Geometrical and dimensional tolerance analysis for the radial flux type of permanent magnet generator design

Mechanical tolerance is something that should be carefully taken into consideration and cannot be avoided in a product for manufacturing and assembly needs, especially in the design stage, to avoid excessive dimensional and geometric deviations of the components made. This paper discusses how to determine and allocate dimensional and geometric tolerances in the design of a 10 kW, 500 rpm radial flux permanent magnet generator prototype components. The electrical and mechanical design results in the form of the detailed nominal dimensions of the generator components, and the allowable air gap range are used as input parameters for tolerance analysis. The values of tolerance allocation and re-allocation process are carried out by considering the capability of the production machine and the ease level of the manufacturing process. The tolerance stack-up analysis method based on the worst case (WC) scenario is used to determine the cumulative effect on the air gap distance due to the allocated tolerance and to ensure that the cumulative effect is acceptable so as to guarantee the generator's functionality. The calculations and simulations results show that with an air gap of 1 ± 0.2 mm, the maximum air gap value obtained is 1.1785 mm, and the minimum is 0.8 mm. The smallest tolerance value allocation is 1 µm on the shaft precisely on the FSBS/SRBS feature and the rotor on the RPMS feature. In addition, the manufacturing process required to achieve the smallest tolerance allocation value is grinding, lapping, and polishing processes.

Toward cost-efficient tolerancing of 3D-printed parts: a novel methodology for the development of tolerance-cost models for fused layer modeling

Tolerance allocation methods significantly contribute to the qualification of Additive Manufacturing (AM) for (small-)series production ensuring high performance and efficiency. However, their usage prerequisites the availability of quantitative, reliable information on the impact of the assigned tolerances on the resulting manufacturing costs. The given article proposes a novel methodology for the systematic development of tolerance-cost curves for a cost-efficient tolerancing of 3D-printed parts. The proposed structured workflow aims at serving as a general guideline for both researchers and practitioners, while the exemplarily chosen perspective from Fused Layer Modeling (FLM) illustrates its adaption to a specific AM technology. The indirect, non-apparent interrelations between tolerances and resulting costs are modelled with the aid of an activity-based cost model, whereas the individual costs elements are mapped as function of the values for the machine-specific process parameters for AM, e.g., layer height or printing speed, which are required to achieve the assigned design tolerances. The total procedure covers all relevant steps, viz. the identification and quantification of the single cost items, the design of benchmark artifacts, adapted to given manufacturing and measuring techniques, the empirical determination of data on cost and geometrical accuracy by design of experiments and tolerance-cost curves. Its exemplary application to an academic use case shows its general applicability and benefits, but also its current limitations.

Tolerance analysis and optimization based on 3DCS

At present, with the increasing requirements of major enterprises on assembly accuracy, the problem of interference and excessive clearance between parts needs to be solved. In order to analyze and optimize the tolerances in the actual assembly of the parts, a three-dimensional vector ring model is proposed on the basis of the dimensional chain model, and the tolerance distribution is optimized by the “dichotomy method”. With the help of 3DCS, the virtual assembly of the automobile headlight is carried out, and the sensitivity analysis is carried out by establishing the measurement of the gap between the turn signal and headlight in the automobile headlight, and the simulation results are used to obtain a reasonable improvement in tolerance allocation that meets the design criteria and saves costs. The results are compared with the traditional method of optimizing the allocation of equal tolerances and are clearly superior, providing a method for optimizing the allocation of tolerances to parts in engineering practice.

Multiobjective Optimization Method and Application of Tolerance Allocation for the Steam Turbine Based on Cooperative Game Theory

Aiming at the optimization problem of multiple objectives with contradictions and conflicts in the process of allocating the tolerance for complex products, taking advantage of the features of coordinating, and balancing contradictions and conflicts of cooperative game theory, this paper uses cooperative game theory to solve the multiobjective optimization problem of tolerance allocation. The quality requirements and cost requirements of assembly products are used as the game decision parties, and the fuzzy clustering method is used to group the design variables of tolerance allocation problem of the steam turbine to form the strategic space of game parties. Take the quality level and cost level of the assembly product as the optimization goals, complete the calculation of the utilities of the two game parties, and establish the multiobjective optimization model of tolerance allocation based on cooperative game theory. Finally, the Shapley value method based on cooperative game theory, the Nash equilibrium method based on noncooperative game theory, and the traditional single-objective optimization method with the quality as the constraint and the cost as the optimization objective are used to solve the tolerance allocation problem of steam turbine. The solution results show that the method of cooperative game realized the balance, coordination, and comprehensive optimization of the quality and cost from the perspective of collective interests, overcame the shortcomings of the traditional single-objective optimization method, and obtained better result than the Nash equilibrium method.

Knowledge creation and application of optimal tolerance distribution method for aircraft product assembly

Purpose This paper aims to illustrate the tolerance optimization method based on the assembly accuracy constrain, precession constrain and the cost of production of the assembly product. Design/methodology/approach A tolerance optimization method is an excellent way to perform product assembly performance. The tolerance optimization method is adapted to the process analysis of the hatch and skin of an aircraft. In this paper, the tolerance optimization techniques are applied to the tolerance allocation for step difference analysis (example: step difference between aircraft cabin door and fuselage outer skin). First, a mathematical model is described to understand the relationship between manufacturing cost and tolerance cost. Second, the penalty function method is applied to form a new equation for tolerance optimization. Finally, MATLAB software is used to calculate 170 loops iteration to understand the efficiency of the new equation for tolerance optimization. Findings The tolerance optimization method is based on the assembly accuracy constrain, machinery constrain and the cost of production of the assembly product. The main finding of this paper is the lowest assembly and lowest production costs that met the product tolerance specification. Research limitations/implications This paper illustrated an efficient method of tolerance allocation for products assembly. After 170 loops iterations, it founds that the results very close to the original required tolerance. But it can easily say that the different number of loops iterations may have a different result. But optimization result must be approximate to the original tolerance requirements. Practical implications It is evident from Table 4 that the tolerance of the closed loop is 1.3999 after the tolerance distribution is completed, which is less than and very close to the original tolerance of 1.40; the machining precision constraint of the outer skin of the cabin door and the fuselage is satisfied, and the assembly precision constraint of the closed loop is satisfied. Originality/value The research may support further research studies to minimize cost tolerance allocation using tolerance cost optimization techniques, which must meet the given constrain accuracy for assembly products.

A Novel Methodology for Simultaneous Minimization of Manufacturing Objectives in Tolerance Allocation of Complex Assembly

Tolerance cost and machining time play crucial roles while performing tolerance allocation in complex assemblies. The aim of the proposed work is to minimize the above-said manufacturing objectives for allocating optimum tolerance to the components of complex assemblies, by considering the proper process and machine selections from the given alternatives. A novel methodology that provides a two-step solution is developed for this work. First, a heuristic approach is applied to determine the best machine for each process, and then a combined whale optimization algorithm with a univariate search method is used to allocate optimum tolerances with the best process selection for each sub-stage/operation. The efficiency of the proposed novel methodology is validated by solving two typical tolerance allocation problems of complex assemblies: a wheel mounting assembly and a knuckle joint assembly. Compared with previous approaches, the proposed methodology showed a considerable reduction in tolerance cost and machining time in relatively less computation time.

Research on the Optimal Allocation of Tolerances of CNC Machine Tools Based on Small Deformation of Grinding Wheel

In order to solve the problem of precision optimization design of CNC machine tools, this paper proposes an optimized allocation method of machine tool tolerance parameters that takes into account the slight deformation of the machine tool. First, establish a tolerance-based geometric error prediction model, and establish a spatial motion error model based on the theory of multi-body systems(MBS); Homogeneously, perform finite element analysis(FEA) on the CNC internal cylindrical compound grinding machine to obtain the slight deformation of the machine tool, and apply the result to the optimal tolerance allocation In the constraint conditions, the final optimal allocation plan is obtained; Finally, the genetic algorithm is used to simulate and analyze the plan, and the optimal tolerance allocation result is obtained. The result shows that most of the tolerance parameters have been relaxed, which means that the machine tool’s manufacturing cost. Through experiments, it is verified that the optimized machine tool machining accuracy pass rates are 98.5%, 98.25%, and 97.85%, respectively. Therefore, the optimal allocation method of tolerances that considers small deformations proposed in this paper is effective.

A Novel Approach to Calculating the Transmission Accuracy of a Cycloid-Pin Gear Pair Based on Error Tooth Surfaces

Transmission error (TE) and backlash are important parameters used to evaluate the transmission accuracy of cycloid-pin drives. Existing calculation methods are mostly based on two-dimensional tooth profile models, and these methods ignore the influence of some abnormal meshing phenomena caused by profile modifications (PMs), manufacturing errors (MEs), and assembly errors (AEs), such as the instantaneous mesh-apart of tooth pairs and the eccentric load on the tooth surface. To fill this gap, a novel approach to accurately calculating the TE and backlash of a cycloid-pin gear pair based on the error tooth surfaces is proposed, and its feasibility and effectiveness are validated by comparison with the theoretical analyses and the results from the literature. Based on this, the effects of the PMs, MEs, and AEs on the transmission accuracy are studied, which will be helpful in optimizing the tooth profile design of a cycloid gear and the tolerance allocation during the installation of a gear pair. The proposed method is also expected to provide accurate error excitation data for the dynamic analysis of cycloid-pin drives.

A Novel Methodology for Simultaneous Minimization of Manufacturing Objectives in Tolerance Allocation of Complex Assembly

A novel methodology is presented in this work to minimize the manufacturing objectives, namely tolerance cost and machining time for allocating optimum tolerance to the components of complex assemblies with considering the proper process and machine selections from the given alternatives. A methodology that provides a two-step solution is developed for this work. First, a heuristic approach is applied to determine the best machine for each process, and then a combined Whale optimization algorithm with a univariate search method is used to allocate optimum tolerances with the best process selection for each sub-stage/operation. The efficiency of the proposed novel methodology is validated by solving two typical tolerance allocation problems of complex assemblies: a wheel mounting assembly and a knuckle joint assembly. Compared with previous approaches, the proposed methodology showed a considerable reduction in tolerance cost and machining time in relatively less computation time.