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Chapter Four Fits and Tolerances: Linear and Geometry

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**Purpose This chapter provides an overview of how to:**

analyse the effect of linear tolerances when applied to fits of mating components competently use standard tables of linear fits and tolerances understand the basic types of geometry tolerances available for common usage select and apply geometry tolerances to component features to ensure a satisfactory performance on assembly.

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**Linear fits and tolerances**

Tolerance – the amount of variation in size which is tolerated. Cost more to produce a narrow tolerance; therefore, use maximum tolerance without sacrificing quality.

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**Linear fits and tolerances**

Shaft – a member that fits into another member; may be stationary or rotating. Hole – the member that fits or houses the shaft; may be stationary, rotating or the space between two restrictions into which a member has to fit. Nominal size – the size by which an item is designated for convenience. Basic size – the size from which the limits of size are derived.

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**Linear fits and tolerances**

Limits of size – extremes of allowable size; that is ‘upper limit of size’ and ‘lower limit of size’. Deviation – difference between basic size and actual size. Tolerance – the difference between the maximum and minimum limits of size for a hole or shaft. Fit – the relative motion between a shaft and a hole resulting from the final size achieved in manufacture.

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**Linear fits and tolerances**

Clearance fit – shaft size is always less than hole size. Transition fit – sizes specified for a matching hole and shaft allow either a clearance of interference fit. Interference fit – shaft size is always larger than the hole size. Note: refer to Figures 4.1 and 4.2, p.67, for comparison between three fits.

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**Linear fits and tolerances**

Allowance – the minimum clearance or maximum interference which exists between mating parts. Grades of tolerance – represents the size of tolerance zone dictating the degree of accuracy of the machining process (18 grades of tolerance in the ISO system). Refer to Figure 4.3, p.68. Bilateral limits – the tolerance is equally disposed above and below the basic size. Refer to Figure 4.5, p.74.

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**Linear fits and tolerances**

Unilateral limits – one limit is the basic size and the other is above or below the basic size. Fundamental deviation of tolerance – determines the maximum and minimum amounts of clearance or interference which are possible for a particular size of tolerance zone. See Figure 4.4, p.69, for an example and Figure 4.5, p.74, for graphical illustration. In the ISO system there are 28 fundamental deviations provided for each of the 18 grades of tolerance on both shafts and holes.

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**Standard tables of linear fits and tolerances**

The hole basis system – the hole is considered a fixed size and the shaft is varied to suit (most commonly used). Table 4.1(a), pp.70–71 is based on this system (also known as the unilateral hole- basis system). Shaft basis system – the shaft is considered a fixed size and the hole is varied to suit (e.g. bearings are a fixed size, hole machined to suit). Table 4.1(b), pp.72–73, is based on this system (also known as the unilateral shaft-basis system).

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**Standard tables of linear fits and tolerances**

A hole is designated by an upper case letter followed by a number (e.g. H9). A shaft is designated by a lower case letter followed by a number (e.g. d10). The complete fit would be H9/d10. A 50mm basic size with a H9/d10 classification would have tolerance limits identified from Table 4.1(a) of:

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**Standard tables of linear fits and tolerances**

A description of each type of fit represented on the data sheet is on p.75. Tolerances are applied where the dimension is critical to the function of the component or dimensions that have unusually large variations. General tolerance – normally recorded in note form and apply when same tolerance is applicable to entire drawing, different tolerances apply to various ranges of sizes or for a particular type of member. Refer to p.76.

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**Standard tables of linear fits and tolerances**

Tolerancing angular dimensions General non-critical tolerances may be selected from Table 4.3, p.76, limits of size, bilateral limits and unilateral limits are shown in Figure 4.7, p.77. Limits of size – the upper limit (maximum) of size is placed above the dimension line, the lower limit (minimum) of size is placed below the dimension line (Figure 4.8, p.77).

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**Standard tables of linear fits and tolerances**

Bilateral tolerances – basic size followed by tolerance limits above and below the basic size. Unilateral tolerances – the basic size followed by an allowable variation in one direction only (variation of size can only occur above or below the basic size). Refer to Figure 4.10, p.77.

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**Standard tables of linear fits and tolerances**

Methods of dimensioning to avoid accumulation of tolerances. Chain dimensioning can result in an accumulation of sizes; this can be avoided by omitting one of the chain of dimensions as shown in Figure 4.11, p.78. Progressive dimensioning from a fixed datum ensures that accumulation of tolerances does not occur; see Figure 4.12, p.78. The method used will depend on the functional relationship of the dimensions.

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**Assembly of components**

In the design of mechanical assemblies, the cumulative effect of assembled component tolerances is controlled to ensure satisfactory operation of the product. Two types of component assemblies is possible, external and internal.

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**Assembly of components**

External assembly – a combination of two or more components which, when added together dimensionally, form an external overall dimension. See Figure 4.13 and ‘Components assembled externally’ on p.79. Internal assembly – a combination of one or more components added together to fit the internal dimension of the final component of the assembly. See Figure 4.14 and ‘Components assembled internally’ CASE 1 and CASE 2 on p.79.

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Geometry tolerancing Dimension size tolerancing takes no account of errors which may occur in the geometrical shape of form of the elements. Interchange ability of components is essential for mass produced components; the control of both size dimensions and the geometrical shape of critical features is of prime importance. Geometry tolerances are used to specify the form, profile, orientation, location and runout of features.

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Geometry tolerancing The type of geometry tolerance to be used is specified on a drawing by the use of symbols applied in accordance with AS1100 Part 101 and shown in Table 4.4, p.83.

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**Geometry tolerancing Terms used in geometry tolerancing:**

Feature – used to identify a part of or a portion of a component. Maximum material condition (MMC) – a feature at its maximum material size allowed by its tolerance; refer to Figure 4.24(b), p.83. Least material condition (LMC) – a feature at its minimum material size allowed by its tolerance; refer to Figure 4.24(c).

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Geometry tolerancing Virtual size – dimension of overall envelope which touches the highest points (Figure 4.24(c) and 4.25). Datum – a point, line, plane or other surface from which dimensions are measured or to which geometry tolerances are referenced. Maximum material principle – the allowable error in geometry of two mating features allowed to increase as the size of the feature decreases from the maximum material condition to the minimum material condition. Governed by the symbol , common uses of this symbol are covered in sections 1–5, pp.84–85.

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**Methods of displaying geometry tolerances**

Two methods are used to display geometry tolerances on a drawing: Tolerance frame method – used when there are no more than three simple groups of geometry tolerance. Tabular method – used when the geometry tolerances are complex or are more than three in number (not described in this book).

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**Methods of displaying geometry tolerances**

Tolerance frame method – comprises a number of boxes readable from the bottom of the drawing. The symbol box and tolerance value box are the minimum necessary to state a geometry tolerance; refer to Table 4.5 no. 1, p.87. A datum feature is a part of a component drawing used as a reference from which to establish a required geometry tolerance.

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**Basic concepts of geometry tolerancing**

A geometry tolerance applied to a feature defines the tolerance zone within which the feature shall be contained (e.g. space between two equidistant lines, space within a circle, etc.). A toleranced feature may take any form or orientation within the tolerance zone, unless it is necessary to apply some restriction which is indicated by an explanatory note.

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**Interpretation of geometry tolerancing**

Flatness – used to control the flatness of a surface. Refer to Table 4.5, no. 3, p.87. Straightness – used to control the straightness of a line, an axis in a single plane or the axes of solids of revolution. Refer to case 1, 2 and 3, p.86, and Table 4.5 no's 4, 5 and 6, p.87.

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**Interpretation of geometry tolerancing**

Perpendicular – used to control the squareness of a lines to a datum line, an axis to a datum line, and a surface to a datum line and/or datum plane. Refer to case 1, 2, 3 and 4, p. 86, and Table 4.5, no's 7, 8, 9, 10 and 11, pp.87–88. Position – used to control the location of a feature by limiting its deviation from a specified true position (i.e. a hole axis, a surface). See Table 4.5, no's 12, 13 and 14, p.89.

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**Interpretation of geometry tolerancing**

Concentricity – used to control two or more features such as circles, spheres, cylinders, cones or hexagons which share a common axis. Refer to Table 4.5, no's 15, 16 and 17, p.89. Symmetry – used to control features symmetrically disposed either side of a centre line or centre plane of another feature which is specified as the datum. Refer to Table 4.5, no’s 18, 19, 20 and 21, p.90.

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**Interpretation of geometry tolerancing**

Cylindricity – specifies tolerance zone between two co-axial cylinders within which the entire cylindrical surface of the feature being controlled must lie. See Table 4.5, no. 22, p.90. Profile – applied to control the profile of a line (Table 4.5, no. 23) or the profile of a surface (Table 4.5, no’s. 24–27, p.91).

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**Interpretation of geometry tolerancing**

Angularity – used to control angular relationships between strait lines or surfaces with straight line elements such as flat or cylindrical surfaces. Refer to Table 4.5, no’s. 28, 29 and 30, p.92. Parallelism – used to control the orientation of features related to one another by an angle of zero degrees. See Table 4.5, no’s. 31, 32, 33 and 34, pp.92–93.

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**Interpretation of geometry tolerancing**

Circularity – specifies the width of an annular tolerance zone, bounded by two concentric circles in the same plane, within which the circumference of the feature must lie. See Table 4.5, no’s 35 and 36. Runout – the allowable deviation in position of a surface of revolution as a part is revolved about a datum axis. See Table 4.5, no’s 37 and 38.

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**Analysis and use of geometry tolerances on a drawing**

Fig 4.33, p.96, illustrates the use of geometry tolerances with linear tolerances to control size and form and geometric tolerances to control true positioning. Principle of independency – the limits control only the size of the feature and provide no other control over its form. Envelope principal (identified by the symbol ) – size and form are both controlled.

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Figure 4.33

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Summary It costs more to produce to a narrow tolerance, therefore the amount of variation in size and form, which is tolerated for an item without sacrificing quality, is ideal and known as linear and geometric tolerancing.

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