Statistical process control of one-side toleranced geometrical features in precision machining

project sponsor: German Research Foundation (DFG)
project leader:  Prof. (em.) Dr. Dr. H. Trumpold
project number:  Special Research Complex (SFB) 326, part P4
researcher Dipl.-Ing. C. Pertuch
research period 01.01.1993 - 31.12.1998

The demands of the customers on the products relating to their quality characteristic (for example accuracy, reliability, safety and life span) rise up more and more. These rising demands lead to smaller dimensions and tolerances of the products, assemblies and components. By smaller dimensions and tolerances not only the deviations of the measures are important but also the deviations of the geometrical tolerances and the surface roughness.
Currently the process control is achieved by measurement of form, location and roughness individually. With this measurement the results are only checked against their tolerance limits. There are no control systems available, that consider the statistical character of these one-sided toleranced features.

The aim of this research project it's, to develop a control system for the moni-toring, the analysis and the control of this one-side toleranced features. The in-vestigations about this one-side toleranced features were supported by grinding examples of the deviations from roundness, from parallelism, from straightness and of the parameters of surface roughness. For that purpose measurements were made of a process in a factory and in our own experimental workshop.

The results of our investigations shown clearly, that the model distributions of one-side toleranced geometrical features can not often described through a normal distribution. The best descriptions for the whole or current distribution of one-sided toleranced features are often the folded normal distribution and the logarithmical normal distribution. For large measuring values of the one-sided toleranced features also the normal distribution can be used approximately. For smaller measuring values is this not longer possible because of the skewness of the distribution due to the accumulation of measuring values in the near of the lower natural limit. The behaviour of the folded normal distribution by different standard deviations is shown in figure 1.

Figure 1: Behaviour of the folded normal distribution by a constant mean value µ = 1 and different standard deviations' 

In the actual working period were also investigated different possibilities for application of statistical methods by one-sided toleranced features. As an example is shown in figure 2 the influence of the assumed model distribution of the capability factors.
Figure 2: influence of the model distribution of the capability factors

The actual works are occupied with investigations about the wearout of a grinding wheel of the roughness. Additional will be investigated the influence of lack of balance of the grinding wheel.

Letzte Änderung: 10. März 2000
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