Pin-Bushing Clearance Tolerance Stack-Up
Pin-in-bushing and shaft-in-hole fits are fundamental to mechanical design. The clearance between mating cylindrical parts determines whether they slide freely, locate precisely, or bind unexpectedly. This guide shows how to build a tolerance stack-up that predicts clearance across all manufacturing variation.
Diametral vs. Radial Clearance
Clearance between a pin and bushing can be expressed two ways:
- Diametral clearance — Difference between hole diameter and shaft diameter (Dhole − Dshaft)
- Radial clearance — Half of diametral clearance, representing the gap on one side when centered
Diametral clearance = Dhole − Dshaft
Radial clearance = (Dhole − Dshaft) / 2
Most tolerance stack-ups work with diametral clearance because that's how ISO fits are specified and how you'll dimension your drawings. Radial clearance is useful when considering how much the shaft can shift off-center.
When Radial Matters
Use radial clearance when the shaft position affects a downstream stack. For example, if a pin locates a lever arm, half the diametral clearance becomes position uncertainty in the 1D loop along the lever's motion axis.
How ISO Fits Feed the Loop
ISO 286 defines standard fits using hole and shaft tolerance zones. Instead of specifying raw dimensions and tolerances, you select a fit code (like H7/g6) and look up the deviations for your nominal diameter.
Common Clearance Fits
| Fit Code | Application | Clearance Character |
|---|---|---|
| H7/g6 | Sliding fit, easy assembly | Small positive clearance |
| H7/f7 | Running fit, free rotation | Moderate clearance |
| H8/f7 | Loose running fit | Larger clearance |
| H11/c11 | Coarse clearance, dirty environments | Large clearance |
The ISO fit directly gives you the min/max clearance for that hole-shaft pair. To integrate it into a larger stack-up, extract the clearance range and treat it as a dimension with tolerance.
From Fit Code to Stack Dimension
For a Ø20 H7/g6 fit:
| Feature | Deviation (μm) | Actual Size (mm) |
|---|---|---|
| Hole H7 | 0 / +21 | 20.000 – 20.021 |
| Shaft g6 | −7 / −20 | 19.980 – 19.993 |
Min clearance: 20.000 − 19.993 = 0.007 mm
Max clearance: 20.021 − 19.980 = 0.041 mm
This clearance range (0.007–0.041 mm) enters your stack-up as a single dimension representing the diametral play.
The 1D Clearance Stack
A simple pin-in-bushing clearance is a two-part stack:
Sign convention:
- + Hole diameter (increases clearance when larger)
- − Pin diameter (decreases clearance when larger)
Multi-Layer Stacks
When a pin passes through multiple parts (e.g., clevis + link + clevis), each hole-pin interface contributes. The effective clearance depends on the worst alignment:
- Pin diameter (one dimension, affects all interfaces)
- Hole 1 diameter
- Hole 2 diameter
- Hole concentricity / position tolerance between holes
Position tolerances on the holes add to the assembly's ability to consume clearance. If holes are misaligned, more clearance is needed to assemble.
Worked Example: Pivot Pin Assembly
A linkage uses a Ø10 pin through two bracket holes and one link hole. The pin must slide freely but with minimal play for position accuracy.
Given Data
| Feature | Specification | Size Range (mm) |
|---|---|---|
| Bracket holes (×2) | Ø10 H7 | 10.000 – 10.015 |
| Link hole | Ø10 H7 | 10.000 – 10.015 |
| Pin | Ø10 g6 | 9.986 – 9.995 |
| Hole position tolerance | Ø0.1 @ MMC | Each hole to bracket datum |
Single Hole-Pin Clearance
At any single interface:
Min clearance = 10.000 − 9.995 = 0.005 mm
Max clearance = 10.015 − 9.986 = 0.029 mm
Assembly Clearance Budget
For the pin to pass through all three holes, the holes must align within the available clearance. The position tolerance (Ø0.1 at MMC) means holes can be off by up to 0.05 mm radially from true position.
With two bracket holes, the worst-case position mismatch between them is:
For assembly to work at worst case:
0.005 mm < 0.10 mm ❌
Assembly Problem
The minimum clearance (0.005 mm) is less than the potential hole misalignment (0.10 mm). At worst case, the pin won't fit. Options: tighten position tolerance, loosen the fit (H7/f7), or use a smaller pin diameter.
Fix: Loosen to H7/f7
Changing to Ø10 f7 pin (9.972–9.985 mm):
Min clearance = 10.000 − 9.985 = 0.015 mm
Max clearance = 10.015 − 9.972 = 0.043 mm
Still not enough—0.015 mm < 0.10 mm position tolerance.
Fix: Tighten Position Tolerance
Changing position tolerance from Ø0.1 to Ø0.02:
Now with H7/g6: Min clearance (0.005 mm) is still less than 0.02 mm. Need both fixes together, or use H7/f7 with the tighter position:
Final solution: Use Ø0.01 position tolerance or switch to H8/f7 for more clearance. This is why tolerance stacks matter—intuition says H7/g6 should work, but the math shows otherwise.
RSS for Production
The worst-case analysis assumes every dimension hits its limit in the worst direction. RSS gives a statistical view:
Hole tolerance: (10.015 − 10.000) / 2 = ±0.0075 mm
Pin tolerance: (9.995 − 9.986) / 2 = ±0.0045 mm
RSS clearance tolerance = √(0.0075² + 0.0045²) = ±0.0087 mm
Nominal clearance: 10.0075 − 9.9905 = 0.017 mm
RSS range: 0.017 ± 0.0087 → 0.008–0.026 mm
Most assemblies will have clearance in this range, but some at the tails will fall outside—hence the need for WC analysis to guarantee assembly.
Common Pitfalls
- Forgetting position tolerance — Hole size alone doesn't determine assembly. Position tolerance eats into available clearance.
- Ignoring MMC bonus — Position tolerance at MMC provides extra tolerance when holes are larger. Include it in the analysis.
- Thermal mismatch — Steel pin in aluminum housing changes clearance with temperature. A press fit at room temp may become a clearance fit when hot.
- Surface finish — Ra values affect functional clearance. A rough bore acts smaller than its measured diameter.
- Coating thickness — Plating, anodizing, or paint adds material. A 10 μm coating per side reduces clearance by 40 μm diametral.
Key Takeaways
- Diametral clearance = Hole − Shaft — Simple subtraction with sign convention
- ISO fits give you the range — Look up deviations for your nominal diameter
- Position tolerance consumes clearance — Multi-hole assemblies need extra margin
- WC ensures assembly — RSS predicts typical production, WC guarantees fit
- Radial = Diametral / 2 — Use radial when position uncertainty matters downstream