The L10 formula
The nominal service life of linear guides with rolling bearings is calculated according to ISO 14728-1 as the running distance that at least 90% of a similarly designed guide series can achieve without fatigue damage:
L10 = (C / P)^p · 10⁵ m
C = dynamic load rating (N) from the catalog · P = equivalent dynamic operating load (N) · p = service life exponent
The exponent p depends on the contact geometry of the rolling elements:
- Balls (point contact): p = 3
- Rollers (line contact): p = 10/3 ≈ 3.33
The higher exponent for rollers means that doubling the C/P ratio increases the service life of rollers by a factor of 2^(10/3) ≈ 10—whereas for balls, it increases by only a factor of 2³ = 8. Roller guides therefore benefit disproportionately from a reduction in the operating load.
- Marked point: Ball: 125 × 10⁵ m
- Marked point: Roll: 214 × 10⁵ m
- Marked point 1: Ball: 125 × 10⁵ m
- Marked point 2: Roll: 214 × 10⁵ m
Description and values of the figure
Both curves rise with the C/P ratio; the roller guide (highlighted because it corresponds to the worked example in this unit) rises faster due to its higher exponent p=10/3 compared to p=3 for the ball guide. At C/P = 5, the roller guide, with a life of approximately 214 × 10⁵ m, lasts about 71% longer than the ball guide, with a life of 125 × 10⁵ m—if C/P were doubled, the factor would be 2^(10/3)≈10 compared to 2³=8.
| C/P ratio | Kugelführung (p=3) (×10⁵ m) | Rollenführung (p=10/3) (×10⁵ m) |
|---|---|---|
| 1 | 1.0 | 1.0 |
| 2 | 8.0 | 10.1 |
| 3 | 27.0 | 38.9 |
| 4 | 64.0 | 101.6 |
| 5 | 125.0 | 213.7 |
| 6 | 216.0 | 392.5 |
From Travel Distance to Operating Hours
L10 initially provides a service life in units of 10⁵ m (= 100 km). For an oscillating axis (back-and-forth motion), the service life in operating hours can be derived from this:
Lh = L10 / (2 · s · n · 60)
Lh = Service life (operating hours) · s = Stroke (m) · n = Double strokes per minute
Mnemonic
Worked example
Given
A roller guide has a dynamic load rating of C = 20 kN at an equivalent operating load of P = 4 kN.
Calculation
- L10 = (C / P)^(10/3) = (20 / 4)^(10/3) = 5^3.33 ≈ 214
- Travel distance: L10 ≈ 214 · 10⁵ m ≈ 21,400 km
This means that 90% of guides of this type achieve a travel distance of at least 21,400 km under this load. For a stroke of, for example, s = 0.5 m and n = 30 double strokes/min, this would result in Lh = 2.14 · 10⁷ m / (2 · 0.5 · 30 · 60) ≈ 11,900 operating hours.
Practical Note: The linked online “Service Life Calculator” is generally labeled for rotating rolling bearings (result in “millions of revolutions,” converted from the speed n). For this worked example, with the same values C = 20, P = 4, and “roller bearing,” it displays the same factor (C/P)^p ≈ 214—only the reference quantity differs: for linear guides, it is ×10⁵ m of travel, while the calculator uses “millions of revolutions.”
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