Trajectory Synthesis for Selective Elimination of High Frequency Actuating Torque Harmonics

1998 ◽  
Author(s):  
Q. J. Ge ◽  
J. Rastegar ◽  
M. Mattice
Keyword(s):  
High Frequency ◽  
Settling Time ◽  
Residual Vibration ◽  
Harmonic Content ◽  
Selective Elimination ◽  
Computer Controlled ◽  
Point To Point ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

Abstract This paper deals with the problem of synthesizing joint trajectories of computer controlled machinery with tailored harmonic content for the actuating torques required to track the trajectories. For point-to-point motions with zero initial and final velocities and accelerations, a method is presented for shaping the harmonic content of the joint trajectories for the purpose of eliminating a specified high-frequency harmonic from the actuating torques. With such trajectories, the machine can perform the synthesized tasks with less residual vibration and increased settling time.

scholarly journals Low-harmonic trajectory synthesis using trajectory pattern method (TPM) for high-speed and high-precision machinery

2021 ◽  
Vol 12 (2) ◽  
pp. 913-922
Author(s):  
Hao Li ◽  
Jahangir Rastegar ◽  
Baosheng Wang
Keyword(s):  
Dynamic Response ◽  
Fundamental Frequency ◽  
High Frequency ◽  
High Speed ◽  
Harmonic Content ◽  
Modes Of Vibration ◽  
Trajectory Pattern ◽  
Trajectory Pattern Method ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

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.

scholarly journals Early Fault Detection Method for Rotating Machinery Based on Harmonic-Assisted Multivariate Empirical Mode Decomposition and Transfer Entropy

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 873 ◽  
Author(s):  
Zhe Wu ◽  
Qiang Zhang ◽  
Lixin Wang ◽  
Lifeng Cheng ◽  
Jingbo Zhou
Keyword(s):  
Fault Detection ◽  
Empirical Mode Decomposition ◽  
High Frequency ◽  
Rotating Machinery ◽  
Transfer Entropy ◽  
Multivariate Empirical Mode Decomposition ◽  
Mode Decomposition ◽  
Coupling Characteristics ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

It is a difficult task to analyze the coupling characteristics of rotating machinery fault signals under the influence of complex and nonlinear interference signals. This difficulty is due to the strong noise background of rotating machinery fault feature extraction and weaknesses, such as modal mixing problems, in the existing Ensemble Empirical Mode Decomposition (EEMD) time–frequency analysis methods. To quantitatively study the nonlinear synchronous coupling characteristics and information transfer characteristics of rotating machinery fault signals between different frequency scales under the influence of complex and nonlinear interference signals, a new nonlinear signal processing method—the harmonic assisted multivariate empirical mode decomposition method (HA-MEMD)—is proposed in this paper. By adding additional high-frequency harmonic-assisted channels and reducing them, the decomposing precision of the Intrinsic Mode Function (IMF) can be effectively improved, and the phenomenon of mode aliasing can be mitigated. Analysis results of the simulated signals prove the effectiveness of this method. By combining HA-MEMD with the transfer entropy algorithm and introducing signal processing of the rotating machinery, a fault detection method of rotating machinery based on high-frequency harmonic-assisted multivariate empirical mode decomposition-transfer entropy (HA-MEMD-TE) was established. The main features of the mechanical transmission system were extracted by the high-frequency harmonic-assisted multivariate empirical mode decomposition method, and the signal, after noise reduction, was used for the transfer entropy calculation. The evaluation index of the rotating machinery state based on HA-MEMD-TE was established to quantitatively describe the degree of nonlinear coupling between signals to effectively evaluate and diagnose the operating state of the mechanical system. By adding noise to different signal-to-noise ratios, the fault detection ability of HA-MEMD-TE method in the background of strong noise is investigated, which proves that the method has strong reliability and robustness. In this paper, transfer entropy is applied to the fault diagnosis field of rotating machinery, which provides a new effective method for early fault diagnosis and performance degradation-state recognition of rotating machinery, and leads to relevant research conclusions.

scholarly journals Double Pendulum Induced Stability

2015 ◽  
Vol 07 (06) ◽  
pp. 1550088
Author(s):  
Bezdenejnykh Nikolai ◽  
Andres Mateo Gabin ◽  
Raul Zazo Jimenez
Keyword(s):  
Theoretical Analysis ◽  
Potential Energy ◽  
High Frequency ◽  
Relative Equilibrium ◽  
Double Pendulum ◽  
Harmonic Vibrations ◽  
Hamilton Equations ◽  
High Frequency Harmonic ◽  
Good Agreement ◽  
Frequency Harmonic

In this work, a study of the relative equilibrium of a double pendulum whose point of suspension performs high frequency harmonic vibrations is presented. In order to determine the induced positions of equilibrium of the double pendulum at different gravity and vibration configurations, a set of experiments has been conducted. The theoretical analysis of the problem has been developed using Kapitsa’s method and numerical method. The method of Kapitsa allows to analyze the potential energy of a system in general and to find the values of the parameters of the problem that correspond to the relative extreme of energy — positions of stable or unstable equilibrium. The results of numerical and theoretical analysis of Hamilton equations are in good agreement with the results of the experiments.

scholarly journals NORMAL FORM AND ENERGY CONSERVATION OF HIGH FREQUENCY SUBSYSTEMS WITHOUT NONRESONANCE CONDITIONS

2013 ◽  
Author(s):  
Dario Bambusi ◽  
Antonio Giorgilli ◽  
Simone Paleari ◽  
Tiziano Penati
Keyword(s):  
Normal Form ◽  
Energy Conservation ◽  
High Frequency ◽  
Harmonic Oscillators ◽  
Fast System ◽  
System Changes ◽  
High Frequency Harmonic ◽  
Slow System ◽  
Frequency Harmonic

We consider a system in which some high frequency harmonic oscillators are coupled with a slow system. We prove that up to very long times the energy of the high frequency system changes only by a small amount. The result we obtain is completely independent of the resonance relations among the frequencies of the fast system. More in detail, denote by ϵ-1 the smallest high frequency. In the first part of the paper we apply the main result of [1] to prove almost conservation of the energy of the high frequency system over times exponentially long with ϵ-1/n (n being the number of fast oscillators). In the second part of the paper we give a new self-contained proof of a similar result which however is valid only over times of order ϵ-N with an arbitrary N. Such a second result is very similar to the main result of the paper [4], which actually was the paper which stimulated our work.

P3P-2 Dual Element Transducers for High Frequency Harmonic Imaging

2006 ◽  
Author(s):  
R. H. Silverman ◽  
K. K. Shung ◽  
R. Liu ◽  
L. Sun ◽  
J. M. Cannata ◽  
...  
Keyword(s):  
High Frequency ◽  
Harmonic Imaging ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

The Rotationally Flexible Pendulum Subjected to a High Frequency Excitation

1990 ◽  
Vol 57 (3) ◽  
pp. 725-730 ◽  
Author(s):  
Bertram A. Schmidt
Keyword(s):  
High Frequency ◽  
Harmonic Excitation ◽  
Flexible Parts ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

A high frequency harmonic excitation is applied to the pivot of a rotationally flexible pendulum. It is found that various equilibrium positions occur depending on the stiffness of the flexible parts.

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