Session: 02-10-01: Variation Simulation and Tolerancing

Paper Number: 70749

Start Time: Friday, 12:25 PM

70749 - Tolerance Analysis on Assembly Parts in Contact Based Upon Parametric Space Envelope 

Tolerance is an essential part of design and manufacturing. Assigning proper tolerance plays a key role for firm to gain a competitive edge. Tighter tolerance ensures high product quality while incurs considerable manufacturing costs. On the other hand, looser tolerance reduces product quality with downward impact on functionality. This paper deals with geometric tolerance analysis between two mating parts by applying Bezier free-form deformation technique. First the two mating parts are represented under Bezier free-form deformation model frame. The deviation of control points can describe the geometric tolerance zone of enclosed manufacturing part. Then the signed distance between the two parts is deduced and represented through a compact set of boundary control points. Thus the contact state (of the two parts) is formulated as an optimization problem, in which the signed distance between the two parts is minimized with constraint of non-negative signed distance (i.e. the two workpieces are not embedded during assembly). Through solving this optimization problem, the translation distance along the assembly direction can be obtained to ensure the least distance between the two parts approaching zero. Then based on the contact state, assembly tolerances can be analyzed.

The validity of the method is verified through two case examples. One involves a plane and a bent plane while the second case involves two quadratic mating surfaces. The initial state of two mating surfaces is assigned, i.e. separated or embedded. By solving nonlinear optimization problem, the translation values along assembly direction are computed. The difference between solved value and theoretical value is less than 10^-10mm. Then based on this contact state, we can analyze the error of assembly through computing the largest gap between the two mating surfaces. Simulating control points random perturbation within its influence zone, the two mating surfaces will deviate from its design intent. Accordingly we can get the geometric deviation of assembling the two deviated surfaces. Conducting this simulation 1,000,000 times, we can get statistics of the assembly error. Based on this, the tolerance of the assembly can be assigned. Further, in order to find how the deformation style affects the assembly tolerance, we analyze the relationship between the deviation of control points and deformation type. Each deformation type observed in assembly line (i.e. bending, stamping, etc.) can be associated with certain pattern of control points’ movement. As such, tighter assembly tolerance for mass production can be achieved under proposed method by selecting complementary mating parts through analyzing control points’ movement pattern.

Presenting Author: Jiaqi Nie Southeast University

Authors:

Jiaqi Nie Southeast University
Chen Luo Southeast University
Yijun Zhou Southeast University