A new method for numerical simulation of 3D motion effects on motion and roundness reconstruction based upon parametric mathematical modelling

Measuring cylinders' out-of-roundness is still a big issue when high accuracy, high velocities or large cylinders are needed. The performance of the methods for roundness detection based on multi-probe scanning are strictly related to both the 3-D motion of the cylinders and the probes mounting configuration. Those effects are currently taken into account only in its 2D simplified form. Due to the lack of methods able to simulate 3D effects, a combined mathematical numerical method was developed. The cylinder is modelled making use of a mathematical description via Discrete Fourier Transform (DFT) of both its cross section and axis deviation. Efficient numerical simulation is employed to estimate the sensors' output taking also into account the cylinder shape effect interaction with unilateral constraints as a function of the cylinder rotation. Some simulations are carried out with the purpose of demonstrating the importance of modelling the entire 3D effects. Simulations show that an inaccuracy on 1° inclination of the probes support can result in an error of 1mm on the sensors output even considering a max amplitude of harmonics of 0.1 mm. Finally a reconstruction using the three point method based on FFT is applied to simulated measures showing that the 3D effects can increase the fluctuating part of the radius reconstruction error by 100 times.