# Fit

Different types of fits

In mechanical engineering, a fit is the dimensional relationship between two parts that should fit together without reworking. Most of the time, these parts have the same contour at the joint, once as an inner shape and once as an outer shape.

A typical example is the shaft in a bore. The diameter of both contours is given as a dimension with a tolerance. Both contours have the same nominal dimension . The two tolerance fields within which the actual dimensions of the bore and shaft that arise during production must lie are different .

There is either a clearance fit or an interference fit (interference fit) on the finished component . If the tolerances allow both play and oversize, one speaks of a transition fit which, depending on the actual dimensions achieved, falls into one of the first-mentioned groups.

## history

Even before 1914, several companies had developed passport systems for their own purposes. After the First World War , the system of DIN fits was developed from this. The International Federation of the National Standardizing Associations (ISA), founded in 1926, standardized the passport systems of different nations in 1928. The ISA fits then replaced the DIN fits. Since 1964, the organization has been called the International Organization for Standardization and the ISO 286-1 and 286-2 standards for round and flat fits were adopted unchanged as DIN standards in the German set of standards.

## standardization

Fits are standardized. The relevant standard is the ISO standard ISO 286. It consists of two parts and was issued in 1988. Basic terms of tolerances and fits are regulated by ISO 286-1 (current new edition 4.2010); ISO 286-2 contains the tables of the basic tolerance levels and tolerance limits for bores and shafts. The standard is published in Germany as a DIN standard .

### Marking of fits

When fitting specifications in technical drawings , internal dimensions (e.g. diameter of a bore ) and external dimensions (e.g. diameter of a shaft ) are considered separately. The fit information can be in the form of the specification of upper and lower dimensions or tolerance symbols.

#### Tolerance abbreviation

Tolerance symbols in technical drawings are standardized according to DIN . The corresponding standard is DIN 406 , which deals with dimension entries.

The fit specification itself always consists of one or two letters and a number. The letter (s) indicates the position of the tolerance field in relation to the nominal dimension, the tolerance position . The number indicates the size of the tolerance field, the degree of tolerance . See: Tolerance (fit information according to ISO) . Capital letters are used to represent the tolerances of internal dimensions (bore) and lower-case letters are used for external dimensions (shaft).

Reminder: The shaft must fit into the hole. Accordingly, the shaft has to be a little smaller (⇒ lower case letters) and the hole a little larger (⇒ upper case letters).

#### Tolerance level

Schematic tolerance field for bores in the same nominal dimension range

The letters A – ZC indicate the position of the tolerance field to the zero line (nominal dimension), the so-called tolerance position. As the letter increases, the position of the tolerance field shifts in the direction of closer fits, i.e. larger external dimensions of the shafts and smaller internal dimensions of the bores.

Examples for an external dimension of a shaft:

${\ displaystyle \ varnothing 10 _ {\ text {h6}} = \ varnothing 10 _ {- 9} ^ {0}}$

Minimum size: ${\ displaystyle 10 \, \ mathrm {mm} -9 \, {\ text {µm}} = 9 {,} 991 \ \ mathrm {mm}}$
Maximum: ${\ displaystyle 10 \, \ mathrm {mm} +0 \, {\ text {µm}} = 10 {,} 000 \ \ mathrm {mm}}$

${\ displaystyle \ varnothing 10 _ {\ text {p6}} = \ varnothing 10 _ {+ 15} ^ {+ 24}}$

Minimum size: ${\ displaystyle 10 \, \ mathrm {mm} +15 \, {\ text {µm}} = 10 {,} 015 \ \ mathrm {mm}}$
Maximum: ${\ displaystyle 10 \, \ mathrm {mm} +24 \, {\ text {µm}} = 10 {,} 024 \ \ mathrm {mm}}$

Examples for an inside dimension of a hole:

${\ displaystyle \ varnothing 10 ^ {\ text {H9}} = \ varnothing 10_ {0} ^ {+ 36}}$

Minimum size: ${\ displaystyle 10 \, \ mathrm {mm} -0 \, {\ text {µm}} = 10 {,} 000 \, \ mathrm {mm}}$
Maximum: ${\ displaystyle 10 \, \ mathrm {mm} +36 \, {\ text {µm}} = 10 {,} 036 \, \ mathrm {mm}}$

${\ displaystyle \ varnothing 10 ^ {\ text {P9}} = \ varnothing 10 _ {- 51} ^ {- 15}}$

Minimum size: ${\ displaystyle 10 \, \ mathrm {mm} -51 \, {\ text {µm}} = 9 {,} 949 \, \ mathrm {mm}}$
Maximum: ${\ displaystyle 10 \, \ mathrm {mm} -15 \, {\ text {µm}} = 9 {,} 985 \, \ mathrm {mm}}$

H fits are directly above the zero line, in contrast to this, h fits are directly below the zero line. The size of the tolerance field is independent of the selected tolerance position.

#### Tolerance level

Size of the tolerance fields for the basic tolerance grades IT 4 to IT 10 in the nominal dimension range from 80 to 120 mm

The degree of tolerance is indicated by numbers from 1 to 18 (formerly called qualities). The larger the number, the larger the tolerance field. Furthermore, the size of the tolerance depends on the nominal size. In the case of small nominal dimensions, the percentage tolerance is greater than that of large nominal dimensions.

The number indicates the size of the tolerance field according to the ISO basic tolerances (IT01, IT 0, IT1, IT2,…, IT18) (IT = ISO tolerance); the tolerance field increases with increasing number. The number assigned to the degree of tolerance is thus the indicator for the quality or accuracy of the fitting element.

Examples for an inside dimension:

${\ displaystyle \ varnothing 10 ^ {\ text {D9}} = \ varnothing 10 _ {+ 40} ^ {+ 76}}$

Minimum dimension: 10 mm + 40 µm = 10.040 mm,
maximum dimension : 10 mm + 76 µm = 10.076 mm

${\ displaystyle \ varnothing 10 ^ {\ text {D11}} = \ varnothing 10 _ {+ 40} ^ {+ 130}}$

Minimum dimension: 10 mm + 40 µm = 10.040 mm,
maximum dimension : 10 mm + 130 µm = 10.130 mm

The minimum for internal dimensions and the maximum for external dimensions are independent of the selected degree of tolerance.

### Nominal dimensions and tolerance unit i

For nominal dimensions greater than 3 mm to 500 mm, the values ​​of the tolerance degrees greater than or equal to 5 are defined as multiples of the tolerance unit i .

The tolerance unit i is calculated as follows:

${\ displaystyle i = 0 {,} 45 \ cdot {\ sqrt [{3}] {D}} + 0 {,} 001 \ cdot D}$

i in µm (micrometers); D in mm (millimeters).

D in mm is the geometric mean from the limit values D 1 and D 2 of the respective nominal size range:

${\ displaystyle D = {\ sqrt [{2}] {(D_ {1} \ cdot D_ {2})}}}$

The formula is empirically determined; it was taken into account that under the same manufacturing conditions, the relationship between manufacturing errors and nominal dimensions has a roughly parabolic function.

The term 0.001 x D takes into account the uncertainty that increases linearly as the nominal dimension increases. The factors 0.45 and 0.001 are therefore empirical values.

## Fit systems

A distinction is made between two basic fitting systems, namely the standard bore system and the standard shaft system . For more information see article Fit system .

### System unit bore

With the standard bore system, all bores are carried out in accordance with DIN 7154 with the same tolerance (e.g. H7). The desired fit is achieved by selecting a shaft with an appropriate tolerance.

### System unit wave

With the standardized shaft system, all shafts are designed in accordance with DIN 7155 with the same tolerance (e.g. h6). The desired fit is achieved by selecting a hole with an appropriate tolerance.

### practice

The production of shafts with an exact diameter is possible on a lathe with relatively little effort. The production of bores with an exact diameter, especially with small bores, is often done by reaming and is more complex since a special tool is required for each diameter and tolerance. It is therefore advisable to design the bore as a unit bore, to use only one reamer per nominal diameter and to adapt the shaft accordingly.

## Quality of a fit (actual and target values)

The actual values ​​of a fit are used as a measured variable and compared with the predefined setpoint values for the corresponding fit system. The result of this comparison is used to assess the quality of a fit. The actual values ​​of a fit are the metrologically determined values ​​of a real fit, i.e. the actual dimensions measured on the corresponding component. The actual dimensions of the fit must lie within the limits tolerated by the dimensions, otherwise the fit and thus U. the entire component scrap .

The subject of rejects due to fits is dealt with in more detail in the section throwing fit .

## Types of fits

There are basically three types of fits. Theoretically, holes and shafts can be combined with one another as required. The choice of tolerance classes results in either play or oversize between the parts to be connected during assembly.

Depending on the selection, a clearance, transition or oversize fit is created . A complete selection of fits for the standard bore system is defined in DIN 7157 . The same standard defines only clearance fits for the unit shaft system.

### Clearance fit

The smallest dimension of the hole is always larger than, in the borderline case also the same as the largest dimension of the shaft.

• combination ${\ displaystyle \ varnothing 30 _ {\ text {f7}} ^ {\ text {H7}}}$
Dimensions of the bore :, the executed bore diameter may be between 30,000 and 30,021 mm. ${\ displaystyle \ varnothing 30 ^ {\ text {H7}} = \ varnothing 30_ {0} ^ {+ 21}}$
Tolerance range: (21 - 0) µm = 21 µm
Dimensions of the shaft :, the executed shaft diameter may be between 29.959 and 29.980 mm. ${\ displaystyle \ varnothing 30 _ {\ text {f7}} = \ varnothing 30 _ {- 41} ^ {- 20}}$
Tolerance range: (41 - 20) µm = 21 µm.
Since the dimensions of the correctly manufactured H7 bore are always greater than or equal to 0 and the dimensions of the f7 shaft are always smaller than at least −20 µm, there is a minimum clearance of
(0 µm of the bore + 20 µm of the shaft) = 20 µm
and a major game of
(21 µm of the bore + 41 µm of the shaft) = 62 µm

#### Selected clearance fits

Selected clearance fits according to the "unit bore" fit system

• ${\ displaystyle d _ {\ text {d9}} ^ {\ text {H7}}}$: Parts with a lot of play : transmission parts , bearings for construction machinery
• ${\ displaystyle d _ {\ text {e8}} ^ {\ text {H8}}}$: Parts with plenty of play: main bearings for crankshafts , pistons in cylinders
• ${\ displaystyle d _ {\ text {f7}} ^ {\ text {H8}}}$: Movable parts with noticeable play: Multi-bearing shaft , piston in cylinder
• ${\ displaystyle d _ {\ text {h9}} ^ {\ text {H8}}}$: Parts hardly have any play and can be moved with manual force: Movable gears and couplings
• ${\ displaystyle d _ {\ text {g6}} ^ {\ text {H7}}}$: Parts can move without noticeable play: gears and clutches
• ${\ displaystyle d _ {\ text {h6}} ^ {\ text {H7}}}$: Parts can just about be moved by hand: Guides on machine tools , adjusting rings

### Transitional fit

With a transition fit, depending on the actual dimensions of the bore and shaft, either a play or an oversize occurs when joining . The largest dimension of the hole is larger, in the borderline case also the same as the smallest dimension of the shaft.

• Combination :${\ displaystyle \ varnothing 6_ {m6} ^ {H7}}$
${\ displaystyle \ varnothing 6 ^ {H7} = \ varnothing 6_ {0} ^ {+ 12}}$
Tolerance range: (12 - 0) µm = 12 µm.
${\ displaystyle \ varnothing 6_ {m6} = \ varnothing 6 _ {+ 4} ^ {+ 12}}$
Tolerance range: (12 - 4) µm = 8 µm.
Here there is a partial overlap between the dimensions of a correctly manufactured H7 bore and the m6 shaft. Depending on the design, there is a maximum play of
(+12 µm of the bore) - (+ 4 µm of the shaft) = 8 µm
or an excess of
(0 µm of the bore + 12 µm of the shaft) = 12 µm

#### Selected transition fits

Selected transition fits according to the "unit bore" fit system

• ${\ displaystyle d_ {j6} ^ {H7}}$: The parts can be moved with light strokes or by hand.
• ${\ displaystyle d_ {m6} ^ {H7}}$: Parts can be joined with little pressure: wheel flanges on wheel centers
• ${\ displaystyle d_ {n6} ^ {H7}}$: Parts can be joined with a machinist's hammer: gears and couplings on pins , also common fit for cylinder pins for precise joining of components

### Interference fit (interference fit)

The largest dimension of the hole is always smaller than the smallest dimension of the shaft.

• combination ${\ displaystyle \ varnothing 3_ {h6} ^ {X7}}$
${\ displaystyle \ varnothing 3 ^ {X7} = \ varnothing 3 _ {- 30} ^ {- 20}}$
Tolerance range: (30 - 20) µm = 10 µm.
${\ displaystyle \ varnothing 3_ {h6} = \ varnothing 3 _ {- 6}}$
Tolerance range: (0 - 6) µm = 6 µm.
Here there is always an overlap between the dimensions of a correctly manufactured X7 hole and the h6 shaft.
Depending on the design, there is a lower (minimal) oversize of
(20 µm of the bore - 6 µm of the shaft) = 14 µm
or an upper (maximum) excess of
(30 µm of the bore - 0 µm of the shaft) = 30 µm

#### Selected interference fits

Selected interference fits according to the "unit bore" fit system

• Interference fits
• ${\ displaystyle d_ {p6} ^ {H7}}$: Parts can be joined with pressure: feather key connections
• ${\ displaystyle d_ {r6} ^ {H7}}$: Parts can be joined with greater pressure: Shaft-hub connections , lever connections
• ${\ displaystyle d_ {s6} ^ {H7}}$: Parts can be joined with greater pressure and additional heating: Shaft-hub connections

## Checking fits

In order to check fitting tolerances after production, so-called gauges are used in measuring and testing technology . Gauges for fits are called limit gauges because they are used to check the dimensional limits of the fit. (see: Category: Teaching (Technology) )

A teaching for holes is z. B. the limit plug gauge, a cylindrical pin with two very precisely manufactured test cylinders on the sides. The fit is only correct if the "good side" of it fits into the fitting hole and the "reject side" (marked by the red ring) does not.

To check waves, for. B. a border throat gauge can be used. This teaching contains an elongated gap on both sides, which is delimited by two flat, parallel surfaces. Here, too, the shaft can and must only fit into exactly one of the two gaps.

It should be noted, however, that a separate plug gauge or snap gauge is required for each individual fit. Gauges do not provide a measured value, which is why inductive measuring probes or pneumatic measuring devices are often used in series production , the results of which are then further processed in the statistical process control.

## Throw fit (scrap)

The term Wurfpassung is a pseudo-technical term used to describe a non noticed particularly unsuccessful fit with undesirable much play. The term comes from the fact that one would trust oneself to get the shaft into the hole by throwing it from a distance.

One or both fitting parts are manufactured outside of the tolerance. Samples are usually taken in production and non-compliant parts are considered faulty production , also called scrap, which cannot be brought to the correct size or only with considerable effort. Such a part is usually unusable and is disposed of for recycling, for example scrap . Are also newly has a defective work produced high in some effort, especially if the error occurs against the production end and the workpiece a high level of vertical adheres.