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Chapter 8: Design of
Mechanical Element 3: Belt
DR. AMIR PUTRA BIN MD SAAD
C24-322
[email protected] | [email protected]
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.
