A probabilistic approach to variation propagation control for straight build in mechanical assembly

Random component variations have a significant influence on the quality of assembled products, and variation propagation control is one of the procedures used to improve product quality in the manufacturing assembly process. This paper considers straight-build assemblies composed of axi-symmetric components and proposes a novel variation propagation control method in which individual components are re-orientated on a stage-by-stage basis to optimise the table-axis error for the final component in the assembly. Mathematical modelling methods are developed to predict the statistical variations present in the complete assembly. Three straight-build assembly strategies are considered: (a) direct build, (b) best build and (c) worst build assembly. Analytical expressions are determined for the probability density function of the table-axis error for the final component in the assembly, and comparisons are made against Monte Carlo simulations for the purposes of validation. The results show that the proposed variation propagation control method offers good accuracy and efficiency, compared to the Monte Carlo simulations. The probability density functions are used to calculate the probability that the eccentricity will exceed a particular value and are useful for industrial applications and academic research in tolerance assignment and assembly process design. The proposed method is used to analyse the influence of different component tolerances on the build quality of an example originating in aero-engine sub-assembly.     

Time-Based Competition in Multistage Manufacturing: Stream-of-Variation Analysis (SOVA) Methodology—Review

Frequency of model change and the vast amounts of time and cost required to make a changeover, also called time-based competition, has become a characteristic feature of modern manufacturing and new product development in automotive, aerospace, and other industries. This paper discusses the concept of time-based competition in manufacturing and design based on a review of on-going research related to stream-of-variation (SOVA or SoV) methodology. The SOVA methodology focuses on the development of modeling, analysis, and control of dimensional variation in complex multistage assembly processes (MAP) such as the automotive, aerospace, appliance, and electronics industries. The presented methodology can help in eliminating costly trial-and-error fine-tuning of new-product assembly processes attributable to unforeseen dimensional errors throughout the assembly process from design through ramp-up and production. Implemented during the product design phase, the method will produce math-based predictions of potential downstream assembly problems, based on evaluations of the design and a large array of process variables. By integrating product and process design in a pre-production simulation, SOVA can head off individual assembly errors that contribute to an accumulating set of dimensional variations, which ultimately result in out-of-tolerance parts and products. Once in the ramp-up stage of production, SOVA will be able to compare predicted misalignments with actual measurements to determine the degree of mismatch in the assemblies, diagnose the root causes of errors, isolate the sources from other assembly steps, and then, on the basis of the SOVA model and product measurements, recommend solutions.     

Optimization of clearance variation in selective assembly for components with multiple characteristics

Quality is an important aspect of any manufacturing process. Only high quality products can survive in the market. The consumer not only wants quality, precision and trouble-free products, but also wants them at attractive prices. When a product consists of two or more components, the quality of that product depends upon the quality of the mating parts. The mating parts may be manufactured using different machines and processes with different standard deviations. Therefore, the dimensional distributions of the mating parts are not similar. This results in clearance or interference between the mating parts. In some high precision assemblies, it may not be possible to have closer assembly clearance variation with interchangeable system. Selective assembly meets the above requisite and gives an enhanced solution. Selective assembly is a method of obtaining high precision assemblies from relatively low precision components. In this paper, a new selective assembly method is proposed to minimize the clearance variation and surplus parts for a complex assembly which consists of the components viz. piston, piston ring. In this assembly, each component will have more than one quality characteristic contributing for the assembly, for e.g., piston diameter will assemble with cylinder inner diameter; piston groove diameter will assemble with piston ring inner diameter, etc. In selective assembly each quality characteristic will fall in different groups. Non-dominated sorting genetic algorithm (NSGA) is used to find the best combination to obtain the minimum clearance variation in this assembly.     

Principle of elastic averaging for rapid precision design

Elastic averaging has worked well throughout history to help create precision machines. With the advent of rapid fabrication processes such as additive manufacturing, abrasive waterjet machining, and laser cutting etc., parts fabricated from these processes can be designed with special elastic features that “average out” the uncertainty in dimension tolerances and manufacturing errors as a collective system at very low cost. This paper presents the principle of elastic averaging and explores simple flexure design to create elastic averaging features within parts for precision alignment and assembly applications. A first-order analytical model and a quick estimation approach is introduced to predict the alignment errors and the repeatability of these parts. Experimental results show that a part with four elastic averaging features was capable of achieving precision assembly with another mating part even after huge errors were purposefully introduced to the mating features. Results also show that the part can achieve sub-micron level repeatability after more than 20 trials of removals and assemblies. Lastly, analytical simulations show that repeatability of the part can be further improved by increasing the number of elastic contacts. All these results suggest that the assemblies of rapid fabricated parts with elastic averaging features can be as precise as those made from conventional machine centers.     

Evaluation of the form errors of axisymmetric components

The form errors of three-dimensional surfaces have an effect on the proper functioning of an assembly. Methods for evaluating form errors of surfaces of spherical and cylindrical components are available. However, in most machines and instruments the functional components are axisymmetric, e.g. spindles, and have varying geometry in the form of steps, tapers etc. Evaluation of the form errors at different zones on the component as well as a form error characteristic of the whole component is required in such cases. To do this coordinate data or circularity traces are obtained at different horizontal sections using a coordinate measuring machine or a roundness measuring instrument respectively and the required form error is then evaluated. Different algorithms developed for fitting the axis of the component which is the first step in the evaluation of form errors are described. The method of normal least-squares fitting was found to be superior to the general least-squares method.     

Optimum manufacturing tolerance to selective assembly technique for different assembly specifications by using genetic algorithm

Tolerance on parts dimension plays a vital role as the quality of the product depends on sub components tolerance. Thus, precision products that are manufactured reflect at high manufacturing cost. To overcome this situation, sub components of an assembly may be manufactured with wider tolerance, measured (using latest technologies like image processing) and grouped in partition and corresponding group components may be mated randomly. This present work is to obtain an optimum manufacturing tolerance to selective assembly technique using GA and to obtain maximum number of closer assembly specification products from wider tolerance sub components. A two components product (fan shaft assembly) is considered as an example problem, in which the subcomponents are manufactured with wide tolerance and partitioned into three to ten groups. A combination of best groups is obtained for the various assembly specifications with different manufacturing tolerances. The proposed method resulted nearly 965 assemblies produced out of one thousand parts with 15.86% of savings in manufacturing cost.     

Particle swarm optimization for minimizing assembly variation in selective assembly

Quality of a product is based on the quality of the mating parts. When the parts are assembled interchangeably, the assembly variation will be the sum of the component tolerances. If the assembly variation is to be less than the sum of the component tolerances, selective assembly is the only solution. In conventional selective assembly, the corresponding selective groups are assembled. In this paper, selective group combinations for assembling the mating parts is obtained using particle swarm optimization (PSO). The combination obtained has resulted in an appreciable reduction in assembly variation. The proposed algorithm has been demonstrated for a linear assembly, which consists of three components having equal dimensional distributions. The assembly variation obtained by interchangeable assembly is 36 μm. By implementing the proposed method, the assembly variations are reduced from 36 to 7.2 μm. However, this algorithm can be extended for assemblies with more number of components and with different dimensional distributions.     

Dimensional management for aerospace assemblies: framework implementation with case-based scenarios for simulation and measurement of in-process assembly variations

Tolerances within an assembly are defined during the setting of engineering specifications in the design phase. However, during assembly process execution, certain assembly variations arise from the individual components, manufacturing imperfections, material compliance, the means by which they are fastened and the assembly sequence used. The implementation work reported in this article utilises in-process assembly measurement information for predicting dimensional variation of the aero structure assembly process. A framework is exploited in the case study for predicting the dimensional influence of (1) designed tolerances, (2) designed assembly processes and (3) component and sub-assembly level measurement data for revising the assembly sequence if any concessions were issued on manufactured components. Considerable learnings are achieved while managing dimensional variation of in-process aerospace assembly structure. Dimensional variation simulation is found to be overestimating variation spread even after considering compliance of non-rigid components. Thus, in-process measurement data (component and sub-assembly level) has to be integrated in the variation analysis in order to reduce variation spectrum. Case-based scenarios are discussed where design and measurement data can be utilised for estimating dimensional variation of the in-process assembly.     

Fuzzy-small degrees of freedom representation of linear and angular variations in mechanical assemblies for tolerance analysis and allocation

Tolerances naturally generate an uncertain environment for design and manufacturing. In this paper, a novel fuzzy based tolerance representation approach for modeling the variations of geometric features due to dimensional tolerances is presented. The two concepts of fuzzy theory and small degrees of freedom are combined to introduce the fuzzy-small degrees of freedom model (F-SDOF). This model is suitable for tolerance analysis of mechanical assemblies with linear and angular tolerances. Based on the fuzzy concept, a new index (called the assemblability index) is introduced which signifies the fitting quality of parts in the assembly. Graphical and numerical representations of tolerance allocation by this method are presented. The goal of tolerance allocation is to adjust the tolerances assigned at the design stage so as to meet a functional requirement at the assembly stage. The presented method is compatible with the current dimensioning and tolerancing standards. The application of the proposed methodology is illustrated through presenting an example problem.     

车身总成组合检具设计方法的研究与应用

基于车身总成件各部件之间的安装关系和各部分的匹配精度,结合实例介绍了一种新型总成组合检具的设计方法。这种总成组合检具能及时发现零件和总成件的设计缺陷,识别和排除存在的问题,同时降低车身制造成本,对车身总成件制造的质量检测和成本控制具有重要的实用价值。     

M-DOF dynamic model for load sharing behavior analysis of PGT

A Multi-degree-of-freedom (M-DOF) nonlinear dynamic model for n-pinion Planetary gear train (PGT) is presented in this paper to investigate load sharing behavior of planet gears. In this dynamic model, manufacturing and assembly errors, elastic deformation and time-varying mesh stiffness are considered. Two sets of elastic compatibility equations are proposed to describe compatibility relationship between displacements, errors and elastic deformations. By means of Ishikawa formula, time-varying mesh stiffness of the gear pair is determined. The dynamic motion equations are solved with Runge-Kutta numerical integral method, which yields the displacements and deformations of each component. With the model, dynamic load sharing behavior of planet gears is evaluated. An example of 3-pinion PGT dynamic modeling is included, for which the influence of floating sun gear and adding flexible planet pin on the load sharing characteristics is analyzed.     

Methods for evaluation of systematic geometric deviations in machined parts and their relationships to process variables

Increasing demands for precision-machined parts put a greater emphasis on achieving a better understanding of the relationships between manufacturing process variables and deviations from perfect geometric forms. To achieve this understanding, it is important to have high-quality metrology data on part features, which (in some sense) span the range of variability in form for the process under study. The problem is complex, involving the machine tool itself, materials, fixtures, cutters, feeds, speeds, and many other factors. In this report, a method is introduced that can identify key deviations from perfect form and can elucidate their dependence on some of the factors enumerated above. This work presents two useful models for form errors of cylindrical features and develops special cases of those models to suit specific requirements. One is an analytical model based on Chebyshev polynomials to model the axial errors and Fourier series to model angular dependencies. The second modeling approach uses the techniques of principal component analysis to extract a basis set of characteristic shapes directly from the measurement data. This report includes a full development of the mathematical basis for the analysis and concludes with some application examples.     

Simulated toleranced CAD geometrical model and automatic generation of 3D dimension chains

In current research of computer aided tolerancing (CAT), how to build models with tolerance and how to generate 3D dimension chains automatically have been tough problems and still unsolved. This paper builds a simulated toleranced CAD geometrical model (STCAD model) based on the feature-based original idealized CAD geometrical model (OICAD model), which can simulate real parts with manufacturing dimension errors from different aspects. Further more, an automatic generation method of 3D dimension chains based on some newly proposed definitions is put forward. In this method, firstly the conception of part instantiation (PI) is realized, secondly performance feature is defined, thirdly through building STCAD models, drive dimensions can be obtained which are vectorized to build drive dimension skeleton model (DDSM), and finally 3D dimension chains can be obtained by DDSM and the method of space projection. This method can generate 1D, 2D, and 3D dimension chains of parts or assemblies. It is verified in our own-developed automatic generation system of 3D dimension chains .     

Optimal tolerance design of assembly for minimum quality loss and manufacturing cost using metaheuristic algorithms

Tolerance allocation is a design tool for reducing overall cost of manufacturing while meeting target levels for quality. An important consideration in product design is the assignment of design and manufacturing tolerances to individual component dimensions so that the product can be produced economically and functions properly. The allocation of tolerances among the components of a mechanical assembly can significantly affect the resulting manufacturing costs. In this work, the tolerance allocation problem is formulated as a non-linear integer model by considering both the manufacturing cost of each component by alternate processes and the quality loss of assemblies so as to minimise the manufacturing cost. Metaheuristics techniques such as genetic algorithm and particle swarm optimisation are used to solve the model and obtain the global optimal solution for tolerance design. An example for illustrating the optimisation model and the solution procedure is provided. Results are compared with conventional technique and the performances are analysed.     

Effect of ultrasonic impact treatment on the ultra high cycle fatigue properties of SMA490BW steel welded joints

This paper presents bi-criteria formulation of a tolerance allocation model for an interchangeable assembly to simultaneously evolve suitable combination of manufacturing facility in multiple facility shaft-hole production environments of medium- and large-scale industries and tolerances to complement the need of customers. An Exhaustive Search Procedure is used to obtain the optimal solution for small and medium size problems and simulated annealing algorithm is used for large size problems. The usefulness of the Pareto front in manufacturing tolerance allocation decisions is demonstrated with three case study problems. The effect of process capability of shaft-hole assembly manufactured from alternative manufacturing machines and the optimality is analyzed in three cases to understand their criticality in decision-making. The models discussed in this paper could be useful for medium- and large-scale manufacturing industries, where there will be a variety of manufacturing facilities (specifications, capabilities, models, and types) for making both shaft-hole assembly and play a key role to meet the tolerance and cost requirements of different customers. This paper further discusses how this formulation and methodologies can be used for two hole and two shaft assemblies and multiple shaft-hole assemblies. Finally, the paper ends with highlighting directions of future research avenues in the shaft-hole assembly.     

Locating Error Considering Dimensional Errors Modeling for Multistation Manufacturing System

Multistation machining process is widely applied in contemporary manufacturing environment.Modeling of variation propagation in multistation machining process is one of the most important research scenarios.Due to the existence of multiple variation streams,it is challenging to model and analyze variation propagation in a multi-station system.Current approaches to error modeling for multistation machining process are not explicit enough for error control and ensuring final product quality.In this paper,a mathematic model to depict the part dimensional variation of the complex multistation manufacturing process is formulated.A linear state space dimensional error propagation equation is established through kinematics analysis of the influence of locating parameter variations and locating datum variations on dimensional errors,so the dimensional error accumulation and transformation within the multistation process are quantitatively described.A systematic procedure to build the model is presented,which enhances the way to determine the variation sources in complex machining systems.A simple two-dimensional example is used to illustrate the proposed procedures.Finally,an industrial case of multistation machining part in a manufacturing shop is given to testify the validation and practicability of the method.The proposed analytical model is essential to quality control and improvement for multistation systems in machining quality forecasting and design optimization.     

基于矢量环装配模型的二维公差分析

在公差分析中，大多数都要求提供描述装配响应函数与零件尺寸设计变量之间关系的函数。然而，复杂的二维公差分析中，这种函数关系通常难于得到。本文提出的基于矢量环装配公差模型，不须提供这些函数关系，而是通过矢量运算得到计算封闭环公差所需的灵敏度系数，进而有效地解决二维尺寸链的公差分析问题。最后给出一个工程应用实例，说明该方法的有效性。     

Design and optimization of concurrent tolerance in mechanical assemblies using bat algorithm

Concurrent designing of tolerance has become a vital concern in product and process development due to the relationship between quality, functionality and product cost. It is one of the well explored areas in combinatorial optimization. In this paper, a recently developed optimization algorithm, called Bat algorithm (BA), is used for optimizing the tolerance based on concurrent objectives to minimize the manufacturing cost, present worth of expected quality loss and quality loss. The mechanical assemblies such as Bevel gear assembly (A), Gear box assembly (B) and Suction union assembly (C) are considered to demonstrate the proposed algorithm. It is found that the BA has produced better results than other methods in initial generations for concurrent tolerance problems.     

Multi-objective optimization for optimum tolerance synthesis with process and machine selection using a genetic algorithm

This paper presents a new approach to the tolerance synthesis of the component parts of assemblies by simultaneously optimizing three manufacturing parameters: manufacturing cost, including tolerance cost and quality loss cost; machining time; and machine overhead/idle time cost. A methodology has been developed using the genetic algorithm technique to solve this multi-objective optimization problem. The effectiveness of the proposed methodology has been demonstrated by solving a wheel mounting assembly problem consisting of five components, two subassemblies, two critical dimensions, two functional tolerances, and eight operations. Significant cost saving can be achieved by employing this methodology.     

Modeling method for assembly variation propagation taking account of form error

The propagation of variations, such as fixture errors and datum errors resulting from assembly and machining processes, has been extensively studied. However, only a few studies that focus on form error propagation in assembly systems have been implemented. Machining errors, especially form errors, have great impact on assembly accuracy and accuracy stability of precision mechanical systems. With form errors being the research object, a method for calculating mating variation and specifying mating coordinate is proposed to improve the accuracy of the variation propagation model. Taking into account the form error of mating surfaces, the assembly variation propagation of a precision mechanical system is analyzed, and the brief derivation procedure of the variation propagation model is introduced afterwards. The variation propagation model involves a new concept of mating variation specified by the two mating surfaces. An innovative method, the difference surface search based method, is proposed to calculate the mating variation amongst the mating surfaces. The obtained mating variation is then utilized to specify the mating coordinate in the variation propagation model. Moreover, FEM is employed to simulate the contact state of the two mating surfaces to demonstrate effectiveness of the proposed method. Meanwhile, the mating variation and mating coordinate obtained are incorporated into the assembly variation propagation model, which is then verified by a following case study through a comparison between the calculated results and the experimental results. The comparing results indicate that the established model improves the prediction of assembly accuracy. The developed model enables the investigation of various fundamental issues in variation reduction, including variation analysis, process monitoring, accuracy prediction, and accuracy control.