# Introduction to Timing Belt Design Methods

Necessary Conditions and Calculation of Design Power for Mechanical Transmission System

Determining Essential Design Conditions
To ensure an accurate mechanical transmission system design, the following key factors must be considered:

① Type of Machinery:
Identify the specific type of machinery or equipment that requires the transmission system.

② Rated Power of Prime Mover or Driving Engine:
Determine the rated power of the prime mover or driving engine that provides the initial power for the system.

For most cases, using the load of the driven machinery as the basis for power comparison is ideal. However, it’s important to note that loads may not always remain stable. In design, the rated power of the motor is often used for calculations.

Take into account the extent to which the load changes, especially during processes involving braking or reversing.

④ Daily Operating Time:
Consider the number of hours the transmission system will operate each day.

⑤ Speed of Small Pulley:
Determine the rotational speed of the smaller pulley.

⑥ Speed Ratio:
Calculate the speed ratio by dividing the number of teeth on the large pulley by the number of teeth on the small pulley.

⑦ Tentative Shaft Distance:
Provide an initial estimation of the distance between shafts.

⑧ Limitations of Pulley Diameter:
Pay attention to the minimum number of teeth and diameter requirements for the pulleys.

⑨ Operating Environment:
Consider the environmental conditions in which the transmission system will operate, such as high/low temperatures, exposure to oil, water, dust, acids, alkalis, etc.

Calculating Design Power
Calculate the design power (Pd) using the following formula:

Formula 1: Pd = Pt × (Ko + Ki + Kr)

Pd: Design Power (kW)
Pt: Transmission Power (kW)
Ki: Idler Correction Coefficient
Kr: Speed Ratio Correction Coefficient

Additionally, when using torque and horsepower, convert efficiency using the following formula:

Formula 2: Pt = Tr × n ÷ 9550

Pt: Transmission Power (kW)
n: Speed (rpm)
Tr: Torque (N·m)

Note: 1 PS = 0.7355 kW

Calculating Design Power for Rapid Stops and Starts:

During rapid stops and starts, the transmission belt experiences abnormal torque due to inertia forces. To account for this, calculate the rotational torque (Trq) using Formula 3. If the belt width is insufficient, corrections must be applied.

Compare the Pd calculated in step 2 (1) with the Pdq calculated through the following formula. Select the higher value as the design power.

Formula 3: Trq = ∑GD2 × (n1 – n2) ÷ (38.2 × t)

Trq: Rotational Torque during Rapid Stops/Starts (N·m)
GD2: Inertia Wheel Effect (Sum of GD2 on the opposite side of the brake) (kg·m2)
n1 – n2: Difference in Speed (opposite side of brake) (rpm)
t: Time required for speed change from n1 to n2 (s)

Convert the torque into efficiency using Formula 2:

Ptq = Trq × n ÷ 9550

Pdq = Ptq × Kq

Kq: Correction Coefficient

Note:

Using the load of the driven machinery as a basis for power comparison is ideal. In cases of uncertainty, use the motor’s rated power.
The tension side and slack side mentioned in the idler correction coefficient are illustrated as follows (clockwise rotation of the drive pulley):
Feel free to reach out for further clarification or adjustments. Title: Belt Selection and Design Steps for Mechanical Transmission System

Belt Model Selection
Select a belt model based on the reference model selection chart, considering the design power and speed of the small pulley. Each supplier typically provides several selection charts, from which the most cost-effective model is chosen.

Pulley Diameter Selection
Choose appropriate pulley diameters and transmission ratios considering design requirements and spatial limitations:

Formula 4: Z2 = n1 ÷ n2 × Z1

Speed Ratio = n1 ÷ n2

Z1: Number of teeth on the small pulley
Z2: Number of teeth on the large pulley
n1: Speed of the small pulley (rpm)
n2: Speed of the large pulley (rpm)

Regarding the relationship between the number of teeth, outer diameter, and pitch diameter of synchronous pulleys:

Formula 5: dp = pt × Z ÷ π

do = pt × Z ÷ π – 2a

dp: Pitch Diameter of pulley (mm)
do: Outer Diameter of pulley (mm)
z: Number of teeth on the pulley
2a: Difference between pitch diameter and outer diameter

When determining pulley diameter, consider:

Check the minimum number of teeth for the pulley.
In general, using pulleys with fewer teeth can lead to increased bending fatigue and reduced belt lifespan. Therefore, the pulley’s number of teeth should be greater than the required minimum.

Check Belt Speed
Ensure that the belt speed does not exceed the maximum speed specified for the belt.

Formula 6: v = dp × n ÷ 19100

v: Belt speed (m/s)
dp: Pitch Diameter of pulley (mm)
n: Pulley speed (rpm)

Belt Length Selection
① Determine Belt Length
Calculate an approximate belt length Lp’ using Formula 7, and select the closest standard length.

Formula 7: Lp’=2C’+1.57（Dp+dp）+（Dp-dp）2/4C’

Where:
Lp’: Approximate belt length (mm)
C’: Tentative shaft distance (mm)
Dp: Pitch Diameter of small pulley (mm)
dp: Pitch Diameter of large pulley (mm)

② Calculate Shaft Distance
Using the chosen standard length Lp, calculate the shaft distance using Formula 8.

Formula 8: C={B+[B2-2（Dp-dp）2]1/2}÷4

B = Lp – 1.57(Dp + dp)

Determine Belt Width
① Determine Basic Transmission Capacity
Calculate the transmission capacity in terms of belt width using the “Basic Transmission Capacity Table.”

② Engagement Correction Coefficient
Calculate the meshing teeth number Zm using Formula 9, and choose the correction coefficient Km based on the meshing teeth number.

Formula 9: Zm = Z × θ ÷ 360
θ = 180 – 57(Dp – dp) ÷ C

③ Calculate Belt Width
Calculate the width correction coefficient Kb using Formula 10.

Formula 10: Kb = Pd ÷ (Pr × Km × Kl)

Kb: Width correction coefficient
Pd: Design power (kW)
Pr: Basic transmission capacity (kW)
Km: Engagement correction coefficient
Kl: Length correction coefficient