Minimum Zone Method Research Articles

Minimum zone evaluation of circles and cylinders

A strategy for minimum zone evaluation of circles and cylinders is proposed in this work. This strategy employs a non-linear transformation to convert a circle into a line and a cylinder into a plane. A straightness or a flatness evaluation scheme was then employed to obtain appropriate control points and minimum zone deviation for the feature concerned. A series of inverse transformation procedures was then implemented to compute desired feature parameters. Computer simulation results revealed that the proposed minimum zone method can yield a smaller tolerance value than the least-squares method. Also, the sensitivity of the proposed method and the least-squares method to an abrupt peak in the measurement data was addressed.

'Z' Approaching Minimum Zone Method for Flatness and Straightness Error Calculation

A computational technique for the minimum zone method, which is used to determine a reference plane from the measured surface data on a precision table or machine bed to verify surface flatness, is introduced. This technique, called the "'Z'approaching method" in this paper, is an analytical method without any assumptions and is simple compared to other techniques. This method can also be applied to the determination of a reference line for straightness measurement of a carriage guide. This method is compared with the graphical solution for the straightness measurement of a straight edge.

Evaluation of spherical form errors—Computation of sphericity by means of minimum zone method and some examinations with using simulated data

Because of the practical difficulties of measuring whole spherical surface form errors, no concrete three-dimensional (3-D) verification has yet been developed. This article deals with the calculation of the value of spherical form errors; that is, sphericity. The iterative least-squares method in which the problem is linearized and the minimum zone method in which the downhill simplex method, one of the nonlinear optimization techniques, is applied are considered. The data to be analyzed are not obtained by actual measurement of a spherical surface, because there is no such a measuring system in my laboratory, but simulated by applying surface harmonics (Laplace's spherical function) with a computer. Then, the application conditions for downhill simplex method are investigated. Furthermore, the roundness values of the spherical surface are compared with the sphericity by means of the minimum-zone method.

球形状誤差の一評価法 シミュレーションデータによる最小領域法真球度の算出といくつかの考察

Due to the difficulties of measuring technique for the whole spherical surface, a concrete three-dimensional verification is not yet developed. This article deals with calculation of the value of spherical form errors, that is sphericity. The iterative least squares method in which the problem is linearized, and the minimum zone method in which the downhill simplex method, one of the nonlinear optimization technique, is applied are considered. The data to be referred is not obtained by actual measurement of spherical surface but simulated by using surface harmonics (Laplace's spherical function) in a computer. Then, their application conditions are investigated. Furthermore, the roundness values of the spherical surface are compared with the sphericity by means of the present method of this article.

A minimum zone method for evaluating flatness error of gage blocks measured by phase‐shifting interferometry

Abstract A new method called “Control Plane Rotation Scheme (CPRS)” has been developed here for the analysis of flatness error in terms of the minimum zone definition, which conforms to the ISO/R1101 specification. An application of the phase‐shifting interferometry was performed for on‐line measurement of gage blocks. Experimental results were quite consistent with the specified grade of the inspected gage block with only an uncertainty of up to 0.005 μm.

A new minimum zone method for evaluating straightness errors

A new minimum zone method for straightness error analysis is proposed in this article. Based on the criteria for the minimum zone solution and strict rules for data exchange, a simple and rapid algorithm, called the control line rotation scheme, is developed for the straightness analysis of planar lines. Extended works on the error analysis of spatial lines by the least parallelepiped enclosures are also described. Some examples are given in terms of the minimum zone and least-squares. Finally, this easy-to-use method is illustrated by an example that demonstrates that, for a planar line, the minimum zone solution can even be found without the use of a computer.

A new minimum zone method for evaluating flatness errors

A new minimum zone method for flatnes error analyis is proposed in this article. Based on the criteria for the minimum zone solution and strict rules for data exchange, a simple and rapid algorithm, called the control plane rotation scheme, is developed for the flatness analysis of a flat surface. Experimental work was performed, and some examples are given in terms of the minimum zone and least-squares solutions.

A Study of the Geometrical Condition and a Calculation Method for the Minimum Zone Method. A Straightness Calculation Method Based on the Geometrical Condition.

It is not always easy to verify work-piece accuracy determined by the minimum zone method even with long calculation time. Therefore the auther clarified the geometrical condition of straightness in another report. According to the report, when there are two points A, B on a straight line of two parallel lines determined by the minimum zone method, and one point H on the other straight line, the angle of ∠HAB and ∠HBA are smaller than π/2. So, this paper showed a calculation method based on the geometrical condition. The calculation method has the advantage that the true solution is get certainly, the algorithm is very simple and the calculation time is much shorter than the standard method.

A Study of the Geometrical Condition and Calculation Method for Minimun Zone Method. The Geometrical Condition of Straightness.

Workpiece accuracy should be evaluated by the minimum zone method. Therefore many techniques were proposed by means of optimization methods. However, it is not always easy to obtain the true solution or approximate value of accuracy even with long calculation time. The true solution exists in the case of the minimum zone method because the solution can be determined theoretically. However, it is not a realistic method because of its calculation time. If the geometrical condition defined by the minimum zone method is clarified, the technique to verify the minimum zone becomes easy. In order to solve this problem, this paper discusses the geometrical condition of the minimum zone straightness.

Geometrical Study of the Minimum Zone Method. Geometrical Condition and Calculation Method of Flatness.

Many techniques of optimization methods to verify the minimum zone accuracy have been proposed, but it is not always easy to obtain the true or approximate solution even with long calculation time is expended. Therefore this paper discusses the geometrical condition of flatness and a calculation method based on the geometrical condition. The results are shown below. 1) When there are two points, a, b on one of two parallel planes determined by the minimum zone method and c, d on the other plane, the segments ab and cd projected on one of the parallel planes intersect each other. 2 ) When there is a point H on one of two parallel planes and three points A, B, C on the other plane, the point H projected onto the opposite plane is in ΔABC.

A Geometrical Study of the Minimum Zone Method. Straightness in Undetermined Directions.

Workpiece accuracy Should be evaluated by the minimum zone method. Therefore many techniques of optimization methods to verify the minimum zone accuracy have been proposed. But it is not always easy to obtain the true or approximate solution even with long calculation time is expended. Hence, this paper disscuses the geometrical condition of straightness in undetermined directions. Because the geometrical condition of finite data points should be determined by the definition of the minimum zone method, the straightness in undetermind directions is determined by three or four points.

A Study of the Geometrical Condition and a Culculatin Method for the Minimum Zone Method. The Geometrical Condition of Roundness.

Many techniques were proposed by means of optimization methods to verify the minimum zone accuracy. It is not always easy to obtain a true solution, even with long calculation time. In order to solve the problem, the geometrical condition of roundness is clarified. The geometrical condition is shown as follows: as shown in Fig. 1, if there are two points A, B on thhe inscribed circle determined by the minimum zone method, and another two points C, D on the circumscribed circle, segments AB and CD intersect each other. This paper proved this geometrical condition determined by the minimum zone roundness.

A Study of the Geometrical Condition and a Calculation Method for the Minimum Zone Method. A Roundness Calculation Method Based on the Geometrical Condition.

A Study of the Geometrical Condition and a Calculation Method for the Minimum Zone Method. A Roundness Calculation Method Based on the Geometrical Condition.