S. Hossein Cheraghi

A unified approach to form error evaluation

Abstract Evaluation of form error is a critical aspect of many manufacturing processes. Machines such as the coordinate measuring machine (CMM) often employ the technique of the least squares form fitting algorithms. While based on sound mathematical principles, it is well known that the method of least squares often overestimates the tolerance zone, causing good parts to be rejected. Many methods have been proposed in efforts to improve upon results obtained via least squares, including those, which result in the minimum zone tolerance value. However, these methods are mathematically complex and often computationally slow for cases where a large number of data points are to be evaluated. Extensive amount of data is generated where measurement equipment such as laser scanners are used for inspection, as well as in reverse engineering applications. In this report, a unified linear approximation technique is introduced for use in evaluating the forms of straightness, flatness, circularity, and cylindricity. Non-linear equation for each form is linearized using Taylor expansion, then solved as a linear program using software written in C++ language. Examples are taken from the literature as well as from data collected on a coordinate measuring machine for comparison with least squares and minimum zone results. For all examples, the new formulations are found to equal or better than the least squares results and provide a good approximation to the minimum zone tolerance.

Straightness and flatness tolerance evaluation: an optimization approach

This paper presents an optimization approach that could be used to calculate exact values of straightness and flatness errors as defined by the ANSI Y14.5M standards on geometric dimensioning and tolerancing. The straightness and flatness error evaluation problems are formulated as nonlinear optimization problems with linear objective function and nonlinear constraints. Because of the special structure of the problem, a linear search method is developed that reduces the nonlinear problem to a linear programming problem with only two constraints. Examples are presented to compare the optimization approach with the least-squares method and some exact methods. The results show that the optimization procedures presented in this paper provide exact values of straightness and flatness errors and are superior to the existing methods in terms of computation time.

Machining Damage in Edge Trimming of CFRP

Conventional machining processes such as turning, milling, drilling, abrasive cutting, and grinding are commonly used to bring composite parts to final shape and assembly requirements. However, due to the layered nature of these materials, their machining may generate undesirable defects such as delamination and high surface roughness. The service life of composite components is believed to be highly dependent on machining quality and damage due to machining may result in scraping expensive parts. In this work, an experimental investigation was conducted to determine the effect of spindle speed, feed rate, and tool condition on machining quality of carbon fiber reinforced polymer (CFRP) composites during edge trimming operation. Machining quality was quantified in terms of average delamination depth and surface roughness. Delaminations were also characterized by their type and frequency of occurrence. It was found that average delamination depth and surface roughness increase with an increase in feed rate and an increase in cutting distance and decrease with an increase in spindle speed. There is a strong relationship between delamination damage and effective chip thickness. The cutting conditions for best machining quality are high spindle speed and low feed rate, which correspond to small effective chip thickness. The most frequent delamination type was found to be Type I/II.

Circularity error evaluation: Theory and algorithm

Many procedures for the evaluation of circularity error based on different criteria have been developed. The procedures that are based on the minimum radial separation criterion are either too complex or lack an algorithmic approach to find optimal solution. This paper presents an optimization-based technique to find the value of circularity error based on the minimum radial separation criterion. The problem is formulated as a nonlinear optimization problem. Based on the developed necessary and sufficient conditions a generalized nonlinear optimization procedure is presented. The performance of the developed procedure is analyzed for different size problems generated using a simulation program. Results indicate that the procedure is accurate and very efficient in solving large size real life problems.

Facility layout design for multiple production scenarios in a dynamic environment

Facility design approaches often focus on a single production demand scenario and develop a layout that minimises the Material Handling (MH) costs for that scenario. In a volatile and uncertain production environment, facility layouts should be designed while taking into consideration multiple demand scenarios to minimise the effects of uncertainty. In a risk-averse situation, where multiple probable demand scenarios exist, designing the layout for any one scenario could lead to high losses if any other scenario occurs. In such situations, all demand scenarios have to be considered and the facility should be designed to minimise the maximum loss (Minmax approach) due to MH costs in a manufacturing plant by considering all possible scenarios. This paper proposes a new facility layout design model to determine a compromise layout that can minimise the maximum loss in MH cost both for single and multiple periods. The model developed has been further modified to address minimisation of the total expected loss as well. The resulting mathematical models are solved to generate improved layouts using Genetic Algorithm (GA) approach. The proposed models are solved for single-period and multiperiod case studies. Results indicate that the proposed models generate compromise layouts which are efficient in reducing maximum possible loss and as well in minimising the total expected loss.

Evaluating the geometric characteristics of cylindrical features

This paper presents mathematical models and efficient methodologies for the evaluation of geometric characteristics that define form and function of cylindrical features; namely cylindricity and straightness of median line. These two problems have similar structures and can be solved by comparable procedures. Based on the proposed methodologies, the cylindricity error evaluation can be performed using any of the following criteria: the least squares cylinders, minimum circumscribed cylinders, maximum inscribed cylinders or minimum zone cylinders. The procedures have been tested for accuracy and efficiency. The results indicate that they provide accurate results quickly.

An optimization approach to shape matching and recognition

Abstract An optimization approach to shape matching and recognition is presented. The technique is a vertex based technique that uses surface contact as a criterion for measuring similarity. Given an object (polygon O) and a reference template (polygon T), the feasible region generated by polygon T is continuously magnified (expanded or contracted) by a factor, e, and polygon O is translated and rotated such that it falls inside T. The objective is to minimize the magnification factor. The problem is formulated as a nonlinear optimization problem with a linear objective function and nonlinear constraints. A search-based procedure is used to solve this problem. To ensure global optimality, the nonlinear constraints are replaced by their linear approximations. The results show that the procedure is very effective in recognizing similar objects.

Evaluation of 3-D feature relating positional error

Position tolerance is a three dimensional geometric specification used to control the location of features of size with respect to a set of datum features or with respect to each other. Among features of size, hole is perhaps most frequently encountered in the production of industrial parts. To control the relationship between a set of holes, feature relating position tolerance (referred to as FRTZ) is used. FRTZ is applied to ensure proper assembly between mating parts. Assessment of feature relating positional error is a difficult task due to the absence of a datum reference frame whose function is to impose translational and rotational constraints on the part. Existing techniques for the assessment of FRTZ are either too expensive, or time consuming and inaccurate. This paper presents a mathematical model of three-dimensional feature-relating positional error and proposes a sound methodology for its evaluation. The results of performance analysis indicate that the proposed methodology is robust, accurate and efficient. The procedure has been implemented in a computer-aided inspection system.

Ant algorithms: web-based implementation and applications to manufacturing system problems

Abstract One of the tools in the gamut of global optimization search procedures is ant algorithms, inspired by the behaviour of the well-known insects—ants. Natural ant colonies exhibit ad-hoc decision-making processes in their day-to-day living activities, such as foraging and brooding. These processes could be modelled and used as tools to solve many practical scheduling problems that are present in current manufacturing environments. This paper proposes web-based ant colony system algorithm (WACSA) optimization procedures to solve several real-world manufacturing systems problems. The problems considered are: (1) single-machine scheduling optimization considering tool wear; (2) drilling sequence optimization; and (3) single-machine scheduling considering total job changeover cost. Results indicate that WACSA provides an optimal solution quickly. It also shows that the ant algorithm is preferred over existing meta-heuristics, as it provides a high level of scheduling flexibility.

Sphericity error evaluation: theoretical derivation and algorithm development

Several methods for the evaluation of sphericity error exist. The Minimum Radial Separation (MRS) spheres method is a method that has been studied by several researchers. In the MRS criterion, two concentric spheres at minimum radial separation must be found such that they contain all points on the actual spherical surface. The existing procedures for finding MRS spheres are either too complex and time consuming or do not provide an optimal solution to the sphericity error evaluation problem. In this paper, mathematical optimization concepts are utilized to develop a theory and an algorithm for the evaluation of sphericity error based on MRS criterion. Results indicate that the algorithm is fast and accurate in providing optimal solution to the sphericity error evaluation problem.