---
title: "Bearing life, load rating and equivalent load"
subject: "Machine Design I"
chapter: 6
key: "semester_6/machine_design_i:bearing-life-load-rating"
source: https://www.bctengineer.com/q/semester_6/machine_design_i/bearing-life-load-rating
site: BCT Engineering
---

# Bearing life, load rating and equivalent load

Machine Design I · Chapter 6: Rolling contact bearing

- Asked in: year not given, 5 marks
- Video: [BEARINGS BASICS and Bearing Life for Mechanical Design in 10 Minutes!](https://www.youtube.com/watch?v=aU4CVZo3wgk) — Less Boring Lectures
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/machine_design_i/bearing-life-load-rating
- Whole chapter: https://www.bctengineer.com/md/semester_6/machine_design_i/chapter-6

## Question

Define bearing life, rated life (L10), basic dynamic load rating and equivalent dynamic load. Write the relation between life and load for ball and roller bearings and the formula for equivalent load, and give the steps for selecting a bearing from a catalogue.

## Short answer

Bearing life: revolutions until fatigue spalling; L10: 90% life in million revs; C: load for 1M rev life; P = X V Fr + Y Fa (V=1). For ball: L10=(C/P)^3; roller: L10=(C/P)^(10/3). To select: determine loads and life, compute P with service factor, required C = P L10^(1/k), choose bearing with suitable bore and C, recheck X,Y.

## Answer

#### Definitions

- **Bearing life:** the number of revolutions (or hours at constant speed) that a bearing completes before the first sign of fatigue (spalling) of the rolling surfaces.
- **Rated life $L_{10}$:** the life, in million revolutions, that 90 percent of a large group of identical bearings will reach or exceed under the same conditions. The median life is about five times $L_{10}$.
- **Basic dynamic load rating $C$:** the constant radial load that a group of bearings can carry for a rated life of one million revolutions with 90 percent reliability.
- **Equivalent dynamic load $P$:** the single radial load that would give the same life as the actual combination of radial and axial loads.

#### Relations

$$
L_{10} = \left(\frac{C}{P}\right)^k \quad \text{million revolutions}
$$

with $k = 3$ for ball bearings and $k = 10/3$ for roller bearings. Life in hours:

$$
L_{10h} = \frac{10^6\, L_{10}}{60\, n}
$$

Equivalent load:

$$
P = X V F_r + Y F_a
$$

where $V = 1$ when the inner ring rotates (1.2 when the outer ring rotates), and $X$ and $Y$ are radial and axial factors from the catalogue, depending on $F_a/F_r$ compared with $e$. If $F_a/(VF_r) \le e$, then $X = 1$ and $Y = 0$. A service (shock) factor multiplies $P$ for rough loads.

#### Selection steps

1. Find the radial and axial loads, speed and required life in hours.
2. Choose the type of bearing from the load direction, speed and space.
3. Assume $X$, $Y$ and calculate the equivalent load $P$ including the service factor.
4. Calculate $L_{10}$ in million revolutions and the required $C = P\,L_{10}^{1/k}$.
5. Choose from the catalogue a bearing of suitable bore with $C$ not less than the required value; check the static rating $C_0$ and the limiting speed.
6. Recheck $X$, $Y$ with the actual $C_0$ and repeat if necessary.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is rated life L10?
   A. Life reached by 50 percent
   B. Life reached or exceeded by 90 percent of a group of identical bearings
   C. Life of the first bearing to fail
   D. Average life of the group
   Answer: B. Median life is about five times L10. (Key point: L10)

2. The life-load relation is
   A. L10 = (C/P)^k with k = 10/3 for ball bearings
   B. L10 = C/P for all
   C. L10 = (C/P)^k with k = 3 for ball and 10/3 for roller bearings
   D. L10 = (P/C)^3
   Answer: C. Roller bearings have line contact so k is 10/3. (Key point: Life-load relation)

3. P = X V F_r + Y F_a; when Fa/(V Fr) <= e,
   A. X = 0.56 and Y = 1.5
   B. X = 0 and Y = 1
   C. X = 1.2 and Y = 1
   D. X = 1 and Y = 0
   Answer: D. Axial load is then ignored. (Key point: Equivalent load)

4. V = 1.2 applies when
   A. The outer ring rotates
   B. The inner ring rotates
   C. The bearing is a roller type
   D. The load is steady
   Answer: A. V = 1 for rotating inner ring. (Key point: V factor)

## Related in Machine Design I

- [Required rating of a tapered roller bearing](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Atapered-roller-bearing-capacity) — Machine Design I, chapter 6
- [Life of a deep groove ball bearing](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aball-bearing-life-check) — Machine Design I, chapter 6

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