Analysis of transmission box vibration characteristics under random road torsional excitation

Random road torsional excitation is a key excitation condition for transmission box vibration of tracked vehicles. In order to accurately analyze influences of random road torsional excitation on the vibration characteristics of the transmission box, a calculation method of this excitation for tracked vehicle is proposed based on the random expression of the roughness of standard road surface. Furthermore, random road torsional excitations under different road grades and vehicle speeds are simulated. With the finite element method and modal superposition method, the box body is discretized, and the elastic characteristics of the box body are characterized to explore the dynamics coupling mechanism of gear shafting and the box body. By considering bending-torsional coupling vibration of gear shafting under multi-source excitations, such as the fluctuated torque of engine and dynamic meshing stiffness of gears, dynamic coupling model of gear shafting and box body under random road torsional excitation is established. The dynamic response of the gearbox under random road torsion excitation is obtained by co-simulation with the variable step length Runge-Kutta method. Influences of different road grades, track preload and vehicle speeds on dynamic response characteristics of the gearbox are analyzed. Real vehicle road test scheme is designed to obtain surface acceleration response of the box body at different speeds on the cement road surface. Both test and simulation results are compared and analyzed to verify the accuracy of the simulation method, which provides a theoretical reference for dynamic optimization of the transmission box.

Comparison of small-strain shear modulus and Young’s modulus of dry sand measured by resonant column and bender–extender element

The small-strain shear modulus and Young’s modulus of dry sand are simultaneously measured by resonant column and bender–extender element tests. Two different methods are adopted to calibrate the resonant column and the results indicate that the conventional calibration method may significantly underestimate the Young’s modulus obtained in flexural excitation, while it only slightly underestimates the shear modulus obtained in torsional excitation. A new calibration method that establishes a calibration curve based on the resonant frequency is used to overcome the error. With this new calibration method, the shear modulus and Young’s modulus from the resonant column agree well with those from the bender–extender element. It convincingly explains the reason why a very small Poisson’s ratio was observed in previous resonant column tests and suggests that the effect of resonant frequency on the calibration results must be considered in flexural excitation.

Dynamic Model and Quantitative Analysis of Stick-Slip Vibration in Horizontal Well

Stick-slip is very harmful to the service life of drillstring. The extended Hamilton principle is applied in the paper. Then, finite element method (FEM) is employed to describe the model. The drillstring-borehole impact and friction, fluid-structure interaction, bit-rock interaction, and gravity are considered in this model. The influence of axial and torsional excitation on stick-slip is analyzed. The nonlinear motion predicted by the model is consistent with the observation results in the experiments. The research shows that the fluctuation amplitude of the bit angular velocity also increases along with the increase of driving angular velocity (torsional excitation). However, both the ratio of the maximum angular velocity of the stick-slip vibration and the fluctuation of the angular velocity are continuously reduced. Meanwhile, the strength of the stick-slip vibration has a tendency to slow down. As the axial load (axial excitation) increases, the fluctuation of the maximum angular speed of the stick-slip vibration does not change significantly, but the smaller load causes a smaller stick duration.

Experimental and numerical studies of bolted joints subjected to torsional excitation

The dynamic response of bolted joints subjected to torsional excitation is investigated experimentally and numerically. First, the effects of the initial preload and the angular amplitude on axial force loss of the bolt were studied. Second, the change of hysteresis loops with the increasing number of loading cycles was found under a larger torsional angle. At last, a fine-meshed three-dimensional finite element model was built to simulate the bolted joint under torsional excitation, from which the hysteresis loops were obtained under varying angular amplitudes. The results of numerical analysis are in good agreement with those of experiments.

Nonlinear Modeling and Qualitative Analysis of Coupled Vibrations in a Drill String

A coupled model for axial/torsional/lateral vibrations of the drill string is presented, in which the nonlinear dynamics and qualitative analysis method are employed to find out the key factors and sensitive zone for coupled vibration. The drill string is simplified as an equivalent shell under axial rotation. After dimensionless processing, the mathematical model for coupled axial/torsional/lateral vibrations of the drill string is obtained. The Runge–Kutta–Fehlberg method is employed for the numerical simulation, and the rules that govern the changing of the torsional and axial excitation are revealed. And the stability domains of the explicit Runge–Kutta method are analyzed. Furthermore, the suggestions for field applications are also presented. It is demonstrated by simulation results that the lateral/axial/torsional vibrations exist simultaneously and couple with each other. The system will obtain a stable period motion with an axial excitation zone before the coupled vibration in the three directions, and continue to increase the axial excitation to cause the coupled vibration easily. The torsional excitation of the drill string mainly contributes to the coupled vibration in the three directions when in a specific rotation speed zone. The system is more likely to obtain a periodic motion through adjusting the torsional excitation out of this zone.

A novel design of the dynamic vibration absorbers for damped main systems under torsional excitation using least squares estimation of the equivalent linearization method

Torsional vibration usually occurs in the working process of machines and equipment such as in transmission drive and working shaft of machine tool. To reduce this vibration, the dynamic balancing method and dual mass flywheel systems are applied. There are fewer researches that used the dynamic vibration absorber for reducing the torsional vibration. However, an analytical solution for designing the optimal parameters of dynamic vibration absorbers attached to the damped main system is found to be difficult and complicated. This paper proposes a novel idea to approximately replace an original damped main system by an equivalent undamped system using the least squares estimation of equivalent linearization method. An explicit closed-form expression of the optimal damping ratio and tuning parameters of dynamic vibration absorber are determined for the undamped main system under torsional excitation. The expressions are quite simple and have effective practical applications. Numerical results for time and frequency responses of the system are presented to reveal stronger effect and accuracy of the proposed solution on the damped main system. It is observed that the torsional vibration of the damped main system has been reduced significantly also in the resonant region. The proposed expressions of the optimal parameters are powerful tools for design dynamic vibration absorber to reduce the torsional vibration of rotary system such as the transmission and working shafts, etc.