Ch4 Belt Drives-1

8/10/2019 Ch4 Belt Drives-1

1/31

Ch 4 Belt Drives

4.1 Types of Belt Drives

4.2 V-belt Drives

4.3 Loading and Stress of Belt Drives

4.4 Belt Creep4.5 V-Belt Drives Design

4.6 Tension Mechanism for Belt Drives

4.7 Timing Belt and Chain Drives


2/31

Examples of belt drives

Agricultural machinery

Automotive engine Precision positioning, 0.05mm

Belt conveyer

Flatbelt

V-belt

Poly-rib belt

Timingbelt


3/31

Introduction

V-Belt DriveFlat Belt Drive

Features of belt drives:

Belt drives can be widely used for power transmission.For a great center distance power drive.

Commonly, the driving shaft and driven shaft are parallel.

Belts are flexible.


Friction causes the belt to turn the driven sheave.
http://localhost/var/www/apps/conversion/tmp/scratch_4/N1702.flchttp://localhost/var/www/apps/conversion/tmp/scratch_4/N1701.flc


4/31

Combination Drive4.1 Types of Belt Drives

12

3 4

5

1- Electrical motor; 2- V-belt drive;

3- Gear reducer; 4- Chain drive;5- Driven machine (Roller).How to arrangethem


5/31

Basic Geometries of Belt Drives

Layout of belt drives


3

12

11 22

CCenter distance

Fig. 4-1 Basic belt drive geometries

1Driving sheave

2Driven sheave

3Belt

1and 2are wrap angles

of driving sheave and

driven sheave. 1>120 .


6/31

Types of sheave arrangement4.1 Types of Belt Drives

a b c

Fig. 4-2 Types of sheave arrangement

a. Open belt drive

b. Cross belt drive

c. Quarter-twist belt drive

Most commonly used

Great center distance;

low belt speed

For twist axis drive


7/31

Types of belt (1)4.1 Types of Belt Drives

Classified by principle of operation

BeltDrive

Friction belt drive

Mesh belt drive

(Synchronous belt)

Positive drive;

Without slippage;

For precise

positioning.

Friction force;

For power drive.


8/31

Types of belt (2)4.1 Types of Belt Drives

Classified by belt crossing section

a. Flat belt

Fig. 4-3 Types of belt

Flat

V-belt

Poly-rib

Round

-More significant driving force than flat belt.Significant driving force, great power, compact structure,

larger speed ratio (10), high belt speed (40 m/s).

Small driving force, for handling devices, instruments,

and household appliances.

b. Round belt d. Poly-rib beltc. V-belt


9/31

Flat belt4.1 Types of Belt Drives

Fig. 4-4 Sectional view of flat belt drive

FQ

FN

Simple structure, convenient

to manufacture, applicablefor large center distance

FQ

=FN

Normal pressure force

Friction force F=FN=FQ


10/31

V-belt4.1 Types of Belt Drives

FQ

FN

FNFN

FN

2 sin cos2 2

Q NF F

2sin cos

2 2

Q

N

F

F

2

sin cos2 2

Q

N e Q

FF F F

Coefficient of friction;

eEquivalent coefficient of friction;

Intersectional angle of belt, 40 ;'Groove angle, 32 , 34 , 36 ,

38 ;

If=0.3,e=0.50-0.53. The V-shape causes the belt to wedge tightly

into the groove, increasing friction and allowing high torques to betransmitted before slipping occurs.

Fig. 4-4 Sectional view of

V-belt drive


11/31

V-belt and Narrow-section V-beltV-belt includes:

Standard V-belt, Narrow-section V-belt, Wide-section V-belt, et al.

Standard V-belts are most widely used.

Standard V-belt: h/bp0.7

4.2 V-belt Drives

Neutral

layer

Narrow-section V-belt: h/bp0.9

Applicable for the

great power with

compact dimensions


12/31

Components: Cords, Top rubber, Bottom rubber, Wrapper.

Layer cord Fabric cord

wrapper

Top rubber

Cords

Bottom rubber

Pitch line

Pitch surface

Pitch line: the circumference of pitch line is constant.Pitch surfaceContaining all of pitch lines

Structure of V-belt4.2 V-belt Drives

By GB/T11544-1997,

Standard V-belt contains 7 different cross section: Y, Z, A, B, C, D, E.

Convenient to

manufactureHigh flexibility, applicable for situation

with high rotational speed, medium loadand small itch diameter


13/31

Section Type Y Z A B C D E

Top width b 6 10 13 17 22 32 38

Pitch width bp 5.3 8.5 11.0 14.0 19.0 27.0 32.0

Height h 4 6 8 10.5 13.5 19 23.5

Wedge angle

Mass/ml(kg/m) 0.02 0.06 0.01 0. 17 0.30 0.62 0.90

Table 4-1 Cross section of V-belt

40

b

bp

When belts pass around sheaves, top rubbers are stretched and

bottom rubbers are compressed. But between top rubber and bottom

rubbers, there is a neutral layer, whose length keeps invariable. We

call this neutral layer as pitch surface of belt or belt pitch.The width of pitch surfacebpkeeps invariable when belts are bent.

Relative height: h/bp0.7 (Standard belt).

On sheave grooves, basic diameter is defined on a cylinder whose

width keeps same with b.

Geometries of V-belt4.2 V-belt Drives


14/31

Table 4-2 Basic length of belt Ld, and coefficient of length kLL d/mm

kL

h f b l


15/31

Advantages:

Smooth movements, low noise, reducing impact and vibration;

When overload, belt slipping occurs, which can be used to

protect other components;

Convenient and low cost to manufacture, assemble and maintain;

Applicable for the situation with great center distance;

Characteristics of V-belt4.2 V-belt Drives

Applications of belt drive:Allowable max power P


16/31

Sheave of V-belt

2. Materials for sheave

Commonly: cast iron, HT150 or HT200

High speed situation: cast steel or steel stamping and welding

Small power: cast aluminum or plastic

4.2 V-belt Drives

1. Requirements of sheave

(1) Light weight;

(2) Convenient to manufacture;

(3) Low interior stress by casting process;

(4) Well-distributed mass, dynamic balance needed if high

rotational speed;

(5) Smooth surface to avoid wear;

(6) Enough precision of groove to distribute load uniformly.

3. Three types for sheave

Solid type, Web type, Spoke type

Sh f b l4 2 V b lt D i


17/31

Solid type

BL

Solid type--for small diameter,

pitch diameter of sheave d 2.5D(dia. of shaft)

Sheave of V-belt4.2 V-belt Drives

h f b l4 2 V b lt D i


18/31

Web type with holes----for medium diameter

pitch diameter of sheave d 300

dh= (1.82)ds dk=( dh+dr) /2

dr= da-2(H+) Hand , see Table 4 - 11

S= (0.2

0.3) B S11.5S S20.5SL=(1.5-2)ds

Web type


Taper1:25

dh d

da

S2

d

s

Sh f V b l4 2 V b lt D i


19/31

h2 =0.8 h1

a1= 0.4 h1

a2= 0.8 a1

f10.2 h1 f2 0.2 h2

P- Power, KW

n- rotational speed, r/minA- No. of spokes

Spoke type--d>350mm


h2

dh

Taper1:25

d

d

a

h1

31 290 P

hnA

Spoke type

T bl 4 11 G di i f h bB


20/31

e/mm 80.3 120.3 150.3 190.4 25.50.5

Groove type Y Z A B C

bd/mm 5.3 8.5 11 14 19

hamin/mm 1.6 2.0 2.75 3.5 4.8

fmin 6 7 9 11.5 16

hmin 4.7 7.0 8.7 10.8 14.3

min 5 5.5 6 7.5 10

60 ---- ---- ---- ----

80 118 190 315

60 ---- ---- ---- ----

>80 >118 >190 >315

32

34

36

38

( )

Table 4-11 Groove dimension of sheavesf

6.3

H

e

b0bd

B

h

ha

dda

F l i f b lt d i4 3 Loading and Stress of Belt Dri es


21/31

Force analysis of belt drive4.3 Loading and Stress of Belt Drives1. Effective circle force

Without the initial tension,

the slack side would go totally loose,

and the belt would not seat in the groove;thus, it would slip.

n1 n2

F0

F0

F0

F0

At rest, the two sides of the belt have the same tension.

F1 = F2 = F0

F1

F2

F1

F2

Tight side

Slack sideDriven sheave

Driving sheave

As power is being transmitted, the tension in the tight side increases

while the tension in the slack decreases.

F1 F2 F1 , Tight side F2, Slack side


22/31

Ignoring the variation of belt length, the tension increment of

tight side equals to the decrement of slack side

F1F0= F0F2 F0= (F1+ F2)/2

Considering the driving sheave,

T1= F1dd1/2 - F2dd1/2 T1=( F1- F2)dd1/2

Effective circle force: driving forceF= F1- F2=F

A relationship among power, effective force and belt speed

1000FvP

If F>F,the belt will slip, which will cause the belt wear, and

decrease the efficiency. Then the belt drive fails.

PTransmitted power by belt drive, kW;FEffective circle force, N; vBelt speed, m/s.

2 Euler formula


23/31

Analyzing a short segment

Normal pressure: dFN

Tension forces at two endsFand F+dF

Force equilibriums in horizontal and vertical axes

d dd sin ( d ) sin

2 2NF F F F

d dd ( d ) cos cos

2 2NF F F F

Friction force: dFN

2. Euler formula

To maximize the efficiency of belt drive and avoid slippage

failure of belt drive, we need to investigate the critical situation.

dFN

F1

F2

F+dF

F

dFN

d

dl

d2

d

2

Ignoring centrifugal force,

d d


24/31

Force equationsd d

d sin ( d ) sin2 2

NF F F F

d dd ( d ) cos cos

2 2N

F F F F

d d dsin , cos 1

2 2 2

dd 0

2

F

d dN

F F d

dF

F

1

2 0

dd

F

F

F

F

1

2

ln F

F

Integration

Tension ratio between slack side and tight side1

2

Fe

F

This is a basic equation about flexible body friction.

d dN

F F

As dis quite small, we have

And ignoring second order term, we have

Eulers formula

3 Maximum efficient circle force F


25/31

max 0

1

12

11

eF F

e

F

(1) To ensure the ability of belt drive, commonly, we have >120 .

(2) is decided by materials of belt and sheave, status of contact

surface and working environment.

Analysis1

2

F eF

F=F1- F2

2F0=F1+ F2

3. Maximum efficient circle force Fmax

(3) If andare already decided, initial tension F0plays an very

important role in Fmax.

(4) It is very important to specify F0. If F0is too small, the belt drive

work under a poor situation and has an inclination to slip. If F0is

too great, the wear of belt will be very serious.

1 2 1

1(1 )F F F F

e


26/31


27/31

2. Stretching stress from tension force

Stretching stress on tight side: MPaA

F11

MPaA

F22 Stretching stress on slack side:

3.Bending stress when passing around sheave

2b

d

yEd

EElasticity of belt, for common V-belt, 250-400Mpa;

yDistance between neutral layer and outside layer;

ddBasic diameter of sheave.

We have the bending stress

When passing around the smaller sheave and bigger sheave

b1

d1

2yE

d

b2d2

2yE

d

b1 b2

4 Combination of three different kind of stress


28/31

4. Combination of three different kind of stress

c b

Belt stress changes with position and time. It is a variable stress.

max 1 1c b

max 1

b2

2n1

n21

b1

2

cSome tips:

1. If the basic diameter of sheave

is reduced by 10%, the life of belt

will be reduced by 50%.

2. If the transmitted power is

increased by 10%, the life of belt

will be reduced by 50%.

3. If the length of belt is reduced by 50%, the life of belt will be

reduced by 50%.

Video

4 4 Belt Creep


29/31

4.4 Belt Creep

If the strain is proportional with the stress, we have

(3) This kind of creep is resulted from the elastic deformation of

materials, We define it as elastic creep, which is the natural

characteristic of belt drive.

For tight side

For slack side:

AEF1

1 AEF2

2

F1 > F2 1 > 2

(1) When belt passes around the driving sheave, the belt length will

become a little shorter, and the belt will slip on groove, which willcause that the speed of belt falls behind the speed of driving sheave a

little.

(2) When belt passes around the driven sheave, the belt length will

become a little longer, and the belt will slip on groove, which willcause that the speed of belt lead the speed of driven sheave a little.

1. Elastic creep of belt

Video of elastic sli a e

Because of the existence of elastic creep


30/31

the linear speed of driven sheave v2 < v1that of driving sheave

Because of the existence of elastic creep,

(1) This will decrease the efficiency of belt drive, and also cause

wear and temperature rise of belt.

(2) The magnitude of elastic slippage is decided by the initial tensio

A greater initial tension means a greater elastic slippage.

d2

d1

11

did

1 d1 2 d2 2 d2 d21 2

1 1 d1 1 d1 d1

11 1

n d n d n d d v v

v n d n d d i

Commonly for V-belt =0.01~0.02we can ignore it.

Definition

2. Creep ratio


31/31

Homework-12

1. Explain why we choose V-belt for power drive instead of flat beltunder the same tension force.

2. Explain the three stress components in the belt drive, and find out

the belt position with maximum stress.

Documents

Ch4 Belt Drives-1