 -‐0,1310 -‐0,1300 -‐0,1290 -‐0,1280 -‐0,1270 -‐0,1260 -‐0,1250 -‐0,1240

3600 7200 10800 14400 displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,00000

0,00200

0,00400

0,00600

0,00800

0,01000

0,01200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Z, displacement in X during work cycle with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

0,00000 0,00500 0,01000 0,01500 0,02000 0,02500 0,03000 0,03500

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

111

0,00000

0,01000

0,02000

0,03000

0,04000

0,05000

0,06000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Z, displacement in Z during work cycle with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

0,0000

0,0020

0,0040

0,0060

0,0080

0,0100

0,0120

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0150 -‐0,0100 -‐0,0050 0,0000 0,0050 0,0100 0,0150 0,0200 0,0250

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

112

-‐0,0250 -‐0,0200 -‐0,0150 -‐0,0100 -‐0,0050 0,0000 0,0050 0,0100 0,0150

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000

0,0020

0,0040

0,0060

0,0080

0,0100

0,0120

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0350 -‐0,0300 -‐0,0250 -‐0,0200 -‐0,0150 -‐0,0100 -‐0,0050 0,0000 0,0050

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

113

-‐0,1000

-‐0,0800

-‐0,0600

-‐0,0400

-‐0,0200

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,04000

-‐0,03000

-‐0,02000

-‐0,01000

0,00000

0,01000

0,02000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)





-‐0,020000

-‐0,010000

0,000000

0,010000

0,020000

0,030000

0,040000

3600 7200 10800 14400 displacemen

t (mm)

ame (s)


glass scale NO 293K

glass scale NO 295K

glass scale NO 298K

114

0,0000 0,0020 0,0040 0,0060 0,0080 0,0100 0,0120 0,0140

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Z, displacement in X during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

0,0000 0,0020 0,0040 0,0060 0,0080 0,0100 0,0120 0,0140

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Z, displacement in Y during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

ball screw Z, displacement in Z during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

115

0,0000 0,0020 0,0040 0,0060 0,0080 0,0100 0,0120 0,0140

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0160

-‐0,0140

-‐0,0120

-‐0,0100

-‐0,0080

-‐0,0060

-‐0,0040

-‐0,0020

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0150 -‐0,0100 -‐0,0050 0,0000 0,0050 0,0100 0,0150 0,0200 0,0250

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

116

0,0000

0,0020

0,0040

0,0060

0,0080

0,0100

0,0120

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0500

-‐0,0400

-‐0,0300

-‐0,0200

-‐0,0100

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0700

-‐0,0600

-‐0,0500

-‐0,0400

-‐0,0300

-‐0,0200

-‐0,0100

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

117

-‐0,0500

-‐0,0400

-‐0,0300

-‐0,0200

-‐0,0100

0,0000

0,0100

0,0200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)





-‐0,0500

-‐0,0400

-‐0,0300

-‐0,0200

-‐0,0100

0,0000

0,0100

0,0200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale NO 293K

glass scale NO 295K

glass scale NO 298K

0,00000

0,01000

0,02000

0,03000

0,04000

0,05000

0,06000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in X during work cycle with iniaal temperature 293K at posaaon BEH

glass scale YES

glass scale NO

118

0,00000

0,02000

0,04000

0,06000

0,08000

0,10000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,00000 0,02000 0,04000 0,06000 0,08000 0,10000 0,12000 0,14000 0,16000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

3600 7200 10800 14400

dispacem

ent (mm)

ame (s)

Tool, displacement in X during work cycle with iniaal temperature 295K at posiaon BEH

glass scale YES

glass scale NO

119

-‐0,0200

0,0000

0,0200

0,0400

0,0600

0,0800

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacemtent in Y during work cycle with iniaal temperature 295K at posiaon BEH

glass scale YES

glass scale NO

-‐0,0400 -‐0,0200 0,0000 0,0200 0,0400 0,0600 0,0800 0,1000 0,1200

3600 7200 10800 14400 displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000 0,0100 0,0200 0,0300 0,0400 0,0500 0,0600 0,0700

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in X during work cycle with iniaal temperature 298K at posiaon BEH

glass scale YES

glass scale NO

120

-‐0,0400

-‐0,0200

0,0000

0,0200

0,0400

0,0600

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,1000 -‐0,0800 -‐0,0600 -‐0,0400 -‐0,0200 0,0000 0,0200 0,0400 0,0600

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,10000

-‐0,05000

0,00000

0,05000

0,10000

0,15000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in Z during work cycle with different iniaal temperatures at posiaon BEH




121

-‐0,100000

-‐0,050000

0,000000

0,050000

0,100000

0,150000

0,200000

3600 7200 10800 14400 displacemen

t (mm)

ame (s)

Tool, displacement in Z during work cycle with different iniaal temperatures at posiaon BEH

glass scale NO 293K

glass scale NO 295K

glass scale NO 298K

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in X during work cycle with iniaal temperature 293K at posaaon CFG

glass scale YES

glass scale NO

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in Y during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

122

0,0000

0,0500

0,1000

0,1500

0,2000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

3600 7200 10800 14400

dispacem

ent (mm)

ame (s)

Tool, displacement in X during work cycle with iniaal temperature 295K at posiaon CFG

glass scale YES

glass scale NO

-‐0,0200

-‐0,0100

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

3600 7200 10800 14400 displacemen

t (mm)

ame (s)

Tool, displacemtent in Y during work cycle with iniaal temperature 295K at posiaon CFG

glass scale YES

glass scale NO

123

-‐0,0200 0,0000 0,0200 0,0400 0,0600 0,0800 0,1000 0,1200 0,1400

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000 0,0100 0,0200 0,0300 0,0400 0,0500 0,0600 0,0700

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in X during work cycle with iniaal temperature 298K at posiaon CFG

glass scale YES

glass scale NO

-‐0,0400

-‐0,0300

-‐0,0200

-‐0,0100

0,0000

0,0100

0,0200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in Y during work cycle with iniaal temperature 298K at posiaon CFG

glass scale YES

glass scale NO

124

-‐0,0800 -‐0,0600 -‐0,0400 -‐0,0200 0,0000 0,0200 0,0400 0,0600 0,0800 0,1000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,1000

-‐0,0500

0,0000

0,0500

0,1000

0,1500

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in Z during work cycle with different iniaal temperatures at posiaon CFG




-‐0,0500

0,0000

0,0500

0,1000

0,1500

0,2000

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Tool, displacement in Z during work cycle with different iniaal temperatures at posiaon CFG

glass scale NO 293K

glass scale NO 295K

glass scale NO 298K

125

-‐0,005

0

0,005

0,01

0,015

0,02

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0 0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Table, displacement in Y during work cycle with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

0

0,0002

0,0004

0,0006

0,0008

0,001

0,0012

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Table, displacement in Z during work cycle with iniaal temperature 293K at posiaon BEH

glass scale YES

glass scale NO

126

0,0000 0,0050 0,0100 0,0150 0,0200 0,0250 0,0300 0,0350

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0100

-‐0,0080

-‐0,0060

-‐0,0040

-‐0,0020

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0132 -‐0,0130 -‐0,0128 -‐0,0126 -‐0,0124 -‐0,0122 -‐0,0120 -‐0,0118 -‐0,0116 -‐0,0114

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

127

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0250

-‐0,0200

-‐0,0150

-‐0,0100

-‐0,0050

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0370

-‐0,0360

-‐0,0350

-‐0,0340

-‐0,0330

-‐0,0320

-‐0,0310 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

128

0

0,01

0,02

0,03

0,04

0,05

0,06

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Table, displacement in X during work cycle with different iniaal temperatures at posiaon BEH

glass scale NO 293K

glass scale NO 295K

glass scale NO 298K

-‐0,0100

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000

0,0001

0,0002

0,0003

0,0004

0,0005

0,0006

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Table, displacement in Y during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

129

0,0010 0,0010 0,0010 0,0010 0,0010 0,0010 0,0010 0,0010 0,0010 0,0010

3600 7200 10800 14400

displacemen

t (mm)

ame (s)

Table, displacement in Z during work cycle with iniaal temperature 293K at posiaon CFG

glass scale YES

glass scale NO

0,0000 0,0100 0,0200 0,0300 0,0400 0,0500 0,0600 0,0700

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0120

-‐0,0100

-‐0,0080

-‐0,0060

-‐0,0040

-‐0,0020

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

130

-‐0,0100

-‐0,0080

-‐0,0060

-‐0,0040

-‐0,0020

0,0000 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

0,0000

0,0200

0,0400

0,0600

0,0800

0,1000

0,1200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0212 -‐0,0210 -‐0,0208 -‐0,0206 -‐0,0204 -‐0,0202 -‐0,0200 -‐0,0198 -‐0,0196 -‐0,0194

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

131

-‐0,0270

-‐0,0260

-‐0,0250

-‐0,0240

-‐0,0230

-‐0,0220

-‐0,0210 3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale YES

glass scale NO

-‐0,0100

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

3600 7200 10800 14400

displacemen

t (mm)

ame (s)





0,0000

0,0200

0,0400

0,0600

0,0800

0,1000

0,1200

3600 7200 10800 14400

displacemen

t (mm)

ame (s)


glass scale NO 293K

glass scale NO 295K

glass scale NO 298K

132

11. References

[1] Heidenhain linear scales http://www.heidenhain.com

[2] Luis Miguel Sanchez-‐Brea and Tomas Morlanes 2008 Metrological errors in optical encoders Meas. Sci. Technol. 19

[3] Ignacio Alejandre and Mariano Artés 2006 Analysis of the Precision Lost in Optical Linear Encoders as a Consequence of Reticule Deformation, Informacion Tecnologica v 17, n6 La Serena 2006.

[4] Thomas P. Moran and John M. Carroll 1996 Design Rationale: Concepts, Techniques and Use Lawerence Erlbaum Associates.

[5] M. Weck, P. McKeown, R. Bonse and U. Herbst: Reduction and compensation of Thermal Errors in Machine Tools, Annals of the CIRP, Vol 44, Issue 2, 1995, pages 589-‐598.

[6] L.K. Kayak, E.E. Sharova and O.V. Yachmentsev: Linear and Angular measurements. Metrological means of increasing the accuracy of precision machine tools, UDC (531.71=531.74).088:621.9

[7] L.K. Kayak: Linear and Angular measurements. Standardization of Linear measurements, UDC 389.6:531.71

[8] P. Compton and R. Jansen 1989 A philosophical basis for knowledge acquisition, European knowledge acquisition for knowledge based systems workshop 1989

[9] Clyde W. Holsapple and Andrew B. Whinston, Manager's Guide to Expert Systems Using Guru

[10] SKF Group, Interactive engineering catalog: http://www.skf.com/portal/skf/home/products?maincatalogue=1&newlink=first&lang=en

[11] Tae Jo Ko, Tae-‐weon Gim and Jae-‐yong Ha: Particular behavior of spindle thermal deformation by thermal bending, International Journal of Machine Tool and Manufacture 43 (2003) 17-‐23

[12] Jong-‐Jin Kim, Young Hun Jeong and Dong-‐Woo Cho: Thermal behavior of a machine tool equipped with linear motors, International Journal of Machine Tool and Manufacture 44(2004) 749-‐758

[13] H.J. Pahk and S.W. Lee: Thermal Error Measurement and Real Time Compensation System for the CNC Machine Tools Incorporating the Spindle Thermal Error and the Feed Axis Thermal Error, , Int J Adv Technol(2002) 20:487-‐494

133

[14] Bernd Bossmanns A Power flow model for high speed motorized spindle, J.Manuf. Sci. Eng. 2001, vol 123, issue 3, 493

[15] Eugene A. Avallone, Theodore Baumeister Marks' Standard Handbook for Mechanical Engineers, McGraw-‐Hill Professional 2006, ISBN: 0071428674

Analyses of Linear Encoder Application (Glass Scale) on Quality of Machining Centre by Santiago M....

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