engineering-skills/tolleranze-iso/references/functional-elements.md

Functional Elements — Tolerances and Fits

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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

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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

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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

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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

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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.

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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

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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)

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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

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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

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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

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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.

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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

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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

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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)

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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