Application of interpolation methods for the determination of position-dependent frequency response functions for the simulation of 5-axis milling processes

Abstract

The occurrence of chatter vibrations in 5-axis milling processes is a common problem and can result in part failure, surface defects and increased wear of the cutting tool and the machine tool. In order to prevent process vibrations, machining processes can be optimized by utilizing geometric physically-based simulation systems. Since the modal parameters of the machine tool are dependent on the position of the linear and rotary axes, the dynamic behavior of milling processes can change along the NC path despite constant engagement conditions. In order to model the pose-dependent modal properties at the tool tip, the frequency response functions (FRFs) were measured at different locations of the workspace of the machine tool for various poses of the rotary axis of the spindle. To take the varying compliance within the workspace of a machine tool into account in a geometric physically-based milling process simulation, different interpolation methods for interpolating FRFs or parameter values of oscillator-based compliance models (OPV) were applied. For validation, the resulting models were analyzed and compared to measured data. In OPV interpolation, the individual oscillation modes were interpolated in their respective characteristics based on the oscillator parameters (eigenfrequencies, modal masses and damping values). In FRF interpolation, however, there was no differentiation between the modes, resulting in a wrong interpolation. It can therefore provide good results when only a small shift of the eigenfrequencies is expected, as in case of the analyzed machine tool, with only small movements of the translatory axes.

Minimisation of Pose-Dependent Regenerative Vibrations for 5-Axis Milling Operations

“…This way, the interaction of process force and deflection and, thus, also the regenerative effect can be modelled. The pose-dependent dynamic behaviour of the system consisting of machine tool, spindle and milling tool was modelled by a linear interpolation of the oscillator parameter values (OPV) between 48 measurement poses for each time step based on the current position of the machine tool axes, as described in [16]. Based on the computed deflections between the milling tool and the workpiece, the workpiece shape is calculated by CSG modelling, while the generated surface location errors are visualised by using a multi-dexel board [33].…”

“…In order to keep the experimental effort for the parameterisation of the dynamics model as low as possible, it is not reasonable to determine the FRF of the machine tool experimentally for every possible position and pose in the workspace. Therefore, linear interpolation methods [16,17] as well as a machine learning approach [17] can be used in order to calculate FRFs at non-measured axis positions or tool poses, respectively. For the simulation-based optimisation of milling processes, several approaches exist which can be used to influence the manufacturing process in a positive way, e.g., the optimisation can be conducted by modifying an already existing NC path [4,18], by adapting process parameters [19][20][21], or by generating a new optimised NC path [22] or milling strategy [12].…”

“…For this purpose, a geometric physically-based simulation system was used to identify tool poses leading to stable or unstable process behaviour. This incorporated the axis position-dependent dynamic properties by means of previously presented models [15,16]. In addition, the kinematic properties of an exemplary machine tool were modelled in Section 2.1 and simulated in a geometric-kinematic model and an acceleration model in Section 2.1.2, taking into account the rotary and swivel axes as well as the machine control system.…”