Instrumentation for the 3D measurement of circular disks and the quantification of warpage

This paper presents an instrument for the measurement of the 3D surface geometry of disks, which enables the quantification of the disk warpage. Discrete basis functions are used to perform surface modelling and filtering, enabling the identification of the different deformation modes. The device is designed for automatic quality control in an industrial environment. The complete system for the measurement and modelling of manufactured plastic disks is presented. The measurement device consists of a motorized rotary stage and a set of six tactile sensors which measure the displacement of the surface during rotation. The data from all six sensor are acquired synchronously, yielding six tracks of data lying on a circular field with a constant number of samples per track. This delivers data in polar coordinates. Each tactile sensor was individually calibrated and a linearizing polynomial was determined. This improves the achievable accuracy of the displacement measurements. The surface is modelled using a set of discrete radial polynomials combined with the Fourier basis functions. The radial polynomials are closely related to the Zernike polynomials; however they are optimized with respect to the propagation of Gaussian noise. This improves the confidence interval of the final measurement. The radial polynomials are subjected to constraints at the origin to ensure a continuous surface. The semi-separable nature of the polynomials enables the implementation of a linear least squares approximation for the individual distortion modes. Measurement results are presented for the surface measurement of manufactured plastic parts, showing the separation of the different surface modes.