•An algorithm is developed to perform the tooth contact analysis of cycloidal gears.•Tolerance parameters for the cycloidal drive are introduced and investigated.•Tolerance design is explored using ...the Monte Carlo method.
This paper presents a method for kinematic error analysis and tolerance design of cycloidal gear reducers. The relationships between parameters concerning geometry, manufacturing, and precision performance for the cycloidal gear reducer are introduced and then investigated via the theory of gearing. First, an algorithm based on the discretization of the cycloidal tooth profile is developed to perform tooth contact analysis of the cycloidal gear reducer. Then, a computer-aided procedure using the Monte Carlo method is established to analyze the distribution of kinematic error once the tolerance distributions of the geometric and manufacturing parameters are known. Finally, the tolerances of the parameters are optimized with the objective of minimizing the manufacturing cost. The reliability of the optimization results is also verified by analyzing samples using the previously developed computer-aided algorithm. Two examples are given to demonstrate the design procedure used in applications of the findings of this study.
It is widely acknowledged that the allocation of part tolerances is a highly responsible task due to the complex repercussions on both product quality and cost. As a consequence, since its beginnings ...in the 1960s, least-cost tolerance allocation using optimization techniques, i.e. tolerance-cost optimization, was continuously in focus of numerous research activities. Nowadays, increasing cost and quality pressure, availability of real manufacturing data driven by Industry 4.0 technologies, and rising computational power result in a continuously growing interest in tolerance-cost optimization in both research and industry. However, inconsistent terminology and the lack of a classification of the various relevant aspects is an obstacle for the application of tolerance-cost optimization approaches. There is no literature comprehensively and clearly summarizing the current state of the art and illustrating the relevant key aspects. Motivated to overcome this drawback, this article provides a comprehensive as well as detailed overview of the broad research field in tolerance-cost optimization for both beginners and experts. To facilitate the first steps for readers who are less familiar with the topic, the paper initially outlines the fundamentals of tolerance-cost optimization including its basic idea, elementary terminology and mathematical formulation. These fundamentals serve as a basis for a subsequent detailed discussion of the key elements with focus on the different characteristics concerning the optimization problem, tolerance-cost model, technical system model and the tolerance analysis model. These aspects are gathered and summarized in a structured mind map, which equips the reader with a comprehensive graphical overview of all the various facets and aspects of tolerance-cost optimization. Beside this, the paper gives a retrospect of the past fifty years of research in tolerance cost-optimization, considering 290 relevant publications. Based thereon, current issues and future research needs in tolerance-cost optimization were identified.
Dimensional tolerance allocation is a very important and difficult task that traditionally seeks to balance cost/productivity and quality. Common tolerance allocation models have two shortcomings: i) ...they are overly reliant on models focused on minimizing cost and tend to ignore waste, and ii) they fail to connect to the root cause of many quality issues: process variation. This paper proposes a tolerance allocation model that addresses these shortcomings. The proposed model considers both product design (tolerance selection) and operation planning (or production rate selection). Relations among production rate, production cost, processing precision, and waste are considered. A gradient-based optimization method is proposed to minimize the cost and waste. A clutch assembly case study is analyzed to evaluate the method. Monte Carlo simulations are employed to validate the accuracy of the proposed cost model. The proposed method is compared with a heuristic method from the literature. The proposed method produced more satisfactory products at a lower cost while producing less waste. For the case study, it is found that when the precision of a process is high, it is not necessary from an economic standpoint to inspect the quality of individual components. For poor precision processes, inspecting the quality of individual components is the preferred approach from a cost/throughput standpoint.
The need for highly reliable and precise products has forced industries to study potential uncertainties during designing needed parts. The reliability and acceptance of the product rely on several ...factors and tolerancing activity plays an important role to assure that the manufactured product meets the requirements. The importance of tolerancing activity can be noticed once designers prefer tight tolerances to ensure product performance and in contrast manufacturers want loose tolerances to reduce manufacturing and assembly complexity and then cost, to decrease the non-conformance rate. Therefore, tolerance allocation and inspection-planning design can be formalized as an optimization problem which the objective function represents the cost impacted by several aspects of the quality management: cost of failure, cost of the inspection. This paper details a modular cost model which includes four components: the manufacturing cost, the inspection cost, the scrap cost (internal failure), and the cost of external failure. Moreover, to improve the efficiency of the cost model, it integrates several factors such as frequencies of the monitoring and inspection activities, probability of conformed product, probability of non-detection of non-conformity, and probability of non-detection of confirmed. The applications of this model are illustrated and demonstrated through an industrial case study.
Tolerance-cost optimisation, i.e. using optimisation techniques for tolerance allocation, is frequently used to determine a cost-efficient tolerance design that can meet the stringent requirements on ...high-quality products. Besides various manufacturing aspects, the selection of available alternative machines and processes hold great potential for an early optimal process planning by identifying their best combination. Although machine/process selection by minimum cost and mixed-integer optimisation is often applied in theory and practice, their proper implementation in tolerance-cost optimisation based on sampling techniques for tolerance analysis, which can statistically consider various individual part tolerance distributions, has not been studied so far. With the aim to overcome this drawback, this article focuses on machine/process selection in sampling-based tolerance-cost optimisation for dimensional tolerances considering the respective machine characteristics of several machine options, e.g. process capabilities and manufacturing distributions. A comparative study proves that machine/process selection by mixed-integer optimisation leads to minimum total manufacturing costs since it covers the whole search space, including all technically feasible machine combinations and thus identifies the global cost minimum.
Tolerances significantly affect the assemblability of components, the product's performance, and manufacturing cost in mechanical assemblies. Despite the importance of product reliability assessment, ...the reliability-based tolerance design of mechanical assemblies has not been previously considered in the literature. In this paper, a novel method based on Bayesian modeling is proposed for the tolerance-reliability analysis and allocation of complex assemblies where the explicit assembly functions are difficult or impossible to extract. To reach this aim, a Bayesian model is developed for tolerance-reliability analysis. Then, a multi-objective optimization formulation is proposed for obtaining the optimum tolerances of components to minimize cost and maximize product performance. Subsequently, Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed for solving multi-objective optimization. Then, the enhanced TOPSIS is used to find the best optimum tolerances from the optimum Pareto solutions. Using the importance vector concept, a sensitivity analysis approach is used to determine the effects of design variables on the product reliability level and improve assembly reliability to the desired level. Finally, to exhibit the applicability of the proposed method, a transmission planetary gear system is considered, and the obtained results are compared and discussed for verification.
In concurrent engineering era, the collaboration between engineering and manufacturing is a vital condition for remaining competitive. For that, an interactive computer-aided design method is ...required for optimal tolerance allocation. In this regard, dimension transfer and tolerance allocation approaches serve as crucial tools for design engineers to reduce the total manufacturing cost of mechanical assembly as well as to ameliorate the product quality. This paper proposes an efficient collaborative hybrid tool for computer-aided integration to an optimal tolerance allocation based on a combination of unique transfer and difficulty coefficient evaluation. The tolerance allocation approach is based on manufacturing difficulty quantification using tools for the study and analysis of reliability of the design or the process, as the Failure Mode, Effects and Criticality Analysis and Ishikawa diagram. The proposed method is performed to produce allocated tolerances according to difficulty requirements to reach a mechanical assembly with high quality and low cost. To validate the proposed concepts and methods, an integrated tool is implemented using graphical user interface in MATLAB. Hence, an Integrated CAT tool for Dimension Transfer and Tolerance Allocation, named CAD_DT&TA, is proposed to expose various tolerance allocation approaches respecting functional and manufacturing requirements. Several examples can be executed using the proposed interface to highlight the benefits of the accomplished integrated tool. The results identify the real benefits of the innovative dimension transfer and tolerance allocation approach as reducing total cost and improving the quality of assembly product.
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