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    Ch4 Belt Drives-2

    Uploaded by

    Abaziz Mousa OutlawZz
    This document discusses the design of V-belt drives, including: 1. The main failure types of belt drives are slippage and fatigue breakdown. Design principles aim to guarantee enough fatigue stress without slippage. 2. The design procedure involves specifying the calculated power, belt type, sheave diameters, center distance, basic belt length, number of belts, initial tension force, and radial force on the shaft. 3. An example design problem is provided to demonstrate applying the procedure to design a belt drive for a fan with a given power rating, motor speed, and center distance limitation. Key steps of the example include selecting an A-type belt, specifying sheave diameters of 125mm and 280mm,

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    Ch4 Belt Drives-2

    Uploaded by

    Abaziz Mousa OutlawZz
    141 views40 pages
    This document discusses the design of V-belt drives, including: 1. The main failure types of belt drives are slippage and fatigue breakdown. Design principles aim to guarantee enough fatigue stress without slippage. 2. The design procedure involves specifying the calculated power, belt type, sheave diameters, center distance, basic belt length, number of belts, initial tension force, and radial force on the shaft. 3. An example design problem is provided to demonstrate applying the procedure to design a belt drive for a fan with a given power rating, motor speed, and center distance limitation. Key steps of the example include selecting an A-type belt, specifying sheave diameters of 125mm and 280mm,

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    Mechanical design

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    This document discusses the design of V-belt drives, including: 1. The main failure types of belt drives are slippage and fatigue breakdown. Design principles aim to guarantee enough fatigue stress without slippage. 2. The design procedure involves specifying the calculated power, belt type, sheave diameters, center distance, basic belt length, number of belts, initial tension force, and radial force on the shaft. 3. An example design problem is provided to demonstrate applying the procedure to design a belt drive for a fan with a given power rating, motor speed, and center distance limitation. Key steps of the example include selecting an A-type belt, specifying sheave diameters of 125mm and 280mm,

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    141 views40 pages

    Ch4 Belt Drives-2

    Uploaded by

    Abaziz Mousa OutlawZz
    This document discusses the design of V-belt drives, including: 1. The main failure types of belt drives are slippage and fatigue breakdown. Design principles aim to guarantee enough fatigue stress without slippage. 2. The design procedure involves specifying the calculated power, belt type, sheave diameters, center distance, basic belt length, number of belts, initial tension force, and radial force on the shaft. 3. An example design problem is provided to demonstrate applying the procedure to design a belt drive for a fan with a given power rating, motor speed, and center distance limitation. Key steps of the example include selecting an A-type belt, specifying sheave diameters of 125mm and 280mm,

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    © All Rights Reserved
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    of 40

    4.

    5 V-Belt Drives Design

    Failure types and design principles

    1. Failure types and Power rating


    The main failure types of belt drive are:
    Slippage and Fatigue breakdown.
    Design principles:
    Enough fatigue stress, non-slippage.

    (1) To guarantee the fatigue stress and life, it is satisfied that

    max c b1 1
    1 c b1

    (1)

    [] Allowable stretching stress of belt

    For a certain belt, when Ld is equal to a certain length, wrap angle


    1=2=180 (speed ratio i=1), under uniform load and load cycle
    number N=108-109, by experiments we have

    CLd
    m
    3600Z ptv
    m Order of root, m=11.1 for common V-belt;
    Ld Basic length of belt, m;
    Zp Number of sheaves, commonly Zp=2;
    t Belt life, h;
    C An constant decided by structure and material of belt.
    (2) To avoid slippage, Euler's formula should be satisfied, and we
    have

    1
    F F1 (1 )
    e

    Combining (1) and (2), we have

    1
    F 1 A(1 )
    e

    (2)

    1
    F c b1 A(1 )
    e

    Further, because
    We have

    Fv
    P
    1000
    1
    c b1 A(1 e )v
    P
    1000

    So this formula is the power capacity of flat belt drive without


    slippage, and with enough fatigue strength.
    If we substitute with e, we can get the power capacity of a
    single V-belt.
    We can find the power rating P0 and added power P0 of Vbelt in Table 4-3 and Table 4-4.

    Table 4-3 P0, Power rating of a single V-belt


    Type

    Dia.
    sheave

    Table 4-4 P0, Added power rating of a single V-belt


    Speed ratio i

    Type

    2. Design procedure of belt drive


    Given rated power P, rotational speed n1 and n2 (or speed ratio i),
    dimension requirements and working conditions.
    To decide: belt type, length, number of belt, center distance, basic
    diameter of sheaves and structure dimension.
    (1) Calculated power
    Considering the properties and service hour of belt drive, the
    calculated power can be decided by

    Pc KA P
    where, Pc Calculated power, kW;
    P Rated power, kW;
    KA Service factor, see Table 4-7

    Table 4-7 Service factor of belt

    (2) Belt type

    Rotational speed of smaller sheave n1, r/min

    Fig. 4-15 Choice of V-belt type

    Z or A
    Z

    Calculated power Pc, kW

    (3) Diameter of sheave and belt speed


    The bending stress is the main reason of fatigue stress. If the
    diameter of sheave is too small, the bending stress in belt will be
    great. So the diameter of sheave can not be too small.
    By Fig. 4-15, we can choose the value of dd1
    We have belt speed vb

    dd1n1
    vb
    60 1000

    where, n1 Rotational speed of small sheave, r/min;


    dd1 Basic diameter of small sheave, mm.
    Belt speed is usually in range of 5-25m/s. So the belt speed
    should satisfy that vb vmax. If the belt speed is too high, the
    centrifugal force will increase to cause instability of belt drive; If
    belt speed is too low, the belt will work under a poor condition
    with small power.
    By dd2=idd1, we have the diameter of bigger sheave. Then see
    Table 4-8, and round up dd2.

    Table 4-8 Minimum diameter of sheave dmin


    Type
    dmin

    20

    50

    75

    125

    200

    315

    500

    dd1 and dd2 should be in recommendation:


    20 22.4 25 28 31.5 35.5 40 45 50 56 63 67 71 75 80 85 90
    95 100 106 112 118 125 132 140 150 160 170 180 200 212
    224 236 250 265 280 300 315 355 375 400 425 475 500 530
    560 630 670 710 750 800 900 1000
    (4) Center distance and basic length of belt
    Wrap Angle: If the center distance is too small, the length of belt
    is also small and the wrap angle is small.
    Belt Life: If the belt speed is given, the number of load cycle will
    increase, which will decrease the life of belt.
    The center distance should be proper value, commonly for V-belt,

    0.55 dd1 dd2 a0 2 dd1 dd2

    After the initial value of a0 is chosen, by the geometrical


    constraints, the calculated basic length of belt Ld

    dd2 dd1

    L 2a0 dd1 dd2


    2
    4a0

    '
    d

    By Table 4-2, the basic length of V-belt Ld can be specified.


    Then by the value of Ld, we can have the actual center distance a.
    In most situation, the center distance can be adjusted, so we
    can use approximating formula,
    '

    Ld Ld
    a a0
    2

    Considering the requirements of adjustment and compensation


    of initial tension, commonly, the center distance can vary in the
    range:
    a a 0.015L
    min

    amax a 0.03Ld

    (5) Checking the wrap angle of driving sheave


    Power capacity of belt drive can be mainly decided by the
    wrap angle. In Fig. 4-17, there exist a relationship between wrap
    angle 1 and other geometrical parameters.
    dd2 dd1

    1 180 2 180
    57.3
    a

    Fig. 4-17 Geometrical relationship of belt drive


    Commonly, the wrap angle of driving sheave should be above
    120. If the wrap angle is too small, we can increase the center
    distance, decrease the speed ratio or add an tension sheave.

    (6) Number of belt


    The power rating of a single V-belt P0 is obtain by experiments
    under certain situations. If the working condition is different
    from that, we need to modify the value of P0.
    After modification, we have

    P P0 P0 k kL
    P0 -- Power rating of a single V-belt, See Table 4-3;
    P0 Added power rating because i 1, kW. See Table 4-4.
    k Coefficient of wrap angle, considering that the actual angle
    is not equal to 180 . See Table 4-9;
    kL Coefficient of belt length, considering the actual belt length
    is not equal to the given length in experiments. See Table 4-2.

    Table 4-9 Factor of wrap angle k

    180 170 160 150 140 130 120 110

    100 90

    80

    70

    Vbelt

    1.00

    0.98

    0.95

    0.92

    0.89

    0.86

    0.82

    0.82

    0.74

    0.69

    0.64

    0.58

    Flat
    belt

    1.00

    0.97

    0.94

    0.91

    0.88

    0.85

    0.80

    0.72

    0.67

    0.62

    0.56

    0.50

    So, the minimum number of V-belt is

    Pc
    Pc
    z

    10
    P P0 P0 k kL

    k : Compensation
    of wrap angle
    kL : Compensation
    of belt length

    To ensure the equal load on each belt, the number of belt


    should be less than 10, commonly in range of 3-7.
    If the number of belt is more than 10, we need to correct the
    belt type.

    (7) Initial tension F0


    We can calculate the initial tension on a single V-belt by
    P 2.5
    F0 500
    1 l v 2
    vz k

    But for a new belt, we need to increase the initial tension by 50%.
    (8) Calculating the radial force acting on shaft
    The tension force will cause a radial force on shaft. The resultant
    force acting on shaft FQ, in Fig. 4-19.
    F0

    FQ 2 zF0 sin

    1
    2
    FQ

    FQ

    F0

    F0
    1
    2

    1
    2

    F0

    Fig. 4-19 Radial force acting on shaft

    Design process
    of belt drive

    (1) Specifying calculated power


    (2) Specifying belt type

    (3) Specifying diameter of sheave and belt speed


    (4) Specifying center distance and basic length of belt
    (5) Checking wrap angle of driving sheave
    (6) Specifying number of belts
    (7) Specifying initial tension force F0
    (8) Calculating force acting on shaft

    2. Design example of belt drive


    Example problem
    Try to design a belt drive for fan ventilation. The power source is
    3-phase AC motor, Power P=7.5kW, rotational speed of motor
    n1=1440r/min; rotational speed of fan n2=630r/min, 16 hours per
    day, creep ration =0.01. The desired center distance is not above
    700mm.
    Solution
    (1) Specifying calculated power
    By Table 4-7, service factor KA=1.2.
    By Pc=KAP, we have Pc=1.2 7.5=9kW.
    (2) Specifying belt type
    According to Pc and n1, by Fig. 4-15, we can choose A type of Vbelt, and specify the diameter of small sheave as dd1=112-140mm

    (3) Specifying diameter of sheave and belt speed


    By Table 4-3, as the belt type is A, we can decide dd1=125mm.
    Diameter of big sheave dd2
    n1
    1440
    dd2 dd1 1
    125 1 0.01 282.86mm
    n2
    630

    So, dd2=280mm.
    Belt speed vb v dd1n1 125 1440 9.4m/s
    b
    60 1000

    60 1000

    The belt speed is within the range of 5-25m/s.


    (4) Specifying center distance and basic length of belt
    As 0.55(dd1+dd2) a02(dd1+dd2)
    We have 222.7 a0810.
    Considering the center distance is not above 700mm, we can
    have a0=650mm.

    By

    L'd 2a0

    dd1 dd2

    We have L'd 2 650

    dd2 dd1

    4a0

    125 280

    280 125

    4 650

    1945.09mm

    By Table 4-2, we can choose the basic length of belt Ld=2000mm.


    '
    L

    L
    d
    d
    By a a0
    2

    2000 1945.09
    a 650
    677.455mm
    2

    We have
    So , we have a=677mm.

    (5) Checking wrap angle of driving sheave


    280 125
    1 180
    57.3 166.88
    677

    1>120. Wrap angle is OK.


    (6) Specifying number of belt

    By Table 4-3, power rating of a single V-belt P0=1.93KW.

    Speed ratio i n1/n2=1440/630=2.29.


    By Table 4-4, Added power rating P0=0.17KW.
    By Table 4-9, factor of wrap angle k=0.97.
    By Table 4-2, factor of belt length kL=1.03.
    z

    Pc
    Pc
    9

    4.29
    P P0 P0 k kL 1.93 0.17 0.97 1.03

    We have z=5.
    (7) Specifying initial tension F0
    By Table 4-1, we have l=0.10, the initial tension
    F0 500

    P 2.5
    9
    2.5

    2
    2

    500

    0.1

    9.4
    159.86N

    vz k
    9.4 5 0.97

    (8) Calculating radial force acting on shaft


    Radial force acting on shaft
    1
    166.8
    FQ 2 zF0 sin 2 5 160 sin
    1589N
    2
    2

    4.6 Tension Mechanism for Belt Drives


    Belt, made from flexible materials, will slack after a period of
    service with initial tension force.
    To avoid slippage failure, we need to check the tension force
    regularly.

    If the tension force is not enough, we need to tension the belt


    again.
    Tension mechanism can be divided into regular tension
    mechanism and automatic tension mechanism.

    1. Regular tension mechanism

    a
    a

    Adjusting
    screw

    Slide way type


    tensioning device

    Adjusting
    screw

    Pendulum type
    tensioning device

    2. Automatic tension mechanism

    pin

    Adding tension sheave


    Automatic tension mechanism
    by gravity

    Tension
    sheave

    4.7 Timing Belt and Chain Drives


    Purpose:
    To introduce basic knowledge about Timing Belt and Chain Drives.

    1. Timing Belt
    Timing belts are constructed with
    rib or teeth across the innerside of belt.

    Driven
    sprocket

    Driving
    sprocket

    The teeth mate with corresponding


    grooves in the driving sprocket and driven
    sprocket, providing a positive drive
    without slippage.
    There is a fixed relationship between the
    speed of driver and the speed of driven
    sprocket, without creep or slippage.

    Side
    flange

    Timing
    belt

    Timing belts are increasingly being considered for applications,


    such as printing, material handling, packaging, and assembly.

    Comparing with the gear drive and chain drive,


    (1) Timing belt drive produces less noise, and absorbs some impact.
    (2) Lubrication is not needed for timing belt.
    (3) Speed ratio can be within 10.
    (4) total efficiency is about 98%.
    (5) Maximum power capacity can be 100kW.
    (6) Timing belt is applicable for high linear speed situation, as
    much as 50m/s.

    2. Types of Timing Belt


    (1) Straight-toothed timing belt

    Types

    Pitch,
    Pb, mm

    Tooth height, Belt thickness,


    ht, mm
    hs, mm

    Angle,
    ,

    MXL

    2.032

    0.51

    1.14

    40

    XL

    5.080

    1.27

    2.30

    50

    9.525

    1.91

    3.60

    40

    12.70

    2.29

    4.30

    40

    XH

    22.225

    6.35

    11.20

    40

    T2.5

    2.5

    0.7

    1.30

    40

    T5

    1.20

    2.20

    40

    (2) Arc-toothed timing belt

    Types

    Pitch,
    Pb, mm

    Tooth height,
    ht, mm

    Belt thickness,
    hs, mm

    2M

    0.75

    1.36

    3M

    1.17

    2.4

    5M

    2.06

    3.8

    8M

    3.36

    6.00

    14M

    14

    6.02

    10.00

    20M

    20

    8.4

    13.20

    3. Chain drives
    Driven
    sprocket

    Driving
    sprocket

    Chain

    A chain is a power transmission element made by a series of


    pin-connected links.
    When transmitting power between rotating shafts, the chain
    engages with toothed sprockets.

    Proper working conditionSpeed ratio: i 8;


    Center distancea 5~6m;
    Power capacity: P 100 kW;
    Linear speed: v 15 m/s;

    Efficiency: 0.95~0.98
    (1) Chain

    Roller chain

    Types

    Tooth chain

    ComponentsRoller, Bushing, Pin, Inner plate, Outer Plate.


    Pin
    Roller
    Bushing
    Inner plate
    Outer plate

    Materials of chain
    Carbon steel or alloy steel, with heat treatments, to improve its
    strength and anti-abrasion performance.

    Pitch of chain p
    Pitch p: the distance between corresponding parts of adjacent links.
    Bigger p means larger dimensions and greater power capacities.
    Types of roller chain: single row chain and multi-row chain.

    pt

    Roller chain is already standardized, including A and B series.


    Series A is commonly used.
    Pitch
    p

    Double row roller chain

    Array
    pitch

    Main parameters of A series roller chain


    Chain

    P
    mm

    Pt
    mm

    d
    mm

    08A

    12.70

    14.38

    7.95

    13800

    0.60

    10A

    15.875

    18.11

    10.16

    21800

    1.00

    12A

    19.05

    22.78

    11.91

    31100

    1.00

    16A

    25.40

    29.29

    15.88

    55600

    2.60

    20A

    31.75

    35.76

    19.05

    86700

    3.80

    24A

    38.10

    45.44

    22.23

    124600

    5.60

    28A

    44.45

    48.87

    25.40

    169000

    7.50

    32A

    50.80

    58.55

    28.58

    222400

    10.10

    40A

    63.50

    71.55

    39.68

    347000

    16.10

    48A

    76.20

    87.83

    47.63

    500400

    22.60

    number

    Q- Average tensile strength (One row), N


    q-mass per meter (one row), Kg/m

    Length of chain can be described by the number of pitches. The


    number of pitch should be even, which is convenient to connect the
    inner plate of first pitch with outer plate of last pitch
    If the number of pitches is odd, we should use a transitional
    pitch. When a stretching force is acting on the chain, an additional
    torque will occur on the transitional pitch. So ,try not to use a
    transitional pitch.

    Cotter

    Transitional pitch
    Spring
    Clamp

    (2) Sprocket
    Standard parameters

    Radius of tooth profilere


    tooth groove angle

    Radius of space profile ri


    min and max

    Recommendation GB

    Pitch of sprocketp chord length

    Geometrical formulas

    Dia. of pitch circle


    p
    d
    sin 180 Z

    360
    Z

    Dia. of outer circle


    da p 0.54 ctg 180 Z

    Dia. of root circle:

    ri

    df=d-d1
    Parameter of roller chain sprocket

    Transverse profile 3 arc + 1 line

    d
    c
    b

    180
    Z

    Transverse profile of roller chain sprocket

    Radial profileArc+Line
    b

    B3

    B2

    (h)

    b
    r5

    r4

    r5
    line

    pt

    Single row sprocket


    Axial profile

    pt

    Multi-row sprocket
    Axial profile

    Materials Carbon steel, Cast iron, Alloy steel for important


    sprocket.
    Heat treatments: improving the contact strength and abrasion
    performance.

    Structure of
    sprocket

    Solid type-Small diameter

    Structure of
    sprocket

    Solid type-Small diameter


    Web type-Medium diameter

    Structure of
    sprocket

    Solid type-Small diameter


    Web type-Medium diameter

    Combined type
    -Large diameter with changeable teeth

    Homework-13
    Try to design a belt drive for fan ventilation. The power
    source is 3-phase AC motor, Power P=7.5kW, rotational
    speed n1=1440r/min; rotational speed of fan n2=630r/min,
    16hours per day, sliding ration =0.01. the desired center
    distance is not above 700mm.

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