scholarly journals A corner smoothing algorithm using Trajectory Pattern Method (TPM) for high-speed and high-quality machining

2021 ◽  
Vol 13 (8) ◽  
pp. 168781402110406
Author(s):  
Hao Li ◽  
Jahangir Rastegar ◽  
Baosheng Wang ◽  
Wenjiang Wu ◽  
Zhuwen Yan
Keyword(s):  
Fundamental Frequency ◽  
High Harmonic ◽  
Transition Curve ◽  
Smoothing Algorithm ◽  
Machining Efficiency ◽  
Modes Of Vibration ◽  
Trajectory Pattern ◽  
Harmonic Components ◽  
Feed Drive System ◽  
Trajectory Pattern Method

In micro-line segments machining, transition curves with high harmonic components are more prone to causing vibration issues in the feed drive system, which affects machining efficiency and quality severely. To construct low harmonic trajectories, this paper proposes a corner smoothing algorithm that uses the Trajectory Pattern Method (TPM). The transition curve construction and axial motion scheduling are performed with a specified fundamental frequency in one step, which reduces the smoothing process time and avoids excitation of natural modes of vibration of the system. The synthesized trajectories and axial kinematic profiles are all smooth and only contain the selected fundamental frequency and its first two odd harmonics, which minimizes the number of high harmonic components in the required actuation forces/torques and avoids excitation of the system modes of vibration. Linear programming is used to synthesize the trajectories. The proposed algorithm is shown to achieve near time-optimal trajectories. The provided experimental analysis and comparisons demonstrate that the proposed algorithm achieves smooth axial kinematic profiles with low harmonic contents, which would improve machining efficiency and quality.

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.

Robot Manipulator Trajectory Synthesis for Minimal Vibrational Excitation

1997 ◽  
Author(s):  
W. Kim ◽  
J. Rastegar
Keyword(s):  
Robot Manipulator ◽  
Vibrational Excitation ◽  
High Harmonic ◽  
Harmonic Excitation ◽  
Tracking Accuracy ◽  
Natural Modes ◽  
Starting Point ◽  
Modes Of Vibration ◽  
Operating Space ◽  
Harmonic Components

Abstract As a robot manipulator is forced to track a given trajectory, the required actuating torques (forces) may excite the natural modes of vibration of the system. Due to their nonlinear dynamics, internally and externally induced high harmonic excitation torques are generally generated even though such harmonics have been eliminated from the synthesized trajectories and filtered from the drive inputs. It is therefore desirable to synthesize trajectories such that the actuating torques required to realize them do not contain higher harmonic components with significant amplitudes. In this paper, a systematic method is presented for synthesizing such trajectories. With such trajectories, a robot manipulator can operate at higher speeds and achieve higher tracking accuracy with suppressed residual vibration. It is shown that in general and for a given starting point, such trajectories can only be synthesized to a portion of the operating space of the manipulator. The method is developed based on the Trajectory Pattern Method (TPM). The application of the method to optimal trajectory synthesis for a plane 2R manipulator is presented.

Pitch related to spectral edges of broadband signals

1992 ◽  
Vol 336 (1278) ◽  
pp. 375-382 ◽  
Keyword(s):  
Fundamental Frequency ◽  
Basilar Membrane ◽  
Comparison Tone ◽  
Harmonic Signals ◽  
Wide Range ◽  
Spectral Components ◽  
Neuronal Processes ◽  
Low Pass ◽  
Harmonic Components ◽  
Hearing System

A complex tone often evokes a pitch sensation associated with its extreme spectral components, besides the holistic pitch associated with its fundamental frequency. We studied the edge pitch created at the upper spectral edge of complexes with a low-pass spectrum by asking subjects to adjust the frequency of a sinusoidal comparison tone to the perceived pitch. Measurements were performed for different values of the fundamental frequency and of the upper frequency of the complex as well as for three different phase relations of the harmonic components. For a wide range of these parameters the subjects could adjust the comparison tone with a high accuracy, measured as the standard deviation of repeated adjustments, to a frequency close to the nominal edge frequency. The detailed dependence of the matching accuracy on temporal parameters of the harmonic complexes suggests that the perception of the edge pitch in harmonic signals is related to the temporal resolution of the hearing system. This resolution depends primarily on the time constants of basilar-membrane filters and on additional limitations due to neuronal processes.

scholarly journals Receptivity of Boundary Layer over a Blunt Wedge due to Freestream Pulse Disturbances at Mach 6

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Jianqiang Shi ◽  
Xiaojun Tang ◽  
Zhenqing Wang ◽  
Mingfang Shi ◽  
Wei Zhao
Keyword(s):  
Boundary Layer ◽  
Fundamental Frequency ◽  
High Frequency ◽  
Pulse Wave ◽  
Second Harmonic ◽  
Acoustic Pulse ◽  
Disturbance Wave ◽  
Acoustic Disturbances ◽  
Disturbance Frequency ◽  
Harmonic Components

Direct numerical simulation (DNS) of a hypersonic compressible flow over a blunt wedge with fast acoustic disturbances in freestream is performed. The receptivity characteristics of boundary layer to freestream pulse acoustic disturbances are numerically investigated at Mach 6, and the frequency effects of freestream pulse wave on boundary layer receptivity are discussed. Results show that there are several main disturbance mode clusters in boundary layer under acoustic pulse wave, and the number of main disturbance clusters decreases along the streamwise. As disturbance wave propagates from upstream to downstream direction, the component of the modes below fundamental frequency decreases, and the component of the modes above second harmonic components increases quickly in general. There are competition and disturbance energy transfer between different boundary layer modes. The nose boundary layer is dominated by the nearby mode of fundamental frequency. The number of the main disturbance mode clusters decreases as the freestream disturbance frequency increases. The frequency range with larger growth narrows along the streamwise. In general, the amplitudes of both fundamental mode and harmonics become larger with the decreasing of freestream disturbance frequency. High frequency freestream disturbance accelerates the decay of disturbance wave in downstream boundary layer.

Joint Wavelet Transform and Time Synchronous Averaging Source Separation Method and its Application on Aero-Engine

2020 ◽  
Author(s):  
Jiqing Cong ◽  
Jianping Jing ◽  
Changmin Chen ◽  
Zezeng Dai ◽  
Jianhua Cheng
Keyword(s):  
Wavelet Transform ◽  
Fault Diagnosis ◽  
Fundamental Frequency ◽  
Averaging Method ◽  
Gaussian White Noise ◽  
Rotating Machinery ◽  
Vibration Source ◽  
Vibration Signals ◽  
Aero Engine ◽  
Harmonic Components

Abstract The reliability and safety of aero-engine are often the decisive factors for the safe and reliable flight of commercial aircraft. Hence, the vibration source location and fault diagnosis of aero-engine are of prime importance to detect faults and carry out fast and effective maintenance in time. However, the vibration signals collected by the sensors arranged on the casing of the aero-engine are generally the mixed signals of the main vibration sources inside the engine, and the components are extremely complicated. Therefore, the vibration source identification is a big challenge for a fault diagnosis and health management of the engine. In order to separate the key vibration sources of rotating machinery such as aero-engine, a Joint Wavelet Transform and Time Synchronous Averaging based algorithm (JWTS) is proposed in this paper. Based on the fact that the fundamental frequency and its harmonic and sub-harmonic components are generally included in the vibration spectrum of shaft fault signal of rotating machinery, wavelet transform and time synchronous averaging algorithm are combined to extract them. The algorithm completes separating the main vibration sources with three steps. First, the source number and fundamental frequency of each source are estimated using the wavelet transform. Second, every source is extracted from each observed signal by the time synchronous averaging method. Time synchronous averaging method can effectively extract a signal of cycle and harmonic rotor components and can suppress noise. Third, the optimal estimation of each source is determined according to signal’s 2-norm. Since the extracted source with a larger energy is closer to the real source, and signal’s 2-norm is a good indicator of the signal energy. Hence, the key vibration sources related to rotary speeds of the engine are obtained separately. The method is verified by synthetic mixed signals first. Three periodic signals of different frequencies are used to simulate the vibration sources of the aeroengine. The fundamental, harmonic and sub-harmonic components of them, as well as Gaussian white noise, are randomly mixed. The results show that the JWTS algorithm can estimate the number of the main sources and can extract each source effectively. Then the method is demonstrated using vibration signals of a real aero-engine. The results indicate that the proposed JWTS method has extracted and located the main sources within the aero-engine, including sources from the low-pressure rotor, high-pressure rotor, combustion chamber and accessory. Therefore, the proposed method provides a new fault diagnosis technology for rotating machinery, especially for a real aero-engine.

Optimal Simultaneous Kinematic, Dynamic and Control Design of High Performance Manipulators Based on Trajectory Pattern Method

1998 ◽  
Author(s):  
J. Rastegar ◽  
L. Liu ◽  
M. Mattice
Keyword(s):  
High Speed ◽  
High Performance ◽  
Optimality Criterion ◽  
Control Design ◽  
Tracking Errors ◽  
Motion Patterns ◽  
Trajectory Pattern ◽  
And Control ◽  
Velocity Tracking ◽  
Trajectory Pattern Method

Abstract An optimal simultaneous kinematic, dynamic and control design approach is proposed for high performance computer controlled machines such as robot manipulators. The approach is based on the Trajectory Pattern Method (TPM) and a fundamentally new design philosophy that such machines in general and ultra-high performance machines in particular must only be designed to perform a class or classes of motions effectively. In the proposed approach, given the structure of the manipulator, its kinematic, dynamic and control parameters are optimized simultaneously with the parameters that describe the selected trajectory pattern. In the example presented in this paper, a weighted sum of the norms of the higher harmonics appearing in the actuating torques and the integral of the position and velocity tracking errors are used to form the optimality criterion. The selected optimality criterion should yield a system that is optimally designed to accurately follow the specified trajectory at high speed. Other objective functions can be readily formulated to synthesize systems for optimal performance. The potentials of the developed method and its implementation for generally defined motion patterns are discussed.

A Real Time Power System Harmonic Estimator Considering Fundamental Frequency Variations

2010 ◽  
Vol 11 (4) ◽  
Author(s):  
Mohammad Reza Dadash Zadeh
Keyword(s):  
Power Systems ◽  
Power System ◽  
Real Time ◽  
Fundamental Frequency ◽  
Digital Signal Processor ◽  
Sampling Rate ◽  
Window Size ◽  
Digital Signal ◽  
Computation Method ◽  
Harmonic Components

A new technique based on orthogonal filters and iterative frequency tracking is proposed to estimate harmonic components in power systems for real time applications. Frequency interpolation is used to estimate fundamental frequency and harmonics when the nominal frequency of the signal is a non-integer value. Fixed data window size and fixed sampling rate are the two advantageous features of the proposed technique. An off-line computation method with linear interpolation is proposed to reduce the number of computations involved during the generation of filter coefficients. The proposed technique was implemented using a real-time DSP (digital signal processor) data acquisition system. The performance of the proposed technique was studied by estimating the harmonic components of various signals. A FFT (Fast Fourier Transform) based technique was also used to estimate harmonic components for comparison. It has been shown that the accurate fundamental frequency is computed using iterative technique, and then accurate harmonic components are estimated when the fundamental frequency is not equal to the power system nominal frequency.

Improved Power Transformer Winding Deformation Fault Diagnosis Method

2014 ◽  
Vol 666 ◽  
pp. 149-153 ◽  
Author(s):  
Hong Zhong Ma ◽  
Ning Jiang ◽  
Chun Ning Wang ◽  
Zhi Hui Geng
Keyword(s):  
Fault Diagnosis ◽  
Fundamental Frequency ◽  
Characteristic Frequency ◽  
Power Transformer ◽  
Vibration Signal ◽  
Frequency Component ◽  
Transformer Winding ◽  
Diagnosis Method ◽  
Winding Deformation ◽  
Harmonic Components

according to analysing the generation principle of transformer winding deformation and its impact on the vibration signal, and make a large number of trial, it can be found in addition to the fundamental frequency component that can reflect the failure, the new characteristic frequency which conclude 50Hz frequency component and some of its harmonic components, the harmonic components of the fundamental frequency can also reflect the failure. Transformer winding deformation fault diagnosis method is proposed based on the relationship between the characteristic frequency, it can not only diagnose whether the failure inside the transformer windings, but also determine the type of fault. In order to verify the proposed method, deformation fault is set to the actual transformer winding. After de-noising, discounted processing, the acquisition monitoring points of vibration signal is used by the proposed method, and the actual transformer is diagnosed, The diagnostic result is same with actual failure. It is shown that the proposed diagnostic method is accurate and feasible.

Linkage Mechanisms With Cam-Integrated Joints for Controlled Harmonic Content of the Output Motion: Theory and Application

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
L. Yuan ◽  
J. Rastegar ◽  
J. Zhang
Keyword(s):  
Closed Loop ◽  
Vibrational Excitation ◽  
High Harmonic ◽  
Harmonic Component ◽  
Linkage Mechanism ◽  
Mechanism Synthesis ◽  
Cam Mechanism ◽  
Harmonic Content ◽  
Harmonic Components ◽  
Four Bar Linkage

In a recent study, the authors presented a systematic method for the modification of the output motion of linkage mechanisms with closed-loop chains using cams positioned at one or more joints of the mechanism. In this paper, the method is applied to the design of a linkage mechanism with an integrated cam mechanism to eliminate high harmonic component of the output motion. The mechanism may be synthesized using any existing linkage mechanism synthesis technique. In the present study, a cam mechanism is synthesized to eliminate all high harmonic components of the output link motion of a four-bar linkage mechanism to illustrate the potentials of the present approach. The mechanism is then constructed and successfully tested. With the present method, selected ranges of high harmonic motions generated due to the mechanisms kinematics nonlinearity can be eliminated by integrating appropriately designed cams, thereby significantly reducing the potential vibrational excitation that the mechanism can impart on the overall system, including its own structure. Such systems should therefore be capable of operating at higher speeds and with increased precision.

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