Abstract
Statistical tolerance analysis based on Monte Carlo simulation can be applied to obtain a cost-optimized tolerance specification that satisfies both the cost and quality requirements associated with manufacturing. However, this process requires time-consuming computations. We found that an implementation that uses the graphics processing unit (GPU) for vector-chain-based statistical tolerance analysis scales better with increasing sample size than a similar implementation on the central processing unit (CPU). Furthermore, we identified a significant potential for reducing runtime by using array vectorization with NumPy, the proper selection of row- and column- major order, and the use of single precision floating-point numbers for the GPU implementation. In conclusion, we present open source statistical tolerance analysis and statistical tolerance synthesis approaches with Python that can be used to improve existing workflows to real time on regular desktop computers.
Highlights
Manufactured components are subject to deviations that reduce the functional and aesthetic quality of the final product
We discuss the results of the Statistical Tolerance Synthesis and determine, based on an appropriate sample size, which of the two best open source implementations is more appropriate for the underlying tolerance problem
With the approaches presented in this study, it is possible to reduce the runtime of vector-chain-based statistical tolerance analysis to real time and to drastically speed up statistical tolerance optimization
Summary
Manufactured components are subject to deviations that reduce the functional and aesthetic quality of the final product. For this reason, tolerances are specified based on the results of statistical tolerance analyses to minimize the degradation of geometrical accuracy and number of rejects in manufacturing. A common approach to satisfying both of these requirements is establishing statistical tolerance analyses based on Monte Carlo simulation to identify the cost-optimal manufacturing tolerance specification based on repeated random sampling and statistical analysis [1]. Monte Carlo simulation has consistently been the preferred choice of the tolerance community to evaluate the statistical implications of manufacturing deviations on the key characteristics of mechanical assemblies. The ongoing digital transformation of manufacturing through the adoption of Industry 4.0 [2,3,4] requires that product characteristics be analyzed after each manufacturing process in order to establish a continuous information flow to enable a self-learning and self-adapting manufacturing process [5,6]
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