Machine Design #01: Bearing and Shaft Load Calculation in Chain and Belt Drives
Loads on bearings and shafts
This article summarizes the calculation methods used to determine the loads acting on bearings and shafts in drive systems that use chains and belts. The content focuses on the basic formulas commonly used in design and load verification, with reference material from the NTN bearing catalog.
① Formula for the load on bearings and shafts
The load calculation is as follows.
This calculation refers to the formula in the NTN product catalog. (Reference: NTN Rolling Bearings General Catalog CAT. NO. 2202-Ⅶ/J, A-23).
In addition, in the reference material, the bearing load formula is based on the transmitted power (kW). In my own case, however, I usually calculate from the actual operating torque, so I convert the torque into transmitted power (kW) and then apply it to the formula.
② Required conditions Please refer to the figure above for the conditions required for the calculation.
2. Load values to calculate for the bearing
① Transmitted power from torque (supplementary calculation) W[kW] = (0.1047 × N × T1) / 1000
② Load acting on the sprocket or pulley Kt[N] = (19.1 × (10⁶ × H)) / (Dp × Ns)
③ Load including the initial tension Kr(F1)[N] = fb × Kt
④ Radial load acting on shaft support A FrA[N] = (((a + b) / b) × F1) + ((d / (c + d)) × F2)
⑤ Radial load acting on shaft support B FrB[N] = -((a / b) × F1) + ((c / (c + d)) × F2)
3. Download the calculation file
Download the Excel sheet for this load calculation formula.
What these formulas assume
A chain of formulas produces a number very quickly, so the risk is not in the arithmetic but in the assumptions. Check these five points before using the result to select a bearing.
| Assumption in the formula | What happens if reality differs |
|---|
| Radial load only | Helical gears, a misaligned V-belt, or shaft misalignment add an axial load that must be calculated separately |
| Forces lie in one plane | If the chain and the pulley pull in different directions, resolve per plane and combine as vectors |
| Dp is the pitch diameter | Using the outside diameter of the sprocket or pulley gives a result smaller than the truth |
| H is the power actually transmitted in service | Taking the motor nameplate rating gives a load that is too high or too low, depending on the real duty |
| f<sub>b</sub> is the initial-tension factor for that drive type | Chain, V-belt and timing belt each have their own factor; one value used for all is wrong from the start |
Beyond that, FrA and FrB are the loads at one steady operating condition. Starting torque, jamming torque and shock loads are not in the formula; they have to be considered separately in the static check on the bearing.
Three places the calculation goes wrong
- The minus sign in FrB. It states the direction of the force relative to the direction
assumed in the figure — not a "negative load". Use the magnitude when selecting the bearing; keep the sign when analysing the shaft, so the terms add correctly.
- Confusing bearing load with bearing life. Kt and Fr are only the applied load. L10 life is
a separate calculation, using the basic dynamic load rating C of the bearing actually chosen.
- Ignoring that a, b, c and d change with the layout. For the same drive, moving the pulley a
few tens of millimetres further from the support raises the load on one bearing noticeably. This is the variable the designer still controls, unlike power and speed, which the process sets.
Input data you should prepare before calculating
Before calculating the load on a bearing or a shaft support, you should gather the following information:
- The actual power, rotational speed and torque.
- The diameter of the pulley, sprocket or gear.
- The distance from the point where the force is applied to each support.
- The direction of the applied force: belt tension, chain force, radial load or axial load.
- The operating conditions: shock load, continuous running, reversing, dusty/hot/humid environment.
- The required life and the internal safety factor of the customer or the factory.
If these data are missing, the calculation may still produce a number, but it is not reliable enough to select a bearing or to evaluate the design.
Frequently asked questions
Should the real operating torque or the motor nameplate rating be used?
Use the real operating torque and convert it to kW, as the article does. Motors are usually selected with margin, so the nameplate tells you what the motor can do, not what the drive is transmitting. Where it cannot be measured, calculate it from the mechanical load and record that the figure is an assumption.
Where does the initial-tension factor come from?
From the catalogue for the drive type in use, matched to the specific chain or belt. It is a value published by the manufacturer for the way that type is tensioned; it should not be carried over from another type, and not set by feel.
The calculated load is small — is a larger bearing still needed?
A small load does not mean the smallest bearing. Shaft diameter, the mounting arrangement, tolerance to misalignment, lubrication conditions and the required life all take part in the selection. The calculated load is an input, not a conclusion.
How is it calculated when two pulleys sit on the same shaft?
Work out the force from each pulley separately, then apply both to the two supports at their actual positions along the shaft. The FrA and FrB formulas in the article already have the form of two forces F1 and F2 added together; a third force follows the same principle of moment balance about each support.
Notes for applying it to real design
In many cases, a bearing failure does not come from choosing the wrong part number at the start, but from under-evaluating the operating conditions. For example: an initial belt tension that is too high, misalignment during assembly, insufficient support-frame stiffness, or dust/oil reducing the actual life.
So after calculating the load, you should also check:
- Does the bearing have enough dynamic and static load capacity?
- Is the shaft deflecting excessively and misaligning the bearing?
- Is the support stiff enough?
- Are there suitable measures for dust protection, water protection or lubrication?
- During maintenance, can the operator replace it without breaking the alignment?
Calculation is only the first step. Good design combines the calculation, the assembly conditions and the real operating conditions.
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