Dynamic Modeling and Analysis of Nonlinear Compound Planetary System

In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.

Nonlinear Dynamics Analysis of Multifactor Low Speed Heavy Load Gear System with Temperature Effect Considered

Low-speed and heavy-duty gears will generate a lot of heat during meshing transmission, which will cause thermal deformation of the gears and affect the transmission performance of the gear system. It is of great significance to explore the influence of temperature effects on the nonlinear dynamics of the gear system. Taking the spur gear system as the research object, considering the nonlinear factors such as time-varying meshing stiffness, tooth backlash and comprehensive error, and introducing the influence of temperature change, the nonlinear dynamic model of the gear system is established, using 4~5th order Runge -Kutta algorithm performs simulation calculation on the model, combined with bifurcation diagram, maximum Lyapunov exponent diagram, phase diagram and Poincare section diagram, etc., to analyze the influence of temperature changes and time-varying stiffness coefficients on the motion characteristics of the gear system. The results show that the influence of temperature change on the gear system is related to the value of the time-varying stiffness coefficient. The larger the value, the more obvious the influence of temperature change; the system will show different dynamic response with the change of the time-varying stiffness coefficient, including four states of single-period motion, multiple-period motion, bifurcation and chaotic motion. The relevant conclusions can provide references for the design of gear systems under special working conditions.

A novel electro-hydraulic servo steering system for Ackermann steering of heavy multi-axle vehicle

Ackermann steering is important for the steering performance of heavy multi-axle vehicle. When Ackermann steering condition is not satisfied, it will lead to abnormal tire wear. Traditional trapezoidal mechanism of heavy multi-axle vehicle is a single degree of freedom (DOF) mechanism, which is difficult to completely realize Ackermann steering. In this paper, a new two DOF electro-hydraulic servo steering system (TDEHSSS) by using a variable length tie rod is proposed for solving the issue. First, a complex nonlinear dynamic model of TDEHSSS is established. This model includes the two DOF mechanical model based on a Lagrange equation, the valve-controlled double steering power cylinders model and the valve-controlled tie rod cylinder model. Then, a simulation model is built through MATLAB/Simulink and the simulation results show that TDEHSSS can realize the proposed requirement. At last, a test bench is founded to verify model. It is indicated that the simulation and experimental curves are consistent, showing that mathematical model is in accordance with the experimental system. This research is valuable for analyzing TDEHSSS, designing advanced controllers, and finally realizing Ackermann steering for heavy multi-axle vehicles.

Adaptive robust precision control of an active spray boom suspension with disturbance estimation

When the boom sprayer works in the field, the boom must be parallel to the undulating ground or crop canopy. Aiming at the problem of low control accuracy and poor stability caused by parameter uncertainties and time-varying disturbances in the electro-hydraulic active boom suspension system, this paper proposes an adaptive robust precision control algorithm based on disturbance estimation. Firstly, the dynamic analysis modeling method is adopted to establish the nonlinear dynamic model and mechanism geometric equation of the pendulum active and passive suspension. Then, the controller was designed based on the nonlinear model of the suspension system. The proposed controller uses the backstepping design method to integrate the disturbance observer into the adaptive robust controller, which can effectively deal with the parameter uncertainties and time-varying disturbances in the suspension system model. Finally, a large number of experiments were carried out by taking a 28 m large boom active suspension driven by a single-rod hydraulic pressure as an example. Using an established rapid control prototype of a large boom suspension, a variety of control algorithm comparison experiments were carried out, and a 6-DOF motion platform was used to simulate the motion coupling interference of the sprayer chassis. The experiment results illustrate the high-performance characteristics of the proposed controller and improve the tracking performance of the active pendulum suspension system under various parameter uncertainties and time-varying disturbances.

Nonparametric Method for Predicting the Trajectory of an Actively Maneuvering Vessel for Unmanned Aerial Vehicle Landing

The article is devoted to the development of algorithms for predicting the trajectory of maneuvering objects based on nonparametric systems theory. The analysis of uncertainties affecting the modeling of the movement maneuvering water objects is presented. An overview of parametric, nonparametric and combined methods for predicting maneuvering water objects trajectory is given. The problem of high-precision autonomous control of the landing unmanned aerial vehicles on the landing vessel in the conditions of its irregular movement caused by meteorological conditions and active maneuvering is being solved. The method for predicting the trajectory of a vessel’s movement based on solving direct problems of dynamics using nonparametric systems theory is proposed. The advantages of the proposed method are that it’s not affected by model errors, due to the fact that it is based only on a retrospective analysis of several consecutive values of the spatial vessel coordinates. The proposed method differs from similar nonparametric methods in that it does not require statistical calculations, own training, or time-consuming tuning. The method does not imply the solution of identification model parameters, state and control actions problems and can be applied with any unknown linearizable input control actions, including when the model of the vessel’s motion dynamics is not identifiable. The results of numerical modeling for solution the problem of predicting the trajectory of an actively maneuvering small-sized landing vessel using a full nonlinear dynamic model with six degrees of freedom are presented. The studies carried out confirm the efficiency, adequacy and very fast adjustment of the developed method under conditions of complete parametric and nonparametric uncertainty. The proposed method can be used to predict the trajectory of any vehicle under the condition of linearizability of its model and control signals over the observed time interval.

Nonlinear Dynamics of the Rigid Drum for Vibratory Roller on Elastic Subgrades

In this paper, a coupling nonlinear dynamic model of the drum and subgrade is established for the vibratory roller. The dynamic characteristics of the rigid drum of the vibratory roller in the process of vibratory compaction are comprehensively investigated by time history, phase diagram, frequency spectrum, Poincare map, and bifurcation diagram. During the compaction process, the stiffness of the subgrade increases and the motion of the rigid drum of the vibratory roller changes from a single period to multiple periods and finally enters chaos by the way of period doubling. Moreover, the roller parameters also significantly affect the dynamic characteristics of the rigid drum and the compaction effect of the subgrade. Based on detailed numerical results, a parameter adjustment strategy about the roller frequency and nominal amplitude is proposed, which can avoid the “bouncing” of the drum during compaction and improve the compaction efficiency.

Influence of Pitch Error on Vibration, Bifurcation, and Chaos Characteristics of the Helical Gear Pair System

Aiming at the problem of pitch error of helical gear pair in engineering practice, the influence of pitch error on vibration, bifurcation, and chaos characteristics of the helical gear pair system is mainly studied. Due to the periodic time-varying nature of pitch error, a method of simulating the pitch error as a sine function is proposed to calculate pitch error. A nonlinear dynamic model of bending-torsion-shaft coupling of the helical gear pair system is established considering the effect of pitch error. The influence of pitch error on the vibration, bifurcation, and chaos characteristics of the system is analyzed by the Runge–Kutta numerical integration method. The research results show that the introduction of pitch error has the most significant impact on the torsional vibration of the system. With the increase in pitch error, the system exhibits rich bifurcation and chaos characteristics in the torsional direction. Moreover, it is also found that the vibration response in the torsional orientation of the system increases or decreases to the same degree when the system is in a periodic motion state, and the pitch error varies by the same extent. Therefore, the impact of pitch error on the dynamic performance of the helical gear pair system should be considered in engineering practice.

Investigation of oil-air flow and temperature for high speed ball bearings by combining nonlinear dynamic and CFD models

An improved nonlinear dynamic model of high speed ball bearings with elastohydrodynamic lubrication (EHL) is adopted to predict the movements of balls and power loss of ball bearings for defining the boundary conditions of computational fluid dynamics (CFD) model. Then, this method of combining nonlinear dynamic and CFD models is are validated through the experimental verification. Subsequently, oil-air flow and temperature distribution inside the bearing chamber are studied at low and high speeds, and light and heavy loads. The effect of nozzle's position on the formation of oil film and heat dissipation is revealed under combined loads. The research results provide a theoretical basis for engineering application of high speed rolling bearings.

Elaborate Modeling and Fragility Assessment of a Multiframe PC Box-Girder Bridge with Intermediate Hinges in California

Multiframe PC box-girder bridge with intermediate hinges is a kind of bridge having complex structural characters, which is very quintessential in California. In this study, a typical bridge was adopted to establish a nonlinear dynamic model through OpenSees platform. Intermediate hinge and inhibiting devices in it were elaborately simulated. Meanwhile, pushover analysis was used to reinstate a specimen of column test, which has the similar ratio of reinforcement to the typical bridge, and the hysteretic model parameters of the longitudinal steels inside columns were obtained. The damage indexes of column and hinge, which are primary components, under different limit states were acquired by moment-curvature analysis. Taking into account the uncertainty, nonlinear time-history analysis of the bridge was carried out through a suite of synthetic ground motions. Subsequently, a probabilistic seismic demand model was developed, and fragility curves were further focused on. According to fragility assessment, the conclusion shows that columns and hinge restrainers exhibit high fragility, and bridge system fragility is gradually determined by column fragility along with aggravating of the damage state. Unseating of girder can hardly occur at abutments and intermediate hinges. Moderate limit state could be exceeded in the positions of plug-type concrete structures in intermediate hinges, which tends to create transverse and vertical cracks, furthermore causing reinforcements yield. It indicates that it would severely underestimate the seismic fragility of intermediate hinges without considering the elaborate simulation of hinges.