International Journal of Automobile Engineering Research and Development (IJAuERD) ISSN(P): 2277-4785; ISSN(E): 2278-9413 Vol. 6, Issue 1, Feb 2016, 15-40 © TJPRC Pvt. Ltd.
RIGID PVC GEARBOX HOUSING FOR AUTOMOBILES VEDAGYA BAKSH1& SHIVOMENDRA PATEL2 1,2
Rajiv Gandhi Technical University, Medi-Caps Institute of Science and Technology, Indore, India
Abstract The present invention relates to gearbox housing for automobiles, and more particularly, it relates to a light weight rigid PVC gearbox housing for automobiles capable of reducing the stress concentration of the gearbox housing. Keyword: Gear box casing, optimization, rigid poly vinyl chloride (PVC), transmission, automobiles, weightreduction, power to weight ratio
Received: Nov 15, 2015 ;Accepted: Oct 19, 2016 ; Published: Feb 15, 2016 ; Paper Id.: IJAuERDFEB20162 INTRODUCTION The gearbox housing is the housing that surrounds the mechanical components of a gear box. It provides
components, and a fluid -tight container to hold the lubricant that bathes those components. Traditionally, the gearbox housing is made from cast iron or cast aluminium, using methods of permanent mould casting or shell moulding. Experimentally, though, composite materials have also been used. The cast iron is one important material which is used for gearbox housing. The cast iron provides string housing to the inner component and lasts long, but it is very cumbersome when it comes to welding it to desired
Original Article
mechanical support for the moving components, a mechanical protection from the outside world for those internal
gearbox design. Also spray painting may cause rusting and lead to low life of the gearbox housing. The cast aluminium is another commonly used material for gearbox housing which is li ghtweight and can be designed easily. Though, cast aluminium is lightweight and design easy, it is heavier as compared to RIGID PVC for gearbox housing. Accordingly, there exists a need to provide a gearbox housing which overcomes above mentioned drawbacks. DETAILED DESCRIPTION •
Objects of the Invention An object of the present invention is to provide a light weight rigid PVC gearbox housing which reduces
the stress concentration which acts on the housing of gearbox. Another object of the present invention is reduction in body weight which increases the power to weight ratio. Yet another object of the present invention is reduction in overall cost of the gearbox housing. Further object of the present invention is to provide an alternative material for gearbox housing.
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Vedagya Bakshi& Shivomendra Patel
•
Brief Description of the Drawing
Figure 1
Figure 2
Impact Factor (JCC): 5.4529
Index Copernicus Value (ICV): 6.1
Rigid PVC Gearbox Housing for Automobiles
17
Figure 3
Figure 4
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Vedagya Bakshi& Baksh Shivomendra Patel
Figure 5
Figure 6
Impact Factor (JCC): 5.4529
Index ndex Copernicus Value (ICV): 6.1
Rigid PVC Gearbox Housing for Automobiles
19
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11 www.tjprc.org
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Vedagya Bakshi& Shivomendra Patel
Figure 12
Figure 13
Figure 14 Figure 1 shows a cross-sectional perspective view of gearbox housing, in accordance with the present invention; Figure 2 shows equation for calculating Centre to Centre distance, in accordance with the present invention; Figure 3shows equation for design of synchronizers, in accordance with the present invention; Figure 4, shows equation for selector mechanism, in accordance with the present invention; Figure 5, shows equation for design of gearbox housing, in accordance with the present invention; Figure 6 shows values of Eigen Modes analysis generated due to Vibration having minimum value of 2.600E-02 and maximum value of 1.400E+01, in accordance with the present invention; Figure 7 shows values of Eigen Modes analysis in X -axis generated due to Vibration having minimum value of 9.911 E+00 and maximum value of 3.051E+00, in accordance with the present invention; Figure 8 shows values of Eigen Modes analysis in Y -axis generated due to Vibration having minimum value of 7.495E+00 and maximum value of 5.139E+00, in accordance with the present invention; Figure 9 shows values of Eigen Modes analysis in Z -axis generated due to Vibration having minimum value of 9.441E+00 and maximum value of 3.806E+00, in accordance with the present invention; Impact Factor (JCC): 5.4529
Index Copernicus Value (ICV): 6.1
Rigid PVC Gearbox Housing for Automobiles
21
Figure 10 shows distribution of Strain Energy Generated in object due to vibration having minimum value of 8.545E-10 and maximum value of 8.417E -10, in accordance with the present invention; Figure 11 shows Density of Strain Energy Generated in object due to vibration having minimum value of 2.600E-11 and maximum value of 3.841E -11, in accordance with the present invention; Figure 12 shows graph of the variation of Thickness of gearbox housing of tw o materials, in accordance with the present invention; Figure 13 shows graph of the variation of Volume of gearbox housing of two materials , in accordance with the present invention; and Figure 14 shows graph of the variation of Mass of gearbox housing of two materials, in accordance with the present invention; •
Detailed Description of the Invention The foregoing objects of the present invention are accomplished and the problems and shortcomings associated
with the prior art, techniques and approaches are overcome by the present invention as described below in the preferred embodiments. Gearbox housing is used to cover the gear box. Also, to prevent it from external undesired objects and dirt. It is also used to retain certain amount of gear lubricant inside it, so that the gear train can run smoothly. The proposed design and analysis is concerned with an alternative material (rigid PVC) which can perform same and has less weight. The novelty of this proposed invention is that by using the gear box housing of rigid PVC, the weight of the gear box housing/housing can be reduced as well as the stress concentration which act on the housing of gear box made up of cast iron/steel/aluminum which are in commercial use today. It can be used for any heavy vehicle and any machines where gear boxes are in use where there is low temperature of about 60 degree and there is no significant space constraint. Refereeing now to figures 1 to 5, it shows a cross-sectional perspective view of a gearbox housing (100) and equations for calculating different units respectively. Following are the parameters for calculating the design of gearbox housing (100). Given: Table 1 Power = P Speed = N Gear = Ratios
µ ,µ ,µ ,µ ,µ ,µ
{
1
2
3
4
5
r}
*5 Forward + 1 Reverse Gears Design of Gearbox Involves the Following Steps •
Estimating the Centre to Centre distance
•
Calculation of gears and their dimensions
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Vedagya Bakshi& Shivomendra Patel
•
Design of synchronizers
•
Design of selector mechanism
•
Design of shafts
•
Design of bearings
•
Design of housing
ESTIMATING THE CENTRE TO CENTRE DISTANCE In order to determine the equation for calculating the Centre distance ‘a’ ; it is here necessary to start with Hertz Contact Stresses at pitch circle. For cylindrical surfaces - eq.7.6 (German Standards DIN 3990)
σH
( Z B D )(σ HW ) k A kV k H β k Hα
=
With Nominal Contact Pressure,
σ H 10
σ H 10
=
( Z H )( Z E )( Zε )( Z β )
Ft ( µ1 + 1) d1bµ1
The torque to be received at the pinion shaft, T1
T1
=
Ft d1 2
And the face width – Diameter relationship be, b
σH
=
=
60 P 2π N
d1
( Z B D )( Z H )( Z E )( Z ε )( Z β )
2T1 ( µ1 + 1) k AkV k H β k Hα d13 (b d1 ) µ1
If the diameter d 1 in above equation is replaced byempirical data
d1
=
2a 1 + µ1
& the surface stress σ H is replaced by the permissible stress
σ H ( perm )
=
σ H ,lim ( Z NT )( Z L )( Z R )( ZV )( ZW )( Z X ) S
Thus, the centre to centre distance is given by
Impact Factor (JCC): 5.4529
Index Copernicus Value (ICV): 6.1
Rigid PVC Gearbox Housing for Automobiles
a
=
3
23
{( Z B D )( Z H )( Z E )( Zε )( Z β )( S H )}2 T1 ( µ1 + 1) 4 3 k k k 3 A V H β kHα 4(b d1 ) µ1 {σ H ,lim ( Z NT )( Z L )( Z R )( ZV )( ZW )( Z X )}2
Provided:
(b d1 )1st gear
=
0.65
(b d1 ) 2st gear
=
0.45
(b d1 )3st gear
=
0.28
(b d1 ) 4st gear
=
0.28
(b d1 )5st gear
=
0.30
(b d1 ) reverse
=
0.65
ka
=
0.65, for passenger cars &
kV
=
0.85, for commercial vehicles
=
kHα
kH β
=
1
ZH
=
ZB/D
=
1
ZE
=
0.175E , For commercial steel = 189.8 N mm 2
Zε
=
0.95
Zβ
=
0.95
2.25
Now we have the following result:-
Z NT , Z L , Z R , ZV , ZW , Z X
=
1
σ H ,lim
=
1800 N mm2 , for commonly used material of shaft (16MCr5)
SH
=
1.2
CALCULATIONS OF GEARS AND ITS DIMENSIONS •
For Permanent Reduction
From empirical data :-
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d1
=
2a 1 + µ1
d1 is the diameter of pinion on input shaft.
Now,
•
•
•
•
d1 + d 2 2
=
a
d1 + d 2
=
2a
d2
=
2a − d1
d9 + d10
=
2a
µ1
=
µ1
=
d 7 + d8
=
µ2
=
µ2
=
d5 + d 6
=
µ3
=
µ3
=
d3 + d 4
=
µ4
=
µ4
=
For first gear
Z9 Z10 d9 d10
For second gear
2a Z7 Z8 d7 d8
For third gear
2a Z5 Z6 d5 d6
For fourth gear
Impact Factor (JCC): 5.4529
2a Z3 Z4 d3 d4 Index Copernicus Value (ICV): 6.1
Rigid PVC Gearbox Housing for Automobiles
•
25
For reverse gear
DC
θ
= =
tan θ
=
DB
=
AD
=
150 mm 80o DC DB DC tan θ AB − DB
In ∆ ADC, By Pythagoras Theorem
AC 2 d9 + d11 2
2
=
AD 2 + DC 2
=
AD 2 + DC 2
d 9 + d11 2
=
d11
=
AD 2 + DC 2
(2
)
AD 2 + DC 2 − d 9
Now, In ∆ BDC, By Pythagoras Theorem
BC 2 d11 + d12 2
•
2
=
BD 2 + DC 2
=
BD 2 + DC 2
d12 + d11 2
=
d12
=
BD 2 + DC 2
(2
)
BD 2 + DC 2 − d11
Face width (b) Let
module
=
m
=
8mm
Helix Angle
=
β
=
35o
Now, from K.MAHADEVAN design datebook, page number 213, equation 12.23(b) According to AGMA, the minimum face width,
bmin
=
(1.15)π m tan β
&Equation 12.23 (c)
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And the maximum value of face width;
20m tan β
=
bmax
Now, from data book page number 214, eq. 12.24 (a) Lewis equation for helical or herringbone gears
σ d CV bYmn
Ft
=
mn
=
m cos β
σd
=
30MPa ,……table-12.22, Page-241
Cw
=
1.15 ,……table-12.22, Page-241
CV
=
Y y
=
πy
=
0.148 ,……table-12.21, Page-232
Cw
6.1 6.1 + v
=
0.378 ,……eq-12.25, Page-241
From data book page number 214, equation number 12.26 (a) Now, According to Buckingham, the inertia force;
k3V (Cb cos 2 β + Ft ) cos β
Fi
=
k3
=
6.60
Dynamic Load Factor , C
=
786.5 ,……table-12.12,
k3V + Cb cos 2 β + Ft
Page-236 The Dynamic Load,
=
Fd
Ft + Fi
Now from equation 12.26 (b) of Databook The dynamic strength of gear is given by following formula;
Fs
=
σ d bYmn
Condition for safe working:
Fs
≥
Fd
Now from data book page number 214;
No. of Teeth, Z Impact Factor (JCC): 5.4529
=
d m Index Copernicus Value (ICV): 6.1
Rigid PVC Gearbox Housing for Automobiles
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πd
Circular Pitch, p
=
Diametrical Pitch, pd
=
1 m
Dedendum Circle Diameter , d r
=
d − 2(t fn + tcn )mn
Tooth Factor for Standard Tooth, t fn
=
Z
tf cos β tc cos β
=
Tooth Clearance Factor , tcn Addendum Circle Diameter , do
=
h
=
= =
1 cos β 0.2 cos β
d r + 2h (2t f + tc )m
=
2.2m
DESIGN OF SYNCHRONIZERS In automobile, a synchronizer is a part of synchromesh manual transmission that allows the smooth engagement of gears. Synchronizers serve to let shafts and gears engage with each other smoothly after their speeds have been synchronized. •
Design of Cones: We know, the friction torque to be transmitted;from design data book page number 259, equation number 13.10 (d)
µ f Fa D m 2sin α
π
T1
=
p
=
0.07
µf
=
0.12
q
=
Dm b
=
2
=
µbpDm2
4.5to8
From equation 13.10(h),page number 260
2Tn 49πµ f p
b
=
Dm
=
7b
Dm
=
D1 + D2 2
3
Now we know,
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Gear Ratio
=
µ1
=
N2
=
µ2 N1 N2
=
N1
µ1
N9
Now we know that;
=
µ2
=
N7
T7
=
( Ft )7
P7
=
2π N 7T7 60
N8 N7 N8
µ2
d7 2
Now
( Dm )2
nd
=
gear
103 3
( Dm )2
=
bc 2
P7 kq π µ f pn 2
nd
gear
q
We already observe that;
( d c 2 ) o − ( d c 2 )i
( bc 2 ) sin α
=
2 ( d c 2 ) o − ( d c 2 )i
=
2 ( bc 2 ) sin α
Since;
≠
( d c 2 )o
( Dm )2
nd