Planar Dynamic Model Research Articles

Development of planar 9-DOF dynamic model with small damping and natural characteristics sensitivity analysis for a double-deck vibrating flip-flow screen

The current double-deck vibrating flip-flow screen (DDVFFS) exhibits swing motion due to an unreasonable structural design, which compromises vibration stability and impacts screen frame displacement response. Therefore, it is essential to investigate the dynamic characteristics of the DDVFFS. For this reason, a 9-degree-of-freedom (DOF) dynamic model of the DDVFFS is established, and a corresponding testbed for the DDVFFS is designed. A sensitivity analysis is conducted to examine the impact of design parameters on the natural frequency and vibration mode, thereby serving as valuable guidance for the design of DDVFFS. The damping matrix in the dynamic model is determined through modal testing, while the displacement response of the testbed is obtained by solving the dynamic model. The test results from the vibration testbed demonstrate that the actual amplitude of each sieve frame closely matches the theoretical amplitude.

Three-dimensional dynamic model of the curved pipe based on the absolute nodal coordinate formulation

Due to the lack of advanced models and analytical methods, the study of pipe conveying fluid usually only considers the in-plane vibration of straight pipe. In order to fully understand the dynamic characteristics of curved pipe, it is necessary to establish the three-dimensional (3D) dynamic model. However, there are still few 3D modeling methods for the curved pipe. In this paper, based on the absolute nodal coordinate formulation (ANCF), a 3D finite element model for the curved pipe is developed. The nonlinear dynamic equations of the pipe system are derived by using the extended Lagrange equations. The natural frequencies and modes are calculated by linearizing the equations. The established model and the adopted method are verified through the comparison with relevant literature and ANSYS simulation. Furthermore, the effects of the relevant parameters on the natural vibration of curved pipe are discussed. The in-plane and out-of-plane natural vibration characteristics of curved pipe are compared and summarized for the first time. Finally, the advantages of the proposed model are outlined by the comparison with the planar dynamic model. The results provide new information about the effect of initial curvatures on the spatial vibration characteristics of pipes. In conclusion, this paper provides a novel dynamic model for studying the spatial vibration of the curved pipe. In the meantime, the results of this paper can also can guide for the research of the vibration of curved pipes in engineering.

Response Sensitivity of Centrifugal Pendulum Vibration Absorbers to Symmetry-Breaking Absorber Imperfections

This paper details an analytical investigation on free and forced vibration response sensitivity of centrifugal pendulum vibration absorbers (CPVA) to symmetry-breaking absorber imperfections. Minor variations in the absorbers’ design due to manufacturing tolerances, errors as well as operational wear and tear tend to break cyclic-symmetry and lead to asynchronous absorber oscillations, unbalanced rotor translations and thus significant vibration amplification. Therefore, an in-depth understanding on the sensitivity of CPVA's vibration response to absorber imperfections is needed to devise an improved absorber tuning strategy for robust vibration and noise reduction from realistic vehicle transmissions and drivelines. In this paper, free and forced vibration response sensitivity of generalized CPVA systems are analytically derived for absorber spacing and mass variations using the perturbation-based eigensensitivity technique in conjunction with modal superposition. The methodology applied in this study is realized through a linearized planar dynamic model, which includes both torsional and translational motions of the rotor along with oscillations of N equally-spaced baseline identical absorbers. Distinct mode distortions and degenerate mode splitting from the known baseline modal structure (with translational, rotational and absorber modes) are investigated for systems with asymmetric absorber spacing and absorber mass variations. The baseline modal structure is modified differently due to having unequal absorber masses or absorber spacing errors, and these differences are analytically derived and demonstrated. Moreover, it was identified that CPVA systems do not exhibit mode splitting with the absorber mass and spacing deviations. Response alterations and localized response patterns due to asymmetric absorber spacing and mass variations are identified and visualized through a case study. Results define a new parametric lower limit for the overtuning of absorbers to avoid localized absorber response and vibration amplification due to absorber imperfections. Additionally, the outcomes are used to locate unique excitation orders, which would help distinguish the alterations in system response due to absorber spacing and mass from each other and serve as a diagnostic tool.

Tuning for robust and optimal dynamic positioning control in BlueROV2

A tuning approach for the robust and optimal dynamic positioning control of BlueROV2 subjected to currents with varying speeds and headings is presented. A 2D planar dynamic model of BlueROV2 is developed in Matlab/Simulink and used for the study. The surge, sway and yaw motions are controlled by individual PID controllers. An extensive sensitivity study is carried out on a total of nine cases with different current speeds, current headings, and measurement noise levels. The results show that tuning a model solely using step responses from a linearized model might not produce optimal results. Further it is important to verify the system responses in time domain after tuning. Finally, it is observed that re-tuning the controllers for each simulation case may lead to better performance. However, it is also shown that the base case controller gains are sufficiently robust and lead to good performances for the other simulation cases.

Turning dynamics analysis of a heavy articulated vehicle by the vehicle planar dynamic model with two steering input signals

The vehicle planar single track dynamic model with two input steering angle parameters is derived by using Lagrange's method with the basis of equations for calculating the tire's force components. Dynamic analysis of a heavy articulated vehicle in case of turing is carried out by the vehicle planar dynamic model, in which two input steering angles are taken into account. Simulation with the selected velocity value to make sure that the stability according to the friction conditions at all axles of the vehicle is satisfied. Turning spacing, lateral forces at each axle of the vehicle are determined and analyzed for all three different cases of steering angles, respectively with steering angle of the semi-trailer is in the same direction, in the opposite direction and is locked or not steered in comparision with the steering angle of the tractor. The obtained results show that the derived model could employ to determine the planar kinematic and dynamic parameters, and analyze the dynamic safety features of an articulated vehicle, too. In addition, the derived mathematical model could also employ to develop a computational model that controls the planar articulated vehicle dynamics.

An analysis of turning stability dynamics of TERA 240 truck by the four - Wheeled planar vehicle dynamic model

The turning dynamic features to ensure stable and safe conditions of the TERA 240 truck are investigated using the four-wheeled planar dynamic model, in which the force components from 4 wheels are taken into account to build a computational model with the time-varying steering angle is used. The necessary input parameters of the TERA 240 vehicle for the vehicle planar dynamic model are determined on the basis of the available actual vehicle, with all 3 loading cases are noload, half-load and full-load. The kinematic and dynamic parameters describing the vehicle's planar turning motion are determined, resulting in the basement for evaluating the vehicle's motion stability. The calculation process is performed in the velocity domain to ensure the ultimate stability condition that the vehicle does not slide or overturn when turning. The obtained results are analyzed to evaluate the vehicle's turning stability performance, based on the variable relationship of the parameters in the investigated cases: turning radius is constant, velocity is constant, and steering angle is constant. The vehicle's turning stability is specifically defined: the vehicle is understeer with no-load case, the vehicle is oversteer with half-load and full-load cases.

Vehicle drifting: mathematical theory and dynamic analysis for stabilised drifting of RWD vehicles

This paper introduces a mathematical definition for drifting of vehicles. A necessary kinematic condition for enabling negative body side-slip angle at centre of the front wheel during a left-hand turn is identified as drifting indicator. Dynamics of the drifting motion is investigated by means of a simplified three-wheel vehicle model in steady-state, focusing on rear wheel drive (RWD) vehicles. Drifting point is identified as an unstable equilibrium point of the nonlinear system. The equilibrium point is made stable by means of direct control only over yaw velocity, as a single key stabilising objective, and using the steady-state model as feedforward. A four-wheel planar dynamic simulation model is used together with a combined slip tyre model to investigate the accuracy of the proposed analysis. Steady-state RWD drifting motion is achieved by using the proposed method, validating the proposed dynamics analysis. Finally, the drifting metric is used to measure the amount of drifting achieved during a manoeuvre and its effectiveness is observed.

Vehicle drifting: mathematical theory and dynamic analysis for stabilised drifting of RWD vehicles

This paper introduces a mathematical definition for drifting of vehicles. A necessary kinematic condition for enabling negative body side-slip angle at centre of the front wheel during a left-hand turn is identified as drifting indicator. Dynamics of the drifting motion is investigated by means of a simplified three-wheel vehicle model in steady-state, focusing on rear wheel drive (RWD) vehicles. Drifting point is identified as an unstable equilibrium point of the nonlinear system. The equilibrium point is made stable by means of direct control only over yaw velocity, as a single key stabilising objective, and using the steady-state model as feedforward. A four-wheel planar dynamic simulation model is used together with a combined slip tyre model to investigate the accuracy of the proposed analysis. Steady-state RWD drifting motion is achieved by using the proposed method, validating the proposed dynamics analysis. Finally, the drifting metric is used to measure the amount of drifting achieved during a manoeuvre and its effectiveness is observed.

Simulation of a Passive Knee Exoskeleton for Vertical Jump Using Optimal Control.

Research on exoskeletons designed to augment human activities and the attendant exoskeleton industry are both rapidly growing areas of endeavor. However, progress in the field is currently being hindered by a lack of understanding of human-exoskeleton interactions. At present, the main method applied to reach such an understanding is to build and test prototypes or end-effectors (that simulate the devices), but this is a very time-consuming and costly process. In this study, we aimed to address this problem by simulating passive exoskeleton-human interactions during a vertical jump. The simulation is based on theoretical and empirical models. Using the simulation, we performed a numerical optimization procedure to determine the muscle excitations and starting postures that would give the maximum jump height. The simulation used a planar 4-DOF dynamic model. The muscles at the joints were modeled as torque actuators, with a flexor and an extensor for each joint and passive torque representing the tendon and muscle properties. We then simulated jumps with a passive knee exoskeleton with five different values of stiffness with the aim to study their effect on the jump height. The optimal excitation for the maximum jump height was found by using a genetic algorithm (GA). To improve our optimization performance and to test the convergence of the GA, the GA optimization was performed several times. For each exoskeleton condition, the GA found the optimal jump more than 400 times, and out of these solutions the one that achieved the highest jump was chosen. The result revealed an increase in jump height as the spring became stiffer. In addition, it was found that the energy that was stored in the spring of the exoskeleton was not fully converted to jump height.

An improved planar dynamic model for vibration analysis of a cylindrical roller bearing

Vibration analysis of cylindrical roller bearings (CRBs) can be useful for controlling the vibration characteristics of the machinery. To overcome this problem, an improved planar dynamic model is presented for calculating the vibrations of a CRB. All components (such as inner raceway, rollers, cage, and outer raceway) of the CRB system and their interactions are considered in the proposed model, as well as the elastic supports of the shaft and housing. An experiment study is presented to verify the proposed model. The effects of the radial load, shaft speed and bearing clearance on the vibrations of the CRB system are evaluated. The results show that the radial load, shaft speed and bearing clearance have great effects on the vibrations of the bearing components. The vibration accelerations of the raceways, rollers, and cage increase with the increments of the shaft speed and the radial load. In addition, the increment of the pocket clearance results in the increase of the roller-cage contact force. The proposed model can provide a method for the dynamic formulations of the CRBs with the rollers and cage. Moreover, this work can be used for the vibration monitoring of CRBS in the rotating machinery.

Nonsmooth Dynamics of a Gear–Wheelset System of Railway Vehicles Under Traction/Braking Conditions

Abstract Gear–wheelset system is a crucial substructure in railway vehicles which affects the operation safety and system reliability, especially in the process of traction and braking conditions. Unlike the general gear transmission system, the gear–wheelset system of railway vehicles operates under an environment with several nonsmooth factors; therefore, it is necessary to analyze the nonsmooth dynamics of the gear–wheelset system for understanding dynamic characteristics better. Herein, a planar dynamic model of the gear–wheelset system of railway vehicles considering motor-driving torque, braking torque, wheel–rail nonlinear interaction forces, nonlinear meshing damping, and piecewise continuous time-varying meshing stiffness is proposed. Then, the proposed model is validated by a simpack model using wheelset's longitudinal velocity. Subsequently, two numerical simulations were performed to reveal the nonsmooth dynamic characteristics under traction and braking conditions. The simulation results indicate that the dynamic stationary point exists in nonsmooth dynamics under traction and braking conditions, which is a critical boundary for transiting any state to a dynamic equilibrium. Besides, the results exhibit the inseparable relationship between time-frequency dynamic characteristics, slip velocity, and wheel–rail nonlinear interaction forces. The effects of harmonic torque under traction conditions and compound braking behavior under braking conditions significantly affect these dynamic characteristics. Additionally, sufficient driving torque can increase the proportion of forward contact and improve the smoothness of the rotation, and the intermittent gear contact phenomenon occurs alternately and frequently in the traction condition. Conversely, only reverse contact occurs in the braking condition.

Sensorless Estimation of the Planar Distal Shape of a Tip-Actuated Endoscope.

Traditional endoscopes consist of a flexible body and a steerable tip with therapeutic capability. Although prior endoscopes have relied on operator pushing for actuation, recent robotic concepts have relied on the application of a tip force for guidance. In such case, the body of the endoscope can be passive and compliant; however, the body can have significant effect on mechanics of motion and may require modeling. As the endoscope body's shape is often unknown, we have developed an estimation method to recover the approximate distal shape, local to the endoscope's tip, where the tip position and orientation are the only sensed parameters in the system. We leverage a planar dynamic model and extended Kalman filter to obtain a constant-curvature shape estimate of a magnetically guided endoscope. We validated this estimator in both dynamic simulations and on a physical platform. We then used this estimate in a feed-forward control scheme and demonstrated improved trajectory following. This methodology can enable the use of inverse-dynamic control for the tip-based actuation of an endoscope, without the need for shape sensing.

Numerical study of the hydraulic excavator overturning stability during performing lifting operations

This article presents a numerical study of the stability of a hydraulic excavator during performing lifting operations. A planar dynamic model is developed with six degrees of freedom, which considers the base body elastic connection with the terrain, the front digging manipulator links, and the presence of the freely suspended payload. Differential equations describing the excavator dynamic behavior are obtained by using the Lagrange formalism. Numerical experiments are carried out to study the excavator dynamic stability under different operating conditions during the motion along a vertical straight-line trajectory. It is shown that the arising inertial loads during the movement of the links along the vertical trajectory, combined with the payload swinging and the motion of the base body, decreases the excavator stability. It was found that the excavator stability during following vertical straight-line trajectory decreases considerably in the lower part of the vertical trajectory. If the stability coefficient is close to 1, the payload swinging can cause the separation of a support from the terrain; nevertheless, the excavator stability can be restored. A method for tire stiffness and damping coefficients estimation is presented. The validation of the dynamical model is performed by the use of a small-scale elastically mounted manipulator.

An Experimental Method to Estimate Upper Limbs Inertial Parameters During Handcycling.

This study proposes an experimental method to estimate personalized inertial parameters of upper limbs during handcycling by using a planar dynamic model. The handle forces are expressed as a product of a matrix describing the kinematics terms and a vector of inertial parameters of arm and forearm. The parameters are estimated by measuring the handle forces during a suitable "passive test" and inverting the mentioned matrix. The data were acquired while an operator actuated the handle and the subject's muscles were relaxed. To validate the estimation procedure, it was applied to a custom-made artificial arm mechanism, and the results were compared with its known parameters. The method was then used to estimate the inertial parameters of 6 human subjects. The estimated parameters were used to compute the exchanged forces and compared with the measured ones obtaining an average error of 14% both for Fx and Fy. These errors are significantly smaller than those obtained using dynamic parameters extracted from the literature to compute the forces, which were 50% for Fx and 19% for Fy. An individual evaluation of inertial parameters better describes interaction forces during handcycling, especially for subjects whose body structures are different from the average population.

Gait Tracking Control of Quadruped Robot Using Differential Evolution Based Structure Specified Mixed SensitivityH∞Robust Control

This paper proposed a control algorithm that guarantees gait tracking performance for quadruped robots. During dynamic gait motion, such as trotting, the quadruped robot is unstable. In addition to uncertainties of parameters and unmodeled dynamics, the quadruped robot always faces some disturbances. The uncertainties and disturbances contribute significant perturbation to the dynamic gait motion control of the quadruped robot. Failing to track the gait pattern properly propagates instability to the whole system and can cause the robot to fall. To overcome the uncertainties and disturbances, structured specified mixed sensitivityH∞robust controller was proposed to control the quadruped robot legs’ joint angle positions. Before application to the real hardware, the proposed controller was tested on the quadruped robot’s leg planar dynamic model using MATLAB. The proposed controller can control the robot’s legs efficiently even under uncertainties from a set of model parameter variations. The robot was also able to maintain its stability even when it was tested under several terrain disturbances.

Lateral & vertical dynamic analysis of a three-wheeled motorbike by the planar single track & 3d vertical dynamic models

To be able to analyze the dynamic features comprehensively and more fully in both the lateral and vertical cases for a threewheeled motorbike (TWM), which have been designed and manufactured by the same group of authors and based on to conduct design improvements, the planar vehicle dynamic model (single track) with 03 degrees of freedom (03-DOF) & the vertical dynamic model with 06 degrees of freedom (06-DOF) have been employed. The parameters used in the calculations are based on existing designs from realistic models manufactured through the combination of experimental measurements and theoretical calculation methods empirically. The lateral dynamic calculated results were based on to investigate the dynamic stability when cornering or steering of a 03-wheeled motorbike. In addition, dynamic calculated results were analyzed also in the frequency domain and basec on to help improve the design featurers with more comfortable and safer.

Velocity and normal tyre force estimation for heavy trucks based on vehicle dynamic simulation considering the road slope angle

A precise estimation of vehicle velocities can be valuable for improving the performance of the vehicle dynamics control (VDC) system and this estimation relies heavily upon the accuracy of longitudinal and lateral tyre force calculation governed by the prediction of normal tyre forces. This paper presents a computational method based on the unscented Kalman filter (UKF) method to estimate both longitudinal and lateral velocities and develops a novel quasi-stationary method to predict normal tyre forces of heavy trucks on a sloping road. The vehicle dynamic model is constructed with a planar dynamic model combined with the Pacejka tyre model. The novel quasi-stationary method for predicting normal tyre forces is able to characterise the typical chassis configuration of the heavy trucks. The validation is conducted through comparing the predicted results with those simulated by the TruckSim and it has a good agreement between these results without compromising the convergence speed and stability.

Performance analysis of jump-gliding locomotion for miniature robotics

Recent work suggests that jumping locomotion in combination with a gliding phase can be used as an effective mobility principle in robotics. Compared to pure jumping without a gliding phase, the potential benefits of hybrid jump-gliding locomotion includes the ability to extend the distance travelled and reduce the potentially damaging impact forces upon landing. This publication evaluates the performance of jump-gliding locomotion and provides models for the analysis of the relevant dynamics of flight. It also defines a jump-gliding envelope that encompasses the range that can be achieved with jump-gliding robots and that can be used to evaluate the performance and improvement potential of jump-gliding robots. We present first a planar dynamic model and then a simplified closed form model, which allow for quantification of the distance travelled and the impact energy on landing. In order to validate the prediction of these models, we validate the model with experiments using a novel jump-gliding robot, named the ‘EPFL jump-glider’. It has a mass of 16.5 g and is able to perform jumps from elevated positions, perform steered gliding flight, land safely and traverse on the ground by repetitive jumping. The experiments indicate that the developed jump-gliding model fits very well with the measured flight data using the EPFL jump-glider, confirming the benefits of jump-gliding locomotion to mobile robotics. The jump-glide envelope considerations indicate that the EPFL jump-glider, when traversing from a 2 m height, reaches 74.3% of optimal jump-gliding distance compared to pure jumping without a gliding phase which only reaches 33.4% of the optimal jump-gliding distance. Methods of further improving flight performance based on the models and inspiration from biological systems are presented providing mechanical design pathways to future jump-gliding robot designs.

In-wheel motor electric vehicle state estimation by using unscented particle filter

Vehicle state parameters are essential for active safety stability control and very valuable in chassis design evaluation. In this paper, a method for vehicle state parameters estimation is developed for in–wheel motor (IWM) electric vehicle (EV). The observer is based on information fusion combining standard sensor suite in today's typical vehicle and feedback signals from IWM. This paper utilise unscented particle filter (UPF) for tyre lateral force, longitudinal velocity, lateral velocity and yaw rate estimation, which is based on a numerically efficient nonlinear stochastic estimation technique. Planar vehicle model and dynamic tyre model are developed to describe behaviour of IWM EV. Detailed simulation verifies the validation and robustness of proposed estimation algorithm.

Energy Balance Associated With a Mixing Process at the Interface of a Two-Layer Longitudinal Atmospheric Model

Several examples illustrating the energy balance associated with a mixing process at the interface of a planar dynamical model describing two-phase perfect fluid circulating around a circle with a sufficiently large radius within a central gravitational field are presented. The model is associated with the spatial and temporal structure of the zonally averaged global-scale atmospheric longitudinal circulation around the Earth. The fluid is supposed to be irrotational and pressure on a outer layer is constant. It is postulated that the total fluid depth is small compared to the radius of the circle and the gravity vector is directed to the center of the circle. Under these assumptions, this problem can be associated with a spatial and temporal structure of the zonally averaged global-scale atmospheric longitudinal circulation around equatorial plane. The model is the subject to the rigid lid approximation to the external boundary conditions for the outer fluid layer. One of the novelties in this work is the derivation of the nonlinear shallow water model by means of the average velocity. This introduction simplifies essentially further potential studies of mixing criteria associated with nonlinear mathematical models representing shallow water equations.