Design of Mechanical Elements

4Tolerances

4.1 Introduction

Manufacturing processes are imperfect, which inevitably leads to variations of the geometry, dimensions, and properties of a mechanical element. Thus, prescribing, controlling, and verifying the allowable variation of the design specifications of a mechanical element is important to ensure that (i) it will perform its function, and (ii) it will fit and operate together with other mechanical elements in a mechanical assembly, such as a device or a machine. In mechanical design, we explicitly control the allowable variation of design specifications by prescribing tolerances.

In this chapter, we discuss how to consider tolerances for design specifications of mechanical elements such that they fit with other elements and reliably perform their function within an assembly with other mechanical elements. We specifically focus on tolerances of dimensions of a mechanical element. Furthermore, we discuss tolerance stacks, i.e. multiple tolerances “in series” or “stacked,” to understand how we determine the tolerance of a dependent variable that is a function of any number of independent variables, each with a prescribed tolerance. Finally, we describe and calculate the worst‐case and statistical error of a dependent variable that relates to any number of independent variables.

4.2 Terminology

A tolerance is defined as the allowable limit of variation of a design specification. We always use the following informal engineering rule: “As coarse as possible, ...