Optimal Tolerance Allocation Research Articles

An integrated hybrid approach for assembly tolerance transfer and allocation

PurposeThis study aims to develop an optimal tolerance allocation strategy involves integrating the unique transfer (UT) approach and the difficulty coefficient evaluation (DCE) routine in an interactive hybrid method. This method combines the strengths of both UT and DCE, ensuring simultaneous utilization for enhanced performance. The proposed tolerancing model manifests an integrated computer-aided design (CAD) tool.Design/methodology/approachBy combining UT and DCE based on failure mode, effects and criticality analysis (FMECA) tool and the Ishikawa diagram, the proposed collaborative hybrid tool ensures an efficient and optimal tolerance allocation approach. The integration of these methodologies not only addresses specific transfer challenges through UT but also conducts a thorough evaluation of difficulty coefficients via DCE routine using reliability analysis tools as FMECA tool and the Ishikawa diagram. This comprehensive framework contributes to a robust and informed decision-making process in tolerance allocation, ultimately optimizing the design and manufacturing processes.FindingsThe presented methodology is implemented with the aim of generating allocated tolerances that align with specific difficulty requirements, facilitating the creation of a mechanical assembly characterized by high quality and low cost. To substantiate and validate the conceptual framework and methods, an integrated tool has been developed, featuring a graphical user interface (GUI) designed in MATLAB. This interface serves as a platform to showcase various interactive and integrated tolerance allocation approaches that adhere to both functional and manufacturing prerequisites. The proposed integrated tool, designed with a GUI in MATLAB, offers the capability to execute various examples that effectively demonstrate the benefits of the developed tolerance transfer and allocation methodology.Originality/valueThe originality of the proposed approach is the twining between the UT and DCE simultaneous in an integrated and concurrent tolerance transfer and allocation model. Therefore, the proposed approach is named an integrated CAD/tolerance model based on the manufacturing difficulty tool. The obtained results underscore the tangible advantages stemming from the integration of this innovative tolerance transfer and allocation approach. These benefits include a notable reduction in total cost and a concurrent enhancement in product quality.

An approach for optimal tolerance allocation of five-axis machine tools by simultaneously considering volumetric error and processing simplicity index

Optimal tolerance allocation (OTA) is one of the most effective ways to improve the machining precision of machine tools. However, the existing OTA methods have the problem that tolerance-cost models are particularly vulnerable to subjective factors, which lead to tolerance allocation scheme with poor applicability and reliability. For this reason, a novel OTA method that simultaneously considers volumetric error and processing simplicity index (PSI) is proposed in this paper. Based on the multi-body system theory and homogeneous transform matrix, the volumetric error prediction model based on tolerance of machine tools’ key parts is firstly established by taking the geometric error as a bridge between tolerance and volumetric error of machine tools. Then, the weight coefficient of each tolerance parameter is calculated based on sensitivity analysis method. Moreover, PSI, which denotes the degree of processing simplicity to reach the required tolerance value, is innovatively proposed to replace manufacturing cost. And the tolerance-PSI model is established to replace tolerance-cost model. Then, an OTA model is established by minimizing volumetric error and maximizing PSI. The NSGA-II is employed to obtain OTA scheme. Finally, simulations and experiments are conducted to validate the feasibility and effectiveness of the presented method.

A collaborative hybrid approach for integrated tolerance allocation

ABSTRACT 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.

Optimal tolerance allocation for non-rigid assembly considering the effect of deformation on functional requirement and quality loss cost

Optimal tolerance allocation for non-rigid assembly considering the effect of deformation on functional requirement and quality loss cost

Associated tolerance optimization approach using manufacturing difficulty coefficients and genetic algorithm

Purpose The purpose of this paper is to establish a tolerance optimization method based on manufacturing difficulty computation using the genetic algorithm (GA) method. This proposal is among the authors’ perspectives of accomplished previous research work to cooperative optimal tolerance allocation approach for concurrent engineering area. Design/methodology/approach This study introduces the proposed GA modeling. The objective function of the proposed GA is to minimize total cost constrained by the equation of functional requirements tolerances considering difficulty coefficients. The manufacturing difficulty computation is based on tools for the study and analysis of reliability of the design or the process, as the failure mode, effects and criticality analysis (FMECA) and Ishikawa diagram. Findings The proposed approach, based on difficulty coefficient computation and GA optimization method [genetic algorithm optimization using difficulty coefficient computation (GADCC)], has been applied to mechanical assembly taken from the literature and compared to previous methods regarding tolerance values and computed total cost. The total cost is the summation of manufacturing cost and quality loss. The proposed approach is economic and efficient that leads to facilitate the manufacturing of difficult dimensions by increasing their tolerances and reducing the rate of defect parts of the assembly. Originality/value The originality of this new optimal tolerance allocation method is to make a marriage between GA and manufacturing difficulty. The computation of part dimensions difficulty is based on incorporating FMECA tool and Ishikawa diagram This comparative study highlights the benefits of the proposed GADCC optimization method. The results lead to obtain optimal tolerances that minimize the total cost and respect the functional, quality and manufacturing requirements.

Minimization of total manufacturing cost of a knuckle joint assembly by means of optimal tolerance allocation using various optimization algorithms

In the present work, the minimization of total manufacturing cost of an assembly considering tolerance allocation using various optimization algorithms have been addressed. Complex assembly which consists of more than one critical dimension with any one dimension of the part involved in more than one dimensional chain has been considered in this work. The manufacturing cost of the various parts of an assembly with tolerance allocation has been minimized using the cost tolerance model. The benchmark solution to the problem has been derived using Lagrange Multiplier (LM) method. The results are improved using Genetic Algorithm (GA) and Artificial Bee Colony (ABC) algorithm by considering the Alternate Nominal Dimension Selection (ANDS). The results have been compared with LM method and found GA outperformed ABC algorithm. Further the research has been extended by considering ANDS and Alternate Process Selection (APS) using Teaching-Learning Based Optimization (TLBO) algorithm and the results have been compared with benchmark solutions. The proposed method is suitable for any type of complex assembly. An Improved Knuckle Joint (IKJ) assembly has been chosen for the illustration of proposed methodology with an implementation strategy. From the results, it was noted that TLBO yielded better results in the aspect of minimizing the total manufacturing cost of IKJ assemblies.

Optimal tolerance allocation for five-axis machine tools in consideration of deformation caused by gravity

Due to the effect of gravity on machine tools, the small deformations inevitably exist. The existing tolerance allocation methods are based on the rigid body assumption, which ignore the small deformations. It will make optimization results inaccurate and increase manufacturing cost. Therefore, a new optimal tolerance allocation method, which integrates the small deformations, is presented in this paper. The establishment of a geometric error model based on tolerance is involved at first. Based on this model and multi-body system theory, the mapping relationship between tolerance and volumetric error of the five-axis machine tool (FAMT) is formulated. Secondly, the small deformations of the FAMT are obtained based on finite element analysis. Then, the optimal tolerance allocation model is established by integrating the small deformations into the constraint conditions. Thirdly, simulation analysis is carried out with this model by using a genetic algorithm. Then, the optimal tolerance allocation scheme is obtained, and the total manufacturing cost after optimization is reduced by approximately 11.5%. Finally, the volumetric errors of the FAMT are calculated based on the two tolerance allocation schemes. The results show that the volumetric errors are within the permitted ranges. Therefore, the proposed method in consideration of the small deformation is feasible and effective.

A framework for tolerance design considering systematic and random uncertainties due to operating conditions

PurposeThe purpose of this paper is to present a novel Kriging meta-model assisted method for multi-objective optimal tolerance design of the mechanical assemblies based on the operating conditions under both systematic and random uncertainties.Design/methodology/approachIn the proposed method, the performance, the quality loss and the manufacturing cost issues are formulated as the main criteria in terms of systematic and random uncertainties. To investigate the mechanical assembly under the operating conditions, the behavior of the assembly can be simulated based on the finite element analysis (FEA). The objective functions in terms of uncertainties at the operating conditions can be modeled through the Kriging-based metamodeling based on the obtained results from the FEA simulations. Then, the optimal tolerance allocation procedure is formulated as a multi-objective optimization framework. For solving the multi conflicting objectives optimization problem, the multi-objective particle swarm optimization method is used. Then, a Shannon’s entropy-based TOPSIS is used for selection of the best tolerances from the optimal Pareto solutions.FindingsThe proposed method can be used for optimal tolerance design of mechanical assemblies in the operating conditions with including both random and systematic uncertainties. To reach an accurate model of the design function at the operating conditions, the Kriging meta-modeling is used. The efficiency of the proposed method by considering a case study is illustrated and the method is verified by comparison to a conventional tolerance allocation method. The obtained results show that using the proposed method can lead to the product with a more robust efficiency in the performance and a higher quality in comparing to the conventional results.Research limitations/implicationsThe proposed method is limited to the dimensional tolerances of components with the normal distribution.Practical implicationsThe proposed method is practically easy to be automated for computer-aided tolerance design in industrial applications.Originality/valueIn conventional approaches, regardless of systematic and random uncertainties due to operating conditions, tolerances are allocated based on the assembly conditions. As uncertainties can significantly affect the system’s performance at operating conditions, tolerance allocation without including these effects may be inefficient. This paper aims to fill this gap in the literature by considering both systematic and random uncertainties for multi-objective optimal tolerance design of mechanical assemblies under operating conditions.

Unique transfer of functional requirements into manufacturing dimensions in an interactive design context

Tolerance allocation and transfer are two important engineering tasks. In fact, the assembly quality improvement and tolerances cost reduction are relied on optimal transfer and tolerance allocation while respecting the functions depend and manufacturing requirements. The traditional approaches reduce the tolerance values during the transfer of the design dimension on the manufacturing dimensions and expand the tolerance manufacturing cost as well. However, these approaches are unsuitable for a concurrent engineering context. This paper proposes a unique transfer approach of mechanism–dimension from the functional requirements to the manufacturing dimensions of parts. The traditional approaches for the transfer of mechanisms–dimensions in parts-dimensions are firstly presented. Then, a case study of the manufacturing dimensions specification based on Bourdet and Wade is detailed. The obtained results lead to avoid the tolerance reduction generated by the double dimensions transfer of traditional industrial approaches. A comparative study of allocated tolerances of manufacturing dimensions is presented for each approach. Therefore, the compared approaches classification is performed according to various criteria as the number of manufacturing dimensions, the values of the allocated tolerance and the calculated total cost based on the tolerances’ manufacturing cost and quality loss. In addition, the proposed method based on the unique transfer promotes the field of interactive engineering. In fact, the unique transfer requires the collaborative work and interactive exchange of expertise between different actors of the product development cycle.

An interactive method for computer-aided optimal process tolerance design based on automated decision making

Interactive and integrated design and manufacturing can be a useful strategy for designers to reach the efficient design through the cognitive or physical interactions. Process tolerance design is a key tool in the integrated design and manufacturing to reach a product with high quality and low cost. Since the optimal tolerance allocation involves several aspects of the design, manufacturing and quality issues, it is always a time consuming and difficult procedure, especially for complex products. Therefore, to overcome these difficulties, a computer-aided approach for optimal tolerance design of manufacturing process is needed in the design stage. In this paper, a novel interactive framework is introduced for computer-aided multi-objective optimal process tolerance design established upon entropy-based decision making. According to the proposed method, the optimal process tolerances of components are allocated through a multi-objective optimization problem where the process capability function and the overall manufacturing cost should be simultaneously optimized. To model the proper objective functions, the new formulations of process capability and manufacturing cost functions are proposed based on the design and customer’s requirements on the virtual model in CAD software, and the experimental observations, respectively. The non-dominated sorting genetic algorithm II is used for solving the multi-criteria optimization. For automated decision making to find the best process tolerances from the optimal Pareto solutions without objective weighting, an improved entropy-based TOPSIS is used. Based on the obtained optimal process tolerances and specifications, the process planning procedure can be carried out. Finally, to illustrate the capability of the proposed method and to validate it, a windmill transmission assembly as a case study is considered and the computational results are compared and discussed.

Two-stage optimization model for process/supplier selection, component allocation, and quality improvement

AbstractA company has to produce a product that gives better value than its competitors. It means the company has to produce a better quality product with lower manufacturing cost. Outsourcing has become a common practice in manufacturing where a company outsources some of their needed components to the suppliers. Supplier selection is not an easy task since it will determine the manufacturing cost and quality of the product. In this research, we develop a two-stage optimization model to help decision maker in determining the optimal suppliers which will give least manufacturing cost and how to improve the quality of the components. In the first stage, a process/supplier selection model was developed to determine the optimal tolerance and component allocation to minimize manufacturing cost and quality loss. In the second stage, investment allocation model was developed to improve the quality of the components. The objective function of the second model is to maximize the return on investment (ROI). The im...

Optimal tolerance allocation based on Difficulty matrix using FMECA tool

The cost and quality of the product depend directly on the tolerance values. Especially, the tolerance allocation is an important engineering function involving a direct impact on compliance with functional and manufacturing requirements. The mastery of this function requires the use of a tool to analysis the reliability of the process as well as a method to optimize the tolerances. Thus, this work proposes an innovative tolerance allocation method based on the Failure Mode, Effects and Criticality Analysis (FMECA) tool as well as a Lagrange Multiplier (LM) approach.The difficulty of obtaining manufacturing dimensions is evaluated through a mathematical coefficient calculated using FMECA tool. The failure causes are the different sources of the manufacturing difficulty. The above sources are identified according to the diagram of Ishikawa. A suitable FMECA worksheet for the analysis is established for each type of manufacturing operation. A CAD model is developed to determine dimension chains as well as to identify manufacturing operations and influenced dimensions. The proposed LM method solves the tolerance allocation problems by quantifying manufacturing dimension difficulty and minimizing the tolerance cost. The results of a case study are compared with those of the standard methods using a cost model. This comparative study confirms that the proposed method reduces the total assembly cost considering manufacturing cost and quality loss.

Concurrent optimal allocation of geometric and process tolerances based on the present worth of quality loss using evolutionary optimisation techniques

Concurrent tolerancing becomes an optimisation problem to find out the optimum allocation of the process tolerances in the given design function constraints. In traditional optimisation methods, finding out the optimum solution for this advanced tolerance design problem is complex. The proposed algorithms (elitist non-dominated sorting genetic algorithm) and differential evolution extensively do better than the previous algorithms for attaining the optimum result. The aim of this paper is to suggest a model for optimal tolerance allocation by considering both tolerance cost and the present worth of quality loss such that the total manufacturing cost/loss is minimised. The suggested model takes into account the time value of money for quality loss and product degradation over time and consists of two new parameters: the planning horizon and the product user’s discount rate. From the outcome of this study, a longer planning horizon results in an increase in both tolerance cost and quality loss; however, a larger value of discount rate gives up a decrease in both tolerance cost and quality loss. Finally, a practical example is brought into reveal the effectiveness of the suggested method.

Optimal Tolerance Allocation in a Complex Assembly Using Evolutionary Algorithms

Tolerance design is a vital factor which influences product and process development. Further, it determines the manufacturing cost, the functionality and quality of a product. It is evident that optimal tolerance normally leads to produce ample parts, better operation of mechanical systems and excellent assembling. In contrast, tight tolerance leads to increase in manufacturing cost for an assembly. An ideal relationship exists among production cost and operation, while determining the optimum tolerance. Based on this relation a new approach by implementing the Non-traditional techniques: Genetic Algorithm (GA), Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Differential Evolution (DE) for determining the optimum tolerance, zero percentage rejection and manufacturing cost considering the varying quality loss constants for an assembly namely overrunning clutch assembly, is discussed in this paper. From the result obtained, it is evident that, the proposed approach is best suitable for solving problems involving complex assemblies. (Received in May 2015, accepted in September 2015. This paper was with the authors 1 month for 1 revision.)

Variable coefficients reciprocal squared model based on multi-constraints of aircraft assembly tolerance allocation

In order to improve product quality and enhance economic returns, the research about tolerance allocation under multi-constraints including assembly and manufacturing accuracy is done. On the basis of cost-tolerance relationship, this paper introduces variable coefficients reciprocal squared model (VCRSM) into tolerance allocation process and thus constructs the tolerance allocation optimization objective model. Aiming at resolving multi-constraints problem within allocation process, the penalty items are added into allocation optimization objective model, and an analytic equation based on multi-constraints is proposed. The equation is solved using the Newton iteration method in consideration of the assembly and manufacturing accuracy constraints. Finally, a tolerance allocation instance about aircraft door component assembly is given. The numerical results show the method can achieve optimal tolerance allocation and the VCRSM is more suitable than other cost-tolerance models in multi-constraints tolerance allocation.

Optimal tolerance allocation for precision machine tools in consideration of measurement and adjustment processes in assembly

The high geometric accuracy requirement of precision machine tools represents a challenge for tolerance design and assembly process planning that guarantee the final assembly accuracy. Component tolerances should be allocated in association with assembly processes. However, tolerance design and assembly process planning are usually considered separately and lack quantitative analysis. In this paper, to integrate the geometric tolerance of components and variation propagation in assembly process, a state space model is developed. The measurement and adjustment process are expressed as observation matrix and control inputs. An optimal control problem is formulated to determine the adjustment process in consideration of the loss of final assembly accuracy and costs of remachining adjustment process. Tolerances of components can be optimally allocated based on the variation propagation in this deterministic assembly process. The generality and effectiveness of this approach are validated by applying the model on a four-axis horizontal machining center.

Optimal statistical tolerance allocation for reciprocal exponential cost–tolerance function

Statistical tolerancing has been widely employed in industry as it is more practical compared with the worst-case tolerancing in achieving lower manufacturing cost while satisfying design specification. As reciprocal exponential function is one of the commonly employed cost–tolerance models in practice and current approach is difficult to allocate statistical tolerances for such a function, this article investigates a method for optimal statistical tolerance allocation with such a cost–tolerance function. The method is to minimize manufacturing cost subject to constraints on tolerance target and machining capabilities. The optimization problem is solved by applying the algorithmic approach. Particularly, a closed-form expression of the tolerance optimization problem is further derived based on the Lagrange multiplier method with integrating the Lambert W function, a multivalue complex function. In addition, for constrained minimization problems with only equality constraints, the optimal tolerance allocation can be obtained by solving simultaneous equations without the time-consuming computing on differentiating while keeping the solution accurate. An example is illustrated to demonstrate the application of this approach. Through comparisons with the regular Lagrange multiplier method applied to reciprocal exponential cost–tolerance type, the result reveals that tolerances can be allocated much faster using this proposed method.

Multi-objective design and tolerance allocation for single- and multi-level systems

In this work we develop a method to perform simultaneous design and tolerance allocation for engineering problems with multiple objectives. Most studies in existing literature focus on either optimal design with constant tolerances or the optimal tolerance allocation for a given design setup. Simultaneously performing both design and tolerance allocation with multiple objectives for hierarchical systems increases problem dimensions and raises additional computational challenges. A design framework is proposed to obtain optimal design alternatives and to rank their performances when variations are present. An optimality influence range is developed to aid design alternatives selections with an influence signal-to-noise ratio that indicates the accordance of objective variations to the Pareto set and an influence area that quantifies the variations of a design . An additional tolerance design scheme is implemented to ensure that design alternatives meet the target tolerance regions. The proposed method is also extended to decomposed multi-level systems by integrating traditional sensitivity analysis for uncertainty propagation with analytical target cascading. This work enables decision-makers to select their best design alternatives on the Pareto set using three measures with different purposes. Examples demonstrate the effectiveness of the method on both single- and multi-level systems.

Optimal Statistical Tolerance Allocation of Assemblies for Minimum Manufacturing Cost

This paper explores a systematic method for optimal statistical tolerance allocation using the Lagrange multiplier method for minimizing manufacturing cost subject to constraints on dimensional chains and machining capabilities. The reciprocal power and exponential cost-tolerance models for statistical tolerancing are investigated for employing this method. The optimization problem is solved by applying the algorithmic approach. Especially, we further derive a closed-form expression of the tolerance optimization problem for reciprocal exponential cost-tolerance model by introducing the Lambert W function. For constrained minimization problems with only equality constraints, the optimum tolerance allocation can be obtained by solving simultaneous equations without further differentiating. An example is illustrated to demonstrate this approach. The result also shows that tolerances can be allocated quickly, economically and accurately using this method.

A Closed-Form Approach for Optimum Tolerance Allocation of Assemblies with General Tolerance-Cost Function

Tolerancing is one of the most crucial foundations for industry development and an index of product quality and cost. As tolerance allocation is based on manufacturing costs, this paper proposes a comprehensive method for optimal tolerance allocation with minimum manufacturing cost subject to constraints on dimensional chains and machining capabilities. The general reciprocal power and exponential cost-tolerance models with equality constraints as well as the worst-case and statistical tolerancings are employed in this method. A closed-form solution for the optimization problem by applying Lagrange multipliers is derived. The optimal tolerance allocation problem for reciprocal exponential cost-tolerance model by introducing Lambert W function is demonstrated. For constrained minimization problems with only equality constraints, the optimum design can be obtained by solving simultaneous equations without differentiating. An example is illustrated to demonstrate this approach. The result also shows that tolerance can be allocated economically and accurately using this method. The contribution of this paper is to solve the optimal tolerancing allocation problem by an efficient and robust method with simultaneous active constraints.