Pitching Vibration Research Articles

Study of the comfortable efficiency of the automobile using the seat’s Negative-Stiffness-Structure via two mathematical models

The isolating performance of NSS (Negative-Stiffness-Structure) on ameliorating the automotive’s comfortable in all vertical, pitching, and rolling directions has been not studied yet. Thus, two vibration models of the automobile including the two-dimensional (2-D) model and three-dimensional (3-D) model are built to evaluate automobile’s comfortable efficiency under various conditions. The reduction of the seat and automobile accelerations has been used as an evaluation index. Results present that seat’s vertical acceleration using NSS is evidently improved compared without NSS in two models of the automobile. Especially, the seat’s root-mean-square acceleration with NSS is strongly deteriorated by 65.1% with 2-D model and reduced by 69.7% with 3-D model in comparison without NSS. However, the seat’s NSS does not affect the pitching vibration of the automobile’s body. Besides, from the comparison results between 2-D and 3-D models, seat’s NSS could strongly ameliorate the comfortable efficiency in both vertical and rolling vibrations while the seat’s NSS does not affect improving the automobile’s pitching angle of the automobile. Therefore, to fully assess NSS’s isolating performance as well as improve the comfortable efficiency of the automobile in all vibration directions, 3-D model of the automobile should be used.

Aerodynamic Characteristics and Its Sensitivity Analysis of a Cylindrical Projectile at Different Incidences

The accurate evaluation of aerodynamic characteristics is a prerequisite and foundation for the design of high-performance aerodynamic shapes, navigation guidance, and strength of projectiles. The nonlinearity of aerodynamic calculations for a projectile is high, and the modeling and simulation are difficult, especially under the high-angle of attack flight conditions. Small variations in flight conditions, and structural parameters, etc., may cause large deviations in aerodynamic responses. Taking a small cylindrical projectile as an example, and to realize its attitude control, it is necessary to conduct aerodynamic characteristics analysis on it and analyze the main influencing factors of its aerodynamic characteristics parameters. In this paper, the finite volume method is used to solve the three-dimensional unsteady N-S equation, combined with the SST k-ω turbulence model, the overlapping grid technology, and the forced pitching vibration method, and the aerodynamic characteristics analysis model of the projectile is established, which realizes the accurate simulation of the surrounding flow field, aerodynamic coefficients, and dynamic derivative of the projectile under different flight conditions. On this basis, the Sobol global sensitivity analysis method based on the augmented radial basis function surrogate model of aerodynamics characteristics and Latin hypercube sampling is used to efficiently analyze and obtain the main influence parameters of cylindrical projectile aerodynamic characteristics. This paper provides a basic theory and fast algorithm for subsequent engineering system design, which has important theoretical and engineering value.

Ameliorating vibratory roller quality based on two methods of cab’s horizontal damper and cab’s active suspension

To reduce both the seat's vertical acceleration and cab pitching vibration in vibratory rollers, an active horizontal seat suspension (AHSS) is proposed and researched based on the dynamic model of the vibratory rollers moving and working and off-road grounds. The fuzzy control is applied to calculate the control force of the AHSS. The indexes in the Root Mean Square acceleration in the seat (RMSas) and cab pitch angle (RMSaφ) have been selected as the objective functions. The isolation performance of the HASS is then compared with the cab isolations controlled (CC) and without control (WC) under two conditions of the vibratory roller moving and working on the off-road surface. The study results show that the vibratory roller’s quality using the AHSS has been strongly ameliorated in comparison with both the CC and WC under both moving/working conditions. Especially, comparison with the WC, both the values of RMSas and RMSaφ with the AHSS are greatly reduced by 54.2 % and 52.6 % under the moving case and by 44.5 % and 50.0 % under working conditions of the vibratory roller. Therefore, the AHSS should be applied to improve both the seat's vertical comfort and shaking in vibratory rollers.

Adaptive control of transonic buffet and buffeting flow with deep reinforcement learning

The optimal control of flow and fluid–structure interaction (FSI) systems often requires an accurate model of the controlled system. However, for strongly nonlinear systems, acquiring an accurate dynamic model is a significant challenge. In this study, we employ the deep reinforcement learning (DRL) method, which does not rely on an accurate model of the controlled system, to address the control of transonic buffet (unstable flow) and transonic buffeting (structural vibration). DRL uses a deep neural network to describe the control law and optimizes it based on data obtained from interaction between control law and flow or FSI system. This study analyzes the mechanism of transonic buffet and transonic buffeting to guide the design of control system. Aiming at the control of transonic buffet, which is an unstable flow system, the control law optimized by DRL can quickly suppress fluctuating load of buffet by taking the lift coefficient as feedback signal. For the frequency lock-in phenomenon in transonic buffeting flow, which is an unstable FSI system, we add the moment coefficient and pitching displacement to feedback signal to observe pitching vibration mode. The control law optimized by DRL can also effectively eliminate or reduce pitching vibration displacement of airfoil and buffet load. The simulation results in this study show that DRL can adapt to the control of two different dynamic modes: typical forced response and FSI instability under transonic buffet, so it has a wide application prospect in the design of control laws for complex flow or FSI systems.

Coupling analysis and vibration control of vehicle vertical vibration and pitching vibration

The decoupling analysis of vertical vibration and pitching vibration is the basis of improving vehicle comfort performance and realizing vehicle body vibration control. In order to study the coupling behavior of vehicle body vibration, the vibration characteristics of the suspension and the body are analyzed through mathematical modeling and vibration tests. The research shows that the vibration characteristics of the front and rear suspensions are the key factors affecting the coupling between the vertical vibration and the pitching vibration. By controlling the difference ξ between the square of the rotating radius of the body and the product of the distance from the center of mass to the front and rear axles, the correlation between front and rear suspension vibration and the coupling of the body vibration can be reduced effectively. Through the reasonable matching of front and rear suspension stiffness, the ξ value can be reduced effectively. The research results provide a theoretical basis and reference for mastering the coupling mechanism between vertical vibration and pitching vibration and for the body vibration control.

A new suppression strategy of pitching vibration based on the magnetic-electric-mechanical coupling dynamic model for superconducting EDS transport system

The superconducting electrodynamic suspension (EDS) train is suitable for high-speed maglev rail transit because of its low drag force, strong levitation force, large suspension gap, and so on. However, the electromagnetic forces of four pairs of superconducting coils on one bogie are dynamically unequal in practical operation. This causes the bogie to vibrate in the pitching axis, which affects the train system's safety, stability, and comfort. Therefore, proposing an appropriate strategy to suppress the bogie pitching vibration is significant. First, based on the dynamic circuit theory, energy method and rigid body dynamics, the magnetic-electric-mechanical coupling dynamic model of eight superconducting high-field coils in the bogie and ground null-flux coils was established to explore the characteristics of fluctuating and unequal electromagnetic forces. The synchronous current and motion responses were further calculated using the Runge-Kutta algorithm. Second, the bogie's vibration characteristics were analyzed and the reasons for the vertical and pitching vibration were discussed. And the accuracy of the model was verified by comparing the levitation force with the experiment data. Third, a non-uniform exciting currents supply strategy for the superconducting coils was proposed under the comprehensive evaluation of the suppressing effect on the pitching vibrations. Finally, several cases were given to prove the effectiveness of the strategy. The results show that the total electromotive force increased by 0.005% after adopting the proposed non-uniform exciting currents supply strategy. But the minimum and maximum amplitude of pitching vibration and the growth rate of pitching vibration decreased by 97.00%, 95.76%, and 81.45%, respectively. This new strategy can effectively suppress the pitching vibration of the bogie without changing the already-designed mechanical structure. This established magnetic-electric-mechanical coupling dynamic model and the suppression strategy provide reference and a new idea for the superconducting EDS system's safety, stability, and comfort.

Pitching vibration suppression of cab system based on the suspension longitudinal coupling effects

<p indent="0mm">The pitching vibration of truck cabs can easily cause driving diseases, such as sciatica and cervical spondylosis, which can seriously disrupt a driver’s normal life. To effectively suppress the pitching vibration of the cab system, a cab’s longitudinal coupled suspension system is proposed. First, the configuration and mechanism of the coupling vibration suppression effect were thoroughly described. The dynamic model of the driver-seat-cab system was then established and verified. The effects of suspension parameters on vibrations were investigated, and a method for matching the parameters for pitch vibration suppression was proposed. Finally, the vibration suppression efficiency of the suspension system was compared and analyzed based on an example. The results showed that compared with the cab-uncoupled suspension system, the RMS (root-mean-square) values of the cab pitch, the driver’s head pitch, and longitudinal acceleration under random road conditions are reduced by more than 28.0%. The RMS values of the cab, the seat, and the driver’s organs vertical acceleration are reduced by approximately 2.0%. Hence, the proposed suspension system can effectively suppress the pitching vibration of the cab system to ensure vertical comfort and significantly improve ride comfort.

Optimized parameters of toroidal tuned liquid column dampers for multidirectional pitching vibration mitigation of structures

Optimized parameters of toroidal tuned liquid column dampers for multidirectional pitching vibration mitigation of structures

A Data Splicing Method for Measuring Rail Corrugation Under Pitching Vibration

Rail corrugation is the geometric structure of the rail top surface, and it directly related to the safety and comfort of rail transportation. The monitoring of rail corrugation is the key work for rail maintenance department. Currently, the 2D laser displacement sensor is being used to measure the rail corrugation. However, the 2D sensor is easily affected by pitching vibration under complex measurement environment, which leads to large errors in the final measurement results. For solving the problem of pitching vibration in dynamic measuring rail corrugation, a data splicing method based on deviation recognition and calibration is proposed in this study. Firstly, the blind recognition of sensor deviation is applied to identify the measurement state of sensor in each data sampling. Then, a mapping method is proposed to position the actual repeated measurement interval according to geometric relationship between the deviation angle and the offset in the longitudinal direction. Finally, the modified DTW model is proposed for data registration and the data splicing can be achieved according to the registration results. Extensive experiments are carried on both indoor experimental platform and outdoor platform. The experimental results indicate that our proposed method can accurately recognize the deviation of sensor and can calibrate the deviated data set, and its performance on the rail corrugation measurement under the pitching vibration case outperforms previous data splicing work. Thus, it is with the potential engineering application.

Effect of mode of vibration on the response of machine foundation on sand

In this paper, the influence of the following parameters on different modes of vibration response of model footings on sand is studied: (vertical, rocking and pitching load amplitude and frequency). To achieve the objective of this study, the model footing was selected to be rectangular footing with an aspect ratio (L/B= 1.33) i.e (L= length and B= width). A physical model was manufactured to simulate a steady-state harmonic dynamic load applied at different operating frequencies with the same load amplitude (0.5 ton). A total of (9) cases was performed taking into account different parameters. The loading frequency ranged from (0.5) to (2) Hz and the footing was rectangular with an aspect ratio (L/B = 1.33). The soil type used was dry sand having a relative density of (50%). The behavior of the soil underneath the footing was examined by measuring the strain using a shaft encoder and the amplitude of displacement using a vibration meter. It was found that the change in vibration mode made little effect of the final strain values under the same frequency and the amplitude of displacement in (Z) direction, while the amplitude of displacement in (Y) is higher, occuring under rocking vibration and higher value amplitude of displacement in (X) direction under pitching vibration under the same frequency.

Consideration of Multi-Degree of Freedom Vibration on Large-Sized Gantry Type Linear Motor Slider

Many transport units for large production devices now incorporate large-sized gantry type linear motor sliders comprising two parallel linear sliders linked by a joint table. This type of linear motor slider develops a unique mechanical distortion, generating a repulsive force between the two axes that can raise the motor output forces higher than their rated limit. A previous study proposed a method to suppress the repulsive force. However, as feedback gains are set high, force references oscillate and the control system becomes unstable. In past study, yawing vibration suppression methods have been proposed. But, we consider that this vibration is not yawing vibration because the force references include same phase vibration with high gains. Therefore, the modal analysis is performed to analyze this vibration. As a result, it was found that the pitching vibration of the slider was greatly affected. This paper considers this vibration phenomenon, and suppression of the vibration by control method which is similar to impedance control is presented. Hence, it is shown that considering multi-degree of freedom vibration which means yawing vibration and pitching vibration included is important in order to control the large-sized gantry type linear motor sliders.

Model analysis of influence of mental workload on vestibulo-ocular reflex

The vestibulo-ocular reflex (VOR), which is a reflexive eye movement generated in the direction opposite to that of the head movement, is affected by mental workload(MWL). A computational model to estimate the VOR from head movement has been proposed. Previous research has shown that when humans perform mental tasks, the error between the measured and the estimated VOR (calculated with the mathematical model) increased. Previously, a computational model for estimating the VOR was proposed; this model, known as the 6DOF-SVC model considered several processes of self-motion estimation. Further, another study revealed that a parameter in this computational model representing self-motion estimation changed as a result of volition of the head movement. This result indicated that the activeness or passiveness of the head movement influenced the outcome.However, the relationship between added mental tasks and the model self-motion estimation parameter has not yet been investigated. Therefore, in this study, an experiment to investigate the effect of mental tasks on the modeling error and the model parameter was implemented. Specifically, movements of the eye and head were measured when participants were exposed to a pitching vibration with and without a mental task to perform.The experimental results showed that the modeling error increased and the model self-motion estimation parameter decreased with the addition of a mental task. Moreover, a positive correlation was found between the model parameter and the VOR gain, which was calculated from the peak eye and head angular velocities.

鉄道車両の車体振動低減のための新たなヨーダンパ取付け構造の開発

It is pointed out that the yaw dampers, which are often installed in between carbody and bogie frame of a high-speed railway vehicle, have such unfavorable points that the damping force is generated not only in the yawing direction but also in other direction. As a result the damping force is generated also to the longitudinal or pitching vibration of a bogie, and the excitation force acts in the longitudinal direction of the carbody resulting in the increase of the carbody vibration of the longitudinal or vertical direction. In this research, to enable the reduction of the excitation of the carbody vibration while maintaining the original function of yaw dampers to prevent bogie hunting motion, a new mounting structure of yaw dampers on railway vehicles has been developed. The new mounting structure enables to reduce the excitation force transmitted from a bogie frame to a carbody through yaw dampers. In this paper, the effect of yaw dampers on the carbody vertical vibration is firstly shown based on the results of an excitation test of a full-scale vehicle, then the outline of the new mounting structure for yaw dampers and the design and manufacture of the prototype device are presented. The vehicle dynamics model based on multi body dynamics was constructed and the suppression effect of the yaw damper force generated to movement in the direction other than the yawing direction of a bogie was verified by the numerical simulation. Moreover, the prototype device was installed on a full-scale test vehicle and a bogie hunting motion test was carried out to verify the running stability.

フォークリフトにおけるピッチング振動制御に関する研究

フォークリフトにおけるピッチング振動制御に関する研究

Dynamics Characterization of Missiles with Control Flaps Based on CFD

Numerical studies were carried out on the dynamics of the Basic Finner missile under supersonic velocity based on the three-dimensional unsteady N-S equation. Second-order upwind NND scheme finite volume was used to discretize the spatial derivative term of the flow-controlled equation group. The LU-SGS containing dual time steps was used to obtain higher efficiency and precision of time solution. A numerical model representing the relationship between the unsteady aerodynamic force/moment coefficients and state variables under single DOF (degree of freedom) pitching and rolling movements was built from the Etkin unsteady aerodynamic model. The numerical algorithm for solving damping-in-pitch derivatives and damping-in-roll derivatives by forced-harmonic analysis was proposed. The M910 target practice, discarding sabot with tracer (TPDS-T) was used as a validation example and proved that the numerical calculation gives the same result as the experiment. By simulating the forced pitching and rolling vibration of Basic Finner, the numerical identification succeeded in obtaining the damping-in-pitch derivative and damping-in-roll derivative to a higher precision than the calculated result obtained by the quasi-steady Euler equation. Besides, to address the longitudinal and horizontal cross coupling induced by the pitching movement, numerical identification was also carried out on the cross coupling derivative of Basic Finner when under forced pitching vibration.

Dynamic Modelling and Analysis of Rectangle-Shaped Plastic-Coated Slideways in Machine Tools

The plastic-coated slideways have been widely used for form-generating movement in machine tools. Its dynamic behavior plays an important role in the vibration properties of the whole machine. In this work, according to the situation that researches on this subject were rather insufficient, a theoretical research was analyzed concerning the stiffness and damping characteristics of rectangle-shaped plastic-coated slideways. The mathematical model was firstly suggested especially based on the assembly of the saddle and worktable. Both stiffness and damping characteristics on vertical and horizontal directions were theoretically determined. To derive the governing motion equation of the slideway system, the carriage and rail were considered as rigid bodies and connected with a series of spring and damping elements at the joint face. Moreover, through the Lagrange’s approach, the frequencies of the carriage at vertical, pitching, yawing and rolling vibration mode were identified.

二連弦で支持された剛体棒系の非線形連成振動解析(&lt;特集&gt;D&amp;D2009)

Analytical results are presented on nonlinear coupled vibrations of a system of a rigid rod supported by parallel strings. The governing equation of the system includes nonlinear coupling between in-plane, out-of-plane and pitching motions. Nonlinear periodic responses are calculated with the harmonic balance method. Time responses of the system are calculated by direct numerical integration with the Runge-Kutta method. As the excitation frequency is increased, vibration form changes from in-plane periodic vibration to whirling, and then quasi-periodic responses appear accompanied by whirling and pitching motion. At the specific frequencies in the region of quasi-periodic responses, chaotic responses are also observed. As the excitation frequency is increased further, the vibration form transits to periodic pitching vibration with the jump phenomenon. It is found that the frequency region of the quasi-periodic response is narrowed as the eccentricity of the rod is increased. Furthermore, the region of the quasi-periodic response is slightly enlarged by the increase of the distance between the two strings. The variation of the frequency region of the quasi-periodic response has close relation with that of the periodic response of pitching motion.

207 二連弦で支持された剛体棒系の非線形連成振動解析

Analytical results are presented on nonlinear coupled vibrations of a system of a rigid rod supported by parallel strings. Nonlinear periodic responses are calculated with the harmonic balance method. Time responses of the system are calculated by direct numerical integration with the Runge-Kutta method. As the excitation frequency is increased, vibration form changes from in-plane periodic vibration to whirling, and then quasi-periodic responses appear accompanied by whirling and pitching motion. At the specific frequencies in the region of quasi-periodic responses, chaotic responses are also observed. As the excitation frequency is increased further, the vibration form transits to periodic pitching vibration with the jump phenomenon. It is found that the frequency region of the quasi-periodic response is narrowed as the eccentricity of the rod is increased. Furthermore, the region of the quasi-periodic response is slightly enlarged by the increase of the distance between the two strings.

1123 玩具'ラトルバック(rattleback)'の奇妙な挙動の直感的説明(メカニカルシステム(1))

When the horizontal rotation is given to the toy called rattleback to have the shape of the boat put on the desk, it rotates only to one direction. When the rotation of the opposite direction is given to the toy, the pitching vibration begins stopping rotating like disliking the direction, and it shifts to the rotation in the opposite direction gradually with the given direction. A dynamic feature of the toy is that the inertial roll axis is a little twisted around the vertical axis, i.e. it is not included in the vertical plane that a lower ridge line forms. Putting this shape feature on the mind, this paper tries to give an intuitive explanation about following two items: reason where direction that rotates easily and direction not rotated easily exist, and cause of pitching vibration generation and reverse-rotating torque generation.

Optimal Performance of the TLCD in Structural Pitching Vibration Control

A detailed optimal parametric study is performed for a tuned liquid column damper (TLCD) in suppressing the pitching vibration of structures. Due to the difficulty of finding analytical solutions for the damped structure, a numerical optimization approach is proposed and applied to the system to find the optimum TLCD parameters. The variations of the optimum control parameter with system parameters are determined and discussed. Using various numerical searching data, a set of practical design formulas for the optimum tuning ratio and optimum head loss coefficient of the TLCD are then derived through regression analysis. The comparison between practical design formula and numerical optimization shows a very close agreement between the two results. The practical design formulas provide a convenient tool for designers. In order to account for the possible effects of structural uncertainties, a parametric sensitivity study on the de-tuning of optimum damper parameters is also carried out. It is found that the detuning effect is more severe for low damped structure with lower ratios of mass moment of inertia, especially for the detuning of tuning ratio.