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.
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.
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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