Chapter 8: Design of

Mechanical Element 3: Belt

DR. AMIR PUTRA BIN MD SAAD

C24-322

amirputra@utm.my | amirputra@mail.fkm.utm.my

mech.utm.my/amirputra

➢ In power transmissions, use of belts, simplify the machine design and reducethe cost.

➢ Is far more economical than buying a motor to run at the speed required bythe driven equipment.

➢ Due to flexibility, it can absorb a good amount of shock and vibration.

➢ It can take care of some degree of misalignment between the driven and thedriver machines and long distance power transmission (compared to gearsystem).

➢ Transmit greater amount of power with higher velocity ratio.

➢ Usually made of cotton, ryon or nylon impregnated with rubber.

8.1 INTRODUCTION

➢ A single V‐belts is less efficient than a flat belt due to the wedging actionbetween belt and pulley (high friction), but multiple v‐belts can be used totransmit higher power.

➢ V‐belts are longer in life due to seamless design (no joint).

➢ V‐belts are used for short centre distance, i.e. compactness.

➢ V‐belts are manufactured in standard lengths.

➢ The groove angle of a sheave is made somewhat smaller than the belt‐sectionangle. This causes the belt to wedge itself into the groove,

thus increasing friction.

➢ Not suitable for constant speed applications due to creep.

8.1 INTRODUCTION

slack

tight

Driver

or

InputDriven

or

Output

Vp

N1 N2

T1

T2

V-Belt

8.1 INTRODUCTION

8.2 V-BELT CONTRUCTION

Refer to Mitsuboshi’s Catalogue (Table 1-2 to Table 1-6) for Belt Code, Outer Length, La and Datum Length, Ld.

8.2 V-BELT CONTRUCTION

1. Set Conditions Required in Design Work:

a. Type of machineb. Transmission Powerc. Running hours in a single dayd. Small pulley speede. Interim center distancef. Special uses and environmental conditionsg. Speed Ratio

𝑆𝑅 =𝑛motor

𝑛machine=

𝐷

𝑑≥ 1

𝐷 = Pulley diameter

𝑑 = Sheave diameter

𝑛motor = Motor speed (rpm)

𝑛machine = Machine speed (rpm)

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

𝐾𝑠 = 𝐾𝑜 + 𝐾𝑖 + 𝐾𝑒

𝐻𝑑 = 𝐻𝑡 × 𝐾𝑠

𝐾𝑜 = Service Correction Factor

𝐾𝑖 = Idler Correction Factor

𝐾𝑒 = Environment Correction Factor

𝐾𝑠 = Service Factor

𝐻𝑡 = Transmission Power

𝐻𝑑 = Design Power

2. Set the Design Power:

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

3. Select the belt type:

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

4. Select the pulley size:

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

i. Datum Length (Belt Length) , 𝐿𝑑:

𝐿𝑑 = 2𝐶 +ሻ𝜋(𝐷 + 𝑑

2+

𝐷 − 𝑑 2

4𝐶

ii. Center-to-Center Length, 𝐶:

𝑏 = 2𝐿𝑑 − 𝜋(𝐷 + 𝑑ሻ

𝐶 =𝑏 + 𝑏2 − 8 𝐷 − 𝑑 2

8

where,

5. Determine the belt length:

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

6. Determine the required number of belts:

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

𝐻𝑐 = 𝐻𝑠 +𝐻𝑎 𝐾𝑐

𝐻𝑐 = Corrected power rating per belt𝐻𝑠 = Basic power rating per belt𝐻𝑠 = Additional power rating per belt𝐾𝑐 = Power rating correction factor𝐾𝜃 = Arc of contact correction factor𝐾𝑙 = Belt length correction factor

𝑁𝑏 =𝐻𝑑

𝐻𝑐

𝐾𝑐 = 𝐾𝜃𝐾𝑙

𝐾𝜃 =𝐷 − 𝑑

𝐶

where,

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

8.3 DESIGN PROCESS FOR CLASSICAL V-BELT

1. Angle of wrap for small pulley:

𝜃𝑑 = 𝜋 − 2 sin−1𝐷 − 𝑑

2𝐶

2. Angle of wrap for large pulley:

𝜃𝐷 = 𝜋 + 2 sin−1𝐷 − 𝑑

2𝐶

(* change Mode D to Mode R)

(* change Mode D to Mode R)

8.4 V-BELT LOADS

3. Tension due to Centrifugal Force, 𝑃𝑐 : *This formula for one belt only

8.4 V-BELT LOADS

𝑃𝑐 = 𝑊.𝑉2 =𝑤𝑒𝑖𝑔ℎ𝑡/𝑙𝑒𝑛𝑔𝑡ℎ

𝑔. 𝑉2

𝑊 = mass per unit length of belt (i.e. kg/m or lb/in)

𝑔 = gravity acceleration (9.81 m/s2, 32.17 ft/s2)

1 ft = 12 in

1 m = 3.28084 ft

lb

8.4 V-BELT LOAD

4. Tension on the tight side, 𝑃𝑡 : *This formula for 𝑜𝑛𝑒 belt only

𝑃𝑡 =33000

𝑛𝑏∙𝐻𝑑

𝑉+𝑊.𝑉2 ∙ 5.8 × 10−6 lb

5. Tension on the slack side, 𝑃𝑠 : *This formula for 𝑜𝑛𝑒 belt only

𝑃𝑡 − 𝑃𝑐𝑃𝑠 − 𝑃𝑐

= 𝑒𝑓𝜃𝑑𝑠𝑖𝑛𝛽From:

𝛽 =𝛼

2=

𝜃𝑑 = Belt wrap angle on the small pulley

𝛽 = 𝐽𝑢𝑣𝑖𝑛𝑎𝑙𝑙′𝑠 𝑏𝑜𝑜𝑘

Half of belt wedge angle𝛼 = 𝑀𝑖𝑡𝑠𝑢𝑏𝑜𝑠ℎ𝑖′𝑠 𝑐𝑎𝑡𝑎𝑙𝑜𝑔𝑢𝑒

8.4 V-BELT LOADS

8.4 V-BELT LOADS

6. Torque transfer: *This formula can be for one belt only or more than one belt.

𝑇 = 𝑃𝑡 − 𝑃𝑠 𝑟

𝑟 = driving pulley radius

𝑃𝑡 = Tight side force

𝑃𝑠 = Slack side force

Step 1: Set conditions required indesign work.

• a. Type of machine ··· Compressor

• b. Transmission power ··· Four pole motor 5 HP/1750rpm

• c. Running hours in a single day ··· 8 hours / day

• d. Small pulley speed ··· 1750rpm

• e. Speed ratio ··· 2 : 1 (Deceleration)

• f. Interim center distance ··· 12"

• g. Special uses and environmental conditions ··· None

Step 2 : Set the design power.

Step 3: Select the belt type.

Step 4: Select Pulley Size

Step 5: Determine the Belt Length

Step 6: Determine the required number of belts.

Step 7: Installation and take-upallowance.