An Approach to the Sensitivity Analysis in Variation Simulations considering Form Deviations

The inevitable presence of geometrical part deviations and their effects on the product function and quality forces companies to manage these deviations along the product life-cycle. Computer-aided tolerancing and variation simulation tools support these activities by enabling the early prediction and assessment of the effects of such part deviations. However, available approaches for the tolerance analysis and variation simulation imply shortcomings regarding the consideration of form deviations, particularly when analysing mechanism and moving systems. This paper presents an approach for the motion tolerancing, i. e. for the tolerance analysis of mechanism and moving systems, employing discrete geometry representations of parts with geometrical deviations (Skin Model Shapes). In this regard, a novel method for the parametrization of form deviations is proposed and the use of meta-modelling techniques for the reduction of the computational effort is illustrated. Moreover, the presented approach is applied on two case studies. Based on the obtained results, it can be found, that the consideration of form deviations in the tolerance analysis for mechanism and moving systems may lead to more purposeful tolerancing decisions.

The modelling of nominal product geometry by computer-aided design tools has gained immense attention in industry during the last decades and is nowadays an integral part of the virtual product development process. However, the established geometry representation schemes for CAD imply severe drawbacks regarding the modelling of geometric part deviations, which are inevitably observed on every manufactured artefact. As a response, the concept of Skin Model Shapes, which stems from international standards for geometric product specification and verification, has been developed as a novel approach for the consideration of product shape variability. It employs discrete geometry methods and computational techniques, such as point clouds, surface meshes and geometric processing, to model shape variability and to facilitate the communication of geometric product information throughout the product design, manufacturing, and inspection processes. This paper highlights the foundations of this concept, demonstrates its potentials for the representation of product geometry considering geometric variations along the product lifecycle, and illustrates main applications in the context of computer aided product and process development. In this regard, a focus is laid upon recent results and contributions, such as contact modelling, tolerance analysis, and motion tolerancing based on Skin Model Shapes. Furthermore, challenges for future research, such as the application to complex shapes and compliant parts, as well as the consideration of novel manufacturing processes, are discussed.

An improved tolerance analysis method for gear mechanisms considering form deviations and elastic-plastic contact behaviors

Skin Model Shapes: A new paradigm shift for geometric variations modelling in mechanical engineering

Nowadays, assembly tolerance analysis has become a challenging problem to predict the accuracy of a final assembly and examine whether specified tolerances satisfy assembly functional requirements (AFRs) for ensuring product assembly performance. Skin model shapes can be addressed to represent part geometric tolerances with manufacturing defects, thereby providing high fidelity surfaces that can replace nominal or ideal surfaces and significantly improve the accuracy and reliability of assembly tolerance analysis. However, their application in easy-to-use assembly simulation is limited by the level of detail required for manufacturing defect simulation and the complicated calculation process for integrating these defects into the tolerance analysis. Therefore, to overcome these issues in predicting assembly deviations in the early design stage, we propose a generic integrated approach of assembly tolerance analysis based on skin model shapes. First, two methods are introduced for modelling and generating skin model shapes according to different mate types of assembly key features. Second, a calculation method of assembly deviation propagation is developed by the integration of skin model shapes and stream-of-variation theory with accuracy and efficiency guarantees. Besides, a slightly modified relative contact positioning method is presented, based on different surface and progressive contact method, to obtain deterministic contact points and contact positioning errors between key mating joint surfaces. And then, the deviation values of AFRs are calculated, considering the inevitable manufacturing and assembly process errors. Finally, a typical mechanical assembly on assembly tolerance analysis is used as a case study to demonstrate the effectiveness of the proposed approach.

Kinematic accuracy analysis for cam mechanism considering dynamic behavior and form deviations

An integrated open source CAT based on Skin Model Shapes

Tolerance analysis methods, which are important to achieve a balance between manufacturing costs and functional requirements, have been studied and improved over the last 30 years. This paper proposes a new method to improve the precision of assembly simulation for statistical assembly simulation; by investigating the effect of the geometric deviations and mechanical behaviors of assembly contact on the stack-up assembly deviation by combining the recent theories on the tolerance analysis of rigid bodies and local contact deformation. To improve the precision of the tolerance analysis, real parts with form defects were simulated with the help of non-nominal skin model shapes. The SMSs were first considered to be rigid, and a quadratic optimization-based method for the rigid body displacement was used to calculate the initial contact points of all the SMSs. Next, contact deformation, following Hertzian contact theory, occurred at the initial contact points, which changed the relative positions of the SMSs in the subsequent interactions. The iteration process was convergent, and the final simulation for tolerance analysis could be generated after several iterations. Case studies demonstrated the practicality of the proposed method. Their actual assembly deviations were simulated by combining the effects of geometric deviations and local surface deformations. Since the proposed tolerance analysis framework based on statistical assembly simulation, it is expected to control the functional requirements of mechanical assemblies with much rough tolerance design and help optimize the tolerance in the future.

DeviationGAN: A generative end-to-end approach for the deviation prediction of sheet metal assembly

Manufacturing signature in jacobian and torsor models for tolerance analysis of rigid parts

Accepting as a basic premise the importance of capital investment decisions for the firm and the significance of risk and uncertainty in forward planning, the research study reviews investment decision theory and examines alternative modifications to this theory to accommodate risk and uncertainty. Recommended modifications to data input, methods of project evaluation, and reporting produce a programme which varies significantly from generally accepted investment theory and practice. Risk and uncertainty is explicitly recognised through their influence on input variables: investment outlays, lifespans, volume of project outputs, selling prices and variable costs per unit of volume, period fixed costs, reinvestment opportunities and residual benefits. In the programme, a range of values (with subjective probabilities for each value) is determined for each input variable. Uncertainty is converted to a risk-equivalent situation. Input data is analysed initially using a Monte Carlo technique to simulate profitability and each range of data is further reduced to an expected value to form the basis for profitability calculations and an evaluation of investment sensitivity to changes in input variables. In both the simulation and sensitivity analyses, four indexes are used to measure investment profitability - internal rate of return, internal rate of return modified to incorporate explicit reinvestment opportunities, accounting rate of return, and the payback calculation. In reporting the results of simulation and sensitivity analyses, extensive use is made of graphs. After illustrating the programme of analysis with a theoretical investment project, the programme is evaluated on the basis of eight case studies - investment projects currently under consideration by executives of Australian manufacturing companies. Experience with the case studies leads to the following conclusions:1) The significance of investment risk and uncertainty is identified for decision-makers if projects are evaluated with a programme incorporating simulation and sensitivity analyses.2) The investment analysis programme provides valuable information for management not currently available from methods in use by accounting executives of Australian manufacturing companies.3) Ranges of values for input variables are readily obtainable from accounting, production and sales executives. Little difficulty is found in assigning subjective probabilities to ranges of values.4) An internal rate of return analysis which explicitly considers reinvestment opportunities, and rule-of-thumb methods of analyses have an important role in identifying risk and uncertainty for investment decisions. When the results of analyses are presented as graphs, management interpretation of these analyses is assisted and subsequent decision-making is most effective.5) Widespread acceptance and implementation of the recommended investment analysis programme by members of the accounting profession must depend on current and future educational policies of professional bodies producing financial executives with a sound knowledge of computer mathematics, statistics and financial analysis.

IBM introduced Copper Column Grid Array (CuCGA) interconnect as the lead-free replacement for the lead-tin solder column on the Ceramic Column Grid Array (CCGA) (Figure 1). Like CCGA, CuCGA offers a high reliability packaging solution, enabling the use of ceramic chip carriers with excellent electrical and thermal performance. The move to eliminate lead in microelectronic packaging increases the complexity of processing large body size, high I/O packages. The development of manufacturable card assembly and rework processes in concert with the development of a new package interconnect structure is key to technology acceptance. Copper column interconnect (CuCGA) has been designed to meet the requirements of manufacturability, reliability, and electrical performance. Optimization of the structure for manufacturability focused on the robustness of the column during manufacturing handling and the ease of card assembly processing. The resulting card-side solder joint is key to the reliability of the interconnect. The interconnect geometry also influences electrical performance [1]. Evaluating these competing factors determined the final column design [2]. This paper focuses on the development and reliability evaluation of the CuCGA card assembly and rework processes. The goal of the process development was to adapt the successful SMT assembly process for CCGA to the developing standards for lead-free SMT processing. Successful integration of the assembly processing of the CuCGA into the developing tin-silver-copper (SnAgCu, or SAC) card assembly process posed challenges in the areas of placement, reflow, and rework. The optimization of these processes, and the proof of successful results demonstrated by reliability evaluations, will be discussed.

Associated with manufacturing and assembly processes, inevitable geometric deviations have a decisive influence on the function and quality of products. Therefore, their consideration and management are important tasks in product development. Moreover, to meet the demand for short development times, the front-loading of design processes is indispensable. This requires early tolerance analyses evaluating the effect of deviations in a design stage, where the product’s geometry has not yet been finally defined. Since such an early tolerance consideration allows quick and economic design changes seeking for robust designs, it is advisable that the design engineer, who is entirely familiar with the design, should take this step. For this purpose, this paper presents an easy-to-use CAD-based tolerance analysis method for skeleton models. The relevant part deviations are represented by varying geometric dimensions with externally driven family tables. The approach comprises the strength of vector-based methods but does not require an expensive set-up of tolerance analysis models. Particularly, the novelty of this method lies in the CAD-internal sampling-based tolerance analysis of simple geometries without the use of expensive CAT software. This enables designers to evaluate the effect of tolerances already at the preliminary design stage. Using a case study, the presented approach is compared with the conventional vector-based tolerance analysis.

Effects of contact behaviors on tolerance analysis of mechanism based on skin model shapes and a boundary element method

While a systematic quality strategy is of crucial importance for the success of manufacturing companies, the universal applicability and effectiveness of implemented quality management practices were called into question by a number of major product recalls in recent years. This article seeks to illustrate how already simple analyses and early stage design methods can help to better understand one of the potential reasons for these failures, namely the variation inherent in manufacturing, assembly, and use processes. Usually thoroughly controlled in production, it seems as if particularly the risk of unanticipated variation effects remain largely underestimated and thus unaccounted for in design practice, sometimes with disastrous consequences. To foster the awareness of this variation and to illustrate the benefits of its early consideration in product development, this paper reviews one of the most infamous recalls in automotive history, that of the GM ignition switch, from the perspective of Robust Design. It is investigated if available Robust Design methods such as sensitivity analysis, tolerance stack-ups, design clarity, etc. would have been suitable to account for the performance variation, which has led to a number of fatal product defects and the recall of 30 million vehicles. Furthermore, the disclosed legal case files were examined, offering a unique opportunity to examine how technical malfunctioning of the ignition switch could stay undetected long enough to result in fatalities.