Viscoelastic damping material has been widely used in engineering machinery to absorb vibration and noise. Dynamic behavior of the viscoelastic damping material is mainly affected by temperature and frequency. Classical dynamic behavior equations of the viscoelastic damping material have complex structures with multiple and ambiguous parameters. So a novel variable-order fractional constitutive model (VOFC) is established based on the variable-order fractional operator. Then the viscoelastic dynamic equations are derived by Laplace transform of the VOFC model. The dynamic thermomechanical analysis tests by the three-point bending mode are carried out at variable temperatures and frequencies, and the frequency spectrum of the dynamic behavior, i.e. the loss modulus, storage modulus and loss factor are obtained. Against the test data, the VOFC model is compared with classical models such as the integer-order Maxwell model, constant fractional-order Kelvin-Voigt model, constant fractional-order Maxwell model and constant fractional-order standard linear solid model. The results show that the VOFC model can describe dynamic behavior of the viscoelastic damping material at different temperatures and frequencies more accurately. And the VOFC model has simpler structure and only two parameters with clearly physical meaning. Finally, a calculation software is designed and developed, which simplifies the process of predicting viscoelastic dynamic behavior in a wide frequency range.

The hydrodynamic lubrication performance of partially textured gas parallel slider bearings with orientation ellipse dimples is investigated in this paper. By using the multigrid finite element method, the pressure distribution between a partially textured slider and a smooth slider is obtained. The geometric parameters of the ellipse dimples are optimized to maximize the average pressure under a given sliding speed. The numerical results show that geometric parameters such as orientation angle, depth, slender ratio, and area density have an important impact on hydrodynamic pressure. Besides, the effect of textured fraction on hydrodynamic pressure is investigated under a given sliding speed. It is observed that the optimum textured fraction for maximizing the average pressure is dependent on the sliding speed.

Traditional viscoelastic constitutive models encounter the problems of massive parameters and ambiguous physical meanings. A new concept variable-order viscoelastic constitutive (called VOVC) model is put forward based on the constant fractional-order constitutive model and viscoelastic theory. The determination methods of the two parameters in the VOVC model, including the material coefficient and viscoelastic coefficient, are discussed both in the tensile and resilient processes. Comparisons are made between the VOVC model and traditional constitutive models, i.e., the constant fractional-order Kelvin–Voigt (CFKV) model, the Zhu–Wang–Tang nonlinear thermo-viscoelastic constitutive (ZWT) model, and the Ogden nonlinear hyper-elastic (Ogden) model. The results show that the VOVC model with the constant material coefficient and the variable viscoelastic coefficient predicts the whole evolution of the constitutive behavior of the viscoelastic material under the constant strain rate more precisely. The constant material coefficient in the VOVC model means the stiffness of the viscoelastic material. The variable viscoelastic coefficient in the model means the distribution of the elasticity and viscosity. The proposed VOVC model contains a simpler structure, fewer parameters, clearer physical meanings, and higher precision.

The prediction for the impact behavior of viscoelastic oscillator (VEO) has a great significance. The fractional Maxwell viscoelastic oscillator (FMVEO) model under impact load is derived by integrating the fractional Maxwell constitutive model into the system vibration equation and further involving the geometric factors of the isolators. The numerical algorithm based on Chebyshev operational matrix is derived. The Split Hopkinson Pressure Bar (SHPB) experiment is conducted to validate the proposed model. The results indicate that FMVEO can fully describe impact properties of the viscoelastic oscillator. The fractional orders α and β are critical to the elasticity-viscosity component of FMVEO and the first amplitude of the impact response, respectively. The response of FMVEO displays an under-damped state for α ≤ 0.5 and over-damped state for α > 0.5. FMVEO degenerates into a pure-elastic system for α = 0 and evolves into a pure-viscous system for α = 1. In frequency domain, there are resonant peaks for the amplitude-frequency response for α ≤ 0.5, while no pronounced peaks exist for α > 0.5. The fractional order β displays a positive correlation with the first amplitude and a weakly negative correlation with the damping. The geometric factor κ should be taken into full consideration in two ways, the relatively small amplitude and the limited installation space, which shows the significant effect of the geometric element on the system response.

Tunnel lighting cleaning is of significant practical importance for improving driving safety. To address the low operational efficiency of tunnel lighting cleaning tasks, a trajectory planning method based on the chaotic adaptive whale–particle swarm optimization (CAW-PSO) algorithm is proposed. Taking the SIASUN GCR16-2000 robotic arm as the research object, the trajectory is constructed using a 3-5-3 polynomial interpolation, with the objective of achieving time-optimal trajectory planning. In the CAW-PSO algorithm, a tent chaotic map is introduced to improve the quality of the population; a linearly decreasing inertia weight is designed to strike a balance between local and global search; dynamic learning factors are defined to strengthen the individual learning ability and global cognitive capability of particles; finally, the exploitation mechanism of the whale optimization algorithm is employed to avoid getting trapped in local optima and improve convergence accuracy. The simulation time is 3.661 s, a reduction of 69.94%. The experimental results yielded a mean relative error of 1.16%, indicating good agreement with the simulation results. The results of the simulation and experiment indicate that the CAW-PSO effectively reduces the motion time of the robotic arm, exhibiting superior applicability in trajectory planning for tunnel lighting cleaning robotic arms.

The influence of grooving parameters and micro-groove cross-section shape on the lubrication performance of partially micro-grooved gas-lubricated parallel slider bearings is investigated in the present study. The solution procedure for the multi-grid finite element method is that the algebraic equations formed by the finite element method are in turn smoothed by the interpolation from the coarse grid to the fine grid and the restriction from the fine grid to the coarse grid. By adopting the multi-grid finite element method, the pressure distribution of partially micro-grooved gas-lubricated parallel slider bearings is obtained. The grooving parameters are optimized to obtain the maximum average pressure for different micro-groove cross-section shapes. The results show that the orientation angle of the micro-grooves, depth of the micro-grooves, width of the micro-grooves, area density of the micro-grooves, micro-grooved fraction, and cross-section shape of the micro-grooves have an important influence on the hydrodynamic pressure of partially micro-grooved gas-lubricated parallel slider bearings. The results of this study demonstrate that the lubrication performance of partially micro-grooved gas-lubricated parallel slider bearings can be obviously enhanced by adopting the appropriate grooving parameters and micro-groove cross-shape. The results of this study is beneficial for the design of partially micro-grooved gas-lubricated parallel slider bearings.