S. Jack Hu

Variation simulation for deformable sheet metal assemblies using finite element methods

Traditional variation analysis methods, such as Root Sum Square method and Monte Carlo simulation, are not applicable to sheet metal assemblies because of possible part deformation during the assembly process. This paper proposes the use of finite element methods (FEM) in developing mechanistic variation simulation models for deformable sheet metal parts with complex two or three dimensional free form surfaces. Mechanistic variation simulation provides improved analysis by combining engineering structure models and statistical analysis in predicting the assembly variation. Direct Monte Carlo simulation in FEM is very time consuming, because hundreds or thousands of FEM runs are required to obtain a realistic assembly distribution. An alternative method, based on the Method of Influence Coefficients, is developed to improve the computational efficiency, producing improvements by several orders of magnitude. Simulations from both methods yield almost identical results. An example illustrates the developed methods used for evaluating sheet metal assembly variation. The new approaches provide an improved understanding of sheet metal assembly processes.

Modeling Variation Propagation of Multi-Station Assembly Systems With Compliant Parts

Products made of compliant sheet metals are widely used in automotive, aerospace, appliance and electronics industries. One of the most important challenges for the assembly process with compliant parts is dimensional quality, which affects product functionality and performance. This paper develops a methodology to evaluate the dimensional variation propagation in a multi-station compliant assembly system based on linear mechanics and a state space representation. Three sources of variation: part variation, fixture variation and welding gun variation are analyzed. The proposed method is illustrated through a case study on an automotive body assembly process.

A Variational Method of Robust Fixture Configuration Design for 3-D Workpieces

Fixtures are used to locate and hold workpieces during manufacturing. Because workpiece surface errors and fixture set-up errors (called source errors) always exist, the fixtured workpiece will consequently have position and/or orientation errors (called resultant errors). In this paper, we develop a variational method for robust fixture configuration design to minimize workpiece resultant errors due to source errors. We utilize both first-order and second-order workpiece geometry information to deal with two types of source errors, i.e., infinitesimal errors and small errors. Using the proposed variational approach, other fundamental fixture design issues, such as deterministic locating and total fixturing, can be regarded as integral parts of the robust design. Closed-form analytical solutions are derived and numerical examples are shown. By employing the nonlinear programming technique, simulation software called RFixDesign is developed. This paper presents a new procedure for robust fixture configuration design that contributes especially to fixture designs where deformation is not influential.

Impact of manufacturing system configuration on performance

Manufacturing systems can be designed in many configurations. Different configurations have profound impact on the performance of the system in terms of reliability and productivity, product quality, capacity scalability, and cost. This paper analyzes these performance measures for different system configurations assuming known machine level reliability and process capability.

Modeling of Manufacturing Complexity in Mixed-Model Assembly Lines

Mixed-model assembly lines have been recognized as a major enabler to handle product variety. However, the assembly process becomes very complex when the number of product variants is high, which, in turn, may impact the system performance in terms of quality and productivity. This paper considers the variety induced manufacturing complexity in manual mixed-model assembly lines where operators have to make choices for various assembly activities. A complexity measure called “operator choice complexity” (OCC) is proposed to quantify human performance in making choices. The OCC takes an analytical form as an information-theoretic entropy measure of the average randomness in a choice process. Meanwhile, empirical evidences are provided to support the proposed complexity measure. Based on the OCC, models are developed to evaluate the complexity at each station and for the entire assembly line. Consequently, complexity can be minimized by making system design and operation decisions, such as error-proof strategies and assembly sequence planning.

Compliant Assembly Variation Analysis Using Component Geometric Covariance

Dimensional variation is one of the most critical issues in the design of assembled products. This is especially true for the assembly of compliant parts since clamping and joining during assembly may introduce additional variation due to part deformation and springback. This paper discusses the effect of geometric covariance in the calculation of assembly variation of compliant parts. A new method is proposed for predicting compliant assembly variation using the component geometric covariance. It combines the use of principal component analysis (PCA) and finite element analysis in estimating the effect of part/component variation on assembly variation. PCA is used to extract deformation patterns from production data, decomposing the component covariance into the individual contributions of these deformation patterns. Finite element analysis is used to determine the effect of each deformation pattern over the assembly variation. The proposed methodology can significantly reduce the computational effort required in variation analysis of compliant assemblies. A case study is presented to illustrate the methodology.

Dynamic Formulation and Performance Comparison of the 3-DOF Modules of Two Reconfigurable PKM—the Tricept and the TriVariant

Utilizing the virtual work principle, this paper presents a method for the inverse dynamic formulation of the 3-degree-of-freedom (DOF) modules of the well-known Tricept robot and a newly invented hybrid robot named TriVariant. The TriVariant is a modified version of the Tricept, achieved by integrating one of the three active limbs into the passive one. Both local and global conditioning indices are proposed for the dynamic performance evaluation and comparison of these two robots. These indices are designed on the basis of the maximum actuated joint force required for producing a unit acceleration of the mobile platform. For a given set of geometrical and inertial parameters, it has been shown that the TriVariant has a similar overall dynamic performance compared with that of the Tricept.

Impact of fixture design on sheet metal assembly variation

This paper presents a new fixture design methodology for sheet metal assembly processes. It focuses on the impact of fixture position on the dimensional quality of sheet metal parts after assembly by considering the effect of part variation, tooling variation and assembly springback. An optimization algorithm combines finite element analysis and nonlinear programming methods to determine the optimal fixture position such that assembly variation is minimized. The optimized fixture layout enables significant reduction in assembly variation due to part and tooling variation. A case study is presented to illustrate the optimization procedure.

Flexible multibody dynamics based fixture-workpiece analysis model for fixturing stability

Abstract The machining force and torque exerted on a workpiece vary as the cutter moves along the tool path, therefore a dynamic approach is essential for fixturing stability analysis. This paper presents a technique to dynamically model and analyze the fixture-workpiece system subjected to time-varying machining loads. Combining the advantages of FEA (Finite Element Analysis) and nonlinear rigid body dynamics, a flexible multibody dynamic model is formulated to incorporate the overall interaction (clamping forces, machining loads, and contact friction) between flexible workpiece and compliant fixture elements. Three major parameters affecting the fixturing stability, namely the magnitude, application sequence, and placement of fixturing clamps, are analyzed. Additionally, the time dependent deformation of a flexible workpiece under clamping and machining loads is estimated. A scaled engine block with the 3–2–1 fixturing scheme subjected to face milling operation is given as an example. Comparison between the simulation result and experimental data shows a reasonable agreement.

An offset finite element model and its applications in predicting sheet metal assembly variation

Dimensional variation in sheet metal assembly affects product fit and functionality. To predict the variation of assembled products, variation simulation analysis has been gradually adopted in the early design stage. However, variation simulation based on rigid body assumptions usually results in over estimation of the assembly variation. In this paper, we propose an offset beam element model for predicting the assembly variation of deformable sheet metal parts joined by resistance spot welding. The purpose of using the offset beam element is to include the shear effect provided by resistance spot weld nuggets that cannot be captured by the conventional beam element. The offset element is then applied to predict sheet metal assembly variation for one-dimensional (1D) models extracted from industrial practice. The first example evaluates the effects of sheet metal thicknesses on assembly variation. The second example shows how the assembly sequence affects assembly variation. These models provide interesting insights into the mechanisms of variation stackup and will lead to the understanding of more complex sheet metal assemblies.