A Proposal of a Spline Filter that Achieves Both Robustness and Lower Compatibility

A spline filter is used to extract roughness profiles for the measurement of surface texture and is useful when sufficient sections before and after a primary profile could not be secured.This is because a spline filter could prevent the end effect,which is the fluctuation of output data that occurs around both ends of the primary profile and depends on the width of the weighting function of a filter.The spline filter is based on the calculation of an inverse matrix instead of the convolution of the weighting function of the filters.When input data include outliers,the output of a spline filter greatly fluctuates.To solve this problem,we propose a robust spline filter.However,output of the robust spline is not in agreement with that of the spline filter when input data do not include outliers.Thus,the robust spline filter has no lower compatibility.In this paper,the"Fast M-estimation Spline Filter(FMSF)"is proposed.FMSF uses the fast M-estimation method.FMGF performs robust to input data including outliers,and gives the same output as that of general spline filters to input data without outliers.The value estimated by this method is in agreement with that estimated by the least squares method if no outlier exists.In order to apply the fast M-estimation method to the spline filter,convolution of weight function is used instead of the inverse matrix.And the input geometry with shear and point-symmetric extensions is pre-processed to prevent the end effect.

A Proposal of Hyperbolic Fitting Method by Applying the Properties of Functions for Plateau Surface Analysis in ISO 13565-3

ISO 13565-3 provides an evaluation method for plateau structure surfaces used as sliding surfaces in machine tools and automobile engines.The evaluation method for plateau structure surfaces of ISO 13565-3 has problems,such as the processing procedure has an ambiguous basis,and the calculation method is not specified.The existing evaluation method that solves these problems requires the implementation of a difficult algorithm.In subsequent evaluation methods,these problems were resolved,and the implementation of complicated calculation algorithms became unnecessary.However,these methods use algorithms that do not conform to the evaluation method of ISO 13565-3.This lack of adherence to the ISO standard may hinder their application in the industrial world.Therefore,in this study,a new method that conforms to the evaluation method of ISO 13565-3 with a more concise algorithm was developed.We concluded that this proposed method can contribute to the formation of plateau surfaces and production control in the industrial world.

Verification of Characteristics of Gaussian Filter Series for Surface Roughness in ISO and Proposal of Filter Selection Guidelines

In surface roughness measurement,if spikes are included in the primary profile,a problem occurs wherein the Gaussian filter(GF)is unable to extract the shape components.To address this problem,the use of a robust filter is proposed.However,ISO16610-31:Gaussian regression filters(GRF)only provide a single method and a few examples,and does not specify the conditions under which the primary profile can be covered.Moreover,the data presented in the example on robustness in ISO16610-31 do not contain roughness components.In actual roughness measurements,no primary profile exists that does not include a roughness component.Because the characteristics of GRFs are unknown,it is not yet clear which filter should be used for which primary profile,and this is an issue that has been raised at ISO and JIS conferences.In addition,the establishment of filter selection guidelines is necessary at measurement sites.Therefore,this paper clarifies the characteristics of GF-series filters,summarizes the points to be considered when using them,and identifies the filter that should be selected according to different situations.Based on the results,a figure that visualizes the characteristics of filters and a flowchart regarding which filter should be used are created;these tools,to the best of the authors’knowledge,did not exist prior to this study.It is believed that these results will help fulfil the needs of measuring job sites and also aid in filter selection.