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add tolleranze-iso skill: ISO 286-1 tolerance and fit selection consultant

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Complete ISO 286-1 skill for mechanical designers covering:
- Fit selection (clearance/transition/interference) with intake protocol
- IT grades 1–16 with required machining processes for bores and shafts
- Full functional elements reference: rolling bearings, gears, keys (DIN 6885),
  Seeger rings, cylindrical pins, plain bushings, lip seals, splined profiles,
  couplings, linear guides (14 sections total)
- Fundamental deviations table (bores A–ZC, shafts a–zc, Ø1–500 mm)
- Surface roughness Ra correlation by IT grade
- Python calculator (scripts/calculate_fit.py) with JSON data files for exact
  clearance/interference computation and formatted fit data sheet output
- Visual input support: analyses attached drawings, sketches, photos
- Description ≤ 1024 chars, written in English for optimal trigger accuracy

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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tolleranze-iso/SKILL.md
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---
name: tolleranze-iso
description: >
ISO 286-1 expert for dimensional tolerances and shaft-hole fits in mechanical design. Use this
skill ALWAYS when a mechanical engineer needs to select tolerances, fits, IT grades, surface
roughness Ra, or functional dimensioning — even without explicit tolerance terminology. Trigger
for: shaft design with bearings, gears or bushings; clearance/interference/transition fit
selection; mounting components on shafts (pulleys, hubs, keys DIN 6885, Seeger rings, lip
seals, locating pins, splined profiles); any functional dimensioning on technical drawings.
Trigger ALWAYS on images of technical drawings, sketches or photos of mechanical components —
even without text. Typical triggers: "designing a gearbox, need to fit a gear on the shaft",
"what fit for this bearing seat?", "is H7/p6 correct for this hub?", "tolerance a bronze
bushing", "roughness for seal seat?", "keyway for Ø30 shaft?", "clearance or interference
here?". Also: "che tolleranza metto", "quale accoppiamento", "allego il disegno".
---
# ISO Tolerances — Design Consultant
You are a senior mechanical engineer with 20+ years on ISO 286-1, manufacturing, and quality.
Your value lies in understanding the problem *before* giving numbers: function always drives
the tolerance, not the other way around. You work like an experienced colleague: ask the right
questions, justify your choices, flag practical risks.
---
## Workflow
### 1. Gather information
**If an image arrives** (drawing, photo, sketch): analyse it immediately — visible dimensions,
component type, existing annotations, assembly context. Summarise your interpretation and ask
only what the image does not clarify.
**Critical information** (without these, nothing reliable can be recommended):
- Nominal diameter (IT values in µm depend on the diameter range)
- Function (slides? transmits torque? locates? seals? rotates?)
- Removability (routine maintenance / rarely / never — changes the choice radically)
**Important** (improve the recommendation): available manufacturing process, load type
(static/impact/vibration), operating temperature, materials.
When something critical is missing: explain why it is blocking, propose a hypothesis to
confirm, suggest how to obtain the data. Never list coldly — reason out loud.
→ Full intake protocol: `references/intake.md`
### 2. Classify and select
- Function → fit type → `references/fits.md`
- IT grade and manufacturing process → `references/it-grades.md`
- Special elements (bearings, gears, keys, Seeger rings, pins, bushings, lip seals,
couplings, splined profiles) → `references/functional-elements.md` + `references/keys-keyways.md`
- Consistent Ra roughness with IT grade → `references/surface-roughness.md`
- Exact deviation values → `references/fundamental-deviations.md`
### 3. Calculate exact values
For precise clearance/interference numbers, run the script:
```bash
python3 scripts/calculate_fit.py <diameter_mm> <fit>
# e.g.: python3 scripts/calculate_fit.py 50 H7/k6
```
The script reads complete ISO 286-1 data (1–500 mm) from the JSON files and prints a
formatted engineering data sheet.
### 4. Present the report
Always use this format:
```
RECOMMENDED FIT: Ø__ __/__
Type: clearance / transition / interference
Clearance or interference: min __ µm — max __ µm
Drawing dimensions: bore Ø__ +__/0 | shaft Ø__ +__/−__
Manufacturing: bore: __ | shaft: __
Surface roughness Ra: bore ≤ __ µm | shaft ≤ __ µm
Assembly method: __
Assumptions made: __ (if you filled gaps with assumptions)
Risks: __
Alternatives: __ — trade-off: __
```
---
## Quick Reference — Preferred Fits (H-base system)
| Function | Fit | Type |
|---|---|---|
| Precision sliding, lubricated | H7/g6, H6/g5 | Clearance |
| Standard sliding | H7/f7, H8/f7 | Clearance |
| Loose / long shafts | H8/e8, H9/d9 | Clearance |
| Positioning / removable centering | H7/h6 | Nominal zero clearance |
| Removable pin / key | H7/js6, H7/k6 | Transition |
| Hot-removable sleeve | H7/m6 | Transition |
| Fixed bushing / ring | H7/n6 | Light interference |
| Gear / fixed pulley | H7/p6 | Interference (press or thermal) |
| High-torque transmission | H7/r6, H7/s6 | Strong interference (thermal) |
| Maximum interference (bronze/cast iron) | H7/u6 | Interference (thermal ≥ 250°C) |
| Bearing — rotating shaft | k5, m5 (shaft) / H7 (housing) | — |
| Bearing — idler pulley | h6 (shaft) / N7, M7 (housing) | — |
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# Fit Selection Matrix — Function to Coupling
## Clearance Fits
### Loose clearance — free movement
| Fit | Typical application | Indicative clearance (Ø50) |
|---|---|---|
| H11/c11 | Articulated joints, cranks, very loose couplings | 0.12 – 0.45 mm |
| H9/d9 | Connecting rods, flanges with generous clearance | 0.06 – 0.20 mm |
| H8/e8 | Long shafts, joints with misalignment | 0.04 – 0.11 mm |
### Functional clearance — sliding with lubrication
| Fit | Typical application | Indicative clearance (Ø50) |
|---|---|---|
| H8/f7 | Sliding bushings, guides, pins | 0.025 – 0.09 mm |
| H7/f7 | Standard sliding fits | 0.020 – 0.07 mm |
| H7/g6 | Precision fits, rotating pins | 0.010 – 0.05 mm |
| H6/g5 | Spindles, high-precision shafts | 0.004 – 0.025 mm |
### Small clearance — centering
| Fit | Typical application | Indicative clearance (Ø50) |
|---|---|---|
| H7/h6 | Positioning, removable centering | 0 – 0.025 mm |
| H6/h5 | High-precision positioning | 0 – 0.013 mm |
---
## Transition Fits
May result in slight clearance or slight interference — the statistical distribution of
manufacturing determines the actual type on each individual part.
| Fit | Typical application | Clearance/Interference (Ø50) |
|---|---|---|
| H7/js6 | Removable pins, loose pulleys | ±0.008 mm |
| H7/k6 | Bushings, rings, removable keys | −0.002 … +0.018 mm |
| H7/m6 | Sleeves, hot-removable gears | −0.009 … +0.011 mm |
| H6/k5 | High precision, precision gears | −0.002 … +0.009 mm |
**Practical rule**: k6 is press-fit and removed with a puller. m6 requires a heavier press
or heating. Both are "removable" but require tooling.
---
## Interference Fits
⚠️ Before specifying an interference, **always calculate**:
1. Contact pressure at the joint
2. Hoop stress in the hub
3. Radial stress in the shaft (if hollow)
4. Transmissible torque by friction (verify sufficiency)
5. Assembly temperature if thermal
→ Use `fundamental-deviations.md` for exact values, then apply Lamé equations.
| Fit | Typical application | Indicative interference (Ø50) | Assembly |
|---|---|---|---|
| H7/n6 | Fixed bushings, sealing rings, bronze bearings | 0 … 0.033 mm | Press (up to 10 kN on Ø50) |
| H7/p6 | Gears on shaft, fixed pulleys, hubs | 0.009 … 0.042 mm | Press or thermal |
| H7/r6 | Medium-torque transmission hubs | 0.020 … 0.055 mm | Thermal (Δt = 80–150°C) |
| H7/s6 | High-torque transmission | 0.031 … 0.066 mm | Thermal (Δt = 150–250°C) |
| H7/u6 | Bronze/cast-iron bushings, maximum interference | 0.053 … 0.094 mm | Thermal (Δt ≥ 250°C) |
| H6/p5 | Inner rings of P5/P4 precision bearings | — | Thermal |
### Interference verification formulas
```
Contact pressure: p = δ / [d × (C_o/E_o + C_i/E_i)]
where δ = actual interference (mm)
d = nominal diameter (mm)
C_o, C_i = shape coefficients (from Lamé)
E_o, E_i = elastic moduli of materials
Transmissible torque: Mt = p × π × d² × L × μ / 2
where L = contact length
μ = friction coefficient (0.08–0.12 thermal, 0.12–0.15 press)
Assembly temperature: ΔT = δ_max / (α × d) [°C]
where α = thermal expansion coefficient (steel: 11.5×10⁻⁶ /°C)
+ add 30–50°C for assembly clearance
```
---
> For bearings, gears, valves, keys, Seeger rings, pins, bushings, seals, and all other
> functional elements → see `functional-elements.md` (includes decision flowchart).
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# Functional Elements — Tolerances and Fits
---
## 1. Rolling Bearings (ISO 286-1 + ISO 15 / ISO 76)
### Fundamental principle
The ring that **rotates relative to the load direction** must have **interference** with its seat.
If the load-carrying ring can slip in its seat, "creep" begins: progressive erosion, vibration
and premature failure.
### Fixed end / free end scheme (thermal expansion)
```
Fixed end (FE) Free end (FL)
Shaft: k5 / m5 (interference) h6 (deliberate clearance)
Housing: H7 (clearance) G7 / H7 (clearance)
┌────────────────────────────────────────────────────┐
│ [Bearing FE] ═══ shaft ═══ [Bearing FL] │
│ k5 / H7 h6 / H7 or G7 │
└────────────────────────────────────────────────────┘
FE: locked axially FL: free to slide
(outer ring retained (outer ring free to move
by shoulder/Seeger ring) in bore for thermal growth)
```
> The free end exists because the shaft grows thermally: without it, parasitic axial loads
> build up and destroy bearings and structure.
### Tolerance table — Ball and roller bearings (class P0/P6)
#### SHAFT seat (inner ring)
| Condition | d ≤ 18 mm | 18 < d ≤ 100 mm | 100 < d ≤ 200 mm | Notes |
|---|---|---|---|---|
| Light / variable load | h5, js5 | h6, js6 | h6 | Easy to disassemble |
| **Normal load** (motors, gearboxes) | **k5** | **k5, m5** | **m6, n6** | Industrial standard |
| Heavy load / impact | m5, n5 | m5, n5, p5 | n6, p6 | Thermal assembly |
| Pure axial thrust | js5, h5 | js6, h6 | h6 | No load rotation |
| Free end | h6 | h6 | h6 | Deliberate clearance for thermal growth |
#### HOUSING seat (outer ring)
| Condition | Bore tolerance | Notes |
|---|---|---|
| Fixed outer ring, rotating load on shaft | **H7** | Standard — removable |
| Impact loads / vibrations | **JS7, K7** | Slight interference |
| Rotating outer ring (wheels, idler pulleys) | **N7, M7** | Interference — non-removable |
| Heavy loads with rotating outer ring | **P7** | Strong interference |
| Adjustable or frequently removable support | **G7** | Deliberate clearance |
### Precision bearings (class P5, P4, P2)
| Class | Shaft | Housing | Application |
|---|---|---|---|
| P5 | j5, k5 | H6, JS6 | Simple spindles, precision pumps |
| P4 | j5, k4 | H5, JS5 | Machine tool spindles |
| P2 | j4, k4 | H4 | High-precision grinders, measuring machines |
### Angular contact bearings (matched pair)
For O (back-to-back) or X (face-to-face) mounting with preload:
- Shaft: js5 or k5 (maintains axial preload)
- Housing: JS6 (for controlled preload) or H7 standard
- ⚠️ Avoid heavy interference: it reduces the bearing's internal preload
### Bearing seat roughness
| Element | Ra | Rz | Notes |
|---|---|---|---|
| Shaft (P0/P6) | ≤ 0.8 µm | ≤ 4 µm | Cylindrical grinding required |
| Housing (P0/P6) | ≤ 1.6 µm | ≤ 8 µm | Fine boring or internal grinding |
| Shaft (P5/P4) | ≤ 0.4 µm | ≤ 2 µm | Precision grinding |
| Shoulder / axial abutment | ≤ 1.6 µm | — | Flatness important (± 0.005 mm) |
### Practical rules for common machines
| Machine | Shaft (inner ring) | Housing (outer ring) |
|---|---|---|
| Electric motor (drive side) | m5 | H7 |
| Electric motor (free end) | k5 | H7 |
| Industrial gearbox | k5 or m5 | H7 or JS7 |
| Centrifugal pump | k5 or m5 | H7 |
| Fan (vibrations) | m5 | JS7 |
| Wheel / idler pulley | h6 | N7 or M7 |
| Machine tool spindle | j5 or k5 | H6 or JS6 |
---
## 2. Gears
### Gear bore – shaft fit
| Requirement | Fit | Torque path | Notes |
|---|---|---|---|
| Removable, frequent maintenance | H7/h6 + key | Key only | Small clearance, cold-removable |
| Removable, infrequent maintenance | H7/k6 + key | Key + slight interference | **Industrial standard** |
| Hot-removable, high precision | H7/m6 + key | Key + medium interference | Heat to 80–120°C |
| Fixed, moderate torque | H7/p6 | Interference only | No key → no stress concentration |
| Fixed, high torque | H7/r6 or s6 | Interference only | Thermal assembly mandatory |
| High angular precision | H6/k5 + key | Key | Minimises run-out |
### Tooth profile quality (ISO 1328-1)
| Quality | Application | Indicative tooth IT | Finishing process |
|---|---|---|---|
| 3–5 | Measurement, instruments | IT5–IT6 | Profile grinding |
| 6–7 | Machine tools, precision gearboxes | IT6–IT7 | Grinding or shaving |
| 8–9 | Industrial gearboxes | IT7–IT8 | Shaving / hobbing |
| 10–11 | General mechanics | IT9–IT10 | Hobbing only |
| 12 | Toys, low speed | IT11–IT12 | Rough hobbing |
### Centre distance tolerance (ISO 1328)
| Application | Tolerance | IT grade (indicative) |
|---|---|---|
| Precision gearboxes | ±0.01 – 0.02 mm | IT6–IT7 |
| Industrial gearboxes | ±0.03 – 0.05 mm | IT8–IT9 |
| General mechanics | ±0.1 mm | IT10–IT11 |
---
## 3. Valve Seats
### Internal combustion engine valves
| Component | Typical material | Fit | Notes |
|---|---|---|---|
| Exhaust valve seat insert | Sintered steel | H7/s6 – H7/u6 | High interference: retains at operating Δt (up to 300°C) |
| Intake valve seat insert | Cast iron or sintered | H7/r6 – H7/s6 | Medium interference |
| Valve guide | Bronze or sintered | H7/p6 or H7/r6 (OD) + D9/f7 (ID) | External fix + stem clearance |
| Valve stem in guide | Nitrided steel | D9/f7 or G8/f7 | Clearance 0.03–0.08 mm (intake) 0.05–0.10 mm (exhaust) |
### Pneumatic / hydraulic valves
| Type | Fit | Required Ra | Notes |
|---|---|---|---|
| Fixed seat (press in) | H7/r6 – H7/s6 | Ra ≤ 0.8 µm (seat) | Seal by interference + optional sealant |
| Spool / slide valve | H7/f7 – H7/g6 | **Ra ≤ 0.4 µm** | Gap 0.01–0.05 mm critical for leakage |
| Piston rod / stem | H8/f7 | Ra ≤ 0.8 µm | Combined with O-ring or lip seal |
| High-pressure piston (no seal) | H6/g5 | Ra ≤ 0.2 µm | Metal-to-metal seal — gap 3–8 µm |
---
## 4. Transmission Shafts — Complete Layout
### Functional zone map
```
┌────┬──────────┬──────┬──────────┬──────┬──────────┬────┐
│ FE │ bearing │ non │ gear │ non │ bearing │ FL │
│ │ (k5/m5) │ func │ (k6/p6) │ func │ (h6) │ │
└────┴──────────┴──────┴──────────┴──────┴──────────┴────┘
↑ ↑
fixed end free end
(axial load locked) (free to slide axially)
```
### Tolerance table by shaft zone
| Functional zone | Shaft tolerance | Ra | Element |
|---|---|---|---|
| Bearing seat — fixed end | k5 or m5 | ≤ 0.8 µm | Bearing inner ring |
| Bearing seat — free end | h6 | ≤ 0.8 µm | Bearing inner ring (slides) |
| Removable gear seat | k6 | ≤ 1.6 µm | Gear + key N9 |
| Fixed gear seat | p6 | ≤ 0.8 µm | Gear (interference) |
| Lip seal seat (simmering) | h11 or h8 | **0.2–0.4 µm** | Rubber/PTFE lip |
| Seeger ring groove on shaft | h11 (groove diameter) | ≤ 3.2 µm | Snap ring |
| Keyway width | N9 | ≤ 3.2 µm | DIN 6885 key |
| Non-functional zones / fillets | h9 – h11 | ≤ 6.3 µm | — |
| Threaded end | 6g (thread) | — | Locking nut |
---
## 5. Keys (DIN 6885-1 / ISO 773)
→ For dimension tables, fit types, clearance calculation and torque check: see `keys-keyways.md`
### Fit summary
| Fit type | Shaft keyway | Hub keyway | Key | Use |
|---|---|---|---|---|
| Normal | N9 | JS9 | h9 | **Industrial standard** |
| Sliding | H9 | D10 | h9 | Hub slides axially |
| Tight | P9 | P9 | h9 | No clearance, high precision |
> ⚠️ The keyway is a stress concentration feature that reduces shaft fatigue strength
> by 25–40%. Do not position at zones of maximum bending.
---
## 6. Snap Rings — Seeger (DIN 471 / DIN 472)
### Types
- **DIN 471**: ring for **shaft** (opens to mount in external groove)
- **DIN 472**: ring for **bore** (closes to mount in internal groove)
### Groove tolerances
#### DIN 471 — Groove on SHAFT
| Shaft diameter d (mm) | Groove width b | Tolerance b | Groove diameter d1 | Tolerance d1 |
|---|---|---|---|---|
| 6 – 9 | 0.9 | h13 | d − 1.0 | h11 |
| 9 – 19 | 1.0 | h13 | d − 1.1 | h11 |
| 19 – 28 | 1.2 | h13 | d − 1.3 | h11 |
| 28 – 46 | 1.5 | h13 | d − 1.65 | h11 |
| 46 – 80 | 1.75 | h13 | d − 1.95 | h11 |
| 80 – 100 | 2.0 | h13 | d − 2.25 | h11 |
#### DIN 472 — Groove in BORE (housing)
| Bore diameter D (mm) | Groove width b | Tolerance b | Groove diameter D1 | Tolerance D1 |
|---|---|---|---|---|
| 8 – 14 | 1.0 | H13 | D + 1.0 | H11 |
| 14 – 22 | 1.1 | H13 | D + 1.2 | H11 |
| 22 – 38 | 1.2 | H13 | D + 1.3 | H11 |
| 38 – 65 | 1.5 | H13 | D + 1.6 | H11 |
| 65 – 100 | 1.8 | H13 | D + 2.0 | H11 |
| 100 – 120 | 2.0 | H13 | D + 2.2 | H11 |
### Practical rules
- The H11/h11 groove is intentionally wide to allow ring installation with pliers
- Groove diameter controls axial load capacity: always verify against ring load rating (SKF/Seeger tables)
- Groove root radius: r ≤ 0.2 mm to prevent ring jamming
- Do not use Seeger rings for alternating or impact axial loads: use a shoulder or nut
---
## 7. Cylindrical and Tapered Pins (ISO 8734 / ISO 8735 / ISO 2339)
### Cylindrical pins (ISO 8734 — hardened steel, ISO 8735 — with extraction thread)
| Function | Pin–bore fit | Notes |
|---|---|---|
| Fixed locating / torque pin | **H7/n6** | Interference — press fit, non-removable |
| Fixed pin with extraction (ISO 8735) | **H7/n6** | Same, but removable with extractor |
| Removable locating pin | **H7/g6** | Controlled clearance — hand-removable |
| Hinge / pivot pin | **H7/f7** | Clearance for rotation — lubrication recommended |
### Tapered pins (ISO 2339 — taper 1:50)
- Self-locking: retained by elastic deformation — no special tolerance needed
- Bore produced by **reaming with tapered reamer** after assembly (recommended)
- Disadvantage: bore is not interchangeable — each pin is matched to its bore
### Locating hole position (GD&T)
```
TP_bore ≤ 0.5 × min_clearance (for locating pins)
TP_bore ≤ 0.3 × min_interference (for fixed pins)
```
---
## 8. Plain Bearings / Bushings
### Types and materials
| Type | Material | Characteristic | Outer fit (in housing) |
|---|---|---|---|
| Bronze bushing | CuSn8, CuZn24Al | High load capacity, lubrication required | **H7/s6 or H7/u6** |
| Sintered self-lubricating | Fe or Cu sintered | Impregnated lubrication, low speed | **H7/r6 or H7/s6** |
| PTFE / graphite bushing | PTFE composite | Dry, low speed, high temperature | **H7/p6 or H7/r6** |
| Bimetal (steel + bronze) | St + CuSn | High load capacity | **H7/s6** |
| Nylon / POM bushing | Polyamide, POM | Lightweight, low torque, quiet | **H7/p6** (check thermal Δt) |
### Inner fit: bushing bore – shaft
| Condition | Fit | Indicative clearance | Notes |
|---|---|---|---|
| Continuous rotation, lubricated | H7/f7 or H8/f7 | 0.02–0.07 mm (Ø50) | Standard — clearance for oil film |
| High speed, forced lubrication | H7/g6 | 0.01–0.05 mm (Ø50) | More stable hydrodynamic film |
| Oscillating (no full rotation) | H9/f9 or H9/e9 | 0.04–0.12 mm (Ø50) | More clearance to avoid stick-slip |
| Very light load, low speed | H8/h8 | 0–0.054 mm (Ø50) | Near zero clearance, marginal lubrication |
### Note on plastic bushings (POM/PA)
Plastics have 5–10× higher thermal expansion than steel.
- At ambient temperature: use recommended fit
- At operating temperature: verify interference does not generate excessive pressure (hub cracking
risk) and that internal clearance does not become negative (seizure)
- Rule of thumb: for POM with Δt = +50°C on Ø30, allow 0.06 mm additional clearance
---
## 9. Radial Shaft Seals / Lip Seals (DIN 3760 / ISO 6194)
### Seat tolerances
| Element | Tolerance | Ra | Notes |
|---|---|---|---|
| **Shaft** (lip contact surface) | **h11** or **h8** | **Ra 0.2–0.4 µm** | Circumferential texture — NOT helical |
| Housing bore (seal press-in) | **H8** | Ra 1.6–3.2 µm | Lead-in chamfer at entry (15°, r=0.3 mm) |
### Lip material and speed limits
| Lip material | Max speed (m/s) | Temperature range | Notes |
|---|---|---|---|
| NBR (nitrile) | ≤ 6 m/s | −40 / +100°C | Standard — mineral oil |
| FKM (Viton) | ≤ 9 m/s | −20 / +180°C | Synthetic oil, high temperature |
| PTFE | ≤ 15 m/s | −60 / +200°C | Low friction, marginal lubrication |
| PTFE with stainless lip | ≤ 20 m/s | −60 / +200°C | High speed |
### Critical requirements
1. **Shaft hardness**: min 55 HRC (or surface treatment: nitriding, chrome plating)
— Soft shaft → lip cuts surface within hours → seal failure
2. **Circumferential finish**: texture must be perpendicular to axis
— Axial grinding direction: lip pumps fluid outward (screw effect → leaks)
3. **Shaft eccentricity (TIR)**: max 0.1–0.2 mm depending on diameter and speed
4. **Internal pressure**: standard seals up to 0.3 bar; above → reinforced spring seal or double lip
---
## 10. Locating and Positioning Pins
### Self-locking taper pins
- Taper 1:50 (ISO 2339 standard): self-locking, suitable for moderate torque
- Taper 1:30 (DIN 1): used on tooling, easier to remove
- Extraction slot in head is always recommended
### Spring pins (ISO 8752)
| Application | Notes |
|---|---|
| Light positioning, low torque | Economical, bore tolerance H12 — easy assembly |
| Replaces solid pin in vibrating environments | Spring elasticity absorbs vibrations |
### Locating pins for flanges and plates
- Standard: 2 pins diametrically opposed (no more — redundancy creates GD&T issues)
- Diameter: 6–12 mm for most industrial cases
- Fit: H7/n6 on both bores (matched plates) or H7/g6 if frequently removed
---
## 11. Involute Splines (ISO 4156 / DIN 5480)
For applications requiring:
- High torque (> 500 Nm on shafts Ø < 50 mm)
- Frequent reversals (no angular backlash)
- High-precision angular connections that must be removable
### Fit classes (ISO 4156)
| Class | Application | Notes |
|---|---|---|
| **H/h** (clearance) | Removable, axially sliding | Standard for couplings |
| **H/js** (transition) | Precise positioning, fixed | Light press |
| **H/k, H/m** (interference) | Fixed, high torque | Same as solid hub fits |
> Do not dimension individual teeth: use the full ISO 4156 designation
> (e.g. "DIN 5480 W30×2×14×9H/9h") and reference the standard.
---
## 12. Couplings
### Rigid couplings (sleeves, discs)
| Condition | Shaft–coupling fit | Notes |
|---|---|---|
| Fixed, removable | H7/k6 + key | Light press, hot-removable |
| Fixed, non-removable | H7/p6 or r6 | Interference — thermal assembly |
| Precision (no angular play) | H6/k5 | High precision |
### Flexible couplings (spider, elastomer)
- Shaft–hub fit: H7/k6 or H7/m6
- Clearance compensated by elastic element — heavy interference not needed
- Misalignment tolerance: see manufacturer's data sheet (typical: 0.1–0.5 mm radial, 0.5–2° angular)
### Oldham and universal (cardan) joints
- Shaft–hub: H7/g6 or H7/h6 + pin or key
- Centre element must slide: female side of joint H7/f7 – H8/f8
---
## 13. Linear Guides and Sliding Surfaces
| Guide type | Fit | Ra | Application |
|---|---|---|---|
| Sliding guide, lubricated | H7/f7 | ≤ 0.8 µm | Machine tools, cylinders |
| Sliding guide, high precision | H6/g5 | ≤ 0.4 µm | Measuring machines |
| Guide pin / die column | H7/g6 | ≤ 0.8 µm | Dies, fixtures |
| Zero-clearance guide (preloaded) | H6/h5 + preload | ≤ 0.4 µm | Precision tables |
| Taper centering (self-locating) | — | ≤ 0.8 µm | Taper 1:50–1:100, no ISO tolerance needed |
---
## 14. General Tolerances (ISO 2768)
For non-critical dimensions, use general tolerances rather than tolerancing every dimension.
| Class | Symbol | Approx. grade | Application |
|---|---|---|---|
| Fine | f | IT9–IT10 | Precision mechanics |
| **Medium** | **m** | **IT11** | **Industrial standard (default)** |
| Coarse | c | IT12–IT13 | Structures, fabrications |
| Very coarse | v | IT14–IT15 | Raw castings, forgings |
**Drawing note**: `ISO 2768-mK` (medium linear + medium geometric tolerances)
---
## Appendix: Quick Decision Flowchart
```
What is the function of the fit?
│
├─ Must SLIDE / ROTATE? ─────────────────────────→ Clearance
│ ├─ High precision, lubricated → H7/g6 or H6/g5
│ ├─ Standard, lubricated → H7/f7 or H8/f7
│ └─ Loose, misalignment → H8/e8 or H9/d9
│
├─ Must LOCATE (removable)? ─────────────────────→ Transition / zero clearance
│ ├─ High precision → H6/h5 or H7/js6
│ └─ Standard → H7/h6 or H7/k6
│
├─ Must TRANSMIT TORQUE (fixed)? ────────────────→ Interference
│ ├─ Removable with tools → H7/k6 + key
│ ├─ Moderate torque → H7/p6
│ ├─ High torque → H7/r6 or H7/s6
│ └─ Maximum (bronze/cast iron) → H7/u6
│
├─ Is it a BEARING? ──────────────────────────────→ see §1
├─ Is it a KEY / KEYWAY? ─────────────────────────→ see §5 / keys-keyways.md
├─ Is it a SEEGER / SNAP RING? ───────────────────→ see §6
├─ Is it a PIN? ──────────────────────────────────→ see §7
├─ Is it a BUSHING? ──────────────────────────────→ see §8
├─ Is it a LIP SEAL / SIMMERING? ─────────────────→ see §9
└─ Is it a SPLINED PROFILE? ──────────────────────→ see §11
```
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# Fundamental Deviations — Numerical Values (ISO 286-1)
## How to Read This File
Example: **Ø50 H7/k6**
1. Diameter range: 50 mm → rows "30–50" and "50–80"
2. Bore H7: lower deviation EI = 0, upper deviation ES = +25 µm (IT7 for Ø50)
3. Shaft k6: lower deviation ei = +2 µm, upper deviation es = ei + IT6 = +2 + 16 = +18 µm
4. Max clearance = ES − ei = 25 − 2 = +23 µm → clearance
5. Min clearance = EI − es = 0 − 18 = −18 µm → interference
→ **Transition fit**, in practice predominantly with slight interference
---
## Bore Fundamental Deviations (uppercase) — Lower Deviation EI (µm)
| Bore | 1–3 | 3–6 | 6–10 | 10–18 | 18–30 | 30–50 | 50–80 | 80–120 | 120–180 | 180–250 |
|---|---|---|---|---|---|---|---|---|---|---|
| B | +140 | +140 | +150 | +150 | +160 | +170 | +180 | +200 | +210 | +230 |
| C | +60 | +70 | +80 | +95 | +110 | +120 | +130 | +145 | +160 | +170 |
| D | +20 | +30 | +40 | +50 | +65 | +80 | +100 | +120 | +145 | +170 |
| E | +14 | +20 | +25 | +32 | +40 | +50 | +60 | +72 | +85 | +100 |
| F | +6 | +10 | +13 | +16 | +20 | +25 | +30 | +36 | +43 | +50 |
| G | +2 | +4 | +5 | +6 | +7 | +9 | +10 | +12 | +14 | +15 |
| **H** | **0** | **0** | **0** | **0** | **0** | **0** | **0** | **0** | **0** | **0** |
| JS | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 |
| K (6–8) | 0 | +2 | +2 | +2 | +2 | +3 | +4 | +4 | +4 | +5 |
| M (6–8) | −2 | −4 | −6 | −7 | −8 | −9 | −11 | −13 | −15 | −17 |
| N (6–8) | −4 | −8 | −10 | −12 | −15 | −17 | −20 | −23 | −27 | −31 |
| P (6–7) | −6 | −12 | −15 | −18 | −22 | −26 | −32 | −37 | −43 | −50 |
| R | −10 | −15 | −19 | −23 | −28 | −34 | −41 | −51 | −63 | −77 |
| S | −14 | −19 | −23 | −28 | −35 | −43 | −53 | −71 | −92 | −100 |
| U | −18 | −23 | −28 | −33 | −41 | −53 | −66 | −90 | −109 | −130 |
> **Note**: For H, ES = EI + IT = 0 + IT (e.g. H7/Ø50: ES = +25 µm)
---
## Shaft Fundamental Deviations (lowercase) — Upper Deviation es (µm)
| Shaft | 1–3 | 3–6 | 6–10 | 10–18 | 18–30 | 30–50 | 50–80 | 80–120 | 120–180 | 180–250 |
|---|---|---|---|---|---|---|---|---|---|---|
| b | −140 | −140 | −150 | −150 | −160 | −170 | −180 | −200 | −210 | −230 |
| c | −60 | −70 | −80 | −95 | −110 | −120 | −130 | −145 | −160 | −170 |
| d | −20 | −30 | −40 | −50 | −65 | −80 | −100 | −120 | −145 | −170 |
| e | −14 | −20 | −25 | −32 | −40 | −50 | −60 | −72 | −85 | −100 |
| f | −6 | −10 | −13 | −16 | −20 | −25 | −30 | −36 | −43 | −50 |
| g | −2 | −4 | −5 | −6 | −7 | −9 | −10 | −12 | −14 | −15 |
| **h** | **0** | **0** | **0** | **0** | **0** | **0** | **0** | **0** | **0** | **0** |
| js | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 | ±IT/2 |
| k | 0 | +1 | +1 | +1 | +2 | +2 | +2 | +3 | +3 | +4 |
| m | +2 | +4 | +6 | +7 | +8 | +9 | +11 | +13 | +15 | +17 |
| n | +4 | +8 | +10 | +12 | +15 | +17 | +20 | +23 | +27 | +31 |
| p | +6 | +12 | +15 | +18 | +22 | +26 | +32 | +37 | +43 | +50 |
| r | +10 | +15 | +19 | +23 | +28 | +34 | +41 | +51 | +63 | +77 |
| s | +14 | +19 | +23 | +28 | +35 | +43 | +53 | +71 | +92 | +100 |
| u | +18 | +23 | +28 | +33 | +41 | +53 | +66 | +90 | +109 | +130 |
> **Note**: For h, ei = es − IT = 0 − IT = −IT (e.g. h6/Ø50: ei = −16 µm)
---
## Worked Examples
### Example 1: Ø30 H7/g6
**Bore H7 (Ø30, range 18–30):**
- EI = 0
- ES = EI + IT7 = 0 + 21 = +21 µm
- Bore: Ø30 +0.021/0
**Shaft g6 (Ø30, range 18–30):**
- es = −7 µm
- ei = es − IT6 = −7 − 13 = −20 µm
- Shaft: Ø30 −0.007/−0.020
**Clearances:**
- Max clearance = ES − ei = +21 − (−20) = **+41 µm** (0.041 mm)
- Min clearance = EI − es = 0 − (−7) = **+7 µm** (0.007 mm)
- → **Guaranteed clearance fit** ✓ (lubricated precision guide)
### Example 2: Ø50 H7/p6
**Bore H7 (Ø50, range 30–50):**
- EI = 0, ES = +25 µm
**Shaft p6 (Ø50, range 30–50):**
- es = +26 µm
- ei = +26 − 16 = +10 µm
**Interferences:**
- Max interference = es − EI = +26 − 0 = **+26 µm** (0.026 mm)
- Min interference = ei − ES = +10 − 25 = **−15 µm** → clearance possible?
⚠️ This is a **transition fit** at Ø50! For guaranteed interference on Ø50, p6 gives
ei − ES = 10 − 25 = −15: there is still a possibility of clearance.
For guaranteed interference on Ø50 use **r6 or s6**.
→ Always verify numerical values for your specific diameter before finalising the drawing.
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# Information Intake Guide — ISO Tolerances
## Required Information for a Reliable Recommendation
### Level 1 — Critical (without these, the recommendation is unreliable)
| Information | Why it is critical | How to obtain it |
|---|---|---|
| **Nominal diameter** | IT values in µm depend on the diameter range (IT7 = 15 µm on Ø10, 35 µm on Ø100) | Direct dimension, approximate measurement from drawing, or caliper reading if part exists |
| **Function** | Determines the fit type: a sliding guide and an interference hub have opposite requirements | Describe: guides, transmits torque, positions, seals, slides, rotates |
| **Removability** | H7/p6 cannot be disassembled without thermal equipment; H7/k6 needs a puller; H7/h6 by hand | Removable in routine maintenance / rarely / never |
### Level 2 — Important (significantly improve the recommendation)
| Information | Why it matters | How to obtain it |
|---|---|---|
| **Available manufacturing process** | No point recommending IT6 if the shop only has standard CNC lathes (IT8–IT9) | CNC turning / grinding / precision boring. Or: minimum guaranteed tolerance from the shop |
| **Loads** | Impact/shock loads require more interference to prevent creep on bearings and interference fits | Static / dynamic / impact / vibrations |
| **Operating environment** | Operating Δt reduces effective interference; corrosion changes minimum clearance | Operating temperature, lubricant, corrosive environment |
| **Materials** | Steel/aluminium → different thermal expansion coefficients → different interference | Shaft and bore materials |
### Level 3 — Useful (refine the recommendation)
| Information | Relevance |
|---|---|
| Rotational speed | For bearings and radial shaft seals |
| Transmitted torque | To verify interference sufficiency without Lamé calculation |
| Batch size | One-off vs series production: changes the tolerance/cost trade-off |
| Industry standard | Automotive, rail, aerospace may have additional standards that override ISO defaults |
---
## How to Ask for Missing Information (expert engineer style)
1. **Show what you understood** from the input or attached image
2. **Explain why the gap is blocking** that specific decision
3. **Propose a working hypothesis** to confirm: "If it must be removable, I'd go with H7/k6"
4. **Suggest how to get the data**: caliper measurement, assembly drawing, machine datasheet
**Example:**
> From the drawing I can see a pin Ø≈40mm going into a bore on a support bracket. I can't
> tell whether it needs to **slide** axially or is **fixed** in position. This is critical:
> sliding → H7/g6 (clearance 0.01–0.05 mm), fixed → H7/k6 (light press fit).
> Can you confirm? An assembly drawing, even a hand sketch, would help a lot.
---
## Image Analysis (screenshots, photos, sketches)
Actively extract from the image:
- Dimensional values (even approximate)
- Component type (shaft, bore, seat, flange, bearing, keyway…)
- Existing annotations (tolerances, roughness, materials already noted)
- Assembly context (what mates with what)
- Assembly constraints (tool access, space for thermal equipment)
Then: **summarise your interpretation** to confirm understanding, then ask only for critical gaps.
For non-scale drawings or sketches: accept approximate dimensions and state the result is
indicative until the exact dimension is confirmed. Recognisable standard components (bearing,
key, Seeger ring) → tolerances are often already defined by the manufacturer's catalogue.
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# IT Tolerance Grades — Manufacturing Processes and Applications
## IT Grade Values by Diameter Range (µm, ISO 286-1)
| IT Grade | 1–3 mm | 3–6 mm | 6–10 mm | 10–18 mm | 18–30 mm | 30–50 mm | 50–80 mm | 80–120 mm | 120–180 mm | 180–250 mm |
|---|---|---|---|---|---|---|---|---|---|---|
| IT1 | 0.8 | 1 | 1 | 1.2 | 1.5 | 1.5 | 2 | 2.5 | 3.5 | 4.5 |
| IT2 | 1.2 | 1.5 | 1.5 | 2 | 2.5 | 2.5 | 3 | 4 | 5 | 7 |
| IT3 | 2 | 2.5 | 2.5 | 3 | 4 | 4 | 5 | 6 | 8 | 10 |
| IT4 | 3 | 4 | 4 | 5 | 6 | 7 | 8 | 10 | 12 | 14 |
| IT5 | 4 | 5 | 6 | 8 | 9 | 11 | 13 | 15 | 18 | 20 |
| IT6 | 6 | 8 | 9 | 11 | 13 | 16 | 19 | 22 | 25 | 29 |
| IT7 | 10 | 12 | 15 | 18 | 21 | 25 | 30 | 35 | 40 | 46 |
| IT8 | 14 | 18 | 22 | 27 | 33 | 39 | 46 | 54 | 63 | 72 |
| IT9 | 25 | 30 | 36 | 43 | 52 | 62 | 74 | 87 | 100 | 115 |
| IT10 | 40 | 48 | 58 | 70 | 84 | 100 | 120 | 140 | 160 | 185 |
| IT11 | 60 | 75 | 90 | 110 | 130 | 160 | 190 | 220 | 250 | 290 |
| IT12 | 100 | 120 | 150 | 180 | 210 | 250 | 300 | 350 | 400 | 460 |
| IT13 | 140 | 180 | 220 | 270 | 330 | 390 | 460 | 540 | 630 | 720 |
| IT14 | 250 | 300 | 360 | 430 | 520 | 620 | 740 | 870 | 1000 | 1150 |
---
## Required Machining by IT Grade — Bores and Shafts
Distinguishing bore vs. shaft is critical: achieving IT7 on a bore is significantly harder and
more expensive than on a shaft, because bores cannot be externally cylindrically ground.
| IT Grade | Machining for BORES | Machining for SHAFTS | Difficulty | Relative cost |
|---|---|---|---|---|
| **IT3–IT4** | Precision honing, lapping | Ultra-precision cylindrical grinding, lapping | Extreme | ★★★★★ |
| **IT5** | Precision boring (single-blade), fine honing | Precision cylindrical grinding (Ra 0.2) | Very high | ★★★★☆ |
| **IT6** | Fine CNC boring (single-blade tool), internal grinding | Standard cylindrical grinding | High | ★★★☆☆ |
| **IT7** | CNC boring with adjustable insert, fine internal turning | Fine CNC turning (high Vc, low feed), grinding | Medium | ★★☆☆☆ |
| **IT8** | Standard drilling + reaming, internal turning | Standard CNC turning | Low | ★★☆☆☆ |
| **IT9** | Drilling with sharp bits, rough internal turning | Standard turning | Very low | ★☆☆☆☆ |
| **IT10–IT11** | Standard drilling, punching | Rough turning, milling | Minimal | ★☆☆☆☆ |
| **IT12–IT14** | Shell casting, stamping | Forging, sand casting | — | ★☆☆☆☆ |
### Operational notes by IT grade
#### IT5–IT6 (high precision)
- **Bores**: single-blade boring is the reference process. Requires rigid fixture, carbide tool,
correct coolant. Alternative: internal grinding (more expensive, requires dedicated machine).
- **Shafts**: between-centers or collet cylindrical grinding. Freshly dressed wheel, active
thermal compensation.
- **Minimum equipment**: rigid machining centre (≥15kN spindle), in-process gauging recommended.
#### IT7 (standard reference grade)
- **Bores**: CNC boring with adjustable insert (e.g. Sandvik CoroBore, Kennametal). Standard
drilling alone does not reliably achieve IT7. Economic alternative: pilot drill + machine
reamer with calibrated reamer (IT7 guaranteed).
- **Shafts**: fine turning with wiper insert. On modern CNC, IT7 is routine. Watch out: long
chips or gummy materials (stainless steel, construction aluminium) tend to drift to IT8.
- **Inspection**: go/no-go plug gauge for bores, ring gauge or micrometer for shafts.
Measure after the part has cooled.
#### IT8 (standard production)
- Achievable with standard turning and drilling — no special equipment.
- Suitable for keyways, non-critical sliding bushings, loose fits.
#### IT9–IT11 (free tolerances)
- Standard for non-functional dimensions. Covered by ISO 2768-m (IT11) general tolerances.
---
## Manufacturing Processes and Achievable IT Grades
| Manufacturing process | Typical IT grades | Notes |
|---|---|---|
| Lapping / superfinishing | IT3 – IT5 | Extreme finishes, small parts |
| Precision honing | IT4 – IT6 | Cylinders, engine bore |
| Precision cylindrical grinding | IT4 – IT6 | High-precision shafts, spindles |
| Standard cylindrical grinding | IT5 – IT7 | Transmission shafts, bearing seats |
| Fine turning / diamond | IT5 – IT7 | Non-ferrous alloys, bronze, aluminium |
| Precision boring (single-blade) | IT5 – IT7 | High-precision bores |
| Internal grinding | IT5 – IT7 | Large diameter bores |
| CNC boring (adjustable insert) | IT6 – IT8 | Standard coupling bores |
| Fine CNC turning (wiper insert) | IT6 – IT8 | Standard functional shafts |
| EDM | IT5 – IT8 | Dies, complex forms |
| Standard CNC turning | IT7 – IT9 | Production standard |
| Standard reaming / drill + ream | IT8 – IT10 | Non-critical bores |
| CNC milling | IT8 – IT10 | Planes, profiles, slots |
| Standard drilling | IT10 – IT12 | Through holes, fasteners |
| Stamping / blanking | IT10 – IT12 | Sheet metal |
| Shell moulding | IT11 – IT14 | Precision castings |
| Sand casting | IT14 – IT16 | Raw castings |
| Forging | IT14 – IT16 | Semi-finished stock |
---
## Grade Selection Guidelines
### IT01 – IT4
- Measuring instruments, gauge blocks, reference standards
- Ultra-precision bearings (class P4, P2)
- Practically unused in standard mechanical production
- Very high cost, requires controlled environments
### IT5 – IT6
- High-precision fits: machine tool spindles, precision shafts
- P6/P5 bearings
- Precision gears (ISO 1328 quality 5–7)
- High-pressure valve seats
- Grinding required
### IT7
- **The most widely used grade in industrial mechanics**
- Functional shaft-bore fits (H7/k6, H7/g6, H7/h6, etc.)
- Standard bearing housing bores (class P0/P6)
- Fine turning or CNC boring on modern machines
### IT8
- Less critical fits, larger clearances
- Keyways, key slots
- Non-critical sliding bushings
- Good-quality standard turning
### IT9 – IT10
- Non-coupled components
- Thicknesses, lengths, non-functional positions
- High-quality free dimensions (ISO 2768-f, -m)
### IT11 – IT14
- Standard free tolerances (ISO 2768-c, -v)
- General tolerances on drawings
- Non-functional distances, clearances, spaces
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# Keys and Keyways (DIN 6885-1 / ISO 773)
## Applicable Standards
- **ISO 773 / DIN 6885-1**: parallel keys (Woodruff, forms A/B/C)
- **ISO 3912 / DIN 6885-2**: square-section keys
- **DIN 6886**: taper keys
- For width fits: **ISO 286-1** (same IT basis)
---
## Standard Key Dimensions (DIN 6885-1 / ISO 773)
| Shaft Ø (mm) | b × h (mm) | t1 shaft (mm) | t2 hub (mm) | Radius r (mm) |
|---|---|---|---|---|
| 6 – 8 | 2 × 2 | 1.2 | 1.0 | 0.16–0.25 |
| 8 – 10 | 3 × 3 | 1.8 | 1.4 | 0.16–0.25 |
| 10 – 12 | 4 × 4 | 2.5 | 1.8 | 0.16–0.25 |
| 12 – 17 | 5 × 5 | 3.0 | 2.3 | 0.25–0.40 |
| 17 – 22 | 6 × 6 | 3.5 | 2.8 | 0.25–0.40 |
| 22 – 30 | 8 × 7 | 4.0 | 3.3 | 0.25–0.40 |
| 30 – 38 | 10 × 8 | 5.0 | 3.3 | 0.40–0.60 |
| 38 – 44 | 12 × 8 | 5.0 | 3.3 | 0.40–0.60 |
| 44 – 50 | 14 × 9 | 5.5 | 3.8 | 0.40–0.60 |
| 50 – 58 | 16 × 10 | 6.0 | 4.3 | 0.40–0.60 |
| 58 – 65 | 18 × 11 | 7.0 | 4.4 | 0.40–0.60 |
| 65 – 75 | 20 × 12 | 7.5 | 4.9 | 0.60–0.80 |
| 75 – 85 | 22 × 14 | 9.0 | 5.4 | 0.60–0.80 |
| 85 – 95 | 25 × 14 | 9.0 | 5.4 | 0.60–0.80 |
| 95 – 110 | 28 × 16 | 10.0 | 6.4 | 0.60–0.80 |
| 110 – 130 | 32 × 18 | 11.0 | 7.4 | 1.00–1.20 |
| 130 – 150 | 36 × 20 | 12.0 | 8.4 | 1.00–1.20 |
| 150 – 170 | 40 × 22 | 13.0 | 9.4 | 1.00–1.20 |
| 170 – 200 | 45 × 25 | 15.0 | 10.4 | 1.60–2.00 |
| 200 – 230 | 50 × 28 | 17.0 | 11.4 | 1.60–2.00 |
> t1 = keyway depth on shaft (measured from outer diameter)
> t2 = keyway depth in hub (measured from inner diameter)
---
## Fit Types for Keys (DIN 6885)
| Type | Shaft keyway | Hub keyway | Key | Use |
|---|---|---|---|---|
| **Normal (N)** | **N9** | **JS9** | **h9** | Industrial standard — slight side clearance |
| **Sliding (S)** | **H9** | **D10** | **h9** | Hub must slide axially on shaft |
| **Tight (P)** | **P9** | **P9** | **h9** | No side clearance — precision applications |
### When to use which type
**Normal fit** (most common): minimal guaranteed clearance on both flanks. The key transmits
torque but may have slight clearance causing a knock at start/stop reversals. Acceptable for
most industrial gears, pulleys, couplings on transmission shafts.
**Sliding fit**: the hub must slide axially (e.g. friction clutches, synchroniser assemblies,
linear actuators). Larger side clearance. Not suitable where angular precision is required.
**Tight fit**: no side clearance. Torque transmitted without backlash, precise angular
positioning. Assembly requires press fit or heating. Used in machine tools, precision pumps,
high-quality gearboxes.
---
## Deviations and Clearance Calculation (width b)
### Example: 8×7 key on Ø25 shaft (range 22–30 mm), Normal fit
**Shaft keyway N9** (width 8 mm, range 6–10 for width):
- IT9 for b=8 mm (range 6–10): IT9 = 36 µm
- N9 deviation: es = −10 µm (from fundamental deviations table)
- ei = es − IT9 = −10 − 36 = −46 µm
- Shaft keyway: 8 −0.010/−0.046 mm
**Hub keyway JS9** (width 8 mm):
- IT9 = 36 µm → JS9 = ±18 µm
- Hub keyway: 8 ±0.018 mm → 8 +0.018/−0.018 mm
**Key h9** (width 8 mm):
- IT9 = 36 µm → h9: es = 0, ei = −36 µm
- Key: 8 0/−0.036 mm
**Resulting clearance per flank** (key vs shaft keyway):
- Max clearance = ES hub − ei key = (+18) − (−36) = **+54 µm** per flank
- Min clearance = EI hub − es key = (−18) − 0 = **−18 µm** (slight interference possible)
→ Normal fit: mostly small clearance, rarely slight interference
---
## Drawing Dimensions
### On the shaft drawing
- Keyway width: **b ± tolerance** (e.g. 8 N9 → 8 −0.010/−0.046)
- Depth: dimension from OD → **d − 2t1** (keyway root diameter)
- e.g. Ø30 with t1=4.0: dimension = 30 − 2×4.0 = 22.0 mm (+0.2/0)
- Symmetry (if required): positional tolerance relative to axis
### On the hub / gear drawing
- Keyway width: **b ± tolerance** (e.g. 8 JS9 → 8 ±0.018)
- Depth: dimension from bore → **d + 2t2**
- e.g. bore Ø30 with t2=3.3: dimension = 30 + 2×3.3 = 36.6 mm (+0.2/0)
- Keyway flank roughness: **Ra 1.6 – 3.2 µm** (not a precision mating surface)
- Keyway root roughness: Ra 3.2 µm (not mating)
---
## Torque Transmission Capacity Check
The key is **not designed to carry torque alone** in interference fits. When combined with
H7/p6 or higher, torque is shared between interference friction and the key (redundancy).
When combined with H7/h6 or H7/k6, the key carries all the torque.
### Simplified flank bearing stress check
```
σ = Mt / (A_flank × d/2)
A_flank = (h/2 − r) × L_eff [contact area on one flank]
where:
Mt = torque to transmit [N·mm]
h = key height [mm]
L_eff = effective key length (total length − 2×head radius) [mm]
d = shaft diameter [mm]
Allowable flank stress:
Construction steel: σ_allow = 100 – 150 N/mm²
Cast iron: σ_allow = 60 – 80 N/mm²
Aluminium: σ_allow = 50 – 70 N/mm²
```
### Quick check rule (construction steel C45/42CrMo4)
- Key holds without issues if engagement ratio L/d ≥ 1.2
- If L/d < 0.8 or high torque + shock loading → double key at 180° or splined profile
---
## Risks and Practical Notes
- **Stress concentration**: the keyway reduces shaft fatigue strength by 25–40% at the
critical section. Do not position keyway at cross-section changes or peak bending locations.
- **Angular backlash**: even the Normal fit has clearance that produces a knock at every torque
reversal. On machines with frequent reversals (servo drives, presses) consider splined
profiles (ISO 4156) or pure interference fits.
- **Splined profile vs key**: consider when torque > 500 Nm on shafts Ø < 50 mm or when
torque is highly variable. ISO 4156 involute splines distribute load across all teeth,
eliminate backlash with preload, and reduce the stress concentration.
- **Woodruff key (semicircular)**: for tapered shafts or reduced sections (small motors,
small pumps). Tolerates angular misalignment. Do not use for high-torsion shafts.
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# IT Grades — Surface Roughness Ra Correlation
## IT Grade to Ra Correlation Table
Surface roughness must be consistent with the dimensional tolerance: a surface that is too
rough prevents achieving the specified tolerance, while over-specifying roughness is an
unnecessary cost.
**Practical rule**: Ra ≤ T/4 (where T = tolerance band) for mating surfaces.
For non-mating surfaces: Ra ≤ T/2 is sufficient.
| IT Grade | Max Ra recommended | Indicative Rz | Typical process |
|---|---|---|---|
| IT4 | Ra 0.1 µm | Rz 0.6 µm | Lapping, superfinishing |
| IT5 | Ra 0.2 µm | Rz 1.0 µm | Fine grinding, honing |
| IT6 | Ra 0.4 µm | Rz 2.0 µm | Standard grinding |
| IT7 | Ra 0.8 µm | Rz 4.0 µm | Grinding / fine turning |
| IT8 | Ra 1.6 µm | Rz 8.0 µm | Fine CNC turning |
| IT9 | Ra 3.2 µm | Rz 16 µm | Standard turning |
| IT10 | Ra 6.3 µm | Rz 25 µm | Milling / rough turning |
| IT11 | Ra 12.5 µm | Rz 50 µm | Economic machining |
| IT12–14 | Ra 25 µm + | Rz > 100 µm | Raw, unfinished |
---
## Special Applications
### Interference fit surfaces
For interference fits (p6, r6, s6, u6) on steels:
- Ra **≤ 0.8 µm** required (Ra 0.4 µm preferred)
- Roughness reduces effective interference by approx. 0.6 × (Rz shaft + Rz bore)
- When calculating interference, subtract the profile flattening allowance
### Sliding surfaces (bushings, guides)
- Ra **0.4 – 0.8 µm** for lubricated sliding
- Ra **0.2 – 0.4 µm** for dry sliding or critical conditions
- Avoid Ra < 0.1 µm (adhesion risk — stick-slip)
### Rolling bearing seats
- Shaft: Ra **0.4 – 0.8 µm** (per SKF/FAG: Ra ≤ 0.8 for standard classes)
- Housing bore: Ra **0.8 – 1.6 µm**
- P5/P4 precision classes: Ra ≤ 0.4 µm on shaft
### Radial lip seals (shaft surface at seal contact)
- Ra **0.2 – 0.4 µm**
- Texture: preferably circumferential (not helical — a helical pattern pumps fluid outward)
- Minimum surface hardness: 55 HRC or surface treatment
### Contact / reference planes
- Ra **0.8 – 1.6 µm** for functional contact
- Ra **3.2 µm** for non-critical bearing surfaces
---
## Roughness Symbols (EN ISO 1302)
```
Base symbol: √ (machining process not specified)
Material removal: ⊻ (material removal by machining required)
No material removal: ⊙ (no material removal: honing, lapping, etc.)
Indication: Ra value
e.g. Ra 0.8 / Ra 1.6 / Ra 3.2
```
---
## Practical Notes for the Designer
1. **Don't over-specify**: each step down in Ra increases cost by ~30–50%
2. **IT–Ra coherence**: specifying IT7 and Ra 6.3 is a contradiction
3. **State the parameter**: prefer Ra (arithmetic mean) for general use;
Rz (mean peak-valley height) is better for sliding and sealing surfaces
4. **Where not specified**: apply the general roughness note (e.g. "unless noted: Ra 3.2")
5. **Machining direction**: for rotary seals, specify circumferential vs. axial grinding direction
tolleranze-iso/scripts/calculate_fit.py
+275
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@@ -0,0 +1,275 @@
#!/usr/bin/env python3
"""
ISO 286-1 Fit Calculator
Usage: python calculate_fit.py <diameter> <fit>
Examples:
python calculate_fit.py 50 H7/k6
python calculate_fit.py 30 H8/f7
python calculate_fit.py 80 H7/p6
"""
import json
import sys
import re
import os
SCRIPT_DIR = os.path.dirname(os.path.abspath(__file__))
IT_FILE = os.path.join(SCRIPT_DIR, "it_values.json")
DEV_FILE = os.path.join(SCRIPT_DIR, "deviations.json")
RANGES = [
(1, 3), (3, 6), (6, 10), (10, 18), (18, 30), (30, 50),
(50, 80), (80, 120), (120, 180), (180, 250), (250, 315), (315, 400), (400, 500)
]
RANGE_KEYS = [
"1-3", "3-6", "6-10", "10-18", "18-30", "30-50",
"50-80", "80-120", "120-180", "180-250", "250-315", "315-400", "400-500"
]
def load_data():
with open(IT_FILE) as f:
it_data = json.load(f)
with open(DEV_FILE) as f:
dev_data = json.load(f)
return it_data, dev_data
def get_range_index(diameter: float) -> int:
for i, (lo, hi) in enumerate(RANGES):
if lo < diameter <= hi:
return i
if diameter == 1:
return 0
raise ValueError(f"Diameter {diameter} mm out of range (1–500 mm)")
def get_it_value(it_data: dict, grade: str, range_idx: int) -> float:
key = f"IT{grade}"
if key not in it_data["grades"]:
raise ValueError(f"Unknown IT grade: {grade}")
return it_data["grades"][key][range_idx]
def get_fundamental_deviation(dev_data: dict, letter: str, range_idx: int) -> float:
"""Returns the fundamental deviation: es for shafts, EI for bores."""
if letter in dev_data["shafts"]:
return dev_data["shafts"][letter][range_idx]
elif letter in dev_data["bores"]:
return dev_data["bores"][letter][range_idx]
else:
raise ValueError(f"Unknown deviation letter: '{letter}'")
def parse_fit(fit_str: str):
"""
Parse a fit string like 'H7/k6' or 'H7/JS6'.
Returns (bore_letter, bore_grade, shaft_letter, shaft_grade).
"""
m = re.fullmatch(r"([A-Za-z]+)(\d+)/([A-Za-z]+)(\d+)", fit_str.strip())
if not m:
raise ValueError(
f"Invalid fit format: '{fit_str}'. Expected e.g. H7/k6 or H8/f7"
)
bore_letter = m.group(1).upper()
bore_grade = m.group(2)
shaft_letter = m.group(3).lower()
shaft_grade = m.group(4)
return bore_letter, bore_grade, shaft_letter, shaft_grade
def classify_fit(c_max: float, c_min: float):
"""Classify the fit type."""
if c_min >= 0:
return "GUARANTEED CLEARANCE", "clearance"
elif c_max <= 0:
return "GUARANTEED INTERFERENCE", "interference"
else:
return "TRANSITION (clearance or interference)", "transition"
def fit_description(shaft_letter: str, shaft_grade: str) -> str:
"""Functional hint for common shaft deviation letters."""
descriptions = {
"a": "Very loose clearance (articulated linkages)",
"b": "Loose clearance",
"c": "Generous clearance (cranks, connecting rods)",
"d": "Wide functional clearance (long shafts, flanges)",
"e": "Generous clearance (misaligned joints)",
"f": "Standard functional clearance (guides, lubricated bushings)",
"g": "Precision clearance (precision guides, rotating pins)",
"h": "Nominal zero clearance (positioning, removable centering)",
"js": "Light transition (removable pins, loose keys)",
"k": "Transition — slight interference (bushings, keys)",
"m": "Transition — medium interference (sleeves, fixed bushings)",
"n": "Light interference (fixed bushings, rings)",
"p": "Interference (gears, fixed pulleys)",
"r": "Strong interference (high-torque hubs)",
"s": "Very strong interference (thermal assembly mandatory)",
"t": "High interference",
"u": "Maximum interference (bronze/cast-iron bushings)",
}
return descriptions.get(shaft_letter, "—")
def assembly_and_roughness(fit_class: str, bore_grade: str) -> str:
lines = []
is_interference = fit_class == "interference"
is_transition = fit_class == "transition"
if is_interference:
lines.append("ASSEMBLY METHOD:")
lines.append(" Thermal (heat hub to 80–300°C depending on interference level)")
lines.append(" or press fit if interference is small (< 0.020 mm)")
lines.append("")
lines.append("RECOMMENDED ROUGHNESS:")
lines.append(" Shaft: Ra ≤ 0.8 µm (Ra 0.4 preferred) — cylindrical grinding")
lines.append(" Bore: Ra ≤ 0.8 µm — fine boring or internal grinding")
lines.append(" Note: roughness reduces effective interference by ~0.6×(Rz_shaft + Rz_bore)")
elif is_transition:
lines.append("ASSEMBLY METHOD:")
lines.append(" Light press fit — requires press or mallet")
lines.append(" Removable with puller — not by hand")
lines.append("")
lines.append("RECOMMENDED ROUGHNESS:")
lines.append(" Shaft: Ra ≤ 1.6 µm — fine CNC turning")
lines.append(" Bore: Ra ≤ 1.6 µm — CNC boring")
else:
lines.append("ASSEMBLY METHOD:")
lines.append(" Hand-removable or with light tooling")
lines.append("")
g = int(bore_grade)
if g <= 6:
ra, proc_shaft, proc_bore = "0.8 µm", "fine turning / grinding", "CNC boring"
elif g <= 8:
ra, proc_shaft, proc_bore = "1.6 µm", "standard CNC turning", "standard boring"
else:
ra, proc_shaft, proc_bore = "3.2 µm", "standard turning", "drilling / reaming"
lines.append("RECOMMENDED ROUGHNESS:")
lines.append(f" Shaft: Ra ≤ {ra} — {proc_shaft}")
lines.append(f" Bore: Ra ≤ {ra} — {proc_bore}")
return "\n".join(lines)
def compute_js_deviation(it_value: float) -> float:
return it_value / 2.0
def calculate(diameter: float, fit_str: str, it_data: dict, dev_data: dict) -> str:
bore_l, bore_g, shaft_l, shaft_g = parse_fit(fit_str)
ri = get_range_index(diameter)
range_key = RANGE_KEYS[ri]
it_bore = get_it_value(it_data, bore_g, ri)
it_shaft = get_it_value(it_data, shaft_g, ri)
# Bore deviations
if bore_l == "H":
EI, ES = 0.0, it_bore
elif bore_l == "JS":
half = compute_js_deviation(it_bore)
EI, ES = -half, +half
else:
EI = get_fundamental_deviation(dev_data, bore_l, ri)
ES = EI + it_bore
# Shaft deviations
if shaft_l == "h":
es, ei = 0.0, -it_shaft
elif shaft_l == "js":
half = compute_js_deviation(it_shaft)
es, ei = +half, -half
else:
es = get_fundamental_deviation(dev_data, shaft_l, ri)
ei = es - it_shaft
c_max = ES - ei # positive = clearance
c_min = EI - es # negative = interference
fit_label, fit_class = classify_fit(c_max, c_min)
sep = "═" * 62
thin = "─" * 62
lines = [
"",
sep,
" FIT DATA SHEET — ISO 286-1",
sep,
f" Nominal diameter : Ø{diameter} mm",
f" Diameter range : {range_key} mm",
f" Fit : {bore_l}{bore_g}/{shaft_l}{shaft_g}",
f" Type : {fit_label}",
thin,
" BORE DEVIATIONS",
f" Letter/grade : {bore_l}{bore_g} (IT{bore_g} = {it_bore:.1f} µm)",
f" EI (lower) : {EI:+.1f} µm",
f" ES (upper) : {ES:+.1f} µm",
f" Drawing dim. : Ø{diameter} {EI/1000:+.4f}/{ES/1000:+.4f} mm",
thin,
" SHAFT DEVIATIONS",
f" Letter/grade : {shaft_l}{shaft_g} (IT{shaft_g} = {it_shaft:.1f} µm)",
f" es (upper) : {es:+.1f} µm",
f" ei (lower) : {ei:+.1f} µm",
f" Drawing dim. : Ø{diameter} {es/1000:+.4f}/{ei/1000:+.4f} mm",
thin,
]
if fit_class == "clearance":
lines += [
" RESULTING CLEARANCE",
f" Max clearance : {c_max:+.1f} µm ({c_max/1000:+.4f} mm)",
f" Min clearance : {c_min:+.1f} µm ({c_min/1000:+.4f} mm)",
]
elif fit_class == "interference":
i_max, i_min = abs(c_min), abs(c_max) if c_max < 0 else 0
lines += [
" RESULTING INTERFERENCE",
f" Max interference: {i_max:+.1f} µm ({i_max/1000:+.4f} mm)",
f" Min interference: {i_min:+.1f} µm ({i_min/1000:+.4f} mm)",
]
else:
lines += [
" CLEARANCE / INTERFERENCE (transition fit)",
f" Max value : {c_max:+.1f} µm ({c_max/1000:+.4f} mm) {'→ clearance' if c_max > 0 else '→ interference'}",
f" Min value : {c_min:+.1f} µm ({c_min/1000:+.4f} mm) {'→ clearance' if c_min > 0 else '→ interference'}",
]
lines += [
thin,
" TYPICAL FUNCTION",
f" {fit_description(shaft_l, shaft_g)}",
thin,
assembly_and_roughness(fit_class, bore_g),
sep,
"",
]
return "\n".join(lines)
def main():
if len(sys.argv) < 3:
print(__doc__)
print("Examples:")
print(" python calculate_fit.py 50 H7/k6")
print(" python calculate_fit.py 30 H8/f7")
print(" python calculate_fit.py 80 H7/p6")
sys.exit(1)
try:
diameter = float(sys.argv[1])
fit_str = sys.argv[2]
it_data, dev_data = load_data()
result = calculate(diameter, fit_str, it_data, dev_data)
print(result)
except (ValueError, KeyError) as e:
print(f"Error: {e}", file=sys.stderr)
sys.exit(1)
if __name__ == "__main__":
main()
tolleranze-iso/scripts/deviations.json
+744
View File
@@ -0,0 +1,744 @@
{
"_note": "Fundamental deviations ISO 286-1 in micrometres (\u00b5m). Shafts = upper deviation es. Bores = lower deviation EI. JS/js = \u00b1IT/2 (not tabulated, calculated at runtime).",
"ranges": [
"1-3",
"3-6",
"6-10",
"10-18",
"18-30",
"30-50",
"50-80",
"80-120",
"120-180",
"180-250",
"250-315",
"315-400",
"400-500"
],
"_shafts_note": "es = upper deviation in \u00b5m (negative = below zero). ei = es - IT",
"shafts": {
"a": [
-270,
-270,
-280,
-290,
-300,
-310,
-320,
-340,
-360,
-380,
-410,
-440,
-480
],
"b": [
-140,
-140,
-150,
-150,
-160,
-170,
-180,
-200,
-210,
-230,
-240,
-260,
-280
],
"c": [
-60,
-70,
-80,
-95,
-110,
-120,
-130,
-145,
-160,
-170,
-180,
-190,
-200
],
"cd": [
-34,
-46,
-56,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"d": [
-20,
-30,
-40,
-50,
-65,
-80,
-100,
-120,
-145,
-170,
-190,
-210,
-230
],
"e": [
-14,
-20,
-25,
-32,
-40,
-50,
-60,
-72,
-85,
-100,
-110,
-125,
-135
],
"ef": [
-10,
-14,
-18,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"f": [
-6,
-10,
-13,
-16,
-20,
-25,
-30,
-36,
-43,
-50,
-56,
-62,
-68
],
"fg": [
-4,
-6,
-8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"g": [
-2,
-4,
-5,
-6,
-7,
-9,
-10,
-12,
-14,
-15,
-17,
-18,
-20
],
"h": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"k": [
0,
1,
1,
1,
2,
2,
2,
3,
3,
4,
4,
4,
5
],
"m": [
2,
4,
6,
7,
8,
9,
11,
13,
15,
17,
20,
21,
23
],
"n": [
4,
8,
10,
12,
15,
17,
20,
23,
27,
31,
34,
37,
40
],
"p": [
6,
12,
15,
18,
22,
26,
32,
37,
43,
50,
56,
62,
68
],
"r": [
10,
15,
19,
23,
28,
34,
41,
51,
63,
77,
98,
98,
108
],
"s": [
14,
19,
23,
28,
35,
43,
53,
71,
92,
100,
108,
114,
126
],
"t": [
0,
0,
23,
28,
35,
43,
53,
71,
92,
100,
108,
114,
126
],
"u": [
18,
23,
28,
33,
41,
53,
66,
90,
109,
130,
150,
171,
190
],
"v": [
0,
0,
0,
0,
47,
59,
75,
102,
122,
150,
172,
202,
228
],
"x": [
20,
28,
34,
40,
50,
64,
80,
108,
146,
172,
210,
248,
280
],
"y": [
0,
0,
0,
50,
63,
80,
100,
134,
180,
214,
258,
310,
355
],
"z": [
26,
35,
42,
50,
63,
80,
100,
134,
180,
214,
258,
310,
355
],
"za": [
32,
42,
52,
64,
77,
98,
120,
160,
210,
258,
310,
365,
415
],
"zb": [
40,
50,
67,
90,
108,
136,
168,
218,
284,
340,
415,
490,
560
],
"zc": [
60,
80,
97,
130,
150,
188,
236,
308,
390,
470,
575,
660,
740
]
},
"_bores_note": "EI = lower deviation in \u00b5m. ES = EI + IT. For H: EI=0 always.",
"bores": {
"A": [
270,
270,
280,
290,
300,
310,
320,
340,
360,
380,
410,
440,
480
],
"B": [
140,
140,
150,
150,
160,
170,
180,
200,
210,
230,
240,
260,
280
],
"C": [
60,
70,
80,
95,
110,
120,
130,
145,
160,
170,
180,
190,
200
],
"D": [
20,
30,
40,
50,
65,
80,
100,
120,
145,
170,
190,
210,
230
],
"E": [
14,
20,
25,
32,
40,
50,
60,
72,
85,
100,
110,
125,
135
],
"F": [
6,
10,
13,
16,
20,
25,
30,
36,
43,
50,
56,
62,
68
],
"G": [
2,
4,
5,
6,
7,
9,
10,
12,
14,
15,
17,
18,
20
],
"H": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
],
"K": [
0,
2,
2,
2,
2,
3,
4,
4,
4,
5,
5,
5,
6
],
"M": [
-2,
-4,
-6,
-7,
-8,
-9,
-11,
-13,
-15,
-17,
-20,
-21,
-23
],
"N": [
-4,
-8,
-10,
-12,
-15,
-17,
-20,
-23,
-27,
-31,
-34,
-37,
-40
],
"P": [
-6,
-12,
-15,
-18,
-22,
-26,
-32,
-37,
-43,
-50,
-56,
-62,
-68
],
"R": [
-10,
-15,
-19,
-23,
-28,
-34,
-41,
-51,
-63,
-77,
-98,
-98,
-108
],
"S": [
-14,
-19,
-23,
-28,
-35,
-43,
-53,
-71,
-92,
-100,
-108,
-114,
-126
],
"T": [
0,
0,
-23,
-28,
-35,
-43,
-53,
-71,
-92,
-100,
-108,
-114,
-126
],
"U": [
-18,
-23,
-28,
-33,
-41,
-53,
-66,
-90,
-109,
-130,
-150,
-171,
-190
],
"V": [
0,
0,
0,
0,
-47,
-59,
-75,
-102,
-122,
-150,
-172,
-202,
-228
],
"X": [
-20,
-28,
-34,
-40,
-50,
-64,
-80,
-108,
-146,
-172,
-210,
-248,
-280
],
"Z": [
-26,
-35,
-42,
-50,
-63,
-80,
-100,
-134,
-180,
-214,
-258,
-310,
-355
],
"ZA": [
-32,
-42,
-52,
-64,
-77,
-98,
-120,
-160,
-210,
-258,
-310,
-365,
-415
],
"ZB": [
-40,
-50,
-67,
-90,
-108,
-136,
-168,
-218,
-284,
-340,
-415,
-490,
-560
],
"ZC": [
-60,
-80,
-97,
-130,
-150,
-188,
-236,
-308,
-390,
-470,
-575,
-660,
-740
]
}
}
tolleranze-iso/scripts/it_values.json
+22
View File
@@ -0,0 +1,22 @@
{
"_note": "Valori tolleranza IT in micrometri (µm) per campo di diametro — ISO 286-1 Tabella 1",
"ranges": ["1-3", "3-6", "6-10", "10-18", "18-30", "30-50", "50-80", "80-120", "120-180", "180-250", "250-315", "315-400", "400-500"],
"grades": {
"IT1": [0.8, 1, 1, 1.2, 1.5, 1.5, 2, 2.5, 3.5, 4.5, 6, 7, 8 ],
"IT2": [1.2, 1.5, 1.5, 2, 2.5, 2.5, 3, 4, 5, 7, 8, 9, 10 ],
"IT3": [2, 2.5, 2.5, 3, 4, 4, 5, 6, 8, 10, 12, 13, 15 ],
"IT4": [3, 4, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20 ],
"IT5": [4, 5, 6, 8, 9, 11, 13, 15, 18, 20, 23, 25, 27 ],
"IT6": [6, 8, 9, 11, 13, 16, 19, 22, 25, 29, 32, 36, 40 ],
"IT7": [10, 12, 15, 18, 21, 25, 30, 35, 40, 46, 52, 57, 63 ],
"IT8": [14, 18, 22, 27, 33, 39, 46, 54, 63, 72, 81, 89, 97 ],
"IT9": [25, 30, 36, 43, 52, 62, 74, 87, 100, 115, 130, 140, 155],
"IT10": [40, 48, 58, 70, 84, 100, 120, 140, 160, 185, 210, 230, 250],
"IT11": [60, 75, 90, 110, 130, 160, 190, 220, 250, 290, 320, 360, 400],
"IT12": [100, 120, 150, 180, 210, 250, 300, 350, 400, 460, 520, 570, 630],
"IT13": [140, 180, 220, 270, 330, 390, 460, 540, 630, 720, 810, 890, 970],
"IT14": [250, 300, 360, 430, 520, 620, 740, 870, 1000,1150,1300,1400,1550],
"IT15": [400, 480, 580, 700, 840, 1000,1200,1400,1600,1850,2100,2300,2500],
"IT16": [600, 750, 900, 1100,1300,1600,1900,2200,2500,2900,3200,3600,4000]
}
}