Minimum Zone Error Research Articles

A Novel Iterative Field Search Approach to Minimum Zone Circle for Roundness Error Estimation

Abstract Roundness is one of the common attributes in the manufacturing industry. Roundness is the most prominent of the extant fundamental forms, as the majority of the fabricated components are round or cylindrical. The examination of roundness error associated with such features is critical since inadequate evaluation might result in the rejection of excellent parts. The performance of any equipment depends on the mating parts. Out-of-roundness components cause the inefficiency of such equipment’s system performance. As a result, roundness error assessment is critical for macro-sized specimens as well as for micro- and nano-sized components. The present article proposes a novel approach to Minimum Zone Circle (MZC) to evaluate the roundness error. An iterative field search methodology is used in the suggested approach. The proposed methodology evaluates the roundness error based on the generated discretized points within the search space and continues the same by decreasing the search space with an increase in the number of iterations to attain the Minimum Zone Error (MZE). The proposed algorithm has been tested with ten CMM (coordinate measuring machine) datasets and ten form datasets available in the literature studies and found to be excellent in comparison to the existing techniques. Further, the proposed methodology was also implemented to estimate the MZE of centerless ground specimens at multiple cross sections, and the roundness error obtained was lesser as compared to the LSC, MCC, and MIC. The number of generated discretized points is flexible and can be varied to reduce the number of iterations and computations. The recommended method is quite effective in assessing the roundness error when compared to the existing techniques. It also works well on data that was both evenly and unevenly spaced. The results suggest that altering the search field area for higher computing efficiency is straightforward, resilient, and versatile.

The minimum zone fitting and error evaluation for the logarithmic curve based on geometry optimization approximation algorithm

The minimum zone fitting and error evaluation for the logarithmic curve has important applications. Based on geometry optimization approximation algorithm whilst considering geometric characteristics of logarithmic curves, a new fitting and error evaluation method for the logarithmic curve is presented. To this end, two feature points, to serve as reference, are chosen either from those located on the least squares logarithmic curve or from amongst measurement points. Four auxiliary points surrounding each of the two reference points are then arranged to resemble vertices of a square. Subsequently, based on these auxiliary points, a series of auxiliary logarithmic curves (16 curves) are constructed, and the normal distance and corresponding range of values between each measurement point and all auxiliary logarithmic curves are calculated. Finally, by means of an iterative approximation technique consisting of comparing, evaluating, and changing reference points; determining new auxiliary points; and constructing corresponding auxiliary logarithmic curves, minimum zone fitting and evaluation of logarithmic curve profile errors are implemented. The example results show that the logarithmic curve can be fitted, and its profile error can be evaluated effectively and precisely using the presented method.

Form Error Evaluation of Noncontact Scan Data Using Constriction Factor Particle Swarm Optimization

Form error evaluation of manufactured parts is one of the crucial aspects of precision coordinate metrology. With the advent of technology, the noncontact data acquisition techniques are replacing the conventional machines like coordinate measuring machine (CMM). This paper presents an optimization technique to evaluate minimum zone form errors, namely straightness, circularity, flatness and cylindricity using constriction factor-based particle swarm optimization (CFPSO) algorithm. Addition of constriction factor helps in accelerating the convergence property of CFPSO. Initially, a simple minimum zone objective function is formulated mathematically for each form error and then optimized using the proposed CFPSO. Primarily, the results of the proposed method for form error evaluation are compared with the literature results. Furthermore, the data obtained from noncontact 3D scanner is processed and the results of form error evaluation using CFPSO algorithm are compared with Steinbichler’s INSPECT PLUS software results. It was found that the results obtained using the proposed CFPSO algorithm are fast and better as compared with other evolutionary techniques like genetic algorithm (GA), previous literatures and software results. Furthermore, to ensure effectiveness of the proposed method statistical analysis ([Formula: see text]-test) was performed. CFPSO results for large dimension of problem show significant difference in computation time as compared with GA. The CFPSO algorithm provides 27.25%, 7.5% and 6.38% improvements in circularity, flatness and cylindricity, respectively, in comparison to RE software results, for determination of minimum zone error. Thus, the methodology presented helps in improving the accuracy and for speeding up of the automated inspection process generally performed by CMMs in industries.

Minimal Exhaustive Search Heuristics (MESH) of point clouds for form tolerances: The minimum zone roundness

MESH is an ɛ-approximate algorithm to find the minimum zone center of a given roundness profile, with ɛ=10−d, where d is the number of required decimal digits.The proposed MESH algorithm is able to provide only the accuracy that is necessary to find the minimum zone error roundness (circularity). The basic principle is to exhaustively assess all MZR center candidates located at the cross points of a mesh, with spacing directly related to the target accuracy. Criteria for the selection of the required manufacturing (designer's) target accuracy (product specifications) are discussed. This result has been made possible by previous work on the limit search space to be searched. The algorithm effectiveness has been shown by computation experiments up to 16,384 cloud datapoints and by comparison with genetic algorithms and an exact method from the literature. The MESH algorithm can also serve for benchmarking purposes to assess the performance of other algorithms in terms of both accuracy and speed. The extension to other form tolerances of the exhaustive mesh based approach is discussed.

Study on straightness error evaluation of spatial lines based on a hybrid ant colony algorithm

Based on the analysis of existing evaluation methods for straightness errors, an intelligent evaluation method for spatial straightness errors is provided in this paper. The evolutional optimum model and the calculation process are introduced in detail. According to characteristics of straightness error for spatial lines evaluation, an improved Ant Colony Optimisation ACO algorithm is proposed to evaluate the minimum zone error. Compared with conventional optimum evaluation methods such as Simplex search and Powell method, it can find the global optimal solution and the precision of calculating result is very high. Then, the objective function calculation approaches for using the ACO to evaluate minimum zone error are formulated. Finally, the control experiment results evaluated by different optimal methods such as the Least Square, Simplex search, Powell search and Genetic Algorithm, indicate that the proposed method does provide better accuracy on spatial straightness error evaluation and it has fast convergent speed as well as using computer.

Study on evaluation of perpendicularity errors with an improved particle swarm optimisation for planar lines

According to characteristics of perpendicularity error evaluation of planar lines, an improved particle swarm optimisation (PSO) is proposed to evaluate the minimum zone error. The evolutional optimum model and the calculation process are introduced in detail. Compared with conventional optimum methods such as simplex search and Powell method, PSO can find the global optimal solution, and the precision of calculating result is very good. Compared to other intelligence computation algorithms such as genetic algorithm (GA), PSO is easier to carry out with fewer parameters to adjust. Then, the objective function calculation approaches for using the particle swarm optimisation algorithm to evaluate minimum zone error are formulated. Finally, the control experiment results evaluated by different method such as the least square, simplex search, Powell optimum methods and genetic algorithm (GA), indicate that the proposed method can provide better accuracy on perpendicularity error evaluation effectively, and is well suited for position error evaluation.

Quasiparticle Swarm Optimization for Cross‐Section Linear Profile Error Evaluation of Variation Elliptical Piston Skirt

Variation elliptical piston skirt has better mechanical and thermodynamic properties and it is widely applied in internal combustion engine in recent years. Because of its complex form, its geometrical precision evaluation is a difficult problem. In this paper, quasi‐particle swarm optimization (QPSO) is proposed to calculate the minimum zone error and ellipticity of cross‐section linear profile, where initial positions and initial velocities of all particles are generated by using quasi‐random Halton sequences which sample points have good distribution properties and the particles’ velocities are modified by constriction factor approach. Then, the design formula and mathematical model of the cross‐section linear profile of variation elliptical piston skirt are set up and its objective function calculation approach using QPSO to solve the minimum zone cross‐section linear profile error is developed which conforms to the ISO/1101 standard. Finally, the experimental results evaluated by QPSO, particle swarm optimization (PSO), improved genetic algorithm (IGA) and the least square method (LSM) confirm the effectiveness of the proposed QPSO and it improves the linear profile error evaluation accuracy and efficiency. This method can be extended to other complex curve form error evaluation such as cam curve profile.

Inclination Errors Evaluation of Planar Lines with a Chaos Optimization

To improve inclination error evaluation of planar lines, chaos optimization is proposed to evaluate the minimum zone error in this paper. The evolutional optimum model and the calculation process are introduced. By using the properties of ergodicity, stochastic property, and “regularity” of chaos, the efficiency of chaos optimization algorithm (COA) is much higher than some stochastic algorithms such as simulated anneal algorithm (SAA) and genetic algorithm (GA) when COA is used to a kind of continuous problems. The chaos optimization algorithm can improve the efficiency of searching in the whole field by gradually shrinking the area of optimization variable. Finally, the control experiment results evaluated by different method such as the Least Square, Simplex search, Powell optimum methods and GA, indicate that the proposed method does provide better accuracy on inclination error evaluation.

Form Error Evaluation: An Iterative Reweighted Least Squares Algorithm*

This paper establishes the equivalence between the solution to a linear Chebyshev approximation problem and that of a weighted least squares (WLS) problem with the weighting parameters being appropriately defined. On this basis, we present an algorithm for form error evaluation of geometric features. The algorithm is implemented as an iterative procedure. At each iteration, a WLS problem is solved and the weighting parameters are updated. The proposed algorithm is of general-purpose, it can be used to evaluate the exact minimum zone error of various geometric features including flatness, circularity, sphericity, cylindericity and spatial straightness. Numerical examples are presented to show the effectiveness and efficiency of the algorithm.

Optimal matching of general polygons based on the minimum zone error

This paper presents a parametric approach for the matching of polygonal profiles based on the tolerancing requirements defined by the ANSI standards. The polygonal matching problem is formulated as a minimax optimization model and a procedure for solving this optimization model is developed.