ch4 belt drives-2

8/10/2019 Ch4 Belt Drives-2

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4.5 V-Belt Drives Design Failure types and design principles

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

1. Failure types and Power rating

max 1 1c b

1 1 (1)c b

[]Allowable stretching stress of belt


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For a certain belt, when Ldis 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

p

3600

dm CL

Z tv

mOrder of root, m=11.1 for common V-belt;

L dBasic length of belt, m;ZpNumber of sheaves, commonly Zp=2;

tBelt life, h;

CAn constant decided by structure and material of belt.

(2) To avoid slippage, Euler's formulashould be satisfied, and we

have

1

1(1 )F F

e

11

(1 ) (2)F Ae

Combining (1) and (2), we have

c b11

(1 )F Ae


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Further, because1000

FvP

We have c b11

(1 )1000

A ve

P

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 P0of V-belt in Table 4-3 and Table 4-4.


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

Type

Dia.

sheave

Z

A

B

C


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

Type

Speed ratioi

Z

A

B

C


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2. Design procedure of belt drive

Given rated power P, rotational speed n1and n2(or speed ratio i),

dimension requirements and working conditions.

To decide: belt type, length, number of belt, center distance, basic

diameter of sheavesand structure dimension.

(1) Calculated power

Considering the properties and service hour of belt drive, thecalculated power can be decided by

c AP K P

where, Pc

Calculated power, kW;

PRated power, kW;

KAService factor, see Table 4-7


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Table 4-7 Service factor of belt


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(2) Belt type

Calculated power Pc, kWRotationalspe

edofsmallersheaven1,r

/min

Fig. 4-15 Choice of V-belt type

Z

Z or A


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(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 d1 1b

60 1000

d nv

where, n1Rotational speed of small sheave, r/min;

dd1Basic diameter of small sheave, mm.

Belt speed is usually in range of 5-25m/s. So the belt speed

should satisfy that vbvmax. If the belt speed is too high, the

centrifugal force will increase to cause instability of belt drive; Ifbelt 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.


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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 530560 630 670 710 750 800 900 1000

dd1and dd2 should be in recommendation:

Type Y Z A B C D E

dmin 20 50 75 125 200 315 500

Table 4-8 Minimum diameter of sheave dmin

(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,

d1 d2 0 d1 d20.55 2d d a d d


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After the initial value of a0is chosen, by the geometrical

constraints, the calculated basic length of belt Ld

2

d2 d1'

d 0 d1 d2

02 2 4

d d

L a d d a

By Table 4-2, the basic length of V-belt L dcan be specified.

Then by the value of L d, we can have the actual center distance a.

In most situation, the center distance can be adjusted, so we

can use approximating formula,'

d d0

2

L La a

Considering the requirements of adjustment and compensation

of initial tension, commonly, the center distance can vary in the

range:min d

max d

0.015

0.03

a a L

a a L


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(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 1and other geometrical parameters.

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.

d2 d11 180 2 180 57.3

d d

a


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(6) Number of belt

The power rating of a single V-belt P0is 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

0 0 LP P P k k

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

P0Added power rating because i1, kW. See Table 4-4.

kCoefficient of wrap angle, considering that the actual angle

is not equal to 180 . See Table 4-9;

kLCoefficient of belt length, considering the actual belt length

is not equal to the given length in experiments. See Table 4-2.


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180 170 160 150 140 130 120 110 100 90 80 70

V-

belt

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

c c

0 0 L

10P P

zP P P k k

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.

Table 4-9 Factor of wrap angle k

k : Compensation

of wrap angle

kL : Compensation

of belt length


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(7) Initial tension F0

We can calculate the initial tension on a single V-belt by

2

0

2.5500 1

l

PF v

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 resultantforce acting on shaft FQ, in Fig. 4-19.

1Q 02 sin

2F zF

F0

F0

1FQ

F0 F0

FQ

12

12

Fig. 4-19 Radial force acting on shaft


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(8) Calculating force acting on shaft

(7) Specifying initial tension force F0

(6) Specifying number of belts

(5) Checking wrap angle of driving sheave

(4) Specifying center distance and basic length of belt

(3) Specifying diameter of sheave and belt speed

(2) Specifying belt type

(1) Specifying calculated powerDesign process

of belt drive


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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.

2. Design example of belt drive

Example problem

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 Pcand n1, by Fig. 4-15, we can choose A type of V-

belt, and specify the diameter of small sheave as dd1

=112-140mm


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(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

1d2 d12

14401 125 1 0.01 282.86mm

630

nd d

n

So, dd2=280mm.

Belt speed vb d1 1b 125 1440 9.4m/s60 1000 60 1000

d nv

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.

2


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By

2

d2 d1'

d 0 d1 d2

0

22 4

d dL a d d

a

We have

2

'

d

280 1252 650 125 280 1945.09mm

2 4 650L

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

By'

d d0

2

L La a

We have2000 1945.09

650 677.455mm

2

a

So , we have a=677mm.

(5) Checking wrap angle of driving sheave

1

280 125180 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.

S d i i / 1440/630 2 29


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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.

c c

0 0 L

94.29

1.93 0.17 0.97 1.03

P Pz

P P P k k

We have z=5.

(7) Specifying initial tension F0

By Table 4-1, we have l=0.10, the initial tension

2 2

0

2.5 9 2.5500 1 500 1 0.1 9.4 159.86N

9.4 5 0.97l

PF v

vz k

(8) Calculating radial force acting on shaft

1

Q 0

166.82 sin 2 5 160 sin 1589N

2 2F zF

Radial force acting on shaft

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

4 6 T i M h i f B l D i


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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 forceregularly.

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

again.

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

1 R l t i h i


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a

Adjusting

screw

Adjustingscrew

Slide way type

tensioning device Pendulum type

tensioning device

a

1. Regular tension mechanism
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Tension

sheave

Adding tension sheave

Automatic tension mechanism

by gravity

pin

2. Automatic tension mechanism

4 7 Ti i B lt d Ch i D i
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4.7 Timing Belt and Chain Drives

Purpose:

To introduce basic knowledge about Timing Belt and Chain Drives.

1. Timing Belt Driven

sprocket

Drivingsprocket

Timing

belt

Timing belts are constructed with

rib or teethacross the innerside of belt.

The teeth mate with correspondinggrooves 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.

Timing belts are increasingly being considered for applications,

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

Side

flange


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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


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2. Types of Timing Belt

(1) Straight-toothed timing belt

Types Pitch,

Pb, mm

Tooth height,

ht, mm

Belt thickness,

hs, mm

Angle,

,

MXL 2.032 0.51 1.14 40

XL 5.080 1.27 2.30 50

L 9.525 1.91 3.60 40

H 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 5 1.20 2.20 40

(2) Arc toothed timing belt


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(2) Arc-toothed timing belt

Types Pitch,

Pb, mm

Tooth height,

ht, mm

Belt thickness,

hs, mm

2M 2 0.75 1.36

3M 3 1.17 2.4

5M 5 2.06 3.8

8M 8 3.36 6.00

14M 14 6.02 10.00

20M 20 8.4 13.20


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3. Chain drives

Drivingsprocket

Chain

Driven

sprocket

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.
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Proper working condition

Speed ratio: i8;

Center distancea 5~6m;

Power capacity: P100 kW;

Linear speed: v15 m/s;

Efficiency: 0.95~0.98

(1) Chain

Types

Tooth chain

Roller chain
http://localhost/var/www/apps/conversion/tmp/scratch_3/N2302.flc


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Materials of chain

Carbon steel or alloy steel, with heat treatments, to improve its

strength and anti-abrasion performance.

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

Pin

Roller

Outer plate

Bushing

Inner plate

Pit h f h i


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Pitch of chain p

Pitch p: the distance between corresponding parts of adjacent links.

Bigger pmeans larger dimensions and greater power capacities.

Types of roller chain: single row chain and multi-row chain.

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

Series A is commonly used.

p

p

pt

Double row roller chainArray

pitch

Pitch

Main parameters of A series roller chain


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Chain

number

08A 12.70 14.38 7.95 13800 0.60

Main parameters of A series roller chain

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

P

mm

Ptmm

Q qdmm

Q- Average tensile strength (One row), N

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

L th f h i b d ib d b th b f it h Th


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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 transitionalpitch. 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.

Transitional pitch

Cotter

SpringClam

(2) S k t


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sin 180p

dZ

(2) Sprocket

Standard parameters

Parameter of roller chain sprocket

Radius of tooth profilere Radius of space profileri

tooth groove angle

min and max

Pitch of sprocketpchord length

Dia. of pitch circle

df=d-d1

Dia. of outer circle

0.54 ctg 180ad p Z

Dia. of root circle:

Recommendation GB

Geometrical formulas

p

ri

360Z

Transverse profile 3 arc + 1 line


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180Z

Transverse profile of roller chain sprocket

Transverse profile

3 arc + 1 line

b

d

c

aa

Radial profile Arc+Line


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b

g

(h)

r5

g

b

B2

B3

pt pt

r5

Radial profileArc+Line

Single row sprocket

Axial profile

Multi-row sprocket

Axial profile

Materials

Carbon steel, Cast iron, Alloy steel for important

sprocket.

Heat treatments: improving the contact strength and abrasion

performance.

line

r4


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Structure of

sprocket

Solid type-Small diameter


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Structure of

sprocket

Solid type-Small diameter

Web type-Medium diameter


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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.

ch4 belt drives-2

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