Correct selection of gearbox synchronous belts
A precisely designed synchronous belt drive is key to efficient and durable power transmission in industrial applications. However, what is important when choosing the right belt? From calculating the rated power to determining the optimum belt width to verifying the center distance between shafts, each step affects the performance and service life of the drive system. Excessive tension can overload components; insufficient tension can cause slippage or tooth failure. That’s why the right belt tension is critical for reliable operation. In this blog post, you’ll learn how to determine the ideal belt configuration step-by-step, which calculation formulas are available to assist you, and what to look for during adjustment and maintenance.
How to Select Gearbox Synchronous Belts
An efficient synchronous belt drive requires precise sizing to ensure optimal power transmission, long service life, and minimal maintenance. In this blog post, we’ll show you step-by-step how to select the right belt based on proven calculation formulas and manufacturer’s specifications, determine the optimal width, and adjust tension correctly to avoid typical malfunctions and maximize the performance of your drive system.
Step 1: Determining the framework conditions
Before selecting a synchronous belt solution, the basic technical requirements must be clearly defined. The sizing of the drive system depends significantly on the force to be transferred, the operating conditions and the service life requirements. Precise specification of these parameters ensures optimal performance, minimal maintenance costs and long belt service life.
The required framework conditions include:
- Machine and drive type
- What type of machine is it? e.g. conveyor, mixer, etc.
- Power transmission of the drive side
- What is the rated output supplied by the motor?
- How many revolutions are provided by the drive on the drive pulley?
- What transfer force Pt is applied to the drive pulley?
- Are there any load variations on the input or output side?
- Operating time per day
- Continuous or intermittent operation?
- Are start-stop operations frequently performed?
- Speeds and gear ratio
- What is the maximum speed reached by the small pulley?
- What rotation ratio/gear ratio is needed?
- What is the actual number of teeth for the large and small pulleys?
- What is the minimum number of teeth on the small pulleys?
- Is the output turning faster than the drive?
- Shaft center distance
- Is there a diameter limit for the pulleys?
- Is there a minimum diameter?
- What is the shaft spacing?
- Are there any interfering attachments?
- Other operating conditions
- Temperature, dust
- Moisture, chemicals, etc.
In many cases, an estimate of the expected belt type is already made when determining the framework conditions. This is usually done by preselecting using the selection guide tables (see step 3). By simply reading these overviews, the belt series can already be narrowed down based on the expected speed of the small pulley and the estimated rated output. With the synchronous belt series selected in this way, the calculation can then be carried out specifically to check the sizing and selection.
Step 2: Calculating the rated power
The rated power of a synchronous belt describes the actual power that the belt must reliably transmit under real-world operating conditions. It takes into account not only the power (Pt) transmitted to the synchronous belt provided in the form of transmission torque (tq) by the motor-driven synchronous pulley. It also takes into account - in the form of an overload factor (Ks)- additional influencing factors such as load fluctuations, operating time and other influencing variables. By contrast, the rated output of the drive only indicates the steady-state power it can deliver under ideal standard conditions. However, this rated output does not take into account external influences such as load variations or operating voltages in the belt drive.
MISUMI offers a wide range of high-quality synchronous belts that are optimized for a wide range of industrial applications. This ranges from synchronous belts for precise drive systems to models for high-performance applications with high loads and speeds. Correct calculation of the rated power is critical to selecting the right belt. The following first explains the calculation of the rated power in general and then goes into more detail using various categories.
Note for the following calculations of the rated power that the calculations apply only to the designated MISUMI synchronous belts and are not necessarily transferable.
General formula
The rated power Pd is calculated by multiplying the transmitted power Pt with an overload factor Ks:
P d: Rated Power
Pt: Transmission power in kW
Ks: Overload factor
Transmission power
The transmission power Pt can be calculated using a range of variables.
Torque and speed:
Pt: Transmission power (kW)
tq: Transmission torque (Nm)
n: Speed (min-1)
9550: Conversion factor for converting torque and speed to kW
with belt speed and tractive force
Te: Effective stress(N)
Pt: Transmission power (kW)
v: Motion speed (m/s)
1000: Converting Watts to Kilowatts
m: Mass (g)
α: acceleration (m/s²)
Overload factor
While the basic formula for the rated power always remains the same, the individual correction factors are adjusted depending on the application. The specific values for these factors depend on the operating conditions as well as the design of the drive system. They are provided in the technical documentation and tables of the belt manufacturers. They contain detailed information related to the use case, operating time and design features. If one of the factors specified in the formula is not required for the respective series, the respective factor is set to zero in the calculation.
The overload factor Ks takes into account additional loads caused by dynamic load changes, different rotation ratios and the use of tension pulleys. Depending on the belt series, the overload factor Ks consists of up to 5 correction factors:
Ko: Overload Correction Factor
Kr: Rotation Ratio Correction Factor
• Number of teeth (large pulley to small pulley)
Ki: Tension pulley Correction Factor
Kh: Operating Time Correction Factor
Km: Engagement Correction Factor
Determining the load correction factor Ko
The necessary tables can be found here:
Determining the tension pulley correction factor Ki
The necessary tables can be found here:
Determining the start/stop correction factor Km
The necessary tables can be found here:
Step 3: Preliminary selection of belt type
The belt guide is provisionally selected using guide tables.
These tables provided by manufacturers include key parameters, such as the rated output, i.e., the maximum transferable power of the belt under standard conditions (in kW). They also consider the pulley speed, which indicates the rotational speed of the driven pulley (in rpm), or the drive pulley speed, which describes the speed of the driving pulley (in rpm).
Selection Tables
The article on selection of V-belts and V-belt pulleys shows parallels when designing belt drives with different belt types and provides comparisons.
Step 4: Calculating the number of teeth, belt length and center distance between shafts
Calculating the number of teeth, belt length and center distance between shafts is another important step for proper sizing of a synchronous belt drive. The following article will give you practical tips on the interaction of timing belts, pulleys and tension rollers, which makes optimal selection and adjustment much easier.
Selecting the minimum number of teeth for large and small pulleys
The gear ratio for synchronous belt drives describes the ratio between the speed of the drive shaft and the speed of the output shaft. It is determined by the sizes of the pulleys used, e.g. their number of teeth. Since synchronous belts have a fixed tooth pitch, the number of teeth must be selected to give a practical and accurate gear ratio.
Calculating the Gear Ratio
i: Speed / gear ratio
Tcg: Number of teeth (large pulley)
Tcs: Number of teeth (small pulley)
| Speed small pulleys (1/min) |
Belt type, minimum number of teeth | |||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| MXL | XL | L | H | S2M | S3M | S5M | S8M | S14M | P2M | P3M | P5M | P8M | UP5M | UP8M | MTS8M | T5 | T10 | 2GT | 3GT | EV5GT | EV8YU | |||
| 900 or less | 12 | 11 | 14 | 16 | 16 | 16 | 16 | 24 | -- | 14 | 14 | 18 | 22 | 18 | 22 | 24 | 12 | 16 | 12 | 14 | 18 | 26 | ||
| Over 900, 1200 or less | 15 | 11 | 14 | 18 | 16 | 16 | 20 | 25 | 40 | 14 | 14 | 20 | 24 | 20 | 24 | 24 | 14 | 18 | 14 | 14 | 20 | 28 | ||
| Over 1200, 1800 or less | 15 | 12 | 16 | 20 | 18 | 18 | 24 | 28 | 48 | 14 | 14 | 24 | 26 | 24 | 26 | 26 | 16 | 20 | 16 | 16 | 24 | 32 | ||
| Over 1800, 3600 or less | 16 | 16 | 19 | 24 | 20 | 20 | 24 | 30 | -- | 16 | 18 | 28 | 28 | 28 | 28 | 28 | 18 | 22 | 20 | 20 | 28 | 36 | ||
| Over 3600, 4800 or less | -- | 16 | 20 | 24 | 20 | 20 | 24 | 32 | -- | 18 | 20 | 30 | 30 | 30 | 28 | 28 | 18 | 22 | 20 | 20 | 30 | -- | ||
| Over 4800, 10000 or less | -- | -- | -- | -- | -- | -- | 20 | 20 | 26 | -- | -- | 20 | 28 | 40 | -- | 40 | -- | -- | -- | -- | -- | -- | -- | -- |
Calculating the Approximate Belt Circumference
Calculating the approximate belt circumference L’p allows for an initial estimate of the required length of the synchronous belt. This takes into account the preliminary shaft spacing and outer diameters of the large and small synchronous pulleys.
The approximate belt circumference L’p is compared to the standard lengths of the available synchronous belts and the closest available belt circumference Lp is selected. Since the actual belt circumference Lp chosen often differs slightly from the approximate circumference, the exact shaft spacing C must be recalculated for that belt circumference.
L'p = approximate belt circumference
C = shaft spacing
D'1 = effective diameter - large pulley
D'2 = effective diameter - small pulley
The effective diameter D' is greater than the outer diameter of the pulley and depends on the selected tooth profile and number of teeth. Refer to the product data provided by the manufacturer for appropriate values.
Calculating the Required Shaft Spacing
Due to their tooth profile, synchronous belts cannot be shortened at arbitrary points. The belt length must therefore always be calculated by rounding up to integer numbers (teeth).
This results in a calculated deviation of the technically feasible shaft spacing from the originally intended shaft spacing. This deviation must be corrected either by an adjustable shaft spacing or an additional clamping element.
C = shaft spacing
b = Auxiliary value for calculation
D'1= effective diameter (large pulley in mm)
D'2= effective diameter (small pulley in mm)
L p = belt circumference
Step 5: Determining the belt width
Belt width significantly affects the performance and service life of a synchronous belt drive. Correct sizing ensures that the transmitted power is optimally distributed, unnecessary loads are avoided, and the belt is reliable.
The belt width must be selected so that the belt can reliably transmit the required power without excessive wear or overload. Depending on the size of the pulleys, a different number of teeth are engaged. The fewer teeth are engaged, the less force can be transferred from the synchronous belt without overload. The number of teeth in engagement is taken into account in the calculation of the required belt width by the correction factor Km.
The required belt width can be calculated by the following formula:
B w’ = approximate belt width (mm)
Pd= rated power
P s= reference transmission capacity
K m= engagement correction coefficient
W p= reference belt width (mm)
The number of teeth in engagement Z m has a direct effect on the engagement correction coefficient K m, which in turn influences the required belt width B’w.
Z m= number of teeth in engagement
Zd= number of teeth of small pulleys
θ = contact angle (°)
C = shaft spacing
D1= outer diameter (large pulleys in mm)
D2= outer diameter (small pulley in mm)
Checking the rated power
In a further step, it must be checked whether the rated power Pd satisfies the following formula:
Pd= rated power
Ps= reference transmission power
Km= engagement correction coefficient
KL= length correction coefficient
If the calculated rated power Pd is less than the product of the other factors, then the selected belt width is sufficient. If the determined power is equal to or greater than the product of the other factors, the current belt width is not sufficient to reliably transmit the required power. In such a case, the belt width must be one size larger and the test must be repeated. This process may need to be repeated until the appropriate width is found.
An overview of the width correction coefficients (Kb) and length correction coefficients (KL) for each series can be found here in the MISUMI web index.
Step 6: Checking the adjustment range of the shaft spacing
After the belt width has been determined, it must be checked whether the adjustment range of the shaft spacing meets the requirements. The adjustment range of the shaft spacing indicates the range within which the center distance between the input and output shafts can be variably adjusted. This check ensures that the belt can be properly tensioned, thus reducing wear and ensuring long drive service life.
Ci: Minimum adjustment range, inner
Cs: Minimum adjustment range, outer
C: Shaft spacing
MISUMI Web Index - Minimum Adjustment Range Tables by Type and Belt Length
If the calculated shaft spacing is within the acceptable range, the design is correct. If not, an adjustment must be made by changing the individual parameters.
Precautions when using synchronous belts
Proper belt tension is critical to the service life and function of a synchronous belt. Excessive or insufficient tension can cause serious problems that affect the efficiency and durability of the drive system. If the belt is over-tensioned, the bearings, shafts and pulleys may be subjected to excessive tractive force. If the belt is not tight enough, the belt may jump out of the pulley groove due to sudden torque or shock loads.
To ensure optimal belt tension, the correct sagging load must be applied.
Td = Load N required for sagging d at center of span length t
Ti = preload
Lp = belt length (mm)
Y = correction coefficient
C = shaft spacing (mm)
δ = deflection: δ=0.016t
t = span length (mm)
dp = diameter of the pitch circle of the small tension pulley (mm)
Dp = diameter of the pitch circle of the large tension pulley (mm)
Table 1a - Ko for MXL, XL, L, H, S_M, MTS_M and T series
Table 1a
Table 1b - Ko for P_M and UP_M series
Table 1b
Table 1c - Ko for 2GT and 3GT series
Table 1c
Table 1d - Ko for EV5GT and EV8GT series
Table 1d
Table 2 - Speed Ratio Correction Coefficient Kr
| Speed ratio | Factor (K_r) |
|---|---|
| 1.00 to 1.25 | 0.0 |
| 1.25 to 1.75 | 0.1 |
| 1.75 to 2.50 | 0.2 |
| 2.50 to 3.50 | 0.3 |
| 3.50 or more | 0.4 |