Sun Jin

A small displacement torsor model for 3D tolerance analysis of conical structures

The small displacement torsor model is a classic three-dimensional tolerance analysis method. It uses three translational vectors and three rotational vectors to represent tolerance information in three-dimensional Euclidean space. However, the target features of this model mainly focused on planes and cylinders in previous studies. Little attention is invested to conical features and their joints which are used widely and more complex than the planar and cylindrical features. The objective of this article is to present a three-dimensional mathematical method of tolerance representation about conical surfaces and their joints based on the small displacement torsor model, and propose a mathematical model of variations and constraint relations of components of the small displacement torsor for conical surfaces caused by geometric tolerances limited by its tolerance zone. In addition, a simple example involving conical structures is used to demonstrate three-dimensional conical tolerance propagation. Both deterministic and statistical results are obtained by this model.

Dimensional variation stream modeling of investment casting process based on state space method

Investment casting process produces high-precision castings, but there is a constant demand for improving the process capabilities, including dimensional accuracy and consistency. In this article, a state space modeling approach of investment casting process for dimensional variation is developed. This research focuses on the linear dimensional change (expansion or shrinkage) in the investment casting process. The generation, propagation and accumulation of the dimensional variation in the investment casting process are interpreted. In order to develop a mathematical model to describe the procedure above, a notion, the dimensional variation stream, is employed, and several key concepts, such as dimensional change rate, state vector and process parameter variation vector, are defined. The inherent relationships among these components are uncovered and finally bring about a State Space Model that describes the dimensional variation stream in the whole investment casting process. In the end, the usages of the developed model are illustrated and summarized via studying a case.

Multistage rotational optimization using unified Jacobian–Torsor model in aero-engine assembly

For revolving components like compressor stages in aero-engine, it is critical to ensure that the overall concentric performance of the assembly is extremely excellent to satisfy the requirements of vibration-free and noise-free. However, in practical production, it is hard to meet the target requirement by manual adjustments; in virtual assembly, it is difficult to build an effective deviation propagation model with traditional methods. This article focuses on two points: one is the assembly technique of multistage rotational optimization and the other is the deviation propagation model for revolving components assembly. The revolution joint was introduced in the unified Jacobian–Torsor model to provide the rotary regulating effects. This modified model has advantages of being able to consider rotating optimization, geometric tolerance, and percentage contribution compared with other mathematical methods. General formulas for the n-stage components assembly were derived including the deviation propagation function and optimization destination expression. Comparisons between three assembly techniques and experiments were made to prove the suggested method was feasible and of high practicability. It can be integrated with computer-aided design systems to propose assistance for operators in assembling stage or redesign parts tolerances where FEs’ percentage contributions can be obtained in design preliminary stage.

The Assembly Variation Modeling for the Rear Casing Wax Part Based on Polar Coordinate

Rear casing is a key part of the aeroplane engine. Its dimensional precision is significant to the quality of the aeroplane engine. In the rear casing manufacturing process, the assembly variation of its corresponding wax dramatically affects the final dimensions. In this paper, a polar-coordinate based model is proposed to calculate the assembly variation of ring-shaped rear casing wax part. It avoids the variation caused by the coupling relationship between Cartesian coordinate systems and locating position. We also compare the polar-coordinate based model with the ordinary one in practical application. The results show that the polar-coordinate based model can simplify the calculating process and improve the computational accuracy for the assembly variation analysis of the ring-shaped part.© 2015 ASME

Variation Analysis for Rigid Workpiece Locating Considering Quadratic Effects Using the Method of Moments

Locators are used to constrain and position workpieces. The proper arrangement of locators, i.e., the locating scheme, is essential for both functionality and quality. In this paper, we propose a quadratic method to calculate the positional and rotational variations of a rigid workpiece using the Method of Moments. First, the workpiece geometry is quadratically approximated (hence allowing the inclusion of the linear and quadratic geometry data) to form the nonlinear constraint equations of the locators through a homogenous coordinate transformation. For a deterministic analysis, these highly nonlinear constraint equations can be solved using the Newton-Raphson method. To calculate the workpiece variations due to the locating source variations, the workpiece positional and rotational errors are first quadratically approximated around the locator positions using the Taylor expansion and then calculated using the Method of Moments. The advantage of the Method of Moment for a variation analysis is its efficiency as compared to the time-consuming Monte Carlo simulations. Examples are presented to benchmark the proposed method with prior research. By using the proposed method, the quadratic geometry effect and the interactions between locating source errors can be captured and hence the analysis results are more accurate, especially when error sources are large.Copyright