Assembly variation analysis of complicated products based on rigid–flexible hybrid vector loop

Abstract

The performance of mechanical products is closely related to their key feature errors. It is essential to predict the final assembly variation by assembly variation analysis to ensure product performance. Rigid–flexible hybrid construction is a common type of mechanical product. Existing methods of variation analysis in which rigid and flexible parts are calculated separately are difficult to meet the requirements of these complicated mechanical products. Another methodology is a result of linear superposition with rigid and flexible errors, which cannot reveal the quantitative relationship between product assembly variation and part manufacturing error. Therefore, a kind of complicated products’ assembly variation analysis method based on rigid–flexible vector loop is proposed in this article. First, shapes of part surfaces and sidelines are estimated according to different tolerance types. Probability density distributions of discrete feature points on the surface are calculated based on the tolerance field size with statistical methods. Second, flexible parts surface is discretized into a set of multi-segment vectors to build vector-loop model. Each vector can be orthogonally decomposed into the components representing position information and error size. Combining the multi-segment vector set of flexible part with traditional rigid part vector, a uniform vector-loop model is constructed to represent rigid and flexible complicated products. Probability density distributions of discrete feature points on part surface are regarded as inputs to calculate assembly variation values of products’ key features. Compared with the existing methods, this method applies to the assembly variation prediction of complicated products that consist of both rigid and flexible parts. Impact of each rigid and flexible part’s manufacturing error on product assembly variation can be determined, and it provides the foundation of parts tolerance optimization design. Finally, an assembly example of phased array antenna verifies effectiveness of the proposed method in this article.

A CAD model for the tolerancing of mechanical assemblies considering non-rigid joints between parts with defects

“…This Platform uses several engineering disciplines such as Monte Carlo simulation as well as the multiobjective genetic algorithm to evaluate the tolerances values attributed to the assembly parts and to find if necessary optimal tolerances. Liu et al 16 proposed a method for the assembly variation analysis using the rigid-flexible hybrid vector loop. First, surfaces and sidelines shapes of parts are determined according to tolerance types and values.…”

“…The approaches proposed in Refs. [11][12][13][14][15][16][17][18][19][20][21][22] overcome the limitations of the above tolerancing methods by taking into account the deformations of non-rigid components. Most of these methods [11][12][13][14] can be applied just in the case of sheets metal assemblies and are not valid for thick parts.…”

Integration of in-plane and out-of-plane dimensional variation in multi-station assembly process for automotive body assembly

“…Ideal part Ni et al, 31 Ghandi and Masehian, 32 Cai and colleagues, 33,34 Liu et al 35 -Non-Ideal part -To be presented in this paper as the gap between parts is closed. Finally, the subassembly is released from the fixtures, and so the springback phenomenon occurs.…”

“…After that, the unified variation model was extended by them 34 for general applicability of sheet metal assembly with 3D generic free surfaces. An assembly variation analysis method based on rigid–flexible VL is proposed by Liu et al 35 Sheet metal part surfaces were discretized into a set of multi-segment vectors to build VL model. The vector set of complaint part was combined with traditional rigid part vector.…”

Tolerance Modeling and Analysis Considering Form Defects for Spaceborne Array Antenna

“…The position errors are mainly determined by the form errors of the reflection plate and the base plate, as a consequence, tolerance analysis without form errors cannot be applied on the antenna design. Many efficient methods such as the matrix model [9] and vector loop method [10] face the same problem. For the convenience of description, a linear array in the whole array antenna (shown in Figure 1a) was analyzed.…”