# Tolerances and fits.

This book includes tables and calculations for easy option of fits of machine parts and determination of their dimensional tolerances and deviations. Using this tool the following tasks can be solved:

1. Selection of suitable fits of machine parts according to the international standard ISO 286.
2. Determination of dimensional tolerances and deviations of machine parts according to the international standard ISO 286.
3. Selection of preferred fits of machine parts and determination of their dimensional tolerances and deviations according to ANSI B4.1.
4. Determination of non-prescribed limit deviations of linear and angular dimensions according to ISO 2768.

5. Automatic design of a fit for the given clearance or fit interference respectively.

The data, procedures, algorithms and specialized literature and standards ANSI, ISO, DIN and others were used in the calculations.
List of standards: ANSI B4.1, ANSI B4.2, ISO 286, ISO 1829, ISO 2768, EN 20286, JIS B 0401

User interface.

Purchase, Price list.

## Control, structure and syntax of calculations.

Information on the syntax and control of the calculation can be found in the document "Control, structure and syntax of calculations".

## Basic terms.

It is necessary that the dimensions, shape and mutual position of surfaces of individual parts of mechanical engineering products are kept within a certain accuracy to achieve their correct and reliable functioning. Routine production processes do not allow maintenance (or measurement) of the given geometrical properties with absolute accuracy. Actual surfaces of the produced parts therefore differ from ideal surfaces prescribed in drawings. Deviations of actual surfaces are divided into four groups to enable assessment, prescription and checking of the permitted inaccuracy during production:

• Dimensional deviations
• Shape deviations
• Position deviations
• Surface roughness deviations

This toll includes the first group and can therefore be used to determine dimensional tolerances and deviations of machine parts.

As mentioned above, it is principally impossible to produce machine parts with absolute dimensional accuracy. In fact, it is not necessary or useful. It is quite sufficient that the actual dimension of the part is found between two limit dimensions and a permissible deviation is kept with production to ensure correct functioning of engineering products. The required level of accuracy of production of the given part is then given by the dimensional tolerance which is prescribed in the drawing. The production accuracy is prescribed with regards to the functionality of the product and to the economy of production as well.

A coupling of two parts creates a fit whose functional character is determined by differences of their dimensions before their coupling.

where:

d=D ... basic size
Dmax , Dmin ... limits of size for the hole
dmax , dmin ... limits of size for the shaft
ES ... hole upper deviation
EI ... hole lower deviation
es ... shaft upper deviation
ei ... shaft lower deviation

Depending on the mutual position of tolerance zones of the coupled parts, 3 types of fit can be distinguished:

1. Clearance fit
2. Transition fit
3. Interference fit

## ISO 286:  ISO system of limits and fits. [1]

This paragraph can be used to choose a fit and determine tolerances and deviations of machine parts according to the standard ISO 286:1988. This standard is identical with the European standard EN 20286:1993 and defines an internationally recognized system of tolerances, deviations and fits. The standard ISO 286 is used as an international standard for linear dimension tolerances and has been accepted in most industrially developed countries in identical or modified wording as a national standard (JIS B 0401, DIN ISO 286, BS EN 20286, CSN EN 20286, etc.).

The system of tolerances and fits ISO can be applied in tolerances and deviations of smooth parts and for fits created by their coupling. It is used particularly for cylindrical parts with round sections. Tolerances and deviations in this standard can also be applied in smooth parts of other sections. Similarly, the system can be used for coupling (fits) of cylindrical parts and for fits with parts having two parallel surfaces (e.g. fits of keys in grooves). The term "shaft", used in this standard has a wide meaning and serves for specification of all outer elements of the part, including those elements which do not have cylindrical shapes. Also, the term "hole" can be used for specification of all inner elements regardless of their shape.

### 1.1 Basic size.

It is the size whose limit dimensions are specified using the upper and lower deviations. In case of a fit, the basic size of both connected elements must be the same.

### 1.2 Tolerance of a basic size for specific tolerance grade.

The tolerance of a size is defined as the difference between the upper and lower limit dimensions of the part. In order to meet the requirements of various production branches for accuracy of the product, the system ISO implements 20 grades of accuracy. Each of the tolerances of this system is marked "IT" with attached grade of accuracy (IT01, IT0, IT1 ... IT18).

##### Field of use of individual tolerances of the system ISO:
 IT01 to IT6 For production of gauges and measuring instruments IT5 to IT12 For fits in precision and general engineering IT11 to IT16 For production of semi-products IT16 to IT18 For structures IT11 to IT18 For specification of limit deviations of non-tolerated dimensions

### 1.3 Hole tolerance zones.

The tolerance zone is defined as a spherical zone limited by the upper and lower limit dimensions of the part. The tolerance zone is therefore determined by the amount of the tolerance and its position related to the basic size. The position of the tolerance zone, related to the basic size (zero line), is determined in the ISO system by a so-called basic deviation. The system ISO defines 28 classes of basic deviations for holes. These classes are marked by capital letters (A, B, C, ... ZC). The tolerance zone for the specified dimensions is prescribed in the drawing by a tolerance mark, which consists of a letter marking of the basic deviation and a numerical marking of the tolerance grade (e.g. H7, H8, D5, etc.). This paragraph includes graphic illustrations of all tolerance zones of a hole which are applicable for the specified basic size [1.1] and the tolerance grade IT chosen from the pop-up list.

Though the general sets of basic deviations (A ... ZC) and tolerance grades (IT1 ... IT18) can be used for prescriptions of hole tolerance zones by their mutual combinations, in practice only a limited range of tolerance zones is used. An overview of tolerance zones for general use can be found in the following table. The tolerance zones not included in this table are considered special zones and their use is recommended only in technically well-grounded cases.

##### Prescribed hole tolerance zones for routine use (for basic sizes up to 3150 mm):
 B8 C8 A9 B9 C9 A10 B10 C10 A11 B11 C11 A12 B12 C12 A13 B13 C13 E5 CD6 D6 E6 CD7 D7 E7 CD8 D8 E8 CD9 D9 E9 CD10 D10 E10 D11 D12 D13 EF3 F3 EF4 F4 EF5 F5 EF6 F6 EF7 F7 EF8 F8 EF9 F9 EF10 F10 FG3 G3 FG4 G4 FG5 G5 FG6 G6 FG7 G7 FG8 G8 FG9 G9 FG10 G10 H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 H14 H15 H16 H17 H18 JS1 JS2 JS3 JS4 JS5 JS6 JS7 JS8 JS9 JS10 JS11 JS12 JS13 JS14 JS15 JS16 JS17 JS18 K3 K4 K5 J6 K6 J7 K7 J8 K8 M3 N3 M4 N4 M5 N5 M6 N6 M7 N7 M8 N8 M9 N9 M10 N10 N11 P3 P4 P5 P6 P7 P8 P9 P10 R3 R4 R5 R6 R7 R8 R9 R10 S3 S4 S5 S6 S7 S8 S9 S10 T5 U5 T6 U6 T7 U7 T8 U8 U9 U10 V5 X5 V6 X6 Y6 V7 X7 Y7 V8 X8 Y8 X9 Y9 X10 Y10 Z6 ZA6 Z7 ZA7 Z8 ZA8 Z9 ZA9 Z10 ZA10 Z11 ZA11 ZB7 ZC7 ZB8 ZC8 ZB9 ZC9 ZB10 ZC10 ZB11 ZC11

Note: Tolerance zones with thin print are specified only for basic sizes up to 500 mm.

### 1.4 Shaft tolerance zones.

The tolerance zone is defined as a spherical zone limited by the upper and lower limit dimensions of the part. The tolerance zone is therefore determined by the amount of the tolerance and its position related to the basic size. The position of the tolerance zone, related to the basic size (zero line), is determined in the ISO system by a so-called basic deviation. The system ISO defines 28 classes of basic deviations for shafts. These classes are marked by lower case letters (a, b, c, ... zc). The tolerance zone for the specified dimensions is prescribed in the drawing by a tolerance mark, which consists of a letter marking of the basic deviation and a numerical marking of the tolerance grade (e.g. h7, h6, g5, etc.). This paragraph includes graphic illustrations of all tolerance zones of a shaft which are applicable for the specified basic size [1.1] and the tolerance grade IT chosen from the pop-up list.

Though the general sets of basic deviations (a ... zc) and tolerance grades (IT1 ... IT18) can be used for prescriptions of shaft tolerance zones by their mutual combinations, in practice only a limited range of tolerance zones is used. An overview of tolerance zones for general use can be found in the following table. The tolerance zones not included in this table are considered special zones and their use is recommended only in technically well-grounded cases.

##### Prescribed shaft tolerance zones for routine use (for basic sizes up to 3150 mm):
 c8 a9 b9 c9 a10 b10 c10 a11 b11 c11 a12 b12 c12 a13 b13 cd5 d5 cd6 d6 cd7 d7 cd8 d8 cd9 d9 cd10 d10 d11 d12 d13 ef3 ef4 e5 ef5 e6 ef6 e7 ef7 e8 ef8 e9 ef9 e10 ef10 f3 fg3 f4 fg4 f5 fg5 f6 fg6 f7 fg7 f8 fg8 f9 fg9 f10 fg10 g3 g4 g5 g6 g7 g8 g9 g10 h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 h12 h13 h14 h15 h16 h17 h18 js1 js2 js3 js4 js5 js6 js7 js8 js9 js10 js11 js12 js13 js14 js15 js16 js17 js18 k3 k4 j5 k5 j6 k6 j7 k7 k8 k9 k10 k11 k12 k13 m3 n3 m4 n4 m5 n5 m6 n6 m7 n7 m8 n8 m9 n9 p3 p4 p5 p6 p7 p8 p9 p10 r3 r4 r5 r6 r7 r8 r9 r10 s3 s4 s5 s6 s7 s8 s9 s10 t5 u5 t6 u6 t7 u7 t8 u8 u9 v5 x5 v6 x6 y6 v7 x7 y7 v8 x8 y8 x9 y9 x10 y10 z6 za6 z7 za7 z8 za8 z9 za9 z10 za10 z11 za11 zb7 zc7 zb8 zc8 zb9 zc9 zb10 zc10 zb11 zc11

Note: Tolerance zones with thin print are specified only for basic sizes up to 500 mm.

### 1.5 Selection of fit.

This paragraph can be used to choose a recommended fit. If you wish to use another fit than the recommended one, define hole and shaft tolerance zones directly in the paragraphs [1.9, 1.10]. When designing the fit itself, it is recommended to follow several principles:

• Design a fit in a hole basis system in a shaft basis system.
• Use hole tolerances greater or equal to the shaft tolerance.
• Tolerances of the hole and shaft should not differ by more than two grades.

### 1.6 System of fit.

Although there can be generally coupled parts without any tolerance zones, only two methods of coupling of holes and shafts are recommended due to constructional, technological and economic reasons.

1. Hole basis system
The desired clearances and interferences in the fit are achieved by combinations of various shaft tolerance zones with the hole tolerance zone "H". In this system of tolerances and fits, the lower deviation of the hole is always equal to zero.
2. Shaft basis system
The desired clearances and interferences in the fit are achieved by combinations of various hole tolerance zones with the shaft tolerance zone "h". In this system of tolerances and fits, the upper deviation of the hole is always equal to zero.

where:

d=D ... basic size
////  ... hole tolerance zone
\\\\  ... shaft tolerance zone

The option of the system for the specified type of product or production is always influenced by the following factors:

• Constructional design of the product and the method of assembly.
• Production procedure and costs for machining the part.
• Type of semi-product and consumption of material.
• Costs for purchase, maintenance and storage of gauges and production tools.
• Machine holding of the plant.
• Options in use of standardized parts.

### 1.7 Type of fit.

Depending on the mutual position of tolerance zones of the coupled parts, 3 types of fit can be distinguished:

1. Clearance fit
It is a fit that always enables a clearance between the hole and shaft in the coupling. The lower limit size of the hole is greater or at least equal to the upper limit size of the shaft.
2. Transition fit
It is a fit where (depending on the actual sizes of the hole and shaft) both clearance and interference may occur in the coupling. Tolerance zones of the hole and shaft partly or completely interfere.
3. Interference fit
It is a fit always ensuring some interference between the hole and shaft in the coupling. The upper limit size of the hole is smaller or at least equal to the lower limit size of the shaft.

### 1.8 Recommended fits.

A sufficient fit can be selected in the pop-up list.

The list of recommended fits given here is for information only and cannot be taken as a fixed listing. The enumeration of actually used fits may differ depending on the type and field of production, local standards and national usage and last but not least, depending on the plant practices. Properties and field of use of some selected fits are described in the following overview. When selecting a fit it is often necessary to take into account not only constructional and technological views, but also economic aspects. Selection of a suitable fit is important particularly in view of those measuring instruments, gauges and tools which are implemented in the production. Therefore, follow proven plant practices when selecting a fit.

#### Clearance fits:

H11/a11, H11/c11, H11/c9, H11/d11, A11/h11, C11/h11, D11/h11
Fits with great clearances with parts having great tolerances.
Use: Pivots, latches, fits of parts exposed to corrosive effects, contamination with dust and thermal or mechanical deformations.

H9/C9, H9/d10, H9/d9, H8/d9, H8/d8, D10/h9, D9/h9, D9/h8
Running fits with greater clearances without any special requirements for accuracy of guiding shafts.
Use: Multiple fits of shafts of production and piston machines, parts rotating very rarely or only swinging.

H9/e9, H8/e8, H7/e7, E9/h9, E8/h8, E8/h7
Running fits with greater clearances without any special requirements for fit accuracy.
Use: Fits of long shafts, e.g. in agricultural machines, bearings of pumps, fans and piston machines.

H9/f8, H8/f8, H8/f7, H7/f7, F8/h7, F8/h6
Running fits with smaller clearances with general requirements for fit accuracy.
Use: Main fits of machine tools. General fits of shafts, regulator bearings, machine tool spindles, sliding rods.

H8/g7, H7/g6, G7/h6
Running fits with very small clearances for accurate guiding of shafts. Without any noticeable clearance after assembly.
Use: Parts of machine tools, sliding gears and clutch disks, crankshaft journals, pistons of hydraulic machines, rods sliding in bearings, grinding machine spindles.

H11/h11, H11/h9
Slipping fits of parts with great tolerances. The parts can easily be slid one into the other and turn.
Use: Easily demountable parts, distance rings, parts of machines fixed to shafts using pins, bolts, rivets or welds.

H8/h9, H8/h8, H8/h7, H7/h6
Sliding fits with very small clearances for precise guiding and centring of parts. Mounting by sliding on without use of any great force, after lubrication the parts can be turned and slid by hand.
Use: Precise guiding of machines and preparations, exchangeable wheels, roller guides.

#### Transition fits:

H8/j7, H7/js6, H7/j6, J7/h6
Tight fits with small clearances or negligible interference. The parts can be assembled or disassembled manually.
Use: Easily dismountable fits of hubs of gears, pulleys and bushings, retaining rings, frequently removed bearing bushings.

H8/k7, H7/k6, K8/h7, K7/h6
Similar fits with small clearances or small interferences. The parts can be assembled or disassembled without great force using a rubber mallet.
Use: Demountable fits of hubs of gears and pulleys, manual wheels, clutches, brake disks.

H8/p7, H8/m7, H8/n7, H7/m6, H7/n6, M8/h6, N8/h7, N7/h6
Fixed fits with negligible clearances or small interferences. Mounting of fits using pressing and light force.
Use: Fixed plugs, driven bushings, armatures of electric motors on shafts, gear rims, flushed bolts.

#### Interference fits:

H8/r7, H7/p6, H7/r6, P7/h6, R7/h6
Pressed fits with guaranteed interference. Assembly of the parts can be carried out using cold pressing.
Use: Hubs of clutch disks, bearing bushings.

H8/s7, H8/t7, H7/s6, H7/t6, S7/h6, T7/h6
Pressed fits with medium interference. Assembly of parts using hot pressing. Assembly using cold pressing only with use of large forces.
Use: Permanent coupling of gears with shafts, bearing bushings.

H8/u8, H8/u7, H8/x8, H7/u6, U8/h7, U7/h6
Pressed fits with big interferences. Assembly using pressing and great forces under different temperatures of the parts.
Use: permanent couplings of gears with shafts, flanges.

### 1.9 Hole tolerance zone.

Limit deviations of the hole tolerance zone are calculated in this paragraph for the specified basic size [1.1] and selected hole tolerance zone.

The respective hole tolerance zone is automatically set up in the listing during selection of any of the recommended fits from the list in row [1.8]. If you wish to use another tolerance zone for the hole, select the corresponding combination of a basic deviation (A ... ZC) and a tolerance zone (1 ... 18) in pop-up lists in this row.

Though the general sets of basic deviations (A ... ZC) and tolerance grades (IT1 ... IT18) can be used for prescriptions of hole tolerance zones by their mutual combinations, in practice only a limited range of tolerance zones is used. An overview of tolerance zones specified for general use can be found in the table in paragraph [1.3]. The tolerance zones which are not included in the selection are considered special zones and their use is recommended only in technically well-grounded cases.

### 1.10 Shaft tolerance zones.

Limit deviations of the hole tolerance zone are calculated in this paragraph for the specified basic size [1.1] and selected shaft tolerance zone.

The respective shaft tolerance zone is automatically set up in the listing during selection of any of the recommended fits from the list in row [1.8]. If you wish to use another tolerance zone for the shaft, select the corresponding combination of a basic deviation (a ... zc) and a tolerance zone (1 ... 18) in pop-up lists in this row.

Though the general sets of basic deviations (a ... zc) and tolerance grades (IT1 ... IT18) can be used for prescriptions of shaft tolerance zones by their mutual combinations, in practice only a limited range of tolerance zones is used. An overview of tolerance zones specified for general use can be found in the table in paragraph [1.3]. The tolerance zones which are not included in the selection are considered special zones and their use is recommended only in technically well-grounded cases.

### 1.11 Parameters of the selected fit.

Parameters of the selected fit are calculated and mutual positions of tolerance zones of the hole and shaft are displayed in this paragraph.

## ANSI B4.1:  Preferred limits and fits for cylindrical parts. [2]

This paragraph can be used for selection of a preferred fit of cylindrical parts according to ANSI B4.1. This standard defines a system of dimensional tolerances and prescribes a series of those preferred fits of cylindrical part, which are specified for preferred use.

### 2.1 Basic size.

It is the size whose limit dimensions are specified using the upper and lower deviations. In case of a fit, the basic size of both connected elements must be the same.

### 2.2 Tolerance of a basic size for specific tolerance grade.

The tolerance of a size is defined as the difference between the upper and lower limit dimensions of the part. The standard ANSI B4.1 implements 10 tolerance grades to meet the requirements of various production branches for accuracy of products. The system of tolerances is prescribed by the standard for basic sizes up to 200 in.

### 2.4 System of fits.

The standard ANSI B4.1 defines two basic methods of coupling of holes and shafts for the selected series of preferred fits.

1. Hole basis system
In this system of tolerances and fits, the lower deviation of the hole is always equal to zero.
2. Shaft basis system
In this system of tolerances and fits, the upper deviation of the hole is always equal to zero.

where:

d=D ... basic size
////  ... hole tolerance zone
\\\\  ... shaft tolerance zone

The option of the system for the specified type of product or production is always influenced by the following factors:

• Constructional design of the product and the method of assembly.
• Production procedure and costs for machining the part.
• Type of semi-product and consumption of material.
• Costs for purchase, maintenance and storage of gauges and production tools.
• Machine holding of the plant.
• Options in use of standardized parts.

### 2.5 Type of fit.

The standard ANSI B4.1 divides the series of preferred fits into three basic groups according to the type and field of use.

1. Running or sliding fits [RC]
This includes fits with guaranteed clearances which are specified for movable couplings of those parts which have to run or slide one against the other.
2. Locational fits [LC, LT, LN]
This includes clearance or interference fits specified for precise locational positioning of coupled parts. The coupled parts must be fixed mechanically to prevent one moving against the other during assembly. Depending on the locational positioning of tolerance zones of the coupled parts, 3 types of these fits may be distinguished: Clearance fits [LC], interference fits [LN] and transition fits [LT].
3. Force or shrink fits [FN]
This includes guaranteed interference fits specified for fixed (non-demountable) couplings of parts.

Each of these groups is marked using a literal abbreviation, which together with a numerical specification of the class of fit unambiguously defines the selected fit.

### 2.6 Fit.

Select a suitable fit from the pop-up list.

Properties and field of use of preferred fits are described in the following overview. When selecting a fit it is often necessary to take into account not only constructional and technological but also economic aspects. Selection of a suitable fit is important particularly in view of those measuring instruments, gauges and tools which are implemented in the production. Therefore, follow proven plant practices when selecting a fit.

#### Running or sliding clearance fits [RC]:

Fits with guaranteed clearance designed for movable couplings of parts (pivots, running and sliding fits of shafts, guiding bushings, sliding gears and clutch disks, pistons of hydraulic machines, etc.). The parts can be easily slid one into the other and turn. The tolerance of the coupled parts and fit clearance increases with increasing class of the fit.

RC 1: Close sliding fits with negligible clearances for precise guiding of shafts with high requirements for fit accuracy. No noticeable clearance after assembly. This type is not designed for free run.

RC 2: Sliding fits with small clearances for precise guiding of shafts with high requirements for fit precision. This type is not designed for free run; in case of greater sizes a seizure of the parts may occur even at low temperatures.

RC 3: Precision running fits with small clearances with increased requirements for fit precision. Designed for precision machines running at low speeds and low bearing pressures. Not suitable where noticeable temperature differences occur.

RC 4: Close running fits with smaller clearances with higher requirements for fit precision. Designed for precise machines with moderate circumferential speeds and bearing pressures.

RC 5, RC 6: Medium running fits with greater clearances with common requirements for fit precision. Designed for machines running at higher speeds and considerable bearing pressures.

RC 7: Free running fits without any special requirements for precise guiding of shafts. Suitable for great temperature variations.

RC 8, RC 9: Loose running fits with great clearances with parts having great tolerances. Fits exposed to effects of corrosion, contamination by dust and thermal or mechanical deformations.

#### Locational clearance fits [LC]:

Fits with guaranteed clearances, designed for unmovable couplings where easy assembly and disassembly is required (precise fits of machines and preparations, exchangeable wheels, bearing bushings, retaining and distance rings, parts of machines fixed to shafts using pins, bolts, rivets or welds, etc.). The coupled parts must be fixed mechanically to prevent one moving against the other during assembly. These fits are defined by the standard in a wide range of tolerances and clearances, from tight fits with negligible clearances designed for precise guiding and centring of parts [LC 1, LC 2] up to free fits with great clearances and maximum tolerances [LC 10, LC 11] where easy assembly is the primary requirement. The tolerance of coupled parts and fit clearance increases with increasing class of the fit.

#### Locational transition fits [LT]:

These types include clearance or interference fits designed for demountable unmovable couplings where precision of fits of the coupled parts is the main requirement. The part must be fixed mechanically to prevent one moving against the other during assembly.

LT 1, LT_2: Tight fits with small clearances or negligible interferences (easy detachable fits of hubs of gears, pulleys and bushings, retaining rings, bearing bushings, etc.). The part can be assembled or disassembled manually.

LT 3, LT_4: Similar fits with small clearances or interferences (demountable fits of hubs of gears and pulleys, manual wheels, clutches, brake disks, etc.). The parts can be coupled or disassembled without any great force by using a rubber mallet.

LT 5, LT_6: Fixed fits with negligible clearances or small interferences (fixed plugs, driven bushings, armatures of electric motors on shafts, gear rims, flushed bolts, etc.). Assembly of parts using low pressing forces.

#### Locational interference fits [LN]:

Fits with small interferences designed for fixed couplings where precision and rigidity of fits of the coupled parts is the main requirement. These fits cannot be used for transfers of torsional moments using friction forces only; the parts must be secured to prevent one moving against the other. The parts can be assembled or disassembled using cold pressing and greater forces or hot pressing.

#### Force or shrink fits [FN]:

Fits with guaranteed interferences designed for fixed (undetachable) coupling of parts (permanent couplings of gears with shafts, bearing bushings, flanges, etc.). These fits are designed, above all, for transfers of torsional moments using friction forces between shafts and hubs. The amount of interference (loading capacity of the fit) increases with increasing class of the fit. Mounting of the parts using cold pressing with great pressing forces at different temperatures of the parts.

FN 1: Light drive fits with small interferences designed for thin sections, long fits or fits with cast iron external members.

FN 2: Medium drive fits with medium interferences designed for ordinary steel parts or fits with high-grade cast iron external members.

FN 3: Heavy drive fits with great interferences designed for heavier steel parts.

FN 4, FN_5: Force fits with maximum interferences designed for highly loaded couplings.

### 2.7 Hole tolerance zone.

The tolerance zone is defined as a spherical zone limited by the upper and lower limit dimensions of the part. The tolerance zone is therefore determined by the amount of the tolerance and its position related to the basic size.

Limit deviations of the hole tolerance zone are calculated in this paragraph for the specified basic size [2.1] and selected hole tolerance zone. The respective hole tolerance zone is set up according to the preferred fit selected in row [2.6].

### 2.8 Shaft tolerance zone.

The tolerance zone is defined as a spherical zone limited by the upper and lower limit dimensions of the part. The tolerance zone is therefore determined by the amount of the tolerance and its position related to the basic size.

Limit deviations of the shaft tolerance zone are calculated in this paragraph for the specified basic size [2.1] and selected shaft tolerance zone. The respective shaft tolerance zone is set up according to the preferred fit selected in row [2.6].

### 2.9 Parameters of the selected fit.

Parameters of the selected fit are calculated and mutual positions of tolerance zones of the hole and shaft are displayed in this paragraph.

## ISO 2768-1:  General tolerances for linear and angular dimensions without individual tolerance indications. [3]

All dimensions of machine parts prescribed in the production documentation should be specified using limit dimensions (tolerances) to avoid any uncertainty and dispute during production, checks and assembly. Important functional dimensions (particularly those that could cause confusion in mounting of the parts) are tolerated usually individually by the addition of a tolerance mark or numerical value of the deviation to the respective basic size. Other dimensions where high precision of production is not required can be tolerated using a general record in the drawing. The standard ISO 2768-1:1989 is an internationally recognized standard for tolerancing of these linear and angular dimensions.

The standard ISO 2768-1 is designed for tolerancing of dimensions of machine parts produced using cutting operations or forming of sheets. It is advisable to use limit deviations defined here also with non-metallic materials. This standard prescribes limit deviations of linear and angular dimensions in four classes of accuracy. When choosing a tolerance class it is necessary (in addition to the constructional aspects) to also take into account, above all, the usual accuracy of the production shop.

General limit deviations according to ISO 2768-1 are divided into 3 groups (tables): Limit deviations for linear dimensions [3.1], limit deviations for broken edges [3.2] and limit deviations for angular dimensions [3.3]. With dimensions up to 0.5mm (tables [3.1, 3.2]) the limit deviations are prescribed right after the respective basic size.

## Design of fit for specific allowance. [4]

This paragraph can be used for a design (matching) of a suitable standardized fit of machine parts for a known clearance or interference respectively. The fit design is based on the standard ISO 286 (see [1]). The fit design is processed automatically and after its completion, the calculation provides the user with a set of 15 fits whose parameters meet the best requirements entered in paragraph [4.1].

### 4.2 System of fit.

Although there can be generally coupled parts without any tolerance zones, only two methods of coupling of holes and shafts are recommended due to constructional, technological and economic reasons.

1. Hole basis system
The desired clearances and interferences in the fit are achieved by combinations of various shaft tolerance zones with the hole tolerance zone "H". In this system of tolerances and fits, the lower deviation of the hole is always equal to zero.
2. Shaft basis system
The desired clearances and interferences in the fit are achieved by combinations of various hole tolerance zones with the shaft tolerance zone "h". In this system of tolerances and fits, the upper deviation of the hole is always equal to zero.

where:

d=D ... basic size
////  ... hole tolerance zone
\\\\  ... shaft tolerance zone

The option of the system for the specified type of product or production is always influenced by the following factors:

• Constructional design of the product and the method of assembly.
• Production procedure and costs for machining the part.
• Type of semi-product and consumption of material.
• Costs for purchase, maintenance and storage of gauges and production tools.
• Machine holding of the plant.
• Options in use of standardized parts.

### 4.3 Type of fit.

Depending on the mutual position of tolerance zones of the coupled parts, 3 types of fit can be distinguished:

1. Clearance fit
It is a fit that always enables a clearance between the hole and shaft in the coupling. The lower limit size of the hole is greater or at least equal to the upper limit size of the shaft.
2. Transition fit
It is a fit where (depending on the actual sizes of the hole and shaft) both clearance and interference may occur in the coupling. Tolerance zones of the hole and shaft partly or completely interfere.
3. Interference fit
It is a fit always ensuring some interference between the hole and shaft in the coupling. The upper limit size of the hole is smaller or at least equal to the lower limit size of the shaft.

### 4.4 Basic size.

Enter a common theoretical size of the coupled parts.

### 4.5, 4.6 Limit deviations for the fit.

Depending on the selected type of fit [1.3], enter desired limit values of clearance or interference resp. of the designed fit in rows [4.5, 4.6].

### 4.7 Design and selection of the fit.

This paragraph can be used for the fit design itself. After setting all desired parameters of the fit in paragraph [4.1], initiate automatic fit design using the button on this row. The design processes all combinations of prescribed hole and shaft tolerance zones (see tables in paragraphs [1.3, 1.4]) and selects 15 optimal standardized fits. The user is informed on processing of the calculations in a dialogue.

The qualitative criterion for selection of a fit includes a sum of deviations (in absolute values) of limit values of the clearance or interference resp. of the designed fit from desired values [4.5, 4.6]. After completion of calculations, the selected fits are transferred to the table. The table of designed fits is divided into two parts. The lower part includes selected fits listed from the best to the least optimal. The upper part of the table gives one of the preferred fits, particularly the one whose parameters best meet the desired limit deviations [4.5, 4.6]. After selection of any fit in the table, its parameters are displayed in paragraph [4.8].

### 4.8 Parameters of the selected fit.

Parameters of the selected fit are calculated and mutual positions of tolerance zones of the hole and shaft are displayed in this paragraph.

## Relationship of tolerance to surface finish. [5]

This paragraph includes a table describing the relationship of surfaces of machine parts to their dimensional tolerances. Individual tolerance grades available for the given method of machining of the parts are marked in the table using a green field.

## Setting calculations, change the language.

Information on setting of calculation parameters and setting of the language can be found in the document "Setting calculations, change the language".

## Workbook modifications (calculation).

General information on how to modify and extend calculation workbooks is mentioned in the document "Workbook (calculation) modifications".