Minimum Zone Tolerance Research Articles

Minimum zone tolerance algorithm to detect roundness error for machined rods using vision system

Inspection of the circular components also include error in its roundness. Errors in roundness create difficulties in assemblies, lubrication distribution and creation unbalanced forces in rotational applications. Non contact approach for roundness measurement use several algorithms like least square algorithm, maximum inscribed circle algorithm, minimum circumscribed algorithm, minimum zone tolerance algorithm etc. These methods are used to find roundness error according to ANSI B89.3.1-1972 standard. The current research makes use of minimum zone tolerance algorithm is heuristic as it gives the precise error value and calculates the roundness error between the zone of two circles. At present this method is employed for measuring the roundness error in camera industries for measuring lens, in gear manufacturing etc. The experiment was carried for the both non contact and contact approach the results were compared. For both methods MZC was used and comparison was made for both the methods. Several contact measurement techniques are employed in industries to inspect roundness and one of the most accurate contact techniques used is CMM technique. The contact method, even though has ability to produce precise results, but it consumes more time. Main problem faced in contact type is wear and tear between the specimen and measuring probe. These disadvantages can be overcome by using image processing technology in measuring error in the roundness of a circular part. This paper gives details on the use of image processing technology in the measurement of roundness error. Finally the results of Both methods revel that there was difference of 9 to 15 µm. But Precession can be improved by using a proper lighting and having high resolution camera.

Sphericity measurement through a new minimum zone algorithm with error compensation of point coordinates

Sphericity is a relevant tolerance of form in many fields of engineering. Measuring sphericity is frequently accomplished through the fitting of the point coordinates obtained from coordinate measuring machines (CMMs) to a substitution sphere. This paper presents a new algorithm for sphericity of minimum zone tolerance. It faces its resolution through the flatness problem associated with the implicit formulation of the polar plane of the sphere. The polarity transformation allows the iterative resolution of the minimum zone sphericity through a simpler flatness problem. Its accuracy is compared with the least-squares solution and some well-known minimum zone algorithms from literature. Its performance reaches or surpasses them. Next, a new error compensation model of point coordinates for sphericity is developed. A model based on the regression of the error by each CMM axis is incorporated into the sphericity measurement model. The explained error propagated allows correcting the sphericity calculated by the CMM indication, but also facilitates the uncertainty estimation by the propagation of the unexplained residual error in the regression through the measurement model. The experimental verification by the Monte Carlo Method shows efficient results. The jointly proposed method of a new algorithm with error compensation and uncertainty estimation can effectively contribute to the improvement of sphericity measurement from point coordinates in precision and accuracy.

A new contouring error estimation for the high form accuracy of a multi-axis CNC machine tool

The evaluation of contouring error is important for multi-axis CNC machines because the tolerance specifications of manufactured parts are directly affected by contouring error. One of the fundamental quality inspections to verify that a manufactured part meets the expected tolerance is via form error evaluations. However, the existing estimation methods of contouring error are based on the position tolerance requirements. To meet the form tolerance requirements for the parts, this paper focuses on developing a high-accuracy estimation method of contouring error that is not related to a datum (ND-contouring error). In the proposed estimation method, at first, the minimum zone tolerance (MZT) method is used to transform the ideal tool tip path to match the actual one. Subsequently, by comparing the position and orientation between the actual point and the nearest point on the transformed ideal tool path, the ND-contouring error and orientation contouring error of the tool can be estimated, respectively. In addition, the difference between the proposed estimation method and previous evaluation methods is comparatively analyzed. Finally, simulations and experiments are conducted by applying the S-shaped and B-shaped machining trajectories, respectively, and the results all verify the estimation accuracy of the ND-contouring error estimation method. By adoption of compensation based on the ND-contouring error estimation, the contouring error could be significantly reduced, which will improve the quality of parts.

Analysis of Methods for Estimation of Machine Workpiece Roundness

One of the parameters most commonly used in the control of workpieces complex form is roundness. Increasing requirements to the workpieces form accuracy determines the relevance of improving methods and instruments for the control of form surfaces. The paper presents the analysis of three methods of roundness calculation by using Maximum Inscribed Circle, Least Squares Circle, Minimum Zone Tolerance Circle. A Matlab software have been developed for this application package. The input data consisted of the coordinates, obtained by the control the external surface of the rollers and the inner surface of the raceways ring bearing on the precision roundness measurement instrument, the toroidal profile of the raceways bearing rings on the Coordinate Measuring Machine. Based on these studies it was revealed that in all cases, the best result is provided at the use of the Minimum Zone Tolerance Circle from the mean value and standard deviation of roundness.

Vectorial method of minimum zone tolerance for flatness, straightness, and their uncertainty estimation

Flatness and planar straightness are fundamental form tolerances in engineering design and its materialization through manufacturing processes. Minimum zone tolerance is a preferred approach of flatness and straightness for widely accepted ISO and ANSI standards. In this paper, we propose a novel accurate method of minimum zone tolerance based on vectorial calculus of point coordinates. The non-linear minimax formulation of the original flatness or straightness problem is transformed into a set of linear problems. Next, the optimal solution of the envelop planes or lines is reached through vectorial calculus for both flatness and planar straightness. Then, the developed algorithms are compared to a selection of methods with published tests in recent and classic literature on the topic, reaching the best attained accuracies or outperforming them in the trials. Finally, we propose a new decomposition of the uncertainty contributions for analysis and the improvement of sampling strategy. We conclude remarking the practical contributions of the proposals.

Optimum Dataset Size and Search Space for Minimum Zone Roundness Evaluation by Genetic Algorithm

Roundness is one of the most common features in machining. The minimum zone tolerance (MZT) approach provides the minimum roundness error, i.e. the minimum distance between the two concentric reference circles containing the acquired profile; more accurate form error estimation results in less false part rejections. MZT is still an open problem and is approached here by a Genetic Algorithm. Only few authors have addressed the definition of the search space center and size and its relationship with the dataset size, which greatly influence the inspection time for the profile measurement and the convergence speed of the roundness estimation algorithm for a given target accuracy. Experimental tests on certified roundness profiles, using the profile centroid as the search space center, have shown that the search space size is related to the number of dataset points and an optimum exists, which provides a computation time reduction up to an order of magnitude.

Roundness: A closed form upper bound for the centroid to minimum zone center distance by worst-case analysis

The minimum zone tolerance (MZT) meets the ISO 1101 definition of roundness error: it determines two concentric circles that contain the roundness profile and such that the difference in radii is the least possible value.This article provides theoretical evidence that the minimum size of the neighborhood of the centroid containing the minimum zone center is π−1EC, where EC is the roundness error related to the centroid, which can be evaluated in closed form.The implications of such linear estimating are twofold: (i) locating the part center with a given tolerance, e.g. for manufacturing tasks, such as handling (peg–hole) or machining (centering) and (ii) providing a search area for minimum zone center-based algorithms, such as metaheuristics (GA, PSO, etc.).

Minimum Zone Evaluation of Symmetry Error for Flatness to Flatness Based on the New Generation GPS

Least square method (LSM) is the most popular method used to evaluate machining error nowadays. However, LSM is likely to overestimate the error value, therefore its solution is only approximate and rather than minimum. In order to obtain the minimum, we study the principle of the minimum zone tolerance method (MZT), analyze the characteristics of the new generation GPS, and give the minimum zone mathematic model of the symmetry error for flatness to flatness. For the purpose of optimizing the mathematical model, this paper describes the application of adaptive genetic algorithm to achieve the best estimation. Simultaneously, the process of optimization is realized by MALTAB. Finally, the experiment shows that the evaluation results of MZT is better than evaluation results of LSM.

Optimal blind sampling strategy for minimum zone roundness evaluation by metaheuristics

Abstract The minimum zone tolerance is a non linear method to find a global solution to the roundness evaluation problem. Metaheuristics such as genetic algorithms, ant colony systems and particle swarm optimization concurrently process a set of solution candidates (chromosomes, ants, particles etc.) within a given search-space. Computation experiments carried out with an effective genetic algorithm have shown that the optimal sampling strategy providing sufficient accuracy at acceptable processing time represents a compromise between number of sample points and search-space size. An estimate of the neighborhood of the centroid containing the minimum zone center is given.

A Dichotomy Searching Algorithm for Planar Straightness Error

The evaluation algorithm of planar straightness error is discussed. A new kind of method that named as Dichotomy Searching Algorithm (DSA) is presented to implement the minimum zone tolerance for evaluating planar straightness errors. The algorithm meets the principle of the minimum zone tolerance. The principle of the algorithm is that two special provision points are constructed based on the starting endpoint and end endpoint respectively firstly, then the four presume centerlines can be established by connecting the preset two special provision points of the starting endpoint to the preset two special provision points of the end endpoint in turn, after that, calculate the distances between all the measured points and the supposed centerlines. The minimum zone straightness error is obtained by means of compare, judgment and set the new special provision points repeatedly. This algorithm is substantiated with typical examples and the results show that the algorithm can be used to achieve precise computation of planar straightness errors.

Fast genetic algorithm for roundness evaluation by the minimum zone tolerance (MZT) method

According to ISO 1101, “A geometrical tolerance applied to a feature defines the tolerance zone within which that feature shall be contained”. The main goal of the minimum zone tolerance (MZT) method is to achieve the best estimation of the roundness error, but it is computationally intensive. This paper describes the application of a genetic algorithm (GA) to minimize the computation time in the evaluation of CMM roundness errors of a large cloud of sampled points. Computational experiments have shown that by selecting the optimal GA parameters, namely a combination of the five genetic parameters related to population size, crossover, mutation, stop condition, and search space, the computation time can be reduced by up to one order of magnitude, allowing real-time operation. Optimization has been tested using seven CMM samples, obtained from different machining features. The performance of the optimized algorithm has been validated using four benchmark samples from the literature and with certified samples.

Flatness tolerance evaluation: an approximate minimum zone solution

This paper is concerned with the problem of flatness tolerance evaluation. First, we introduce the concepts of width and inner radius of point sets, and establish the equivalence between the width of a point set and the inner radius of the convex hull of the self-difference of the set. On this basis, we present an algorithm for calculating the exact minimum zone tolerance of flatness. Second, we prove that an approximation of the inner radius of a convex set can be obtained from the inner radius of the set in fixed direction. On this basis, we present an algorithm for calculating the ‘almost exact’ minimum zone solution. This algorithm is implemented by solving a single linear programming problem, of which the computational complexity is O( n). Numerical examples are given to validate the proposed algorithms.

A unified approach to form error evaluation

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.

A new convex-hull based approach to evaluating flatness tolerance

In this paper, we consider a minimum-zone evaluation problem for flatness to determine the minimum tolerance zone enclosing all the measurement points obtained from a surface. For the problem, a new geometric approach called the ‘convex-hull edge method’ (CONHEM) is proposed. The method guarantees the minimum zone tolerance for a given set of measurement points. Several examples discussed by other researchers are illustrated to compare the method with some existing approaches.