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    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

    mechanical support for the moving components, a mechanical protection from the outside world for those internal

    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

    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.

     Or i   gi  n al  Ar  t  i   c l   e 

     

    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.

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    16 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

    •  Brief Description of the Drawing

    Figure 1

    Figure 2 

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    Rigid PVC Gearbox Housing for Automo

     

    www.tjprc.org 

    biles

    Figure 3

    Figure 4 

    17

    [email protected]

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    18

     Impact Factor (JCC): 5.4529

    Veda

     In

    Figure 5

    Figure 6 

     ya Bakshi& Shivomendra Patel

    ex Copernicus Value (ICV): 6.1

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    Rigid PVC Gearbox Housing for Automobiles 19

    www.tjprc.org  [email protected]

    Figure 7

    Figure 8 

    Figure 9 

    Figure 10 

    Figure 11 

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     20 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

    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;

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    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 1Power = P

    Speed = N

    Gear

    Ratios=

    { 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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    a   =  

    24

    1 1 33 32

    1 1 ,lim

    {( )( )( )( )( )( )}( 1)

    4( ) { ( )( )( )( )( )( )}

     B D H E H 

     A V H H 

     H NT L R V W X 

     Z Z Z Z Z S T k k k k  

    b d Z Z Z Z Z Z  

    ε β 

     β α 

     µ 

     µ σ 

     Provided :

    1 1( )  st 

    gear b d    =   0.65  

    1 2( )   st gear b d   

    =   0.45  

    1 3( )   st 

    gear b d    =   0.28  

    1 4( )   st 

    gear b d    =   0.28  

    1 5( )   st gear b d   

    =   0.30  

    1( )reverseb d   =   0.65  

    ak   =  

    0.65, for passenger cars &

    0.85, for commercial vehicles 

    V k   =  

     H k  α   =  

     H k   β   =   1 

     H  Z   =   2.25  

     /  B D Z    =   1 

    Z E 

      =   0.175 E , For commercial steel =2

    189.8   N mm  

     Z ε   =   0.95  

     Z  β   =   0.95  

    Now we have the following result:-

    , , , , , NT L R V W X  Z Z Z Z Z Z   =   1 

    ,lim H σ    =  21800 N mm , for commonly used

    material of shaft (16MCr5)

     H S   =   1.2  

    CALCULATIONS OF GEARS AND ITS DIMENSIONS 

    •  For Permanent Reduction 

    From empirical data :-

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     24 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

    1d   =  

    1

    2

    1

    a

     µ + 

    1

    d  is the diameter of pinion on input shaft.

    Now,

    1 2

    2

    d d + 

    =   a  

    1 2d d +  =   2a  

    2d   =  

    12a d −  

    •  For first gear

    9 10d d +  =   2a  

    1 µ    =  

    9

    10

     Z 

     Z  

    1 µ    =  

    9

    10

    d  

    •  For second gear

    7 8d d +   =   2a  

    2 µ    =  7

    8

     Z 

     Z  

    2 µ    =  7

    8

    d  

    •  For third gear

    5 6d d +  =   2a  

    3

     µ   =  

    5

    6

     Z 

     Z  

    3 µ    =  5

    6

    d  

    •  For fourth gear

    3 4d d +  =   2a  

    4 µ    =  3

    4

     Z 

     Z  

    4

     µ   =  

    3

    4

    d  

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    •  For reverse gear

     DC    =   150 mm  

    θ   =   80o  

    tanθ   =   DC 

     DB  

     DB   =  tan

     DC 

    θ   

     AD   =    AB DB−  

    In ∆ ADC, By Pythagoras Theorem

    2 AC    =  

    2 2 AD DC +  

    2

    9 11

    2

    d d +

      =   2 2 AD DC +  

    9 11

    2

    d d +

     =   2 2

     AD DC + 

    11d   =   (   )2 2 92   AD DC d  + −  

    Now,

    In ∆ BDC, By Pythagoras Theorem

    2 BC    =  

    2 2 BD DC +  

    2

    11 12

    2

    d d +

      =   2 2 BD DC +  

    12 11

    2

    d d +

     =   2 2

     BD DC +  

    12d   =   (   )2 2 112   BD DC d  + −  

    •  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,

    minb  =  

    (1.15)

    tan

    mπ 

     β  

    &Equation 12.23 (c)

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     26 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

    And the maximum value of face width;

    maxb  =  

    20

    tan

    m

     β  

    Now, from data book page number 214, eq. 12.24 (a)

    Lewis equation for helical or herringbone gears

    t F  =  

    d V n

    w

    C bYm

    σ  

    nm  =   cosm   β   

    d σ    =   30 MPa ,……table-12.22, Page-241

    wC   =   1.15 ,……table-12.22, Page-241

    V C    =  

    6.1

    6.1   v+  =   0.378 ,……eq-12.25,

    Page-241

    Y   =    yπ   

     y   =   0.148 ,……table-12.21, Page-232

    From data book page number 214, equation number 12.26 (a)

    Now, According to Buckingham, the inertia force;

    iF   =  

    2

    3

    2

    3

    ( cos )cos

    cos

    k V Cb F  

    k V Cb F  

     β β 

     β 

    +

    + + 

    3k   =   6.60  

    , Dynamic Load Factor C   =   786.5 ,……table-12.12,

    Page-236

    The Dynamic Load,

    d F   =  

    t iF F +  

    Now from equation 12.26 (b) of Databook

    The dynamic strength of gear is given by following formula;

    sF    =   d nbYmσ   

    Condition for safe working:

    sF    ≥  

    d F   

    Now from data book page number 214;

    . , No of Teeth Z   =   d m

     

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    ,Circular Pitch p   =  d 

     Z 

    π  

    , d  Diametrical Pitch p   =  1

    , r  Dedendum Circle Diameter d    =   2( ) fn cn nd t t m− +  

    ,n

    Tooth Factor for Standard Tooth t    =  cos

     f t 

     β   =  

    1

    cos β  

    ,cnTooth Clearance Factor t   

    =  

    cos

    ct 

     β  

    =   0.2

    cos β  

    , o Addendum Circle Diameter d   =   2r d h+  

    h   =   (2 ) f c

    t t 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)

    1T   =  2sin

     f a mF D µ 

    α   =  

    2

    2  m

    bpDπ 

     µ   

     p   =   0.07  

     f  µ    =   0.12  

    q   =   m D

    b  =   4.5 8to  

    From equation 13.10(h),page number 260

    b   =   32

    49

    n

     f 

     pπµ  

    m D   =   7b  

    Now we know,

    m

     D   =   1 2

    2

     D D+ 

      For Second Gear 

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     28 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

    Gear Ratio   =   2 µ   

    1 µ    = 

    1

    2

     N 

     N  

    2 N   =   1

    1

     N 

     µ   =   9 N   

    Now we know that;

    8

    7

     N 

     N  

    =  2 µ   

    8

    2

     N 

     µ   =  

    7 N   

    7T   =   ( ) 77 2t 

    d F   

    7P  =  

    7 72

    60

     N T π  

    Now

    ( )2nd m   gear 

     D   =  3 7

    32

    10 f 

    P kq

     pnπ µ  

    2cb   =  ( )

    2

    nd m  gear 

     D

    We already observe that;

    ( ) ( )2 22

    c co id d −

      =  ( )2 sincb   α   

    ( ) ( )2 2c co id d −  =   ( )22 sincb   α  

    Since;

    ( )2c   od   ≠  

    7d   

    ( )2nd m   gear  D   <   ( )2c   od    <   7d   

    Taking average value

    ( )2c   od   =   ( ) 72

    2

    nd m   gear  D d +

     

    ( )2c   id   =   ( )

    ( )72

    22 sin2

    nd m   gear 

    c

     D d b   α 

    +

    −  

      For Third Gear 

    Gear Ratio   =   3 µ   

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    1 µ    = 

    1

    2

     N 

     N  

    2

     N    =   1

    1

     N 

     µ   =  

    6

     N   

    Now we know that;

    6

    5

     N 

     N   =  

    3 µ   

    6

    3

     N 

     µ   =  

    5 N   

    5T   =   ( ) 55 2t 

    d F   

    5P  =  

    5 52

    60

     N T π  

    Now

    ( )3rd m   gear 

     D   =  3 5

    32

    10 f 

    P kq

     pnπ µ  

    3cb  =  

    ( )3rd m   gear 

     D

    We already observe that;

    ( ) ( )3 32

    c co id d −

      =  ( )3 sincb   α  

    ( ) ( )3 3c co id d −  =   ( )32 sincb   α   

    Since;

    ( )3c   od   ≠  

    5d   

    ( )3rd m   gear 

     D   <   ( )3c   od    <   5d   

    Taking average value

    ( )3c   od   =   ( ) 53

    2

    rd m   gear  D d +

     

    ( )3c   id   =   ( )

    ( )53

    32 sin2

    rd m   gear 

    c

     D d b   α 

    +

    −  

      For Fourth Gear 

    Gear Ratio   =   4 µ   

    1 µ    =   1

    2

     N 

     N  

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     30 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

    2 N   =   1

    1

     N 

     µ   =   4 N   

    Now we know that;

    4

    3

     N  N 

      =  4 µ   

    4

    4

     N 

     µ   =  

    3 N   

    3T   =   ( ) 33 2t 

    d F   

    3P  =  

    3 32

    60

     N T π  

    Now

    ( )4thm   gear 

     D   =  3 3

    32

    10 f 

    P kq

     pnπ µ  

    4cb   =  

    ( )4thm   gear 

     D

    We already observe that;

    ( ) ( )4 4

    2

    c co id d −

      =  ( )4 sincb   α   

    ( ) ( )4 4c co id d −  =   ( )42 sincb   α  

    Since;

    ( )4c   od   ≠  

    3d   

    ( )4thm   gear 

     D   <   ( )4c   od    <   3d   

    Taking average value

    ( )4c   od   =   ( ) 34

    2

    thm   gear  D d +

     

    ( )4c   id    =  ( ) ( )

    34

    42 sin2

    thm   gear 

    c

     D d b   α 

    +−  

    •  Design of Lockers

      Between 2nd and 3rd Gear

    As we know that diameter of 3rd gear is smaller than that of 2nd gear and the diameter of annular ring of

    slider is to be constant.

    Therefore, we need to design the cotter corresponding to that of 3rd

     gear. Therefore torque loses to be neglected

    and;

    3rd Torque on gear   =   5T   

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    Now,

    Shifting Force is given by

    sF   =  

    3

    2 sin

    ( )   rd 

    s m Gear 

    α 

     µ 

     

    Now, from reference, AT by Gisbert Lechner and Herald Naunheimer

    page number 252,equation 9.18

     Z T   =   ( )2

    2

    cFd Cot 

      β 

     

    105o   <    β    <   125o  

    Now we know

     Z T    ≤   r T   

    Neglecting the loses,

    Let us assume

     Z T    =   r T   

    cd    =   ( ){ }2

    2

    r T 

    F Cot   β  

    cd    =   ( ){ }

    2tan

    2r 

     β  

    Let ZB be the number of teeth’s on synchronizers

    Therefore, pitch of synchronizers

    From databook page number 205,equation 12.8, Bachi's formula for beam strength of tooth

    m   =   532

    0.88s

    k kz 

    Where

    k   =   s

    s

    b

    Strength Coefficient   =  2k    =

      ( )24.90 M m for bronze  

    6   ≤   k   ≤   20  

    k   =   7  

    Therefore

    ,s

    Circular Pitch P   =   s

    s

     z

    π  

    ( ), d    s Diametrical Pitch P  =   s

    s

     z

    d  

    ( )  , o   s Addendum Circle Diameter of Synchronizers d    =   (2 )r f cd t t + +  

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     32 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

    ( )  , r    s Dedendum Circle Diameter of Synchronizers d   =   2( )

     f c st t m+  

     f t    =   1 

    ct   =   0.2  

    Here addendum of synchronizer is the dedendum for synchronizer ring,

    s z  =  

     R z  

    DESIGN OF SELECTOR MECHANISM

    Let the angle of contact of selecting fork over synchronizer ring be:

     f θ    =   180o  

    Let the selecting fork arms have a T-cross section.

    • 

    Selector Mechanism 

    In manual transmissions, an interlock mechanism prevents the engagement of more than one gear at any one

    time and a decent mechanism holds the gear in the, in detention, in the selected position.

    σ    =   55 MPa  

    sF   =  

    (1.5 )

     f 

     f l t 

    σ  

    l   =  360

    cd θπ 

     

    t   =  

    (1.5)

     f 

    sl F 

    σ  

    Here,

    l   =   Length of Fork

    sF    =   Force of Shift

    •  Design of shifting lever :

    Let L be the affective length of the lever and P be the manual force applied at the handle.

    Let B and t be the height and thickness of handle near the boss assuming that the lever is extended to the centre

    of shaft (for strength of lever).

    We get,

    . Max Bending moment on the lever   =   PL  

    Section Modulus near the boss   =  2

    6

    tB 

    As we know,

     M    =   b Z σ   

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    PL   =  2

    6

    btB  σ 

     

    bσ    =   Permissible Bending Stresses In Material

    Also, for empirical data

     B   =   5t  

    Also,

    1 B  =  

    2

     B 

    Where

    P  

    =   70 100 N −    for Continuous Shifting  

    =   200 250 N −    for Intermittent Shifting  

    =   350 400 N −    for Instantaneous Shifting  

    The diameter d2 is subjected to combined bending and twisting.

    Therefore by GUEST’S FORMULA:

    3

    216

      bd 

    π σ    =   2 2

    b t  M M +  

    3

    216

      bd 

    π σ    =   2 2( ) ( )Pl PL+  

    3

    216

      bd 

    π σ    =   2 2P l L+  

    2d   =  

    13

    2 216

    b

    Pl L

    πσ 

    +

     

    Or by  RANKINE formula

    2d   =   (   )

    1

    32 232

    b

    P l l L

    πσ 

    + +

     

    Now for dimension of boss,

    We know,

    PL   =  2

    2 22

    d t l t  σ 

      +

     

    Now,

    2

    2

    l

    t   =   ( )1.25 Standard ratios  

    Let

    2t   =   ( )3 mm General considerations  

    Therefore,

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     34 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

    2l  =   5.75 mm  

    P   =   ( )25.625

    t sbd t 

     Lσ    +  

    sbd   =   2

    5.625t 

    PL t σ 

    −  

    DESIGN OF SHAFTS 

    •  Design of Main Shaft: 

    As we know, size of gear synchronizers increase gradually, consider the load as UVL.

    We know,Deflection in simply supported beam subjected to UVL is,

    δ    =  

    ( )

    4 2 2 47 10 3360

    o x

    l l x xlEI 

    ω − +  

    For UVL,

    maxδ    =  

    4

    0.00652   o sl

     EI 

    ω  

    Here

    oω    =    Identity of load  

    As we know for standard gearbox max. Permissible deflection of shaft

    maxδ    =   0.0003

    s L  

    0.0003   =  3

    0.00652 o sl EI 

    ω   

    3

    0.4601

    s

     EI 

    l  =  

    oω   

    Net load acting on shaft

    nω    =   o s

    lω   

    nω   =  

    2

    0.4601

    s

     EI 

    l  

     A B R R+   =   nω   

    Taking moments about A

     B R   =   2

    3  n

    ω   

     A R   =   1

    3  nω   

    ( ) Bc

     BM    =   2

    3

     B s R l  

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    ( ) Bc

     BM    =   2 1. .3 3

      n slω   

    ( ) Bc

     BM    =   2

    9

      n slω   

    Considering A

    ( ) Ac

     BM    =   2

    3 A n s

     R lω   

    Maximum bending moment of main shaft

    ( )b   m M    =   2

    9  n s

    lω   

    Since first gear is subjected to maximum torque i.e T9.

    Therefore using GUEST’S THEORY

    eT    =   2 2

    9b M T +  

    3916   ms

    T d π 

      =  2

    2

    9

    2

    9  s nl T ω 

    +

     

    Let

    s

    ms

    l

    d   =   10  

    2

    6

    916

      msT d 

    π 

     =  

    ( )22 2

    9

    410

    81  n msd T ω    +  

    2

    32 2

    256  s msd π  τ      =   2 2 29

    40081

      n msd T ω    +  

    Thus diameter of the main shaft is determined and hence length of the shaft is also determined.

    •  Design of counter shaft:

    Approx. Volume of gears

    V    =   2

    4   nad b

    π  

    Let the density of material be  ρ  ,

    g Mass of Gears m   =   V  ρ   

    ( )g nm  =   2

    4   na

    d bπ 

     ρ  

     

    Weight of Gears   =   ( )g nw   =   ( ) .g nm g  

     AC BC  R R+   =   1 2 3 4 5 6 g g g g g gW W W W W W  + + + + +  

    Taking moment about Ac 

     BC s R l  =  

    1 2 3 4 5 63 6 9 12 15

    2 2 2 2 2 2

    b b b b b bw w b w b w b w b w b

    + + + + + + + + + +

     

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     36 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

     BC s R l  =  

    1 2 3 4 5 6

    7 13 19 25 31

    2 2 2 2 2 2

    b b b b b bw w w w w w

    + + + + +

     

     BC s R l   =   [ ]1 2 3 4 5 67 13 19 25 31

    2

    bw w w w w w

      + + + + +

     

     B R   =   [ ]1 2 3 4 5 67 13 19 25 31

    2 s

    bw w w w w w

    l

    + + + + +

     

     AC  R   =   ( )g Bnw R∑   −  

    BM will be max either at 3 or at 4.

    ( )3

     BM    =   ( ) ( ) ( )2 13 6 62

     A

    bw b w b R b

    + − +

     

    ( )4 BM   =  

    ( ) ( )( )5 63 6 6 2 BC b

    w b w b R b

    + − +

     

    The greater of ( )3

     BM   or ( )4

     BM   is equal to equivalent bending moment, ( )b   c M   Considering torque maximum due to first gear only

    ceT    =   2 2

    9bc M T +  

    csd    =  

    1

    3

    16

    ce

    s

    T π 

    τ 

     

    •  Design of idler shaft: 

    Approx. Volume of gears

    igV    =   2

    4   na

    d bπ 

     

    Let the density of material be  ρ  

    ,ig

     Mass of Ge s mar    =   igV  ρ   

    igm   =   2

    4   na

    d bπ 

     ρ  

     

    Weight of Gears  =

     ig

    w   = 

    igm g  

    igw   =    Ai Bi R R+  

    Taking moment about A

     B s R l  =  

    2

    sig

    lw  

    2

    igw 

    =   A

     R   =   B

     R  

    Also, we know

    isl   =   2

    2

    bb +  

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    bi M   =  

    4

    ig

    is

    wl  

    Torque is considered to be maximum

    ieT    =   2 29ib M T +  

    isd   =  

    1

    3

    16

    ie

    s

    T π 

    τ 

     

    DESIGN OF BEARINGS

    Design of bearings is purposed for selection of bearings of standard sizes.

    Since there is no axial motion on shaft thus radial roller bearing is design.

    From data book page number 373, equation number 16.7(b).

    The equivalent load P for radial roller bearings

    P   =  r a XVF YF +  

    From data book page number 384, table number 16.5

    Considering rotating inner ring

    V    =   1.0  

    Considering, Maximum Permissible Force r F   in gearbox, is due to first gear.

    From databook page number 206, equation 12.8(b)

    1r F    =  

    1tan

    t F    α  

    And from databook page number 211, equation 12.21

    aF    =   F tant    β   

    Now,

    Bearing number is selected from databook page number 394; table number 16.13(a).

    On the basis of diameter of shaft

    aF   =   F tant    β   

    •  For Main Shaft: 

    Series NU22,

    5

    msd 

     

    • 

    For counter shaft: 

    Series NU22,

    5

    csd 

     

    •  For Idler Shaft:

    Series NU22,

    5

    5

    id 

     

    From the table corresponding value of basic load factors,

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     38 Vedagya Bakshi& Shivomendra Patel

     Impact Factor (JCC): 5.4529 Index Copernicus Value (ICV): 6.1

    Static Co and dynamic C are selected.

    Now,

    e   =   1.5tanα    =   0.545  

     X   =  

    0.4  Y   =   0.4cot α    =   1.098  Now,

    Life of roller bearings is given by following formula,

    nl  =   ( )

    10

    3c p

     

    DESIGN OF HOUSING 

    The gear housing is the housing that surrounds the mechanical components of a gear box. It provides

    mechanical support for the moving components, a mechanical protection from outside world for those

    internal components, and a fluid-tight container to hold the lubricant that bathes those components.

    Maximum vertical measure of gearbox element is measured by considering all the following terms

    H = (radius of countershaft permanent reduction gear) + (centre to centre distance) +

    (radius of synchronizer ring) + (total height of selecting fork cross section) +

    (diameter of boss of shifting shaft).

     H   =  ( )

    ( )2 1.52 2

    o   ssb

    d d a t t d  + + + + +  

    Now, since it is clear that vertical measure of gearbox elements is dominant on horizontal thus, inner

    diameter of the housing can be

    i D  =    H Clearances+  

    Now, thickness of housing is given by t,

    From databook page number 113 equation numbers 8.10

    t   =  1   i

    PC D

    σ  

    Let

    1C   =   0.54  

    mid  and cid   are determined as the outer diameter of the bearing outer case.Therefore selecting the value of D from databook page number 394, table number 16.13(a).

    Now

    mod   =   3mid mm+  

    cod   =   3

    cid mm+  

    The number of studs required

     I    =   0.015 4id   +  

    The core diameter of studs

    c

     D   =   maxi

    P

    d  nσ   

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    Rigid PVC Gearbox Housing for Automobiles 39

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    Nominal diameter of the studs

     N  D   =  

    0.84

    cd 

     

    From databook page number 433, equation number 21.2(a)

    ,g

    Thickness of gasket t    =   0.25 1.5mm to mm   =   1.5 mm  

    CONCLUSIONS 

    This invention has various advantages. Some of them are as follows :

    •  Reduced weight

    •  Simplified design

    •  Increased power to weight ratio of the vehicle

    •  Alternate material for manufacturing of gear box casing.

    The foregoing descriptions of specific embodiments of the present invention have been presented for purposes of

    illustration and description. They are not intended to be exhaustive or to limit the present invention to the precise forms

    disclosed, and obviously many modifications and variations are possible in light of the above teaching.

    The embodiments were chosen and described in order to best explain the principles of the present invention and

    its practical application, to thereby enable others skilled in the art to best utilize the present invention and various

    embodiments with various modifications as are suited to the particular use contemplated. It is understood that various

    omission and substitutions of equivalents are contemplated as circumstance may

    Suggest or render expedient, but such are intended to cover the application or implementation without departing

    from the spirit or scope of the present invention.

     REFERENCES 

    1.  The refences of the article were cited from the following :

    2. 

     A Textbook of Machine Design by R.S. Khurmi& J.K. Gupta ,S.Chand Publication

    3. 

     Design Data Handbook for Mechanical Engineers in SI and Metric Units by K. Mahadevan & K. Balaveera Reddy.

    4. 

     Automotive Trasnmission, Gisbert Lechner and Herald Naunheimer.

    5.   MASTER'S THESIS IN THE INTERNATIONAL MASTER PROGRAMME IN APPLIED MECHANICS

    6.  “Synchronization Processes and Synchronizer Mechanisms in Manual Transmissions” , ANA PASTOR

    7. 

     BEDMAR, Department of Applied Mechanics,CHALMERS UNIVERSITY OF TECHNOLOGY, Göteborg, Sweden.

    8. 

     Machine Design,Mubeen and Mubeen.

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