# A new method for Numerical Simulation of 3D motion effects on Motion and Roundness reconstruction

Measuring cylinders out-of-roundness is still a big issue when high accuracy, velocity 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 in its 2D simplified form.  Due to the lack of methods able to simulate 3D effects, we developed a combined mathematical numerical method. The cylinder is modelled making use of a mathematical description via DFT of its cross section and axis deviation. Efficient numerical simulation is employed to estimate the sensors output while taking into account the cylinder shape effect interacting on unilateral constraints as a function of cylinder motion.

The study gave the following results:

a) A mathematical parametric model of the shape and the axis of a generic cylinder is realized. This parametric model gives the possibility to easy model a wide range of cylinders.
b) An algorithm for simulating the measurement process in 3-D environment by generically oriented probes is implemented. The main point of the algorithm is the 3-D recursive search of the contact point between sensor and surface of the moving cylinder.
c) A model that reconstruct the motion of the cylinder during the measurement process is realized focusing on systems for grinding of rolling mill cylinders. The model take into account the contact constraints on the supports and reconstruct the motion from this assumption with geometrical consideration.
d) The entire kinematic of the measurement system is modeled and the positioning errors are integrated in the model giving the possibility to study theirs effect.
e) Some simulation are reported demonstrating the importance of modeling either the motion, the kinematics of the support tool and the mounting errors of the probe. Comparing the measures obtained with this aspects modeled and without is clear that conspicuous error are reached.
f) Finally a three point method is employed only with the purpose to demonstrate how the effect of the features modeled are influent in the performance of a reconstruction algorithm. A mean error of 100μm can be reached if mounting errors are considered.