Printed from Kezuriba (kezuriba.net/en/maintenance/life/)

Bearing and ball screw life

Calculates bearing L10 life in hours, and ball screw life in hours and travel distance, from basic dynamic load rating, load and speed. Load factors and guide values for required life.

If the load is halved,
ball bearing life is
8 times longer!

÷Life calculation

Rolling bearings: L10 = (C / P)^p, L10h = 10⁶ / (60n) × (C / P)^p

Basic dynamic load rating CNDynamic equivalent load PNLoad factor fwRotational speed nmin⁻¹Bearing typeOperating hours per dayh

Ball screws: L = (Ca / (fw × Fa))³ × 10⁶

Basic dynamic load rating CaNAxial load FaNLoad factor fwRotational speed nmin⁻¹Lead lmm

When the load varies, enter the mean load Fm (formula below) as Fa. For preloaded ball screws, the preload must also be considered.

What is basic rating life L10?

The total number of revolutions that 90% of a group of identical bearings, run under the same conditions, can complete without rolling-contact fatigue flaking. Fatigue life varies widely, so this value is used rather than the mean.^[1][2][3]

What is basic dynamic load rating C?

A constant load, in constant direction and magnitude, at which the basic rating life is exactly 1 million revolutions. Written Cr for radial bearings and Ca for thrust bearings. Values are given in each manufacturer's dimension tables.^[1][2][3]

Bearing life (total revolutions)

L10 = (C / P)^p

L10: Basic rating life (×10⁶ revolutions)
C: Basic dynamic load rating (N)
P: Dynamic equivalent load (N)
p: Ball bearings 3, roller bearings 10/3

^[1][3][2]

Bearing life (hours)

L10h = 10⁶ / (60 × n) × (C / P)^p

L10h: Basic rating life (h)
n: Rotational speed (min⁻¹)

^[3][2]

If the load is halved

Ball bearing life becomes 8 times (2³) longer, and roller bearing life about 10 times (2^(10/3)) longer.^[1](1 source, for reference)

Life factor fh and speed factor fn

fn = (0.03 × n)^(−1/p) / fh = fn × C / P / L10h = 500 × fh^p

A formulation based on 500 hours; the content is the same as L10h = 10⁶/(60n)(C/P)^p. JTEKT also gives a simple nomogram method.^[3](1 source, for reference)

Bearing load factor fw

F = fw × Fc

Condition	fw
Almost no vibration or shock (electric motors, machine tools, instruments)	1.0〜1.2
Normal operation, light shock (rail vehicles, automobiles, blowers, compressors, etc.)	1.2〜2.0
Heavy vibration or shock (rolling mills, crushers, construction machinery, etc.)	2.0〜3.0

Multiply the calculated load Fc by this factor to get the actual load F.^[3](1 source, for reference)

Guide to required bearing life by machine type

Application	Required life
Home appliances, power tools, agricultural machinery, etc. (short or intermittent use)	4,000〜8,000 h
Factory electric motors, general gear units	12,000〜20,000 h
Machine tools, vibrating screens, crushers	20,000〜30,000 h
Compressors, pumps, critical gear units	40,000〜60,000 h

Excerpted from the table "Empirically adopted required life (reference)" in the JTEKT catalog. The catalog notes that making the life longer than necessary is not economical.^[3](1 source, for reference)

Ball screw life (total revolutions)

L = (Ca / (fw × Fa))³ × 10⁶

L: Basic dynamic load life (revolutions)
Ca: Basic dynamic load rating (N)
Fa: Axial load (N)
fw: Load factor

THK gives two forms: L10 = (Ca/Fa)³ × 10⁶ without fw, and L10m = (α × Ca/Fa)³ × 10⁶ with a correction factor α = 1/fw (the two are equivalent). For a preloaded ball screw, the preload must also be taken into account.^[4][5]

Ball screw load factor fw (categories differ by source)

Source	Condition	fw	Notes
NSK	Smooth operation without shock	1.0〜1.2	^[4][6](1 source, for reference)
NSK	Normal operation	1.2〜1.5	^[4][6](1 source, for reference)
NSK	Operation with shock and vibration	1.5〜3.0	^[4][6](1 source, for reference)
THK	Very slight vibration and shock, speed V ≤ 0.25 m/s	1〜1.2	^[5](1 source, for reference)
THK	Slight, 0.25 < V ≤ 1 m/s	1.2〜1.5	^[5](1 source, for reference)
THK	Moderate, 1 < V ≤ 2 m/s	1.5〜2	^[5](1 source, for reference)
THK	Heavy, V > 2 m/s	2〜3.5	^[5](1 source, for reference)

^[4][6][5]

Ball screw life in hours

Lt = L / (60 × n)

Lt: Life (h)
n: Rotational speed (min⁻¹)

For reciprocating motion, the THK formula Lh = L10 × Ph / (2 × 60 × n × ℓs) also works (Ph: lead in mm, n: reciprocations per minute, ℓs: stroke in mm).^[4][5]

Ball screw life in travel distance

Ls = L × l / 10⁶

Ls: Travel distance life (km)
l: Lead (mm)

^[4][5]

Mean load when the load varies

Fm = ∛( (Fa1³·ℓ1 + Fa2³·ℓ2 + … + Fan³·ℓn) / ℓ )

Fm: Mean axial load (N)
Fan: Load in each section (N)
ℓn: Distance traveled under that load
ℓ: Total travel distance

Instead of distance, you can use revolutions × time (THK). NSK also gives how to find the mean load and mean speed when load and speed change in steps.^[5][4]

Target fatigue life of ball screws (NSK reference values)

Application	Required life
Machine tools	20,000 h
Industrial machinery	10,000 h
Automatic control equipment	15,000 h
Measuring equipment	15,000 h

^[4](1 source, for reference)

Checking static safety (at rest or at low speed)

At rest or at low speed (10 rpm or less), use the basic static load rating C0a rather than life (NSK). For the static safety factor fs = C0a / Famax, the lower limit is 2 without vibration or shock and 5 with them (THK), and 1–2 for normal load and 2–3 for shock load (NSK); the sources differ.^[6][5]

When the raceway hardness is low

The raceway of a hardened ball screw is HRC58–62. Below HRC58, multiply by a hardness factor to reduce the basic dynamic and static load ratings (NSK).^[6](1 source, for reference)

📚Sources

Items without a mark are those on which two or more materials from different publishers agree. For product values, each manufacturer's documentation takes precedence. The text is summarized in Kezuriba's own words.