Parametric Vibration Analysis of a Six-Degree-of-Freedom Electro-Hydraulic Stewart Platform

Electro-hydraulic Stewart 6-DOF platform is a 6-DOF parallel mechanism combined with the electro-hydraulic servo control system, which is widely used in the field of construction machinery. In actual working conditions, the flow and pressure pulsation of the hydraulic oil output from the hydraulic leg of the electro-hydraulic Stewart platform are inevitable, so the equivalent stiffness of the platform leg will change, and the stiffness parameters of the transmission system will change, resulting in vibration, which will affect the accuracy of the platform. This paper considering the fluid unit equivalent stiffness cyclical fluctuations and leg, on the basis of the relationship between hydraulic stiffness, constructs the electric hydraulic Stewart platform machine vibration dynamics equation, fluid coupling parameters of vibration parameters using the method of the multiscale approximate analytic formula of the main resonance and combination resonance are derived, and the system parameters vibration time-domain response and frequency response under two different poses are discussed. Results show that the system first to six order natural frequency and the first to the sixth order natural frequency and frequency of hydraulic oil equivalent stiffness of the combination of frequency will have an effect on the parameters of the system vibration. In the main resonance, the dominant frequency is mainly the first to sixth order natural frequency of the system; in the combined resonance, the dominant frequency is the combined frequency. Through the parameter vibration analysis of two different positions of the platform, it is concluded that when the platform is in an asymmetric position, each leg of the system is more involved in vibration. This study can provide the reference for the subsequent dynamic optimization and reliability analysis of the electro-hydraulic Stewart platform.

Analysis and Control of Vibrations of a Cartesian Cutting Machine Using an Equivalent Robotic Model

The vibrations of a Cartesian cutting machine caused by the pneumatic tool are studied with a sub-system approach. The cutting head is modeled as an equivalent robot arm which is able to mimic the measured resonances, The Cartesian structure is modeled according to the mode superposition approach. The full model is able to predict the variations in the response of the machine to tool excitation that are caused by the motion of the head along the rails of the Cartesian structure. Comparisons with experimental results are made. Finally, the mathematical model is used for assessing the effectiveness of a vibration absorber tuned to main resonance frequency of the cutting head.

Model-Based Analysis and Regulating Approach of Air-Coupled Transducers with Spurious Resonance

As an essential characteristic of air-coupled transducers, electrical impedance can provide valuable information for quality control during manufacturing of transducers. It is also found feasible to directly read the optimal operating frequency from the impedance plots when the resonance is independent of the others. However, the spurious resonance emerges when two neighboring resonances are closely spaced, resulting in distorted impedance and ambiguous optimal operating frequency. In this paper, the electrical impedance of air-coupled transducers with spurious resonance is modeled using the Butterworth–Van Dyke (BVD) equivalent circuit. Then model-based sensitivity analysis is performed to evaluate the mutual interference between adjacent resonances. Based on the analysis results, the prestress method is proposed to regulate and suppress the spurious resonance by adjusting the equivalent parameters of the BVD model. Experimental study was carried out on the response of the electrical impedance and the vibration velocity of the transducer with spurious resonance to pre-tightening force. The results show that the spurious resonance disappeared when the pre-tightening force was initially loaded. Moreover, the vibration velocity of two main resonance peaks increases about 45.6% and 33.9% as the pre-tightening torque increases to 0.25 N∙m. Hence it is validated that the proposed prestress method is efficient to suppress the spurious resonance and improve the transducers performance.

Nonlinear Vibration Mitigation of a Beam Excited by Moving Load with Time-Delayed Velocity and Acceleration Feedback

The time-delayed velocity and acceleration feedback control are provided to mitigate the resonances response of a nonlinear dynamic beam. By use of the method of multiple scales, the primary resonance and the 1/3 subharmonic resonance response of the controlled beam are analyzed. The excitation amplitude response peak and critical expression are obtained, and numerical simulations are also given. The effect of the feedback gains and time delayed on the steady-state response of the two types of resonances are investigated. The result show that time-delayed acceleration feedback control can effectively mitigate amplitude, and the main resonance response is affected periodically. Selecting reasonable control gain and time delay quantity can avoid the main resonance region and unstable multi-solutions, and can improve the efficiency of the vibration control.

Two types of scale effects on the nonlinear forced vibration of axially moving nanobeams

Various non-classical continuum mechanics models appearing in previous studies cannot perfectly explain the mechanical properties of micro- and nanomaterials. Establishing a reasonable continuum mechanics model that comprehensively reflects the scale effect on material deformation is of great practical significance for objectively explaining the variation law of mechanical properties of micro- and nanomaterials under the combined action of different scale effects. Based on nonlocal strain gradient theory, a new scale-dependent model is proposed for axially moving nanobeams. In this study, an asymptotic expansion is performed using the multiscale time method to obtain the amplitude-frequency response curve of the equilibrium solutions for the forced vibration problem. Afterwards, the effects of various system parameters, especially the scale parameters, on the resonance curve are examined. Finally, the effects of nonlocal parameters and material characteristic length parameters on the amplitude-frequency response curves are investigated through typical numerical examples. The numerical results show that the nonlocal parameters promote the emergence of the main resonance, whereas the material characteristic length parameters suppress the emergence of the main resonance. Moreover, these parameters also affect the response amplitude and the skewness and jumping point of the amplitude-frequency characteristic curve.

Study on Vertical Vibration Characteristics of the 2-DOF Strip Rolling Mill Model with a Single Weak Defect on the Work Roll Bearing Outer Raceway

Considering the influence caused by a early single pit defect on the outer raceway of the work roll bearing, a 2-DOF plate strip rolling mill vertical vibration model with a single point weak fault on the outer raceway was established. With the practical parameters of the roughing mill of the 1780 hot continuous rolling mill, the vertical vibration characteristics of the rolling mill work roll with different rotating speed and different single pit defect area on the bearing outer raceway are analyzed by numerical simulation. It is found that with the change of the rotation speed of the work roll, different nonlinear vibration behaviors occurred, such as superharmonic resonance, main resonance, combined resonance and sub-harmonic resonance. Especially the subharmonic resonance of the work roll is more harmful than the main resonance when the work roll speed is twice the rotation speed corresponding to the first and second natural frequency of the rolling mill. This work provides a theoretical basis for further clarifying the effect caused by a early defect of the work roll bearing on the mill vibration.