Maximum Material Condition Research Articles

Impact of Temperature Variations on Torque Capacity in Shrink-Fit Junctions of Water-Jacketed Permanent Magnet Synchronous Motors (PMSMs)

This study investigates the impact of temperature variations on the torque capacity of shrink-fit junctions in water-jacketed permanent magnet synchronous motors. Focusing on both baseline and improved designs; torque capacities were evaluated across a temperature range from −40 °C to 120 °C under different material conditions: Least material condition, nominal, and maximum material condition. The baseline design exhibited torque capacities from 7648 Nm to 9032 Nm at −40 °C, decreasing significantly to 549 Nm to 1533 Nm at 120 °C. The improved design showed enhanced performance, with torque capacities ranging from 8055 Nm to 9247 Nm at −40 °C and from 842 Nm to 1618 Nm at 120 °C. The maximum improvement was observed at 120 °C for least material conditions, with a 55.4% increase, and the minimum improvement at −40 °C for maximum material conditions, with a 2.4% increase. Our findings demonstrate a significant increase in torque capacity by up to 20% under varied thermal conditions. These results underscore the effectiveness of design modifications in enhancing thermal stability and torque capacity, making the improved design a more reliable choice for high-performance applications subject to significant thermal fluctuations. This research highlights the critical role of material selection, thermal management, and precise design adjustments in optimizing the performance and reliability of permanent magnet synchronous motors.

Computer-Aided Design/Tolerancing Integration: A Novel Tolerance Analysis Model of Assemblies With Composite Positional Defects and Deformations of Nonrigid Parts

Abstract Nowadays, the tolerancing integration in computer-aided design (CAD) tools remains among the major goals of mechanical manufacturers. In the virtual product development, ideal and rigid models are used in the digital mockup (DMU). Hence, research works developed integrated CAD models for tolerance analysis, while considering manufacturing defects. However, the tolerance analysis in the case of composite positional tolerance for feature patterns, commonly used in the industry, becomes a difficult activity with the consideration of parts deformations. Thus, this paper presents a novel CAD model for the tolerance analysis considering composite positional defect of features set and nonrigid component deformations due to external mechanical loads. The modeling of rigid components with dimensional defects is established based on the numerical perturbation method. Indeed, the relationships between driving and driven dimensions are determined to obtain the configurations in maximum and least material of the CAD model. Thereafter, the geometrical deviations are modeled by face displacements. The modeling of composite positional errors is performed while respecting the feature relating position tolerance zone framework and the pattern-location tolerance zone framework constraints, as well as the maximum or least material condition. The deviations caused by nonrigid part deformations are considered by the integration of finite element results into the CAD model. The realistic configurations of the assembly are obtained after the updating of mating constraints between rigid and nonrigid parts with defects. The composite positional tolerance is analyzed with the simulation of relative motion between parts. A case study is proposed to evaluate the developed tolerancing method.

The Calculation Method of the Inspection Tolerance Zone When Two Datum Features Apply MMC/LMC

When the datum features apply the maximum or least material condition (MMC/LMC), the shift tolerance, because of the departure of the actual mating size of the datum features from their extreme condition, can be added to the stated tolerance of the related feature, thereby improving the acceptance rate of the parts. However, it is difficult to calculate the shift tolerance when more than one datum feature applies MMC/LMC. In this paper, a general calculation method of the inspection tolerance zone (ITZ) based on the linkage mechanism model is proposed. The Datum Feature Simulators (DFSs) at actual virtual condition are used to construct the measurement datum reference frame (DRF), and the DFSs at the stated MMC/LMC condition are used to construct the design DRF. In the proposed methodology, the relative position between the design DRF and the measurement DRF is simulated by the series combination of two linkage mechanisms, the measurement DRF is fixed at the mechanism frame, the design DRF is fixed at target linkage, and the kinematic envelope of the design tolerance zone at design DRF corresponds to the ITZ. The combination of the datum features for applying MMC/LMC is investigated, and the combination principles of the representation mechanism for different combinations of the datum features are discussed. An example is given to demonstrate the proposed method.

Intelligent DMU Creation: Toleranced Part Modelling to Enhance the Digital Environment

This paper describes a method for the consideration of tolerance stack ups in the computer-aided design (CAD) environment as design concepts are developed into digital mock ups (DMUs). The method functionality includes the capability to create maximum (MMC) and least material condition (LMC) versions of the nominally sized components, allowing the three sets of entities to co-exist while respecting the positional constraints of the nominal master model. As the user switches between MMC and LMC combinations across a number of components, the overall dimensions of the assembly within the DMU change accordingly. The assembly constraints are regenerated through an equivalencing method based on surface properties, to respect the assembly intention. The new DMU, therefore, is an improved reflection of ‘as manufactured’ part forms making assembly analysis and the allocation of tolerances more accurate at the conceptual design stage, a novel function not currently available in commercial CAD software.

A comprehensive fuzzy feature-based method for worst case and statistical tolerance analysis

Tolerance analysis is an analytical tool for the estimation of accumulating effects of the individual part tolerances on the functional requirements of a mechanical assembly. This article presents a comprehensive feature-based method for tolerance analysis of mechanical assemblies with both dimensional and geometric tolerances. In this method, dimensional and geometric tolerance zones are described by the combination of fuzzy modelling and small degrees of freedom (SDOF) concept. In this model, the uncertainty in dimensions and geometric form of features is mathematically described using fuzzy modelling, and the kinematic effects of tolerances in assemblies are expressed by SDOF concept. In the proposed method, complicated GD&T concepts such as various material modifiers (maximum material condition, least material condition and regardless of feature size), envelope requirement, bonus tolerances and Rule No. 1 (Taylor principle) in several conditions are accurately modelled. Compatible with the proposed model, a procedure for modified worst case and statistical tolerance accumulation analysis is introduced. An algorithm is laid out that describes the steps and the procedure of tolerance analysis. The application of this method is demonstrated through an example, and the results are compared with experimental results.

Position Tolerance Process Capability Prediction under Maximum Material Condition

Process capability prediction methods for position tolerance under maximum material condition were discussed in this paper. Due to application of maximum material condition the position tolerance specification varied individually for each part, percentage normalization and minimum gap methods were introduced to calculate the position process capability index. Link was taken as an example, true position percentage normalization and minimum gap of 30 parts were calculated. Considering the true position constitution relative to position tolerance at maximum material condition, related individual percentages were used to express the result and the same tolerance size 100% was obtained as for a unilateral tolerance. Set the acceptable value was 0, minimum gap between a hole and a simulated position gauge pin is studied instead of position. The process capability prediction results of two methods were calculated by Minitab software.

Calculation Method on Process Capability Index of True Position Based on Maximum Material Condition

This paper focuses on process capability evaluation method for position tolerance under maximum material condition. Due to application of maximum material condition the position tolerance specification varies individually for each part, the approach of percentage normalization is introduced to calculate position process capability index. Bush is taken as an example, and true position percentage normalization of 30 parts are calculated. Considering the true position constitution relative to position tolerance at maximum material condition, related individual percentages are used to express the result and the same tolerance size 100% is obtained as for a unilateral tolerance. Process Capability index is calculated with Minitab software.

Evaluating the effect of tolerances on the functional requirements of assemblies

In order to improve digital mock-up, a tolerancing phase should be integrated in the geometric models. However, in CAD software, tolerances are represented by annotations, which are neglected as well as the tolerance impact. Thus, the system malfunction is generated. For these reasons, in this paper a tolerancing phase is integrated in the numerical model to form a realistic model, where worst case configurations of assemblies are determined from the tolerances assigned to the nominal model. The proposed model incorporates tolerances on CAD models in the case of planar face, cylindrical face and planar face with non quadratic loop. In addition, the model ability to respect the maximum material condition (MMC) and the requirement of datum priority order in the CAD models is shown. Finally, functional requirement of a linear guide mechanism is inspected by using the proposed model.

Sphericity Evaluation Based on Minimum Circumscribed Sphere Method

The search of sphericity evaluation is a time-consuming work. The minimum circumscribed sphere (MCS) is suitable for the sphere with the maximum material condition. An algorithm of sphericity evaluation based on the MCS is introduced. The MCS of a measured data point set is determined by a small number of critical data points according to geometric criteria. The vertices of the convex hull are the candidates of these critical data points. Two theorems are developed to solve the sphericity evaluation problems. The validated results show that the proposed strategy offers an effective way to identify the critical data points at the early stage of computation and gives an efficient approach to solve the sphericity problems.

Sphericity Evaluation Using Maximum Inscribed Sphere Method

The maximum inscribed sphere (MIS) method is an important method to evaluate sphericity error suitable for the sphere with the maximum material condition of a concave. It is proven that the MIS of a data point set is decided only by four points in the paper. An algorithm of sphericity evaluation based on the MIS is proposed. Six points with extreme coordinates are selected as an initial subset and the MIS is constructed by four of them. Another point which is the farthest from the center among the set replaces one of the former four points each time. According with the minimum criterion, the final sphere is just the MIS of the data point set when all data points is outside the sphere. The validated results show that the proposed strategy offers an effective way to identify the control data points at few iterative turns and gives an efficient approach to solve the sphericity problems.

Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MI-SDOF) concepts

Tolerance analysis is a key analytical tool for estimation of accumulating effects of the individual part tolerances on the design specifications of a mechanical assembly. This paper presents a new feature-based approach to tolerance analysis for mechanical assemblies with geometrical and dimensional tolerances. In this approach, geometrical and dimensional tolerances are expressed by small degrees of freedom (SDOF) of geometric entities (faces, feature axes, edges, and features of size) that are described by tolerance zones. The uncertainty of dimensions and geometrical form of features due to tolerances is mathematically described using modal interval arithmetic. The two concepts of modal interval analysis and SDOF are combined to describe the tolerance specifications. The algorithm is presented which explains the steps and the procedure of tolerance analysis. The proposed method is compatible with the current GD&T standards and can incorporate GD&T concepts such as various material modifiers (maximum material condition, least material condition, and regardless of feature size), envelope requirement, and bonus tolerances. This method can take into account multidimensional effects due to geometrical tolerances in tolerance analysis. The application of the proposed method is illustrated through presenting an example problem and comparing results with tolerance charting method.

Statistical Tolerance Allocation for Tab-Slot Assemblies Utilizing Tolerance-Maps

A new mathematical model for representing the geometric variations of tabs/slots is extended to include probabilistic representations of 1D clearance. The 1D clearance can be determined from multidimensional variations of the medial-plane for a slot or a tab, and from variations of both medial-planes in a tab-slot assembly. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map (Patent No. 6963824) (T-Map), a hypothetical volume of points that models the range of 3D variations in location and orientation for a segment of a plane (the medial-plane), which can arise from tolerances on size, position, orientation, and form. Here it is extended to model the increases in yield that occur when the optional maximum material condition (MMC) is specified and when tolerances are assigned statistically rather than on a worst-case basis. The frequency distribution of 1D clearance is decomposed into manufacturing bias, i.e., toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is built from geometric bias, and it is presumed that manufacturing bias is uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled tab and slot. A comparison is made between the effects of specifying the optional MMC and not specifying it with the tolerance that determines the allowable variations in position of a tab, a slot, or of both in a tab-slot assembly. Statistical tolerance assignment for the tab-slot assembly is computed based on initial worst-case tolerances and for (a) constant size of tab and slot at maximum material condition, and (b) constant virtual-condition size.

Using Tolerance-Maps to Generate Frequency Distributions of Clearance and Allocate Tolerances for Pin-Hole Assemblies

A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of one-dimensional (1D) clearance, which arise from positional variations of the axis of a hole, the size of the hole, and a pin-hole assembly. The model is compatible with the ASME/ ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map (T-Map) (Patent No. 69638242), a hypothetical volume of points that models the 3D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here, it is extended to model the increases in yield that occur when maximum material condition (MMC) is specified and when tolerances are assigned statistically rather than on a worst-case basis; the statistical method includes the specification of both size and position tolerances on a feature. The frequency distribution of 1D clearance is decomposed into manufacturing bias, i.e., toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is built from geometric bias, and it is presumed that manufacturing bias is uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole. A comparison is made between the effects of choosing the optional material condition MMC and not choosing it with the tolerances that determine the allowable variations in position.

Establishing Conformity to Tolerances by Coordinate Measuring Machines: A First Step for a Statistical Approach

Conformity to tolerances is currently assessed taking into account the maximum material condition. Coordinate measuring machines do not however operate accordingly, a small sample only of points on workpiece surface being actually contacted, with a fairly low chance of hitting the outmost point. That problem should therefore be properly addressed using statistical methods, as currently considered also by the ISO Technical Committee on “Geometrical Product Specifications and Verification.” This paper proposes to associate maximum material with the statistical distribution of maximum; typical examples of saw-tooth and round grooved surface profiles are theoretically examined. An actual surface with a good finish, representing the common case of normal distribution, was experimentally evaluated, showing that the method proposed produces consistent results. Furthermore, the method proposed readily associates results obtained with a statistical confidence interval; the uncertainty of results obtained can thus be assessed at any given confidence level.

Process capability requirement under maximum material condition

A frequently used geometrical tolerance is the position tolerance. When it is assigned at the maximum material condition (MMC), an increase in the position tolerance is allowed, equal to the departure of the particular feature from the maximum material condition size. Neither concept - position tolerance and maximum material condition - analytically related with the exact coordinate dimensions that locate the feature. A feature position is usually allocated on the basis of its theoretically exact co-ordinate dimensions, whereas positional accuracy is pursued through an appropriate planning of the machining process in conjunction with appropriate machine tool(s) and/or jig(s). Exploitation of the MMC tolerance bonus is taken into account mainly during part inspection in order to reduce rejects. Such an approach is not systematic, considering that the MMC benefits are not taken directly into account in the process planning stage in order to control the overall process cost. In this paper, the permitted manufacturing errors of a feature size and position are considered and studied simultaneously in an analytical way. It is shown that a lower process capability (PC) requirement can then be established that leads to a significant process cost reduction. An application example demonstrates the use of the method and the obtained results are discussed.

Maximum material condition in process planning

Appropriate and cost effective assignment and interpretation of dimensional and geometrical tolerances, in conjunction with tolerancing principles such as the maximum material condition (MMC), constitute a major area of concern for manufacturing SMEs. This is particularly true for the process planning stage, where production operations and parameter values establish the final product quality and cost. A frequently used geometrical tolerance is the position tolerance. It allows at least 57% more space for feature allocation without affecting product quality and is very useful for accurate specification of multiple-hole assemblies. Feature allocation becomes further relaxed in case a position tolerance is assigned to the MMC. This assignment is mainly exploited during inspection, because it permits fewer rejections. In terms of cost, it is advantageous to systematically integrate the MMC tolerance bonus into the position tolerance at the process planning stage. A methodology that allows a new MMC-adapted position tolerance to be calculated is presented in this paper. The new, increased, position tolerance can then be taken into consideration early in the process planning stage, in order to achieve lower production cost, without affecting the quality.

A scheme for mapping tolerance specifications to generalized deviation space for use in tolerance synthesis and analysis

Tolerances impose restrictions on the possible deviations of features from their nominal sizes/shapes. These variations of size/shape could be thought of as deviations of a set of generalized coordinates defined at some convenient point on a feature. Any tolerance specification for a feature imposes some kind of restrictions or constraints on its deviation parameters. These constraints, in general, define a bounded region in the deviation space. In this paper, a method has been presented for converting tolerance specifications as per maximum material condition (MMC)/least material condition (LMC)/regardless of feature size (RFS) material conditions for standard mating features (planar, cylindrical, and spherical) into a set of inequalities in a deviation space. Both virtual condition boundaries Virtual condition boundary: A constant boundary generated by the collective effects of a size feature's specified MMC or LMC material condition and the geometric tolerance for that material condition. (VCB) and tolerance zones are utilized for these mappings. The mapping procedures have been illustrated with an example. Note to Practitioners-This paper deals with methods to convert tolerance specification as per ASME Y14.5M into a set of generalized deviation of features and vice-versa. These are intermediate relationships that are required for use in deviation-based tolerance synthesis methods. In this work, different examples have been presented to show how different tolerance specifications (such as positional tolerance at maximum material condition (MMC), least material condition (LMC), etc.) applied to different features could be treated on a generalized basis for tolerancing of manufactured parts.

Mathematical Analysis of Three-dimensional Geometric Tolerances of Mechanical Products : Analysis under Maximum Material Condition(Digital design and digital manufacturing (continued))

Mathematical Analysis of Three-dimensional Geometric Tolerances of Mechanical Products : Analysis under Maximum Material Condition(Digital design and digital manufacturing (continued))

Tolerance synthesis: quantifier notion and virtual boundary

The purpose of functional tolerancing process is to define the geometrical specifications of parts ensuring functional requirements. For automotive and aircraft industries, the tolerance synthesis has become an important issue in product design process. Indeed, designers need methods and rules to determine the tolerances. To define rules, a mathematical formulation of tolerance synthesis is detailed. This mathematical formulation of tolerance synthesis simulates the influences of geometrical deviations on the geometrical behavior of the mechanism, and integrates the quantifier notion (existential quantifier ‘there exists’ and universal quantifier ‘for all’). It takes into account not only the influence of geometrical deviations but also the influence of the types of contacts on the geometrical behavior of the mechanism; these physical phenomena are modeled by convex hulls (compatibility hull, interface hull and functional hull) which are defined in parametric space. With this description by convex hulls, a mathematical expression of the admissible deviations of parts integrates the quantifier notion. This notion translates the concept that a functional requirement must be respected in at least one acceptable configuration of gaps (existential quantifier there exists), or that a functional requirement must be respected in all acceptable configurations of gaps (universal quantifier for all). With this approach, some rules are formalized to determine the modifier (maximum material condition or minimum material condition) function from the type of quantifier. These rules have been performed with success in French automotive industries.

A Statistical Approach to Process Planning

Abstract This paper presents a formal method for the process planning of machined components using a statistical methodology that can be used in design to determine the percent defective for feature-based tolerance specifications when used in conjunction with a process planning system or more specifically a process tolerance chart. The paper begins with an approach for process selection and then goes through an illustration of a tolerance specification for hole features under a location specification of Regardless of Feature size. Once a formal process plan has been developed, a probability model is used in conjunction with a process tolerance chart to determine the effects of feature size and location specification on percent defective and product cost. A discussion is presented and the model is expanded to include location specification under Maximum Material Condition and Least Material Condition.