Tohru Kanada

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 (Laplaces 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.

Evaluation of minimum zone flatness by means of nonlinear optimization techniques and its verification

Abstract This article deals with the application of some nonlinear optimization techniques for minimum zone flatness. The convergence criteria of the techniques, namely the downhill simplex method and the repetitive bracketing method, are considered. The least-squares method is also applied, and subsequently the three methods are compared from the viewpoint of computational accuracy. A surface profile measuring system and a noncontact sensor are used to obtain three-dimensional data. The measured data are expressed by means of perspective mapping. Subsequently, the relationship among the above three methods is clarified according to accuracy and efficiency of the computation. Furthermore, some examples of the relationship between the manufacturing method and the flatness value, and the technique of a skilled hand are described.

Application of several computing techniques for minimum zone straightness

Abstract This research deals with the application of several algorithms to calculate the minimum zone straightness. Generally, in the evaluation of the minimum zone value of form errors such as straightness, flatness, roundness, and cylindricity, nonlinear optimization techniques are usually applied. The problem with the nonlinear technique that depends on computing algorithm is that the computing time may be prolonged. Therefore, some linear search techniques that are relatively easy to program are applied for straightness in this article. Furthermore, the problem can also be linearized by considering the characteristics of the measured profile for straightness; thus, the reduction of computing time will be achieved. Then, the problems caused by the above consideration are clarified. Consequently, the convergence criteria and comparison of results by means of several computing methods are investigated. The relationship between flatness and straightness values in some machining conditions and the comparison with the least-squares values are studied.

Estimation of sphericity by means of statistical processing for roundness of spherical parts

Abstract In the industrial standard of “balls for rolling bearings,” deviation from spherical form (sphericity) is defined as follows. It is usually determined by numerically evaluating the ball profiles, in two or three equatorial planes at 90° to each other, and recording them on a polar chart. Furthermore, the standard indicates that the minimum circumscribed circle method is relatively simple and generally satisfactory for ball profiles, and the method is also based on the assumption that two or three equatorial profiles at 90° to each other are a good indication of the deviation from spherical form. The measurement method for three-dimensional (3-D) spherical profiles is two-dimensional (2-D), because a practical (3-D) measuring system for spherical forms remains to be developed. This is another important problem. Using the method recommended in the standard, the deviation value is significantly underestimated, because the major part of the 3-D surface is not measured. Verification of the above-mentioned assumption is also difficult in general. If numerous measurements of 2-D profiles are performed, the degree of underestimation decreases. However, this requires much time and labor. In this study, a 3-D deviation value from spherical form is calculated from a few 2-D roundness values obtained using a general roundness measuring system with a statistical technique. Furthermore, an appropriate number of measuring cross sections necessary to estimate the sphericity with high reliability are presented.

Evaluation of two- and three-dimensional surface roughness profiles and their confidence

Abstract Surface roughness values, in general, vary a little owing to the measuring positions on a surface. Therefore it is hard to guarantee the roughness values indicated in a drawing of an overall surface from a few measuring positions. Investigated in this research were the scatters of the specific values of R max , R z , R a and r.m.s. roughness measured at many positions on a surface and the confidence interval of these values. Some characteristics of twodimensional surface roughness values were compared with three-dimensional values for ground and lapped surfaces.

Method for the evaluation of form errors of conical tapered parts

Abstract This paper deals with a measuring technique for conical tapered parts using cylindrical form measuring equipment. In order to evaluate the form errors of such parts, a special algorithm is developed to remove eccentricity and tilting errors of the specimen due to the measuring centre axis. The algorithm proposed is the modified Newton-Raphson method. It is established in this paper that, for a required computational accuracy of 0.1 μm, the number of iterations by this algorithm is typically two or three. In addition, it is shown that the form errors may be represented by a perspective projection and a contour map.

Development of tapered roller bearing with low torque: Reduction of sliding friction between large flange and roller end faces machined by precision powder shot peening

A taper roller bearing can support both radial and axial loads and is available for the differential gear mechanism of a vehicle. Since the inner and outer rings can be separated, the axial force should be loaded to some extent as preload even if the bearing is used for supporting the radial load. However, when the axial force is loaded, the rotational torque becomes larger owing to the sliding friction between the roller end face and the large flange surface of the inner ring. In this research, to reduce the sliding friction inside the taper roller bearing, precision powder shot peening was performed on the large flange surface of the inner ring. Thus the bearing torque was reduced considerably by increasing the surface hardness and residual compressive stress and by smoothing the surface protrusion by grinding Shot Machine A. one Polish treatment. Furthermore, it was confirmed that the wear of the taper roller end face was the same as before and that of the large flange surface could be inhibited.

The development of a computer-aided centring and levelling system for cylindrical form measurement

Abstract In the measurement of a cylindrical form by the radial deviation method using a rotating table, the measured data have some errors arising from the setting of the specimen, such as eccentricity and tilting. These errors should be removed by manual operation or automatic equipment before the measurement in order to obtain accurate data. The former method requires a high degree of skill, and the latter brings higher costs. This paper deals with a new control system to remove the setting errors. The automatic centring and levelling equipment, which is controlled by a microcomputer, is placed external to the rotating table. This newly developed system has a simple mechanism and its cost is very low. Further, this equipment can be easily adapted to a conventional measuring machine.

Control of a flexible master-slave manipulator using dual compliance models

This paper presents a newly developed bilateral controller of a flexible master-slave manipulator (FMSM) system. A FMSM consists of a conventional compact rigid master arm and a flexible slave arm, and will be used in outer space and in the construction field in the future. There are two problems in controlling a FMSM. One is the vibration of a flexible link. The other is the deformation of a flexible link when a slave link contacts with an object. The proposed controller is effective in restraining the vibration of a flexible link and in protection from adding too much force to a flexible link. For this purpose, the key idea of the proposed method is that this controller has dual compliance models, and the design is done for each model considering the elasticity of a master and a slave arm. Each arm moves along the desired path which was calculated in this model. Also, a slave controller has a vibration controller. As the initial study, a 1 d.o.f. system was considered. The effectiveness of the proposed ...

The development of a multi-turn absolute encoder. A new concept in accordance with a design insensitive to accuracy

Abstract A new design concept of a multi-turn absolute rotary encoder which is insensitive to the accuracy of encoder components is proposed. This new design does not demand high accuracy of the encoder structure other than the fundamental pattern to produce the least significant digit. The allowable error in the encoder structure is compensated by electronic light circuits. This absolute encoder has been applied to the measurement of height position in a cylindrical form-measuring system. The new encoders can be connected in series by reduction gears whose accuracy is fairly rough, so that a multi-turn device in realized. The allowable tolerances in the encoder structure are presented.