Tolerance analysis
The tolerance analysis is a method of describing and analyzing the effects of manufacturing defects in multi-stage production processes. The result of a tolerance analysis is a mathematical model that describes the relationship between the process capabilities of individual manufacturing steps and the resulting process capabilities for higher-level product features.
Every manufacturing process has a finite manufacturing accuracy . Every component produced therefore shows small deviations from its ideal geometry . If components with geometric deviations are further processed in a multi-stage production process, the geometric errors of the individual parts add up. If components are joined in an assembly process, for example, the geometric errors of the individual parts are transferred to the assembly. The geometric quality of the end product is determined by the quality of the individual parts.
The geometries of the individual parts and the parameters of the manufacturing processes must be tolerated in such a way that the overarching quality requirements of the customer with regard to function and appearance are met. The tolerance analysis is used to forecast the achievable manufacturing quality based on the tolerances of the individual parts and processes involved. The causal relationship between the relevant contributors and a technical parameter to be examined is also referred to as a tolerance chain. If it is a question of geometric dimensions, then according to DIN 7186 , one speaks of individual dimensions and closed dimensions . The tolerance chain describes the relationship between the individual dimensions and the respective closed dimensions.
Arithmetic tolerance calculation
The classic arithmetic tolerance calculation is based on the approach of complete interchangeability. It ensures compliance with the required tolerance for the examination feature for any combination of components. This procedure results in very small tolerances for the geometric elements of the individual parts and the parameters of the manufacturing process. These small tolerances can only be maintained through the use of complex manufacturing processes. Due to the associated high production costs, this type of tolerance calculation is used for particularly function-critical or safety-relevant features.
Statistical tolerance calculation
The exact characteristics of a finished workpiece cannot be predicted. However, the behavior of a large number of manufactured components can be described statistically. The statistical tolerance calculation provides a forecast of the distribution of an examination feature based on the statistical distributions of the elements of the tolerance chain. By taking into account the stochastic distribution of the elements of the tolerance chain, the statistical tolerance calculation represents reality better than the arithmetic tolerance calculation.
The need for process and design optimization measures can be derived from the prognosis of the manufacturing quality through the tolerance analysis. The optimization process is supported by the mathematical model of the tolerance chain, as it quantifies the effects of individual tolerances on the examination feature. According to the Pareto principle , the optimization process should focus on the main contributors, i.e. H. the individual tolerances, which have a strong effect on the expression of the examination characteristic.
Individual evidence
- ↑ Stefan von Praun: Tolerance analysis of flexible assemblies in the product creation process. (PDF) January 24, 2002, accessed October 30, 2019 .