Tolerance analysis method considering multifactor coupling based on the Jacobian–torsor model

Abstract

Assembly quality affects the performance of mechanical products and reasonable tolerance designs are central to assembly quality. Unreasonable tolerance design leads to the mechanical equipment performance degradation under complex operating conditions. This study developed a novel tolerance analysis method that considers the influence of temperature, load, and other environmental factors based on the Jacobian–torsor and skin models. First, the deformation caused by multifactor coupling was analyzed using the finite element method, and the feature surface of deformation is extracted. Second, the deformation extraction and tolerance conversion based on the new generation geometrical product specification theory was used to convert the deformation of the feature into the dimension, orientation, and form tolerance. Third, the modified Jacobian–torsor model considering multifactor coupling was constructed by superimposing the converted tolerance with the design tolerances. Finally, the abrasion problem of the airborne actuator was considered as an example to verify the effectiveness and accuracy of the novel method. Through the accurate calculation of tolerances, it accurately analyzes the assembly state of the product under the influence of environmental factors, and provides more accurate guidance for the design and optimization of product tolerance in complex working conditions.

Optimization Method of Assembly Tolerance Types Based on Degree of Freedom

“…The value of the element r ij in the matrix T B is related to the rotational coordinate axis; C B is the rotation matrix. When the G-coordinate system is rotated around the X-axis only and the rotational displacement is α, the expression C B is as shown in Formula (7) [38].…”