Accuracy and Time in Surface Measurement, Part 2: Optimal Sampling Sequence

While commonly practiced, the uniform and random distribution of sample points are shown to be far from optimal. This part of the paper presents a sequence for measurement and demonstrates by simulation that, for the same level of accuracy, a nearly quadratic reduction in the number of sample points can be achieved.

[1]  N. O. Myers,et al.  Characterization of surface roughness , 1962 .

[2]  van der Ach Wolf,et al.  Modelling of a Coordinate Measuring Machine for Analysis of Its Dynamic Behaviour , 1988 .

[3]  G. M. Zhang,et al.  Dynamic Generation of Machined Surfaces, Part 2: Construction of Surface Topography , 1991 .

[4]  H. Woxniakowski Information-Based Complexity , 1988 .

[5]  Neil A. Duffie,et al.  Error Diagnosis and Compensation Using Kinematic Models and Position Error Data , 1987 .

[6]  Tadao Tsukada,et al.  An optimum sampling interval for digitizing surface asperity profiles , 1982 .

[7]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[8]  J. Meijer,et al.  Accuracy of Surface Plate Measurements — General Purpose Software for Flatness Measurement , 1990 .

[9]  K. F. Roth On irregularities of distribution , 1954 .

[10]  T. Thomas Characterization of surface roughness , 1981 .

[11]  H. Wozniakowski Average case complexity of multivariate integration , 1991 .

[12]  K. F. Roth,et al.  On irregularities of distribution IV , 1979 .

[13]  H. Niederreiter Quasi-Monte Carlo methods and pseudo-random numbers , 1978 .

[14]  J. Hammersley MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS , 1960 .

[15]  H. Kunzmann,et al.  Performance of CMMs , 1988 .

[16]  B A Cipra The breaking of a mathematical curse. , 1991, Science.

[17]  Ian Sherrington,et al.  Parameters for Characterizing the Surface Topography of Engineering Components , 1987 .

[18]  Grzegorz W. Wasilkowski,et al.  On the average complexity of multivariate problems , 1990, J. Complex..

[19]  The Digital Measurement of Peak Parameters on Surface Profiles , 1978 .

[20]  S. R. S. Kalpakjian Manufacturing Processes for Engineering Materials , 1984 .

[21]  M. Kowalski,et al.  The influence of kinematic errors on the profile shapes by means of CMM , 1989 .

[22]  Lauwerens Kuipers,et al.  Uniform distribution of sequences , 1974 .

[23]  Takeshi Kishinami,et al.  A New Method for Detecting the Contact Point between a Touch Probe and a Surface , 1989 .

[24]  D Y Yim,et al.  Optimum Sampling Interval for Ra Roughness Measurement , 1991 .

[25]  K. J. Stout,et al.  The Analysis of the Three Dimensional Topography of the Grinding Process , 1989 .

[26]  P. Whittle ON STATIONARY PROCESSES IN THE PLANE , 1954 .

[27]  S. K. Zaremba,et al.  The extreme and L2 discrepancies of some plane sets , 1969 .

[28]  T. Treib,et al.  Error Budgeting — Applied to the Calculation and Optimization of the Volumetric Error Field of Multiaxis Systems , 1987 .

[29]  B. Lu,et al.  A Displacement Method for Machine Geometry Calibration , 1988 .

[30]  H. Davenport Note on irregularities of distribution , 1956 .

[31]  O. A. Gorlenko Assessment of surface roughness parameters and their interdependence , 1981 .

[32]  David J. Whitehouse Comparison Between Stylus and Optical Methods for Measuring Surfaces , 1988 .