Decomposition of trajectory errors caused by flexibility outside the control loop based on the frequency-domain machine tool mechatronics model

Under high-speed and high-acceleration conditions, flexibility outside the control loop (FOCL) is one of the critical incentives for trajectory errors (TEs). Because the FOCL will deform and vibrate under the action of inertial forces, which leads to TEs. FOCL contains multiple components, and the contribution of each component to TE needs to be evaluated. This paper first proposes a frequency domain dynamic model-based multi-axis machine tool trajectory tracking simulation method and a FOCL-induced TE decomposition method. Then using the proposed methods, quantitatively evaluates the contribution of different components of FOCL to TE caused by FOCL and discusses the dominant influencing factors. The mechatronics model of the machine tool is established in the frequency domain. This allows the lead screw to be equivalent to the spectral beam element, which is generated using the exact solution of the governing differential equations and can describe the lead screw's higher-order dynamics with fewer degrees of freedom. The TE of the test trajectory is calculated using a setpoint-trajectory-based numerical method. Using this method, the calculated TEs have the same reference and can be directly subtracted to achieve TE separation. Hence, the decomposition of TE caused by FOCL can be achieved by further calculating the TE of the tool center point (TCP) trajectory that only considers part of the FOCL components and subtracting it from the TE of the feedback trajectory.