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Calculation of Tolerance Stacks Using Direct-Position Approach in Geometric Dimensioning and Tolerancing Abstract

Formulas for the calculation of position tolerance stacks of Geometric Dimensioning and Tolerancing (GD&T) are presented. This direct-position approach shows that the formulas can be observed directly from the extreme positions of the holes specified in an engineering drawing. When compared to other approaches for tolerance stacks, this method can be applied to all three material conditions (Maximum Material Condition, Least Material Condition, and Regardless of Feature Size.) and is easier for students to learn and remember the formulas. A graphical demonstration using position control on two holes in an engineering drawing is applied to explain the approach.

1. Introduction

Tolerance stacks are used to describe the problem-solving process in calculating the effects of the accumulated variation that is allowed by specified dimensions and tolerances, which are typically specified on an engineering drawing. Arithmetic tolerance stacks use the worst-case maximum or minimum values of dimensions and tolerances to calculate the maximum and minimum distances between holes or between a hole and the edge of a part1,2. The application is particularly important in the design stage to maintain a specified minimum solid distances in the part. In addition, stack analysis enables parts to be made precise enough to be assembled interchangeably with the largest possible tolerances permitted by part specification.

Several methods are proposed to calculate tolerance stacks using the approaches of graphs, charts, tables, and formulas3,4,5. However, they are all very complicated for students to learn. A graphical approach called gage method, using the concept of functional gages, seems to provide an effective way for this purpose2. However, as the functional gages can only be applied to the Maximum Material Condition (MMC), this method can not be applied to other two material conditions: Least Material Condition (LMC) and Regardless of Feature of Size (RFS). In this paper, the direct-position method is proposed to derive the formulas for tolerance stacks. The method not only is easier for students or designers to understand and remember, but can be applied to three material conditions, which are explained in the following session. A graphical example using position control on three material conditions is applied to demonstrate the approach.

2. Three Material Conditions

Based on the design and manufacturing needs, geometric tolerances can be specified with different material conditions, which include Maximum Material Condition (MMC), Least Material Condition (LMC), and Regardless of Feature Size (RFS). Characteristics of each material condition are described in the following paragraphs.

2.1. Maximum Material Condition (MMC)

To indicate that a geometric tolerance is specified with MMC, a symbol m is added to either a geometric characteristic or a datum. Maximum Material Condition is particularly defined as having the maximum solid volume for a part. Therefore, for internal parts (such as holes or grooves, etc.), MMC is at its minimum feature of size (FOS). For external parts (such as pins or studs, etc.), MMC is at its maximum feature of size. When a geometric characteristic is specified with MMC, the geometric tolerance may have a bonus tolerance when its FOS is approaching to its Least Material Condition (LMC). Figure 16 shows a design drawing using MMC Position Tolerance with Datum A as the center axis of the φ0.8 hole. From the table shown in this figure, when the diameter of a part is measured at 1.02, which is the MMC, there is no

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Lin, C. (2009, June), Calculation Of Tolerance Stacks Using Direct Position Approach In Geometric Dimensioning And Tolerancing Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--4568