Chapter 5 Belt Drive.pdf

Microsoft PowerPoint Chapter 5 BELT DRIVE 14/3/2023 1 14 Mar 23 1 THEORY OF MACHINE AND MACHINE DESIGN Chapter 4 BELT DRIVES DEPARTMENT OF EDUCATION AND TRAINNING HOCHIMINH CITY UNIVERSITY OF TECHNOLO[.]

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THEORY OF MACHINE AND MACHINE DESIGN

Chapter 4: BELT DRIVES

DEPARTMENT OF EDUCATION AND TRAINNING

HOCHIMINH CITY UNIVERSITY OF TECHNOLOGY

AND EDUCATION

TS Phan Công Bình binhpc@hcmute.edu.vn binhpc.tpm@gmail.com

Target

I Overview of belt drives

II Understand the mechanism of transmission problems

III Calculation and design drives belts

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Theoretical contents

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I Overview

II Sequence of calculation and design the belt drives

III Exercise

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TS Phan Công Bình binhpc@hcmute.edu.vn binhpc.tpm@gmail.com 14-Mar-23

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Overview

1 Structure.

1 Driving pulley 2 Driven pulley 3 Belt 4 Idler pulley

4 3

1

2

3

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2 Operating principle.

Depend on friction force between belt and pulley

Movement and energy are transmitted from driving pulley to driven pulley

Overview

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Belt tension generates friction force

2 Operating principle.

Overview

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3 Classification.

Cross-section of belt:

• Flat belt

• V belt

• Ribbed belt

• Round belt

• Timing belt

Overview

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Flat belt :

• Cross section 𝑏𝑥𝛿 𝑚𝑚

• Include: leather belt, rubber belt,

3 Classification.

Overview

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V belt :

• Isosceles trapezoid section, contact the belt groove with two sides

• In structure, V-belt include:

Top fabric 1

Tension cords

Cushion rubber

Compression rubber 4

3 Classification.

Overview

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V belt :

• Cross-section is standardized

3 Classification.

Overview

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V belt:

3 Classification.

Overview

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4 Advantages, disadvantages and range of use

Disadvantages:

• Large structural framework

• Belt ratio is not stable

• Large force acting on shaft

• Low lifetime(1000h - 5000h)

Advantages:

Overview

• Working with high speed range

• Simple structure

• Smooth working

• Against overload

• Drive transmission for two far axes

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Theoretical contents

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I Overview

II Sequence of calculation and

design the belt drives

III Exercise

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2 Select belt and cross section.

the cross section of V belt

is selected by the Figure based on the given parameters:

+ Power P + Rotating speed n

Sequence of calculation and design the belt drives

P (kW) Power of driving shaft

n (rpm) Rotation speed of driving shaft

u Ratio

1 Initial parameters

A

B

C

D E

5000

3150

2000

1250

800

500

315

200

2 3.15 5 8 12.5 20 31.5 50 80 125 200 400

Power P, kW

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d1, d2(mm) : Pitch circle diameters

a (mm) : Center distance

α1, α2 : Angle of wrap

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4 Select diameter of pulley.

Select diameter of

driving pulley 𝒅𝟏

according to Table

4.13

Standardized to

select 𝑑 (mm): 63,

71, 80, 90, 100,

112, 125, 140, 160,

180, 200, 224, 250,

280, 315, 335, 400,

450, 500, 630, 710,

800, 900, 1000,

Nên chọn 𝑑 ≈

1,2 𝑑 , chỉ khi

nào yêu cầu kích

thước thật nhỏ

𝑑 = 𝑑

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a) Validation velocity of the belt

4 Select diameter of pulley.

1

60.1000

d n

v

1



Calculation and select pitch circle diameter of the driven pulley d2:

v1< 25 m/s for V - belts

v1< 40 m/s for Narrow V belts

Chọn 𝑑 𝑡ℎ𝑒𝑜 𝑑ã𝑦 𝑡𝑖ê𝑢 𝑐ℎ𝑢ẩ𝑛 𝑔ầ𝑛 𝑣ớ𝑖 𝑔𝑖á 𝑡𝑟ị 𝑡í𝑛ℎ 𝑡𝑜á𝑛 𝑛ℎấ𝑡

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5 Length and center distance.

Select center distance asbased on table and can be obtained by the formula

Assumed Centre distance (a):

0,55dd   h a 2dd

Length of belt (l):

2

s

Based on the assumed center distance as, the length of belt is obtained by

following Equation:

Then, the belt length is standardized and given in Table 4.13

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6 Determine center distance

Calculation exactly center distance (a):

2 2

l









Based on the selected length of belt, the center distance is re-defined by

4

where,

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Condition: 𝛽 ≤ 10° ⇒ 𝛽 ≈ sin 𝛽 =

𝑑 − 𝑑

 Validation of the wrap angle: 𝛼 ≥120°for the V belt

𝛼 ≥150°for the Flat belt

7 Angle of wrap.

𝛼 = 𝜋 − 2𝛽 𝑟𝑎𝑑

𝛼 = 𝜋 + 2𝛽 (𝑟𝑎𝑑)

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8 Calculation the number of belt.

Number of belt is calculated by formula:

1 0

[ ]

d

l u z

PK z

P C C C C





+ Cz: Coefficient of load’s effect Table 4.18

+ Cα: Coefficient of angle wrap’s effect Table 4.15

Or calculation according to formula:

+ Cu: Coefficient of ratio’s effect Table 4.17

+ Cl: Coefficient of length’s effect Table 4.16

l: Real length of belt

l0: Experimental length of belt on Table 4.19 and 4.20

+ P0 (kW) Power permit on Table 4.19 for V- belt

Table 4.20 for Flat belt + Kd: Coefficients of dynamic load Table 4.7

+ P1 (kW) Power of driving pulley

0

1 0,0025(180 )if150 180 (≤ 6)

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Table 4.17

Cu 1 1,07 1,11 1,12 1,13 1,135 1,14

Table 4.18

Cz 1 0,95 0,9 0,85

Table 4.15

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

Cα 1 0,98 0,95 0,92 0,89 0,86 0,82 0,78 0,73 0,68 0,62 0,56

Table 4.16

l/l0 0,5 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,4

Cl 0,86 0,89 0,95 1,0 1,04 1,07 1,10 1,13 1,15 1,20

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Cross section

and laboratory

length lo (mm)

Diameter of

driving pulley

d1(mm)

Velocity (m/s)

O

lo = 1320

63

112

0,33 0,48 0,49 0,75 0,83 1,33 1,04 1,78

1,14 1,8 2,12 1,88 2,3 A

lo = 1700

112

140

180

0,7 0,78 0,8 0,84

1,08 1,25 1,38

1,85 2,0 2,20 2,47

2,4 2,75,2,9 2,3,14 3,27

2,73 3,44 4,06

2,85 3,75 4,46

lo = 2240

125

224

0,92 1,2 1,35 1,38 2,30 2,25 4,0 4,47

2,61 5,53

-5,34 7,38

-5,93 8,22

Table 4.19 Value allowable power [P0] of V belt

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Cross section

and laboratory

length lo (mm)

Diameter of

driving pulley

d1(mm)

Velocity (m/s)

B

lo = 3750

200

280

355

1,83 2,3 2,46 2,84

2,73 3,77 4,29

4,55 6,59 7,57

5,75 8 8,82 10,51

6,28 10,27 12,42

-9,69 11 12,27 15,62 Г

lo = 6000

355

630

-6,67 10,76 11,17 17,46 14,91 23,60 16,5 27,89 17,51 32,19

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Cross section

and laboratory

length lo (mm)

Diameter of

driving pulley

d1(mm)

Velocity (m/s)

YO

lo = 1600

63

90

112

180

0,71 0,93 1,46

0,93 1,46 1,88

1,46 2,74 3,54 4

1,77 3,74 4,93

1,85 4,23 6,14

-2,69 5,85 7 7,28

YA

lo = 2500

180

224

2 2,12 2,34

3,05 3,26 5,33 6,02 7,53 8,46 9,15 10,3 10,85

10,26 11,85

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 Sliding curve ε(ψ) – effect curve η(ψ)

9 Sliding phenomenon of belt drive.

Set coefficient of tension:

F F



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Elastic Sliding :

Cause of the belt is

elastic strain The more

flaccid of belt, the more

stretched so sliding

increase

Slippery Sliding :

Cause of the belts chains is overload, tangential force Ftis higher than friction Fms,

The sliding slippery occurred atACB arcon pulley

AC Sliding arc BC Static arc

9 Sliding phenomenon of belt drive.

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Tension in the belt:

10 Tension in the belt

Or Fr= 2.F0.sin(α1/2)

(Common Fr= ( 2 – 3)Ft

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10 Tension in the belt

F0 Initial force is necessary for transmitting power P1 or torqueT1.

• Tangential force cause by T1:

• Tension of the side F1: F1 = F0 + Ft /2

• Tension of the side F2: F2 = F0 – Ft /2

According to Euler’s formula about friction,

We have: F1= F2.efα

0

fα

F



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Bending stress:

Stress diagram:

11 Stresses in belt.

If belt material according Hook’s law: σu= E.ε

(E: Young module; ε Elongation)

ε =δ 𝑑

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11 Stresses in belt.

Tensile stress:

Stress due to initial tension:

Stress tension on driving side:

Stress tension on driven side:

Stress due to centrifugal forces: (condition v>20m/s)

0 0 F A

  1

2

t F F



    2

t F A



  

2

V

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Exercise

Q.1

There is the flat belt drives with Power P1=6,5kW and the rotation speed of

the faster shaft n1=1420 rpm and the remained shaft n2=565 rpm The

center distance a is 1800mm The velocity of belt is from 14,5 m/s to 15,5

m/s The pitch circle diameter of pulleys are standardized in the given

range: 160, 180, 200, 224, 250, 280, 315, 400, 450, 500, 560, 630, 710

(mm)

1) Determine diameter of driving pulley d1and driven pulley d2?

2) Validate the wrap angle α1?

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1

60000 60000 14,5

195,12

πn



1

60000 60000 15,5 208,57

πn



1 3 1

1 (1100 1300) P 182,64 215,85( )

n

1) Determine diameter of driving pulley d1:

Exercise

Solution 1: Based on velocity of belt

Select d1based on standard values: d1= 200mm

Solution 2: Based on Savơrin formula

Select d1based on standard values : d1= 200mm

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1 2 1

2 1 2

502,65

1

500 200

1800

d d

α

a

1) Determine diameter of driven pulley d2:

Select d2base on standard values : d2= 500mm

2) Checking the condition of wrap angle α1:

Exercise

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Q2:

The flat belt drive includes the pulleys with pitch circle diameters

d1=150mm, d2=600mm Width belt b=50mm and thickness= 6mm The

friction coefficient between the pulley and belt is 0,32; Initial stress

0=2MPa Angle of wrap1=1600and rotating speed n1=1000v/ph

Determine center distance a of belt drives?

Determine initial tension F0andtangential forceFton driving pulley?

Calculating max power P1?

Exercise

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 Determine center distance a of the belt drives :

𝛼 = 180 − 57𝑑 − 𝑑

𝑎

𝑎 = 57 𝑑 − 𝑑

180 − 160 = 57

600 − 150

20 = 𝟏𝟐𝟖𝟐, 𝟓𝑚𝑚

 Determine initial tension 𝐹 and tangential force 𝐹 on driving pulley :

• Cross-section: 𝐴 = 𝑏 ∗ 𝛿 = 50 ∗ 6 = 𝟑𝟎𝟎𝑚𝑚

• 𝐹 =A0= 300x2=600 N

 tangential force Ft:

• Condition tension belt 2𝐹 : 𝑒 − 1 ≥ 𝐹 𝑒 + 1

𝐹 =2𝐹 𝑒 − 1

𝑒 + 1 =

2 ∗ 600 ∗ 𝑒, ∗ , − 1

𝑒, ∗ , + 1 = 𝟓𝟎𝟑, 𝟏𝑁 Exercise

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 Calculating max power P1 :

• Velocity on driving pulley:

𝑣 = 𝑑 𝑛

60 10 =

3.14 ∗ 150 ∗ 1000

60 10 = 𝟕, 𝟖𝟓(m/s)

• Power on the driving pulley:

𝑃 =𝐹 𝑣

1000=

503,1 ∗ 7,85

1000 = 𝟑, 𝟗𝟓𝑘𝑊 Exercise

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Q3:

Flat belt drives has center distance a=1800mm, pulley diameter

d1=200mm, d2=600mm Friction coefficient between pulley and belt

f=0,30;Power P1=6,5kWand rotating speed n1=1200rpm

Determine and checking the condition of wrap angle α1?

Determine initial tension F0to the belt chains disappear sliding

slippery

Replace the belt by the other type with the fiction coefficient f=0,35

How the tangential force Ftis increasing?

Exercise

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Exercise 1) Determine and validation the condition of wrap angle α1

1

600 200

1800

α

a

α1=167,30 = 2,92 rad

1

0,3 2,92

0 0,3 2,92

fα

t

fα

e e





6 1 6 1

1

6,5

1200 P

n

1

2

517,3

t

T

d

where,

Hence,

2) Determine initial tension F0to satisfy the working basic condition

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Exercise

1

0,35 2,92 ' 0

0,35 2,92

fα

t fα

e e





'

591,04

1,143

517,3

t

F

3) How is the tangential force Ftchange?

The tangential force Ftincreasing

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Tiêu đề	Belt Drives
Tác giả	TS. Phan Công Bình
Trường học	Hochiminh City University of Technology and Education
Chuyên ngành	Theory of Machine and Machine Design
Thể loại	chapter
Năm xuất bản	2023
Thành phố	Hochiminh City

Định dạng
Số trang	14
Dung lượng	2,91 MB