~ Pergamon Int. J. Mach. Tools Manufact. Vol. 36, No. 1. pp. 33-46. t996 Elsevier S~nce Ltd Printed in Great Btitaia 0890-~55/~S,tg.50 + .00 IN-PROCESS EVALUATION OF WORKPIECE GEOMETRICAL TOLERANCES IN BAR TURNING A. M. SHAWKYt and M. A. ELBESTAWlt~t (Received 10 June 1994; in final form 15 February 1995) Abstract--This paper presents the development of an on-line system for the evaluation of workpiece size and geometrical tolerances in bar turning. The measurement is performed using three ultrasonic non-contact proximity sensors which operate in a wet cutting environment. Data conditioning of radius measurements based on spectral analysis and error separation methods are used in order to eliminate errors due to spindle runout and workpiece axis translation. Analytical formulation of cylindricity tolerance is presented. Nun- linear numerical optimization techniques are used to fit the data. Two different fitting functions are compared: the least squares and the minimax fit. The sufficiency of the sampled data set is investigated. The determination of cylindricity tolerance of the workpiece from given experimental data is presented and recommendations are given. AB b d~.i. dr, e, F f fc |,j,k Lp L p, Px P~ q R R, Rm r, It $, V Xa~Ya,Za NOMENCLATURE axis of substitute cylinder vector representing control variables minimum distance from q to AB high frequency form error data smallest residual objective function tool feed, rev/min cut-off-frequency, Hz unit vectors in the x, y, z directions distance function with index p, 0 < p < circumferential distance of workpiece surface elapsed per measurement distance measured by the ith sensor vector representation of a point x tangent vector at point x vector representation of a measured point nominal radius of the workpiece ith radius measurement mean value of radius measurements radius data with low frequency form error parametric variable, u • [0, 1] distance from ith sensor to machine center line cutting speed, m/rain Cartesian coordinates of point A 1. INTRODUCTION Today more stringent requirements are being imposed on the machining process to diminish the effects of machining errors on the product in order to meet tighter tolerances. Due to quality control requirements, diameters are often measured in workshop conditions. Measurements are performed both as post-process inspection and while the workpiece is still on the machine. Measurement is generally costly and in some cases the costs of part inspection by conventional methods equal or exceed machining costs. The current trend is to bring quality control closer to the machining process by means of on-line dimensional sensing. The full (or partial) replacement of off-line measurement and statistical quality control by full on-line part inspection would greatly reduce "quality costs" and improve process control. The ultimate goal is the tDepartment of Mechanical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4N2. ~To whom correspondence should be addressed. 33