Wine Name Class Class Name Medal Class Award Texas Class ...
Automobile Class 2
-
Upload
ruchin-chahwala -
Category
Documents
-
view
218 -
download
0
Transcript of Automobile Class 2
-
8/3/2019 Automobile Class 2
1/33
-
8/3/2019 Automobile Class 2
2/33
9/20/2011
2
x y
L
mg
CG
H
Fi=ma
a=3 m/s2
A B
R2R1
P
-
8/3/2019 Automobile Class 2
3/33
9/20/2011
3
-
8/3/2019 Automobile Class 2
4/33
9/20/2011
4
VEHICLE MECHANICS
1.1 Laws of Equilibrium : If a body is inEquilibrium then :-
(a) The resultant of all the forces acting on it is
zero.
And
(b) The resultant of all the couples and themoments of all the forces taken about
any axis whatsoever is zero.
In the most general case, the laws of
equilibrium will enable us to write down
six equations,
Three by equating to zero the force along
the three axis
Three by taking moment about the
three axis
But the majority of problems do not require
the formulation of all six equation.
-
8/3/2019 Automobile Class 2
5/33
9/20/2011
5
1.2 Weight/Force Distribution in Two wheeler :-
a b
L
R2R1
CGFront Rear
W
x
x
Fy = 0, R1 + R2 = W ....... (i)
Taking moment about x-x,
(ii)
(iii)
Substituting (iii) in (i),
(iv)2 * *[1 ]W b b R W W L L
= =
1 * * R L W b=
1*W b
RL
=
-
8/3/2019 Automobile Class 2
6/33
9/20/2011
6
Example 2 :
A two wheeler has an unladden weight of 100.3 kg and a
wheel base of 1230mm. If the CG is displaced by 575 mmfrom rear wheel axis. Determine the load shared by front and
rear wheels.
1
* 983.943*0.575
459.971.230
W b
R NL= = =
20.575
*[1 ] 983.943*[1 ] 523.9731.230
b R W N
L= = =
Soln. :
W= 100.3 * 9.81 = 983.943 N
L = 1.230 m, b = 0.575 m
we know that:
Example 3 :
During experimental measurement of the height ofCG, the above two wheeler was kept on an inclined
surface at 15 and the load distribution at front &
rear wheels was found to be 52.3 kg & 48 kg
respectively. Determine the height of CG of this
vehicle.
The mean tyre radius is 0.225 m. Also state the
limiting value of slope on which the vehicle will
be stable.
-
8/3/2019 Automobile Class 2
7/33
9/20/2011
7
R2
R1
W
Taking moment about A,
2*cos * *sin * * *cos R L W H W a + =
2*sin * * *cos *cos *W H W a R L =
* si nW
2[ * ]* cot
R H a L
W
=
2*cot * *cot
R H a L
W =
48*9.81[0.655 *1.23]* cot15 0.2477
983.943H m = =
.. (1)
.. (2)
.. (3)
Ans.
Dividing by
-
8/3/2019 Automobile Class 2
8/33
9/20/2011
8
Now R2COS is a reaction at rear wheel.
When this reaction tends to zero, the
vehicle becomes unstable & may over-
turn about pt. A.
2*cos * * *cos *sin * R L W a W H =
2*
*cos *cos * *sinW a W
R HL L
=
Now Rewriting Equation no. (2)
Thus limiting value of may be obtained as:
2 ** cos 0 * cos * * sinW a WR HL L
= =
( * cos * sin ) 0W
a HL
= =
0W
L
*cos *sina H =
0.655
tan 2.6440.2477L
a
H = = =
lim] 69.28 =
[Note: In practice, this is
limited by road adhesion]
-
8/3/2019 Automobile Class 2
9/33
9/20/2011
9
These equations very clearly signifies two
facts:
(i) For better stability of vehicle, the CG
disposition must as further as possible
from front axle
(ii) CG must be as lower as possible.
Example 4 :
A bike driver takes his bike to weigh bridge
for determination of its correct CG, he
intends to take part in a bike race, when
front wheel alone enters the weigh bridge,
the load indicated is 78 kg when both
wheels are taken to weighbridge, the
indicated load is 170 kg.
-
8/3/2019 Automobile Class 2
10/33
9/20/2011
10
Now he takes out front wheel from the bridge
on level road & raises the rear wheel by 10cms on weighbridge. The load indicated is 88
kg. If wheel base is 1.208 m & tyre radius is
225 mm.
Determine
(i) CG Position.
(ii) Limiting value of slope on which vehicle
will be stable.
a b
L
W
CG
A B
R2R1
Case : 1
-
8/3/2019 Automobile Class 2
11/33
9/20/2011
11
Data:Case : 1
R1 = 78 kg = 765.18 NW= 170 kg = 1667.7 N
Fy = 0; W = R1 + R2
R2 = 902.52 NNow taking moments about A,
R2*L = W*a
2* 902.52*1.208 0.65371667.7
R La mW
= = =
1.208 0.6537 0.5543b L a m = = =
W
A
B
R2
R1
LCOS
x
aCOSh=0.10 m
Case : 2
-
8/3/2019 Automobile Class 2
12/33
9/20/2011
12
Selecting AB as a moment arm and taking moment
about point A,
2 * * cos *{ *cos ( ) *sin } R L W a h r =
2* *cos * *cos *( )*sin R L W a W h r =
2( ) * co t * * co t
Rh r a L
W =
Dividing by W*sin
2
( * ) * cot
R
H r a LW = +
863.280.225 (0.6537 *1.208) *cot
1667.7= +
4.7585 =
cot 4.7585 12.0385 =
0.566H m =
Now we know that Limiting value of slope,
0.6537
tan 0.5666La
H ==
tan 1.153L =
49.08L =
0.100
sin 0.082781.208
h
L = = =Now
-
8/3/2019 Automobile Class 2
13/33
9/20/2011
13
Weight Distribution in aWeight Distribution in a
ThreeThree--Wheeled VehicleWheeled Vehicle
a b
L
W
CG
A B
R2R3R1
C
C
R3
R2
H
R1
x
x
z
z
y yB=2c
-
8/3/2019 Automobile Class 2
14/33
9/20/2011
14
Fy = 0; W = R1 + R2 + R3 (i)
Now taking moments about x-x,R1*L = W*b (ii)
Now taking moments about y-y,
R3*c = W*x +R2*c
R3 - R2 = (iii)
Now taking moments about z-z,
R2*L+ R3*L = W*a
R2 + R3 = (iv)*W a
L
*W x
c
1 2 3 R W R R=
2 [ ]2
W a xR
l c=
(iii) + (iv)
. (v)
(iv) - (iii)
(vi)
(vii)
3 [ ]2
W x aR
c l=
-
8/3/2019 Automobile Class 2
15/33
9/20/2011
15
Example 5:
A three-wheeler has a wheelbase of
1524 mm and its CG is 900 mm behind
front wheel axle and 160 mm from the
longitudinal axis of vehicle on near
side. The track of rear wheel is 870
mm. Determine the wheel loads, iftotal weight of the vehicle is 411 kg.
Sol.Given Data:
L=1.524 m
a=0.900 m
X=0.160 m, c= = 0.435 m
W=411 x9.81=4031.91 N
we know that,
0.870
2
2 2 [ ]
W a x
R l c=
24031.91 0.900 0.160
[ ] 449.024 45.7722 1.524 0.435
R N kg= = =
-
8/3/2019 Automobile Class 2
16/33
9/20/2011
16
3
2
[ ]W x a
Rc l
=
4031.91 0.160 0.900[ ]
2 0.435 1.524= +
1932.025 196.944 N kg= =
1 2 3 R W R R=
4031.91 449.024 1932.025
1650.86 168.28 N kg
=
= =
Example 6:
It is required to determine the CG of a threewheeler experimentally when one of the nearsiderear wheel is taken to weigh bridge, the loadrecorded is 160 kg while when opposite rearwheel is taken to weigh bridge the load is foundto be 80 kg. When both the rear wheels weretaken on weighbridge and raised by 110mm theload recorded was 235 kg.
Determine (i) CG position
(ii) limiting slope for stability.
The wheelbase and rear wheel track for this vehicleare 1.6m and 1m respectively while total weightof the vehicle is 425kg. The wheel diameter is 250mm.
-
8/3/2019 Automobile Class 2
17/33
9/20/2011
17
Solution:
Given data:
= 160 kg = 1569.6 N
D = 0.250 m
W = 425 kg
L = 1.6 m
C =1/2 = 0.5 m
Raised condition: [R2 + R3]=235 kg=2305.35 N
3R
For a three wheeler we know that :
22
[ ]W a xRl c
=
4169.25784.8 [ ]
2 1.6 0.5
a x=
4169.251569.6 [ ]2 1.6 0.5
a x= +
32
[ ]W a x
Rl c
= +
784.8 = 1302.891*a 4169.25*x . (1)
And
1569.6=1302.891*a + 4169.25*x . (3)
-
8/3/2019 Automobile Class 2
18/33
9/20/2011
18
Adding (1) + (3)
2354.4 = 2605.782*a
a=0.9035 m
b= L-a = 1.6 - 0.9035 = 0.6965 m
(3) - (1)
784.8 = 8338.5 * x
x=0.0941 m
W
A
B
R2,3
R1
x
h
h
r
-
8/3/2019 Automobile Class 2
19/33
9/20/2011
19
Selecting A-B as moment arm & taking moments
about A,
2,3* *cos *{ *cos ( )*sin } R L W a H r =
* *cos *( )*sinW a W H r =
Dividing by sinW
2, 3( ) * cot * * cot
R H r a L
W
=
2, 3[ * ]* cot
R H r a L
W = +
Now0.11
sin 0.068751.6
h
L= = =
3.942 =
2305.350.125 [0.9035 *1.6]*14.511
4169.25H = +
0.3977H m =
0.9035tan 2.272
0.3977
a
H = = =
66.24L =
-
8/3/2019 Automobile Class 2
20/33
9/20/2011
20
Weight Distribution in a Four-wheeled
Vehicle:
L
a b
CG
W
R3,4R1,2
R2
R1 R3
R4B
c
d
x
B
d c
R1,3 R2,4
y = B/2 -x
H
y B/2 +
xW
Data Given:
W=1000 kg
L=2.3 m
B=1.3 m
a=1.3 m
b=1.0 m
x= 0.1 m
c=0.75 m
d=0.55 m
-
8/3/2019 Automobile Class 2
21/33
9/20/2011
21
Taking moment about A,
3 4( ) * * R R L W a+ =
1 3( )* * R R B W c+ =
2 4( )* * R R B W d + =
Taking moment about C,
Taking moment about D,
1 2( )* * R R L W b+ =
Taking moment about B,
3 4( ) *a
R R W L
+ =
1 2( ) *b
R R W L
+ =
2 4( ) *d
R R W
B
+ =
1 3( ) *c
R R W B
+ =
From (i) to (iv),
-
8/3/2019 Automobile Class 2
22/33
9/20/2011
22
From method of Superimposition:
From (vi) to (viii)
From (vi) to (vii)
From (v) to (vii)
From (vi) to (vii)
1 * *b cR WL B
=
2 * *b d
R WL B
=
3 * *a c
R WL B
=
4 * *
a d
R W L B=
1 2460.7R N=
4 2345.8N=
2 1804.5R N=
3 3198.9R N=
-
8/3/2019 Automobile Class 2
23/33
9/20/2011
23
Example:2
A four wheeled vehicle has a wheel base of 2.36m and mean track of 1.32 m. It is designed in
such a manner that front axle shares 48% of
vehicle load. The CG of this vehicle is displaced
by 0.075 m from longitudinal axis away from
driver side. Determine load distribution if
vehicle load is 790 kg under unladden
condition.
[Fiet-UNO]
L
a b
CG
W
R3,4R1,2
R2
R1 R3
R4
B = 1.32mC = 0.735m
d = 0.585m0.075m
B
d cR1,3 R2,4
-
8/3/2019 Automobile Class 2
24/33
9/20/2011
24
Given data:
L=2.36 mB=1.32 m
W=790 kg = 7749.9 N
c = 0.735
1 2( ) 0.48* 3719.952 R R W N + = =
2
By= +
0.5852
Bd y m= =
3 4 1 2( ) ( ) 4029.948 R R W R R N + = + =
Taking moment about A,
3 4( ) * * R R L W a+ =
3 4( )* 4029.948* 2.361.2272
7749.9
R R La m
W
+ = = =
2.36 1.2272 1.1328b L a m= = =
-
8/3/2019 Automobile Class 2
25/33
9/20/2011
25
Now we know that:
1 * *b c
R WL B
=
1.1328 0.7357749.9* *
2.36 1.32=
2071.337 211.145 N kgf = =
2 * *b dR WL B
=
1.1328 0.5857749.9* *
2.36 1.32=
1648.615N=
168.055kgf=
-
8/3/2019 Automobile Class 2
26/33
9/20/2011
26
3 * *
a c
R W L B=
1.2272 0.7357749.9* *
2.36 1.32=
2243.948N=
228.741kgf=
4 * *a dR WL B
=
1.2272 0.5857749.9* *
2.36 1.32=
1785.9997N=
182.059kgf=
-
8/3/2019 Automobile Class 2
27/33
9/20/2011
27
1st check: W=R =790 kgf
2nd check:
3rd check:
------------------------------------------------------------
3 4 *a
R R W L
+ =
410.8 410.8=
2 4( ) *d
R R W B
+ =
350.114 350.114=
Example 3: A four wheeled vehicle stands on a weighbridge
such that only front wheels are on the bridge.
The load recorded is 614 kgf. The vehicle is now
taken on weighbridge & the load was found to
be 1180 kg. The vehicle then was kept on a
weighbridge in such a way that its rear wheels
were on the weighbridge raised by 10 cms.
-
8/3/2019 Automobile Class 2
28/33
9/20/2011
28
R2
R1
W
Case : 2
3 4
1 2
1
2
3
4
2 4
1 3
3 4
1 2
2 4
1 3
1 2 3
( )* *
( )* *
2460.7
1804.5
3198.9
2345.8
( )* *
( )* *
( ) *
( ) *
( ) *
( ) *
R W R R
R R L W a
R R L W b
R N
R N
R N
R N
R R B W d
R R B W c
a R R W
L
b R R W
L
d R R W
B
c R R W
B
=
+ =
+ =
=
=
=
=
+ =
+ =
+ =
+ =
+ =
+ =
-
8/3/2019 Automobile Class 2
29/33
9/20/2011
29
cot 14.511
0.9035tan 2.272
0.3977
66.24L
a
H
=
= = =
=
x y
L
mg
CG
H
Fi=ma
a=3 m/s2
A B
R2R1
P
-
8/3/2019 Automobile Class 2
30/33
9/20/2011
30
x y
L
mg
CG
H
Fi=ma
a b
L
R2R1
CGFront Rear
W
-
8/3/2019 Automobile Class 2
31/33
9/20/2011
31
R2
R1
W
a b
L
W
CG
A B
R2R1
-
8/3/2019 Automobile Class 2
32/33
9/20/2011
32
W
A
B
R2
R1
LCOS
x
aCOSh=0.10 m
R2
R1
W
-
8/3/2019 Automobile Class 2
33/33
9/20/2011
a b
L
W
CG
A B
R2R3R1
C
C
R3
R2
H
R1
x
x
z
z
y yB=2c
8 6 3 .2 80 .2 2 5 ( 0 .6 5 3 7 * 1 . 2 0 8 ) * c o t
1 6 6 7 .7
0 .1 0 0s in 0 .0 8 2 7 8
1 .2 0 8
4 .7 5 8 5
c o t 4 .7 5 8 5 1 2 .0 3 8 5
0 .5 6 6
2( * ) * c o t
h
L
H m
R H r a L
W
= +
= = =
=
=
=
= +