| Link errors on machine tools are the mechanical linkage offsets between its axes of displacements. Propagated through the kinematic chain, their combined effect results in a failure to reach the desired position and orientation of the tool relative to the workpiece, hence an imperfectly machined part. These errors are independant from the position within the machine, as opposed to other kinds of errors which are position-related, such as the pitch error for example. The machine tool taken as a case study for this research had eight link errors that contribute to making the actual pose unknowable. First, three perpendicularity errors define the orientation of the prismatic axes. Then both rotation axes orientations can be described with two angles. Finally there is a gap between those rotation axes which should normally intersect.;There are three main types of uncertainty estimation. The first is the simplest one since it just associates uncertainty with the standard deviation of a pool of results from repeated experiments, assuming the variability among the experimental population comprises every error source. Consequently, the risk of oversimplification is the principal flaw of this method. In some cases final results are the only accessible values. This was the case for all perpendicularity diagnostic methods of this research. A "type A evaluation of uncertainty", as it is called, hence was the most appropriate strategy. A "type B evaluation of uncertainty", on the other hand, calls for a more elaborate approach. First an equation of the output as the result of the interaction of all the inputs must be written. Partial derivatives of this equation are taken as correlation coefficients applied to the standard deviation attributed to each uncertainty component. The final result is a standard uncertainty that can be multiplied by specific factors in order to obtain a larger coverage value. This method can be adapted to numerical simulation of populations of each input based on statistical properties in order to get an accurate probability distribution of the output (result).;There are two procedures dedicated to rotational axes orientation. First the telescopic ball bar is used for data acquisition only, data being analyzed with the help of algorithms developed by the user. For this application, the longitudinal axis of the instrument is kept nominally parallel to the axis being diagnosed for orientation and its reference spheres are maintained respectively into the toolholder and on the pallet of the machine. A circular interpolation of the two prismatic axes forming a plane normal to the rotational axis is realized and synchronized with a rotation of the latter. As the machine moves, micro-displacements of the sensor are acquired. They are later converted to cartesian coordinates used to calculate a least squares plane. The two director angles defining this plane also define the orientation of the rotational axis. A similar method is used to estimate the same link errors. However, the coordinates are obtained differently. A masterball is mounted on the machine table and probed using the built-in machine probing system in order to get the coordinates of its center. The studied axis is rotated according to a fixed angular increment. The sphere is probed again into this new pose. Those operations are repeated to cover the full axis range. A least squares plane is calculated with the coordinates acquired.;Experimental tests are repeated in two different thermal states of the machine, which are called "cold" and "warm". Thermal expansion and static friction affect the structural elements of the axes as well as joint components. These effects are propagated through the kinematic chain and hence on the link errors. This is why particular care is taken to characterize the errors in both thermal states. The experimental results are analyzed to compare the link errors in both states and obtained using different methods based on expanded uncertainties. When issued from Monte Carlo simulations, the relative contribution of each uncertainty component is calculated. (Abstract shortened by UMI.)... |
