On Functional Tolerances in Machine Design
Doctoral thesis, 1995
This thesis describes a method that allows tolerances on critical dimensions to be assigned with respect to both quality and manufacturing cost. To be able to quantify and include customer needs in the process of assigning tolerances, the concept of functionality loss is used. Functionality loss, as used here, differs from the concept of quality loss suggested by Taguchi. Loss functions are here determined using known (or quantifiable) physical relations between critical dimensions and quality aspects of interest. Here, only parameters (in this case dimensions) that have a major influence on an important quality aspect of a product are studied. Functionality loss caused by a critical dimension may, for example, be the maintenance cost related to the life of a component, or the operating cost related to the efficiency of a component.
A minimum manufacturing cost curve is used to describe the minimum manufacturing cost for every tolerance of a critical dimension. This curve represents the manufacturing cost on a competitive market, and the price of a product is assumed to be a function of the minimum manufacturing cost.
The total loss to customer is here defined as the total potential cost, due to the choice of tolerances a product will cause the user over a certain period of time. The total loss is defined as the sum of the functionality loss and the tolerance-dependent part of the product price. The optimal tolerance of a critical dimension is the one representing the minimum total loss for the customer.
If the functionality loss is asymmetrical with respect to the functional target, a manufacturing target that deviates slightly from the functional target may allow somewhat looser manufacturing tolerances without compromising the function of the product. This may result in lower manufacturing cost and may also increase the robustness to the design. The optimal combination of nominal value (manufacturing target) and tolerance is again the one that minimizes the total loss to customer. A worst case approach is used throughout this work to determine the total tolerance-dependent loss to customer that may occur.
The implementation of the method in an integrated CAD/CAM system is discussed and a prototype system is developed. The prototype system allows the designer to graphically define tolerance chains on the drawing. Tolerances in a tolerance chain may then be determined using cost minimization or by cost/loss optimization.
computer aided tolerancing