Bearing Endplay & Preload Tolerance Stack-Up
Bearing endplay and preload are controlled by the axial stack of components along the shaft. Too much endplay causes noise and wear; too much preload causes heat and early failure. This guide shows how to build a tolerance stack-up that predicts—and controls—the result.
Endplay vs. Preload
Endplay is axial free movement of the shaft when the bearings are installed. The shaft can slide back and forth within the housing. Some applications need endplay to accommodate thermal expansion.
Preload is the opposite—the bearings are compressed axially, eliminating all free play and putting the rolling elements under load even at rest. Preload increases stiffness and precision but generates heat.
| Condition | Stack Result | Use Case |
|---|---|---|
| Endplay | Gap > 0 | Gearboxes, long shafts, thermal expansion |
| Zero play | Gap = 0 | Theoretical ideal (hard to hit) |
| Preload | Gap < 0 (interference) | Spindles, precision equipment, zero backlash |
The tolerance stack-up calculates the range of endplay or preload across all tolerance combinations. Your spec defines acceptable limits for both extremes.
Axial Stack Contributors
A typical shaft-in-housing bearing arrangement includes these axial dimensions:
Housing Side
- Housing bore depth — Distance from face to bearing seat shoulder
- Outer race widths — From bearing catalog (usually with tight tolerance)
- Spacers / shims — If used between bearings or against housing shoulder
- Retaining ring groove position — Or end cap face if bolted
Shaft Side
- Shaft shoulder positions — Locating surfaces for inner races
- Inner race widths — From bearing catalog
- Spacer sleeves — Between bearings on the shaft
- Locknut / retaining ring position — Axial constraint on the shaft
Bearing Race Widths
Inner and outer race widths are often (but not always) equal. Check the bearing spec sheet—some designs have different inner and outer widths. Angular contact and tapered roller bearings behave differently than deep groove ball bearings.
Building the Signed 1D Loop
The endplay/preload calculation is a signed 1D tolerance chain. You're comparing two "stacks":
- Housing stack — Total axial space available for the bearings
- Shaft stack — Total axial length the bearings occupy on the shaft
Endplay = Housing stack − Shaft stack
If the result is positive, you have endplay. If negative, you have preload (interference).
Sign Convention
Pick a direction along the shaft axis (e.g., left to right). Dimensions that increase the available space get a positive sign. Dimensions that decrease it (by occupying space) get a negative sign.
- + Housing bore depth, housing spacers
- − Bearing widths (inner and outer races combined effect)
- − Shaft spacer sleeves
The key is consistency. Once you establish your sign convention, apply it to every dimension.
Worked Example: Two-Bearing Shaft
Consider a shaft supported by two deep groove ball bearings (6205) in a housing. The goal is 0.05–0.15 mm endplay.
Given Dimensions
| Dimension | Nominal (mm) | Tolerance | Sign |
|---|---|---|---|
| Housing bore depth | 45.00 | ±0.05 | + |
| Bearing A width (6205) | 15.00 | ±0.02 | − |
| Spacer sleeve | 14.90 | ±0.03 | − |
| Bearing B width (6205) | 15.00 | ±0.02 | − |
Nominal Endplay
Worst-Case Analysis
Sum all tolerances to find the total variation:
- Maximum endplay: 0.10 + 0.12 = 0.22 mm
- Minimum endplay: 0.10 − 0.12 = −0.02 mm (preload!)
Problem Identified
The worst-case minimum is −0.02 mm, meaning some assemblies will have preload instead of endplay. The spec requires 0.05–0.15 mm endplay. Either tighten tolerances or adjust the spacer nominal.
Fixing the Stack
Reduce the spacer nominal from 14.90 to 14.80 mm:
- Maximum endplay: 0.20 + 0.12 = 0.32 mm
- Minimum endplay: 0.20 − 0.12 = 0.08 mm ✓
Minimum endplay is now 0.08 mm—within spec. Maximum is 0.32 mm, which may be acceptable depending on the application. If not, tighter tolerances or selective assembly may be needed.
RSS Analysis for Production
Worst-case assumes every part is at its limit in the worst direction simultaneously. In production, that's unlikely. RSS (Root Sum Square) gives a statistical estimate:
With the adjusted spacer (14.80 mm nominal, 0.20 mm nominal endplay):
- RSS Max endplay: 0.20 + 0.065 = 0.265 mm
- RSS Min endplay: 0.20 − 0.065 = 0.135 mm
The RSS range (0.135–0.265 mm) represents ~99.73% of assemblies assuming normal distributions. Most production assemblies will fall comfortably within spec.
Common Pitfalls
- Forgetting thermal expansion — Long aluminum housings with steel shafts will have different expansion rates. At operating temperature, endplay changes.
- Ignoring bearing internal clearance — Bearings have their own internal clearance (C2, CN, C3). This adds to or subtracts from the stack depending on the mounting.
- Missing the locknut — The locknut (or snap ring) axial position contributes to the shaft-side stack. Its tolerance matters.
- Race width assumptions — Don't assume inner and outer race widths are identical. Check the bearing drawing.
- Confusing preload with interference fit — Shaft-to-bore interference (press fit) is radial. Preload is axial. They're different analyses.
Key Takeaways
- Endplay is a 1D axial stack-up — Housing space minus shaft-side dimensions
- Sign convention is critical — Positive for space-adding, negative for space-occupying
- WC predicts the extremes — Use it to verify spec compliance at limits
- RSS reflects production reality — Most assemblies land near nominal
- Adjust nominals first — Changing spacer length is cheaper than tightening tolerances