## Geometry and tolerances

In many instances the geometry associated with tolerances is of significance and the geometry itself needs to be defined by tolerances such that parts fit, locate and align together correctly. Tolerances must therefore also apply to geometric features. The table in Figure 5.13 shows the commonly used geometric tolerance (GT) classes and symbols. These are a selection from ISO 1101:2002. The use of geometric tolerances is shown by three specific examples that are discussed in detail in the following paragraph.

 Features and tolerance Toleranced characteristics Symbols Single features Form tolerances Straightness — Flatness O Circularity O Cylindricity a Single or related features Profile of any line r\ Profile of any surface Related features Orientation tolerances Parallelism // Perpendicularity _L Angularity ¿L Location tolerances Position Concentricity & coaxiality 1 @ Symmetry • Run-out tolerances Circular run-out / Total runout | //

Figure 5.13 Geometric tolerance classes and symbols

### Figure 5.13 Geometric tolerance classes and symbols

Figure 5.14 shows the method of tolerancing the centre position of a hole. A 10mm diameter hole is positioned 20mm from a corner. The dimensions show the hole centre is to be 20,00 ± 0,1mm (i.e. a tolerance of ±100um) from each datum face. This means that to pass inspection, the hole centre must be positioned within a 200um square tolerance zone. However, it would be perfectly acceptable for the hole to be at one of the corners of the square tolerance zone, meaning that the actual centre can be 140um from the theoretical centre. This is not what the designer intended and GTs are used to overcome this problem. The method of overcoming this problem is shown in the lower diagram in Figure 5.14. In this case the tolerances associated with the 20mm dimensions are within a GT box. Thus, the 20mm dimensions are only nominal and are enclosed in rectangular squares. The GT box is divided into four compartments. The first compartment contains the GT symbol for position, the next compartment contains the tolerance, and the next two boxes give the datum faces (A and B), being the faces of the corner. Using this GT box, the hole deviation can never be greater than lOOum from the centre position.

Figure 5.15 is another example of hole geometry but in this case, the axis of the hole. A dowel is screwed into a threaded hole in a plate. Another plate slides up and down on this dowel. If the axis of the threaded hole is not perpendicular to the top face of the lower plate, the resulting dowel inclination could prevent assembly. By containing the hole axis within a cylinder, the inclination can be limited. The geometrical tolerance box shows the hole axis limits

Figure 5.14 Two methods of tolerancing the centre position of a hole

Figure 5.14 Two methods of tolerancing the centre position of a hole

Case 1 - Dowel perpendicular: Case 2- Dowel inclined: assembly possible. assembly impossible.
Figure 5.15 Method of geometric tolerancing the axis perpendicularity of a hole

which allow assembly. In this case the GT box is divided into three compartments. The left-hand compartment shows the perpendicularity symbol (an inverted 'T') which is shown to apply to the M10 hole, via the leader line and arrow. The right-hand compartment gives the perpendicularity datum that in this case is face 'A'. This is the upper face of the lower plate. This information says that the inclination angle is limited by a cylindrical zone that is 30um in diameter over the length of the hole (the 15mm thickness of the

Maximum limit o( size

| Drawing

Maximum limit o( size

[Interpretation

Figure 5.16 Method of geometric tolerancing straightness and roundness ofa cylinder

[Interpretation

Figure 5.16 Method of geometric tolerancing straightness and roundness ofa cylinder lower plate). Thus, the dowel inclination is limited and the upper plate will always assemble.

Figures 5.14 and 5.15 relate to the hole position and axis alignment but nothing has been said about the straightness of the dowel. This situation is considered in the example in Figure 5.16. The dowel has the dual purpose of screwing into the lower plate and locating in the upper plate. If the dowel has a non-circular section or is bent, it may be impossible to assemble. In Figure 5.16, GTs are applied to the outside diameter of the dowel which limits the deviation from a theoretically perfect cylinder. In this case three things are specified using two geometric tolerance boxes and one toleranced feature (the diameter). These are the diametrical deviation, the out-of-roundness and the curvature. The left-hand drawings show the theoretical situation with the cylinder dimensioned in terms of the above three factors. The nominal diameter is 10mm with an h7 tolerance (i.e. 0 and -0,015mm). This means in that whatever position the two-point diameter is measured, the value must be in the range 9,985 to 10,000mm. The out-of-roundness permitted is given in the lower geometric tolerance box. It has two compartments. The left-hand compartment shows the circle symbol (referring to circularity) and the right-hand compartment contains the value of 20um. This means that the out-of-roundness must be contained within two concentric circles that have a maximum circularity deviation of 20um. The upper tolerance box gives the information on straightness. It has two compartments. The left-hand compartment shows the symbol for straightness (a straight line) and the right-hand compartment contains the value 60um. This means that the straightness deviation of any part of the outside diameter outline must be contained within two parallel lines which are separated by 60um.

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### Responses

• proserpina
How to use geometric tolerances in engineering drawing?
8 years ago
• paul
How to show tolerances on a engineering drawing?
8 years ago
• eyob
What does a 3 box geometrical tolerance mean?
8 years ago