Bearing Load Analysis and Size Selection

Given $d$, $F_r$, $F_a$, $P$, $P_0$, $L_{10}$, $L_H$, $R$, $f_s$, you can determine $C$, $C_0$, $D$, and $B$ based on tables.

• $C$: dynamic load rating. This is the hypothetical load that will give a standard life of 1 [million revolutions]. It is used to compute the (surface) fatigue life.
  • Example, if C=10kN, it means that this class of bearings should survive at least 1M cycles under this load
  • We can compute $C$ from $C\ge P\sqrt[3]{L_{10}}$ for ball bearings or $C\ge P{L_{10}}^{3/10}$ for roller bearings!
• $C_0$: static load rating (Calculate using equation below)
• $f_s=\frac{C_0}{P_0}$: static safety factor
• $P_0$: Static load calculated from $F_a$ and $F_r$ (could be $P_0\ge X_0{F}_r+Y_0{F}_a$)
• $P$: equivalent dynamic load (could be $P=X{F}_r+Y{F}_a$) Where $X$ is the radial factor and $Y$ is the axial factor. If we have an axial load, we just recompute $P$ and $P_0$ using the equations instead of the straight load
• $d$: shaft size
• $F_r$: radial applied load
• $F_a$: axial applied load
• $L_{10}$: bearing life [millions of revolutions]
• $L_h$: bearing number of hours

The bearing life is denoted by $L_R$ [M Rev] where the subscript $R$ denotes a failure rate $\left[\%\right]$.
The $L_{10}$ life is the life of a bearing that 90% of the batch is expected to survive the design load.

• Here, reliability is 90% and failure is 10% The bearing life could also be given in $L_H$. Given a speed [rpm] and the $L_{10}$ [M Rev], the hours of operation life $L_h$ [h] can be calculated as…
• $L_h=\frac{L_{10}\cdot 10^6}{60\cdot n}$
• There are other equations that relate these two that you can check the lectures for or derive

Alt Failure

Note that alternative failure is based on $L_{aR}=C_R{L}_{10}$ found from a table.
The higher the desired reliability, the lower the expected bearing life at that reliability level will be

Solving

1. Select possible bearings based on given constraints
2. Find forces on bearings (axial or radial) and solve for them
3. Find bearing loads for static and dynamic conditions $P_0$ and $P$
4. Use $P$’s and the given conditions to solve for stuff (maybe $f$ to find the minimum static and dynamic load ratings for each bearing)
5. Pick one bearing based on basic load ratings now (you typically select the smallest bearing)