Tolerance Charts Research Articles

Statistical quality control charts: new tools for studying the body mass index of populations from the young to the elderly.

Statistical quality control charts (SQCCs) have been widely used in numerous manufacturing processes to keep fluctuations within the acceptable limits but no applications have been applied to weight management studies yet. The aims of the present study were (1) to show that using the mean Body Mass Index (BMI) values as the only indicator to assess the weight status of populations might be misleading in clinical weight management studies; and (2) to introduce a powerful tool, SQCCs, to keep fluctuations in BMIs within acceptable limits in a given population for healthy aging. The study design was cross-sectional. The distributions of individual BMIs (n=829) between specified limits (USL=24.9 and LSL=18.5) and the pattern of BMI change by age were studied using X-charts, tolerance charts and a capability analysis. The mean BMI increased in both genders by age. In some groups, although a significant number of people were outside the normal weight BMI limits the mean BMI values were within the normal limits (18.5<BMI < 24.9). In addition, although the number of overweight individuals was greater in some groups, their mean BMIs were lower compared to the groups with fewer overweight individuals. Capability tests clearly show that each group, even the groups with a mean BMI in the normal weight ranges and also the groups which are referred as being "under control" according to the X-charts, was not in energy balance (Cp<1 and Cpk<1). The results clearly indicate that using the mean BMIs as the only indicator might be misleading in weight management studies. This study introduces SQCCs as a potential tool for clinical nutrition studies to maintain the fluctuations of individual BMIs within acceptable limits for healthy aging populations.

Automatic generation of min/max tolerance charts for tolerance analysis from CAD models

The so-called min/max tolerance charts are popular for analysing tolerance accumulation in parts and assemblies, despite the fact that this method is limited to one-dimensional worst-case analysis. Since different chart construction rules apply to different tolerance classes, the user has to remember all the different rules to construct a valid tolerance chart. Constructing the charts manually, as is common practice in industry today, is time-consuming and error-prone. This paper presents procedures for automating tolerance charting. It requires a computer aided design (CAD) model with GD&T specifications as input. The automation is based on a data model called the constraint-feature-tolerance (CTF) graph and machine interpretable representation of charting rules specific to each tolerance class. This paper also presents procedures for automatically extracting dimension and tolerance stacks for any user defined analysis dimension, and automatic part arrangement in assemblies corresponding to worst case analyses. Important implementation issues are also discussed and several case studies are presented, the results of which have been verified by manual chart construction.

Dimensional and geometrical tolerance balancing in concurrent design

In conventional design, tolerancing is divided into two separated sequential stages, i.e., product tolerancing and process tolerancing. In product tolerancing stage, the assembly functional tolerances are allocated to BP component tolerances. In the process tolerancing stage, the obtained BP tolerances are further allocated to the process tolerances in terms of the given process planning. As a result, tolerance design often results in conflict and redesign. An optimal design methodology for both dimensional and geometrical tolerances (DGTs) is presented and validated in a concurrent design environment. We directly allocate the required functional assembly DGTs to the pertinent process DGTs by using the given process planning of the related components. Geometrical tolerances are treated as the equivalent bilateral dimensional tolerances or the additional tolerance constraints according to their functional roles and engineering semantics in manufacturing. When the process sequences of the related components have been determined in the assembly structure design stage, we formulate the concurrent tolerance chains to express the relations between the assembly DGTs and the related component process DGTs by using the integrated tolerance charts. Concurrent tolerancing which simultaneously optimizes the process tolerance based on the constraints of concurrent DGTs and the process accuracy is implemented by a linear programming approach. In the optimization model the objective is to maximize the total weight process DGTs while weight factor is used to evaluate the different manufacturing costs between different means of manufacturing operations corresponding to the same tolerance value. Economical tolerance bounds of related operations are given as constraints. Finally, an example is included to demonstrate the proposed methodology.

A Comparative Study Of Tolerance Analysis Methods

This paper reviews four major methods for tolerance analysis and compares them. The methods discussed are: (1) one-dimensional tolerance charts; (2) parametric tolerance analysis, especially parametric analysis based on the Monte Carlo simulation; (3) vector loop (or kinematic) based tolerance analysis; and (4) ASU Tolerance-Map® (T-Map®) (Patent pending; nonprovisional patent application number: 09/507, 542 (2002)) based tolerance analysis. Tolerance charts deal with worst-case tolerance analysis in one direction at a time and ignore possible contributions from the other directions. Manual charting is tedious and error prone, hence, attempts have been made for automation. The parametric approach to tolerance analysis is based on parametric constraint solving; its inherent drawback is that the accuracy of the simulation results are dependent on the user-defined modeling scheme, and its inability to incorporate all Y14.5 rules. The vector loop method uses kinematic joints to model assembly constraints. It is also not fully consistent with Y14.5 standard. The ASU T-Map® based tolerance analysis method can model geometric tolerances and their interaction in truly three-dimensional context. It is completely consistent with Y14.5 standard but its use by designers may be quite challenging. The T-Map® based tolerance analysis method is still under development. Despite the shortcomings of each of these tolerance analysis methods, each may be used to provide reasonable results under certain circumstances. Through a comprehensive comparison of these methods, this paper will offer some recommendations for selecting the best method to use for a given tolerance accumulation problem.

A CAD/CAM Representation Model Applied to Tolerance Transfer Methods

This paper presents the adaptation of tolerance transfer techniques to a model called TTRS for Technologically and Topologically Related Surfaces. According to this model, any three-dimensional part can be represented as a succession of surface associations forming a tree. Additional tolerancing information can be associated to each surface association represented as a node on the tree. This information includes dimensional tolerances as well as tolerance chart values. Rules are then established to infer tolerance chains or stack up along with tolerance charts directly from the graph. This way it becomes possible to combine traditional one dimensional tolerance transfer techniques with a powerful three-dimensional representation model providing high technological contents.

A Matrix Method for Calculating Working Dimensions and Offsets for Tolerance Charting

This paper presents a new matrix method for calculating working dimensions and offsets for tolerance charts. The method is part of a more general datum hierarchy tree technique for tolerance planning and control. The matrix method is suitable for both manual and computer-aided computation. It has been implemented in an industrial program, CATCH, and a prototype artificial intelligence (AI) program for process planning. The method has been successfully taught to engineering students in New Zealand and Finland. Worked examples are provided to illustrate the method. The examples show how to calculate working dimensions without offsets, and how to calculate an offset working dimension and an offset resultant dimension.

Extending the algebraic method to identify dimensional chains for angular tolerance charting

Tolerance charting, as a practical tool to determine nominal working dimensions and their tolerances for the process operations of a product, has been used in manufacturing industry for many decades. In the past years, many researchers have made great efforts on the tolerance charts for products with square-shouldered features (that is, 1D tolerance charting) and a few researchers have discussed tolerance charts for products with angular features, which are more complicated than the former. A few researchers have even presented an approach to identifying dimensional chains for angular tolerance charting. This paper proposes an algebraic method to establish dimensional chains for angular tolerance charting, which is the extension of the previous algebraic approach for 1D tolerance charting. The problems and characteristics of angular tolerance charting and the new algebraic approach are discussed. Both the forward and the reverse dimensional chains can be obtained from the algebraic method, so the nominal values and tolerances of the working dimensions can be determined. An example is presented to illustrate the method.

Optimal process plans for manufacturing and tolerance charting

A graph theoretical approach is presented that permits the calculation of optimal process plans from datum hierarchy trees, which are elegant representations of tolerance charts. The theory is developed for a cost function that minimizes machine and datum changes. Restrictions on the sequence of machining operations arising from technical constraints or the layout of a group cell are taken into account. The process plans are optimal with respect to a specified datum hierarchy tree, manufacturing constraints and cost function. It is shown that the number of possible plans for real industrial trees is very large, and therefore this kind of optimization is beyond the ability of a human process planner. Trial runs with industrial parts indicate that optimization can be performed by a computer within a time period that is acceptable for industrial use.

Evaluation of alternative tolerance allocations for multiple machining sequences with geometric tolerances

The purpose of tolerance charting is to allocate working dimensions and tolerances such that the designed blueprint dimensions and tolerances can be achieved. For a given part description, there may exist multiple machining sequences that can be used to produce the same part. In tolerance charting, the multiple machining sequences represent different ways that the working dimensions and tolerances can be allocated. In this research, the alternative tolerance allocations for the multiple machining sequences with geometric tolerances are evaluated. First, the geometric tolerances are transformed into equivalent linear specifications and constraints. Second, the linear tolerances and geometric tolerances are combined in an integrated model and solved based on the objective of maximizing the cumulative sum of working tolerances. Finally, the integrated tolerance charting methodology is performed to evaluate the multiple machining sequences. The goal is to find the machining sequence that can be performed with the best objective value. The three-dimensional (3-D) prismatic parts are defined by solid modelling data and the machining sequences are described using featurebased models. The three-dimensional tolerance charts are developed for the 3-D prismatic parts. The new idea is to integrate linear and geometric tolerances in an integrated tolerance charting methodology for finding the most suitable machining sequences. The developed methodology is implemented on a personal computer. Example parts are tested and discussed.

CAPP and its integration with tolerance charts for machining of aircraft components

Computer-aided process planning (CAPP), indispensable for industry automation, is credited the technical index for the aerospace industry. The objective of this research lies in developing a CAPP system to co-operate with fabrication of aircraft components, which are complicated and manifold in geometric shapes and manufacturing processes. Process charts are sheets output from a CAPP system and are typically used in the aerospace industry to assist machine operators in carrying out workshop machining tasks. Its contents include part name, part number, operation number, machining department, machining tool, machining operation, operation illustration, etc. Among these, operation illustration is the most tedious, yet important, data to make in illustrating the part machining processes. As a result, the CAPP system addressed in this paper possesses a special feature of integrating operation illustration with process database. In this paper, the development of a variant process planning system will first be addressed. The methodology for automatic generation of operation illustration, and its integration with process planning, is then discussed.

The Noded graph approach to stack analysis

The tolerance chart is a graphical method for representing the manufacturing dimensions of a workpiece or assembly, at all stages of its manufacture. The chart provides an intermediate control system of checks and balances to ensure that processing dimensions and tolerances will meet those specified on the print. Tolerance charts are generally used in studying the dimensional problems on individual parts. However, they have proved tedious in their application to assemblies. This paper presents a simple and systematic approach to the process of tolerance stack analysis. The “Noded graph” model is constructed, representing the given and the unknown dimensions. Links are then established, using the model, which help to formulate the stack path of interest into a linear equation. The equation is used to complete the tolerance stack analysis module. This will be explained using a variety of geometric dimensioning and tolerancing examples. In addition, it is simple and hence easy to practise and very logical.

Statistical process control application to weld process

A statistical weld process monitoring system is described. Using data collected while welding, the welding statistical process control (SPC) tool provides weld process quality control by implementing techniques of data trending analysis, tolerance analysis, and sequential analysis. The SPC system computes the mean, standard deviation, and range of each of the parameters sampled by the data collection system. Changes in the mean, standard deviation, and range are displayed using control (or trend) charts. The control chart displays a function of a parameter with respect to the ordering of the weld records (for a single weld) or weld number (for multiple welds). The SPC tool also permits plotting tolerance charts of the mean, standard deviation, and range for each of the sampled parameters. The tolerance chart is plotted versus the record number (or weld number) and consists of a vertical line for each record (or weld number) showing the minimum and maximum value of that parameter for that record (or weld number). The upper control limit (UCL), lower control limit (LCL), and nominal value may also be displayed on the tolerance chart printout. The SPC also performs sequential analysis, which allows the user to examine the process as it goes along, which in turn may permit the user to locate a possible change in the process before it goes out of control. Work directed toward developing an expert interpreter of the voluminous statistical output generated by the SPC is also described.

An object-oriented system for tolerance charting

This paper presents a scheme to automate the entire process of tolerance charting. An object-oriented database called TOLCHAIN is developed to support this scheme. TOLCHAIN stores all the necessary information for tolerance charts to determine the intermediate machining tolerance values automatically. It is assumed that the part is stored as a boundary model. Feature volumes are then constructed from the boundary model to perform the tool accessibility analysis and to determine the process sequence. The intermediate machining tolerances are derived automatically from the boundary model.

Tolerance Stack Analysis for Assembly

Studies have indicated that design for manufacture and design for assembly have a significant impact on the success of a product. One of the key issues is tolerance specification and thus it is important for the designer to consider tolerance analysis thoroughly in the early stages of product development. With minor modifications and if used properly, tolerance charting can be a valuable tool to the product designer. This paper illustrates two methods used to tackle tolerance balancing for assembly and provides an insight into the considerations to be taken into account. A manual method first demonstrates the fundamental concepts while a computer aided version further enhances the charting process. The latter is easy to apply and renders greater flexibility during problem formulation. Consequently, what–if analysis is possible and thus better results can be achieved. However, it should be cautioned that tolerance charts are merely tools; the results they produce can only be as good as the inputs they receive and thus a ‘perfect’ solution cannot be guaranteed. Nonetheless, tolerance charting is an effective diagnostic tool as it provides tolerance analysis in the early stage of products development.

Tolerance control for dimensional and geometrical specifications

The development of tolerance charts has come a long way from the past manual methods to the current computer-aided models. As a result, many techniques have emerged over the years. However, the area of geometrical tolerance charting has not been given much attention. In view of this, this paper addresses both linear and geometrical tolerance control.

Optimal allocation of process tolerances and stock removals

Tolerance charts have been used as an effective tool to ensure that a specific processing sequence is appropriate for a product of the required dimensions. Different arrangements of manufacturing tolerances and amount of stocks to be removed at each machining operation result in different production costs. Instead of existing heuristic, experience-based methods, this paper presents a new approach by means of which process tolerances and stock removals are simultaneously allocated through an optimization program, In approaching the optimal design, a cost function, the value of which varies with design variables (process tolerance and stock removal at individual cuts), is chosen as the objective to be minimized. During the searching process, the variables are subject to the constraints derived from dimension chains associated with a tolerance chart.

A list approach to tolerance charting

Tolerance charts for mechanical components are essential to the planning of manufacturing processes as well as to the assurance of product quality. The design of such a chart, however, is not only a time-consuming job but also highly reliant upon engineer's expertise. This paper presents a new approach which utilizes list representation to assist the analysis as well as the computation during the generation of tolerance charts. The method has been successfully implemented on a computer-aided design software based on a personal computer.

A complete tolerance charting system

Abstract Manual computation of tolerance charts is both tedious and time-consuming. This paper presents an efficient method of automatically determining the working dimensions and their balanced tolerances. With this method, the feasibility of different process plans can be evaluated efficiently and economically. A unique algorithm, based on a special path tracing technique, is developed to reduce the unknown working dimensions to a system of linear equations. The Gauss elimination technique is then employed to solve for the working dimensions. The tolerance balancing process is accomplished using a separate mathematical model. The complete system, comprising the tolerance charting and optimization modules, is finally tested on an example.

A rule-based system for angular tolerance charting

Different manufacturing processes and their sequences have different effects on tolerance build-ups. An oversight on the effect of tolerance build-up often leads to rework and excessive scrap. This paper describes a rule-based system for developing angular tolerance charts. Mathematical equations for computing the mean working dimensions and their tolerances for typical manufacturing processes are presented. The procedures involved in calculating the mean working dimensions, mean stock removal and their tolerances are shown. The general rule-sets adopted to compute the above are also presented.

A graph-theoretic approach to tolerance charting

A major problem for manufacturing companies is the effective integration of design and production. Tolerance charts provide one means of aiding this integration. Manually produced charts are time-consuming and have not been widely adopted. This paper presents an elegant graph-theoretic approach to tolerance charting suitable for use with a microcomputer. The approach has the potential to significantly reduce the amount of work required in charting, and so it can be used by small companies as well as large ones.