Abstract
Abstract. In high-speed and high-precision machinery, trajectories with high-frequency harmonic content are one of the main sources of reduction of operational precision. Trajectories with high-frequency harmonic content generally demand even higher-harmonic actuating forces/torques due to the nonlinear dynamics of such systems, which may excite natural modes of vibration of the system and/or be beyond the dynamic response limitation of the actuation devices. In this paper, a global interpolation algorithm that uses the trajectory pattern method (TPM) for synthesizing low-harmonic trajectories is presented. The trajectory synthesis with the TPM is performed with a prescribed fundamental frequency and continuous jounce boundary condition, which would minimize the number of high-harmonic components in the required actuation forces/torques and avoid excitation of the system modes of vibration. The minimal curvature variation energy method, Lagrange multiplier method, and contour error control are used to obtain smooth kinematic profiles and satisfy the trajectory accuracy requirements. As an example, trajectory patterns that consist of a fundamental frequency sinusoidal time function and its first three harmonics are used to synthesize the desired trajectories for a selected dynamic system. The synthesized trajectories are shown to cause minimal system vibration during its operation. A comparison with a commonly used trajectory synthesis method clearly shows the superiority of the developed TPM-based approach in reducing vibration and demand on the actuator dynamic response, thereby allowing the system to operate at higher speeds and precision.
Highlights
For the trajectory synthesis (Chu et al, 2020; Dai et al, 2020; Van Loock et al, 2015) of high-speed machinery, such as CNC machinery, robot manipulators and other computer-controlled machines, polynomial-based curves (Analooee et al, 2020; Liang and Su, 2019; Shen et al, 2020) are still the most widely used trajectories
The synthesized trajectory is a unique combination of a fundamental frequency harmonic and its second harmonic, which results in the minimum number of harmonics in the required actuation forces/torques and minimizes excitation of the system modes of vibrations
The path segments are presented as lines as shown in Fig. 2, and since the segment trajectories are synthesized with a fundamental frequency time function and its three harmonics, by checking contour error at a limited number of intervals in each segment the maximum contour error is accurately estimated
Summary
For the trajectory synthesis (Chu et al, 2020; Dai et al, 2020; Van Loock et al, 2015) of high-speed machinery, such as CNC (computerized numerical control) machinery, robot manipulators and other computer-controlled machines, polynomial-based curves (Analooee et al, 2020; Liang and Su, 2019; Shen et al, 2020) are still the most widely used trajectories. The sine series method constructed jerk profiles with sinusoidal functions with an appropriate fundamental frequency and all harmonics, which contained considerable high-harmonic content. The synthesized trajectory is a unique combination of a fundamental frequency harmonic and its second harmonic, which results in the minimum number of harmonics in the required actuation forces/torques and minimizes excitation of the system modes of vibrations. This method is only used for pointto-point motions with zero end point velocity, acceleration, and jerk. The synthesized trajectories and axis kinematic profiles are smooth and only contain the fundamental frequency and its first three harmonics, which are designed to minimize vibration of the high-speed machinery.
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