Abstract
Assembly variations are unavoidable due to parts’ geometrical errors. Statistical variation analysis is an effective method to quantitatively predict product quality in the original design stage. However, traditional methods can’t handle the problem of abnormal distribution of the actual variation variables. Meanwhile, they are underdeveloped in regard to the complex geometrical errors in spatial 3D state. To overcome this problem, firstly, Jacobian-Torsor model is used to build the variation propagation, which is well suited to a complex assembly that contains large numbers of joints and geometric tolerances; secondly, Pearson distribution family is adopted to determine probability distribution pattern and build probability density function. By comparing results of the suggested method to the Monte Carlo method, it is observed that this novel method has the same accuracy, but much higher efficiency. The results also demonstrate that probability distribution types of the parts variations have a significant impact on the final assembling variation.
Highlights
Variation is inherent during any manufacturing and assembly process owing to the variability of the part, datum, positioner, fixture, etc
To verify the influence of probability distribution types on the final assembly variations, we suppose the distribution types of functional elements (FEs) follow normal distribution, skewed distribution and uniform distribution respectively, and four probability combinations will be used as shown in Table.4, where skewed distribution is simulated by virtue of Beta approximation
Based on Eq (5) to (10), we can further obtain the values of a0, b0, b1, b2, and deduce the variation distribution pattern by reference to Table.1, which has been shown in the last column of Table
Summary
Variation is inherent during any manufacturing and assembly process owing to the variability of the part, datum, positioner, fixture, etc. They cause minor variations in components from the nominal geometry [1]. The results obtained by extremum method are overly pessimistic which will cause high fabricating cost, while the mean square root method only gives results for the mean-square variation which is primarily used to solve the plane size-chain problem. These methods are underdeveloped in regard to the geometrical errors in spatial 3D state. It combines the advantages of the torsor model which is suitable for tolerance representation and the Jacobian matrix which is suitable for tolerance propagation
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