For engineers who already know the math—but still lose projects. For the last few years, I’ve been sharing technical guides here on Mechanical Design Handbook —how to size a motor, how to calculate fits, and (as you recently read) how to choose between timing belts and ball screws. But after 25 years in industrial automation, I realized something uncomfortable: Projects rarely fail because the math was wrong. They fail because: The client changed the scope three times in one week. A critical vendor lied about a shipping date (and no one verified it). The installation technician couldn’t fit a wrench into the gap we designed. University taught us the physics. It didn’t teach us the reality. That gap is why I wrote my new book, The Sheet Mechanic . This is not a textbook. It is a field manual for the messy, political, and chaotic space between the CAD model and the factory floor. It captures the systems I’ve used to survive industrial projec...
Figure 1: Fundamental deviations for shafts and holes relative to the Zero Line. (Click image to search for the Standard Reference)
In the world of Precision Metrology and CNC machining, adhering to the ISO 286 standard for limits and fits is non-negotiable. Whether you are designing a bearing press fit or a sliding shaft, understanding these metric standards is the difference between a smooth assembly and expensive scrap.
Essential Reference: Most professional engineers rely on the Machinery's Handbook for the complete tables of tolerances and allowances. It is the industry standard for verifying these calculations.
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1. The Big Picture: Hole Basis vs. Shaft Basis
Before calculating numbers, you must choose a system.
- Hole Basis System (Most Common): We keep the hole size constant (e.g., exactly 20.00 mm with a tolerance of H7) and machine the shaft to fit. This is preferred because drills and reamers come in standard sizes.
- Shaft Basis System: We keep the shaft size constant (e.g., standard cold-rolled steel bar) and bore the hole to fit. Used for long shafts like textile rollers.
2. Common Fits for Design Engineers
While the standard lists thousands of combinations, 95% of engineering uses just these three:
A. Clearance Fit (Slide)
Code: H7/g6The shaft is always smaller than the hole. Used for:
Sliding gears, clutch discs, and pivot pins.
B. Transition Fit (Tap)
Code: H7/k6The zones overlap. It might be tight or loose. Used for:
Locating dowels, pulleys on shafts, and coupling hubs. Requires a light tap with a mallet.
C. Interference Fit (Press)
Code: H7/p6The shaft is always larger than the hole. Used for:
Permanent bearing mounts, bushings, and seal rings. Requires a hydraulic press or thermal shrink fitting.
3. Decoding the Numbers: IT Grades
The "Number" in the code (e.g., the '7' in H7) tells you the Cost of Manufacturing.
| IT Grade | Typical Process | Application |
|---|---|---|
| IT 01-4 | Lapping / Superfinishing | Gauge blocks, Fuel injectors |
| IT 5-7 | Precision Grinding / Reaming | Bearings, Engine pistons |
| IT 8-11 | Turning / Milling | General brackets, keyways |
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4. Mathematical Calculation (IT Formula)
For general engineering (IT6 - IT16), the standard tolerance unit (i) in microns is calculated as:
i = 0.45 × ∛D + 0.001D
Where D is the geometric mean of the size range.
Tolerance Grade Multipliers
| Grade | Tolerance Value |
|---|---|
| IT6 | 10i |
| IT7 | 16i |
| IT8 | 25i |
| IT9 | 40i |
5. Thermal Considerations (Shrink Fits)
For heavy interference fits (like a railway wheel on an axle), simple pressing is dangerous. We use Shrink Fitting.
By heating the hole (expanding it) and freezing the shaft (shrinking it) using liquid nitrogen, we create a temporary clearance gap.
Formula: ΔL = L × α × ΔT
6. Real-World Calculation Example
Let's calculate the limits for a standard 25 mm diameter shaft with a sliding fit (H7/g6).
Step 1: Identify the Parameters
- Basic Size: 25.000 mm
- Hole Tolerance (H7): For 25mm, IT7 = 21 µm (0.021 mm). Since it is 'H', the lower deviation is 0.
- Shaft Tolerance (g6): For 25mm, IT6 = 13 µm (0.013 mm). The fundamental deviation for 'g' is -7 µm (-0.007 mm).
Step 2: Calculate Limits
| Component | Max Limit | Min Limit | Result |
|---|---|---|---|
| Hole (H7) | 25.000 + 0.021 | 25.000 + 0 | Ø25.000 - Ø25.021 |
| Shaft (g6) | 25.000 - 0.007 | (25.000 - 0.007) - 0.013 | Ø24.980 - Ø24.993 |
Step 3: Determine the Fit
Max Clearance: 25.021 - 24.980 = 0.041 mm
Min Clearance: 25.000 - 24.993 = 0.007 mm
Result: The shaft will always slide freely with a small lubricating gap.
Conclusion
A design engineer must balance precision with cost. Specifying an H7 fit on a garden gate hinge is a waste of money; specifying H11 on a turbine bearing is a catastrophe.
📚 Related Engineering Guides
If you found this guide on Limits and Fits useful, check out these related practical design articles:
- 👉 The Engineer's Guide to Precision Alignment - Learn when to use transition fits for locating pins.
- 👉 Ball Detent Torque Limiters - How to design safety couplings using precision fits.
- 👉 Standards of Limits and Fits (Part 2) - Advanced calculations using Excel.
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