INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY Meas. Sci. Technol. 13 (2002) 1924–1930 PII: S0957-0233(02)34773-8 Ambiguities in the definition of spacing parameters for surface-texture characterization Richard K Leach 1 and Peter M Harris 2 1 Centre for Basic, Thermal and Length Metrology, National Physical Laboratory, Queens Road, Teddington, Middlesex TW11 0LW, UK 2 Centre for Mathematics and Scientific Computing, National Physical Laboratory, Queens Road, Teddington, Middlesex TW11 0LW, UK Received 12 March 2002, in final form 10 July 2002, accepted for publication 17 September 2002 Published 1 November 2002 Online at stacks.iop.org/MST/13/1924 Abstract A range of instruments is available for surface-texture measurement. The instruments record the (x , z ) coordinates of data points that represent a surface profile, and apply software to filter the data and compute various surface-texture parameters that aim to describe the properties of the surface. However, many current and proposed parameters are not unambiguously defined. The focus of this paper is on one such parameter, namely, the spacing parameter RSm . It is shown that the definition of the RSm parameter given in standards is ambiguous, leading to the possibility of different algorithms for calculating RSm whose implementations can give results that differ considerably. Results obtained from three algorithms for calculating RSm applied to a real measurement data set are presented. Keywords: surface-texture measurement, spacing parameters, traceability 1. Introduction Knowledge of the topography of a machined surface is necessary in order to understand the functional performance of a surface, and is consequently essential to the manufacturing process. The use of a parameter to associate a numerical value to the measured topography of a surface was proposed many years ago (e.g. Hume (1980) gives a brief history). A single numerical value allows different surfaces to be readily compared and facilitates the interpretation of surface-texture tolerances on engineering drawings. Subsequently there has been a proliferation in the number of parameters that have been adopted by the various standards bodies (Whitehouse 1982). The current ISO specification standard (ISO 4287 1997) lists 11 parameters for two-dimensional (profile) measurements, nine of which are calculated from profile height data (z -values), one from profile spacing data 3 (x -values) and one that is a hybrid of height and spacing data. Communicating information about a surface using a defined set of surface-texture parameters is effective 3 The definition also requires the measurement of a height parameter—see section 2. only if those parameters have unambiguous mathematical definitions. Without such definitions there is scope for different interpretations of how the parameters should be calculated and, consequently, the danger that different software engineers would design (mathematically) different algorithms to calculate the parameters. The spacing parameter RSm (ISO 4287 1997) would appear to be an example of a parameter for which such an ambiguity exists, and is the subject of this paper. It is not the intention here to single out the problems associated with the definition of this particular parameter, but to use the RSm parameter to highlight the generic problems associated with defining surface-texture parameters. Note that the mathematical ambiguities inherent in the definition of RSm also apply to the spacing parameters defined in older specification standards (including previous versions of ISO 4287), such as the peak count Pc, the mean spacing of profile irregularities Sm, the mean spacing of local peaks of a profile S , and the high spot count HSC (see Leach (2001, appendix A)). Ambiguities in the definitions of surface-texture param- eters can lead to serious problems in ensuring traceability of 0957-0233/02/121924+07$30.00 © 2002 IOP Publishing Ltd Printed in the UK 1924