In this paper, an analytical model is proposed to study the behavior of defective bearing and rotor system. An overhung rotor system and defective roller bearing are considered for the study. Rotor is considered with unbalanced mass and bearing is taken as the cylindrical roller bearing having localized surface defect. To analyze all the system components’ effect at one node, finite element method is used to predict exact system vibrations. Euler–Bernoulli’s beam element is used to discretize the shaft. Gyroscopic effect of overhung rotor is also taken into account and governing equations of motion have been modified according to our system. Hertz contact stress theory is used for every roller–race contact to calculate the overall nonlinear bearing force. Governing differential equation is solved by Newmark-β time integration method. Nonlinear matrix equation, which is generated at each time-step in Newmark’s method, is solved by Broyden’s method. Results for defective bearing are obtained and plotted in the time and frequency domain. Poincare map has been plotted to view the system’s minimum stability time. An experiment has been carried out to validate the proposed analysis work. In this paper, it has been shown how rotor dynamic analysis can be achieved numerically with minimum calculations.
With increase in the axle load and wagon speed, the cost of damage to rail track and wagon components increases significantly. This leads to widespread interests in the investigation of the dynamic interactions of the rail track and the wagon. Rail irregularities are one of the important vibration sources of the rail track structure and train. These irregularities have generally random distribution that are assumed to be stationary random and ergodic processes in space, with Gaussian amplitude probability densities and zero mean values. In this paper, the dynamic response of the railway vehicle due to random irregularity of rail track is analysed. The wagon is modelled as a two degrees-of-freedom non-linear model where includes non-linear spring and linear damper of primary suspension system. The Hertzian contact theory is used to obtain the relationship between normal contact force and the displacement of the mass centre of the wheel. Using the method of multiple scales the analytical approximate response of the railway vehicle due to track irregularities is obtained. The amplitudes of vibrations of the vehicle and the interaction forces between the vehicle and the rail for different line grades and train speeds have been analysed analytically by this model. According to the results, rail irregularities have more effect on the vertical acceleration of the vehicle than the train speed.
In this paper, an analytical mechatronic dynamic design model of a full rail vehicle system is developed. Based on the rail vehicle motion, its degree of freedom can be reduced to only 38. This reduction is necessary for the model simplicity. The developed model is validated with experimental result and compared with other one from literature. The real characteristics of the actuators are discussed, and its controller is designed. A mechatronic model that expresses the controlled tracking error as function of the vehicle dynamics and the actuator characteristics is developed. This model is used by the linear quadratic regulator approach to identify the mechatronic rail vehicle proportional–integral–derivative controller’s gains. The mechatronic rail vehicle comfort is evaluated in terms of the passenger displacement, acceleration and frequency as a response of a rail irregularities caused by a lateral and two vertical track irregularities. The simulations of vibration analysis are obtained in time and frequency domains and compared with railway vehicle status. The robustness of the designed mechatronic rail vehicle is verified by simulations, carried out for the cases of car body mass variations. The results show the effectiveness of the proposed mechatronic rail vehicle design which improves significantly the transportation of passengers.
This paper is dedicated to investigate the nonlinear free vibration analysis of prestressed orthotropic membranes. The fundamental frequency of the system is obtained asymptotically by employing a modern analytical approach. The effects of different parameters such as vibration amplitude, initial conditions and geometric parameters on the frequency ratio and nonlinear frequency of membrane are investigated. Comparison between the obtained results in the present study, the reported results in the literature, and Runge–Kutta fourth-order numerical method verify the strength of the analytical procedure.
In this paper, an adaptive sliding mode controller is proposed to improve the vehicle yaw stability and enhance the lateral motion by direct yaw moment control method using active braking systems. As the longitudinal and lateral velocities of the vehicles as well as many other vehicle dynamics variables cannot be measured in a cost-efficient way, a robust control method combined with a state estimator is required to guarantee the system stability. Furthermore, some parameters such as the tyre–road friction coefficient undergo frequent changes, and the aerodynamics resistance forces are often exerted as a disturbance during the wide driving condition. So, an adaptive sliding mode controller is applied to make vehicle yaw rate to track its reference with robustness against model uncertainties and disturbances and a non-linear estimator based on unscented Kalman filter is used to estimate wheel slip, yaw rate, road friction coefficient, longitudinal and lateral velocities. The estimation algorithm directly uses non-linear equations of the system and does not need the linearization and differentiation. The designed controller, which is insensitive to system uncertainties, offers the adaptive sliding gains to eliminate the precise determination of the bounds of uncertainties. The sliding gain values are determined using a simple adaptation algorithm that does not require extensive computational load. Numerical simulations of various manoeuvres using a non-linear full vehicle model with seven degrees of freedom demonstrate the high effectiveness of the presented controller for improving the vehicle yaw stability and handling performance.
In this study, a new method to improve ride comfort, vehicle handling, and workspace was presented in multi-objective optimization using nonlinear asymmetrical dampers. The main aim of this research was to provide suitable passive suspension based on more efficiency and the low cost of the mentioned dampers. Using the model with five degrees of freedom, suspension system parameters were optimized under sinusoidal road excitation. The main functions of the suspension system were chosen as objective functions. In order to better illustrate the impact of each objective functions on the suspension parameters, at first two-objective and finally five-objective were considered in the optimization problem. The obtained results indicated that the optimized viscous coefficients for five-objective optimization lead to 3.58% increase in ride comfort, 0.74% in vehicle handling ability, and 2.20% in workspace changes for the average of forward and rear suspension.
A forwarder is an off-road working machine that is used to transport logs from logging sites to a landing area that is accessible by trucks. Soil damage and operator comfort, especially whole-body vibrations when operating on hard and rough terrain, are crucial issues when developing novel forest machines. Most forwarders on the market are heavy machines with articulated steering and they are equipped with pairs of wheels mounted on bogies. For such bogie machines, only the flexibility and the dynamic dissipation in the tyres contribute to the "chassis damping". The roll and lateral motions are the most severe components of the whole-body vibrations. So, developing new traction units, chassis suspensions and/or cabin suspension are in focus. Model-based design relies on focused models that are as simple as possible, but not too simple. This paper presents a 12 degrees-of-freedom multi-body dynamics simulation model of a standard eight-wheeled bogie type of medium-sized forwarder. The presented model is targeted for assessing and comparing different design solutions. It is shown that a configuration of seven rigid subsystems and eight flexible tyres represented with the simple and computer efficient Fiala tyre model enables the forwarder dynamic simulation model to be used to predict the roll and lateral motions of a forwarder operating on hard and rough terrain.
In this paper, a novel pulse active steering system for improving vehicle yaw stability is developed. In the proposed method, pulses are sent to the steerable rear wheels whenever the error between the expected and actual yaw rate is outside a predetermined range. The proposed method and its performance are verified experimentally by full vehicle testing. For this purpose, a simplified vehicle model and a rear suspension model are developed. Vehicle stability is investigated and the steering pulse parameters on the vehicle’s stability are studied. A control system is designed and numerical simulations are performed. Moreover, the active rear steering system is implemented on a Lexus for performing road experiments. Results from simulations and experiments indicate that considerable improvement in the yaw stability performance can be achieved by the proposed system. The proposed method is more cost effective and simpler for vehicle stability control.
Computational multibody system (MBS) method is a practical technique utilized for modeling, simulation, and optimization of mechanical systems. In the methodology of computational multibody system, equations of motion are derived, formulated, and solved through a systematic, generalized, and well-structured computational-mathematical approach. In this paper, the computational multibody system formulation, based on the appended Lagrangian method, is implemented to establish the governing equations of ride dynamics for a nonlinear ride model that represents a versatile half-car two-track model of a road vehicle. The input to the system is a simulated road surface model based on the ISO road surface classification. The solution of the equation of motion is obtained using the direct integration approach along with constraint violation elimination and control techniques. Following the simulation, a time-domain multiobjective design optimization procedure is performed to improve the ride quality of the model. The ride quality comprises both ride comfort and ride safety. The optimization considers relevant objective functions including vibration isolation, suspension travel, road holding, and force index. The results of work show that the proposed method could acceptably estimate the optimal values of design variables for specific road classes and vehicle driving speeds. The simulation-based ride quality optimization performed here could facilitate improvement of suspension and tyre.
In this paper to improve manoeuvrability and jackknifing prevention, as well as increasing rollover stability of an articulated vehicle carrying liquid, a new control system coupled with an active roll control system and an active steering control system is presented. First, a 16-degrees-of-freedom nonlinear dynamic model of an articulated vehicle is developed. Next, the dynamic interaction of the liquid cargo with the vehicle is investigated by integrating a quasi-static liquid sloshing model with a tractor semi-trailer model. Initially, to improve the roll stability of the vehicle, an active roll control system is presented. The active anti-roll bar is employed as an actuator to generate the roll moment. Furthermore, the manoeuvrability increment and jackknifing prevention are targeted using the active steering control system. The main purpose of using the active steering controller is to track the desired values of tractor yaw rate, articulation angle and tractor lateral velocity in different roads, various filled volumes and different speeds. The active steering control system is designed based on a three-degrees-of-freedom dynamic model of the articulated vehicle carrying liquid and on the basis of sliding mode control. Simulation results confirmed robust performance of the control system for different filled volumes, especially during the critical manoeuvre. Further studies show that the tracking of the desired articulation angle has not only eliminated the off-tracking path, but also has made the semi-trailer rear end follow the fifth wheel path.
When a train passes over bridges, the magnitude of forces and accelerations is altered due to sudden changes in the track stiffness. These forces can change with the variation in operational parameters and are effective particularly in high-speed passenger trains, when studying ride index parameter. In addition, by increasing the speed, old bridge structures could fall into resonance, which has harmful consequences for both bridge and ride comfort index. Moreover, to harmonize the old bridges with the new operational conditions dynamic behavior of the vehicle and ride comfort need to be taken into account. In this paper, coupled vertical and roll vibration of a horizontally curved bridge are considered. During pass over the bridge, acceleration and ride comfort of a passenger vehicle are studied. The eccentric vertical and lateral forces are the major excitation sources in the analysis, an issue that is rarely noticed in the literature. A multi-body model of a normal wagon is built in three dimensions, passing over a horizontally curved bridge. The governing equations of the vehicle–bridge system are written, taking into account the wheel–rail interactions. The major variables are the cant, train speed, track quality, and radius of curvature. The paper studies the effects of the prescribed variables on ride comfort. The results show that track quality and cant have considerable influences on ride comfort index. The ride comfort is improved when the speed is approached to a so-called equivalent speed.
As an important structure parameter, contact angle is also a judgement factor for the working performance of ball bearings. However, under some conditions, the ball may roll over the raceway shoulder, and contact angle is not enough for estimating this phenomenon. Thus, edge angle and edge distance are proposed as compensatory judgement factors in the current study. A six-degree dynamic model with time-varying contact stiffness was developed for investigating effects of initial contact angle, raceway groove curvature factors, number of balls, axial load, shaft speed, friction coefficient and raceway misalignment on contact angle, contact stiffness, edge angle and edge distance. Inapposite initial contact angle may make the ball roller over the raceway shoulder, inner raceway misalignment have significant influences on the stable motion of ball bearings, and more harmonics frequencies about contact angle appear. Comparison of contact angle from presented model with Jones–Harris model under axial load shows reasonable qualitative agreement.
In this study, several new stiffened plate element models are proposed based on the absolute nodal coordinate formulation. The stiffened plate elements with different geometrical continuity conditions and performances are developed by a full parametrized plate element and three different beam elements of absolute nodal coordinate formulation. The effect of stiffener is incorporated by internally constraining the stiffener displacement fields to the relevant plate displacement fields. The displacement compatible conditions of plate and stiffener are investigated to obtain the transformation matrix of nodal coordinates. The mass and stiffness of a stiffener is reflected at all the nodes of the plate element in which it is placed. Accordingly, the stiffener can be positioned anywhere within the plate element along lines of local coordinates and need not necessarily be placed on nodal lines, which gives a great flexibility in the choice of mesh size. The stiffened plate elements also achieve a better continuity condition with the slope constraint equations. Static, dynamic, and free vibration analyses are conducted to validate the proposed elements and to study the performance of the stiffeners. The results show that the new elements can be applied to describe mechanical behaviors of stiffened structures in both static and dynamic situations. The effects of the dimension of cross section and the number of stiffeners are also numerically investigated for both linear and nonlinear deformation problems.
Lightly damped non-linear dynamic driveline components are subjected to excitation with rapid application of clutch and/or throttle. Modern thin-walled driveshaft tubes respond with a plethora of structural-acoustic modes under such impulsive conditions, which are onomatopoeically referred to as clonk in the vehicle industry. The underlying mechanisms for the occurrence of this phenomenon are investigated, using combined experimentation and flexible multi-body dynamics under impulsive impact conditions. The coincidence of high-frequency structural modes, coupled with acoustic response is highlighted for the broad-band spectral response of the hollow driveshaft tubes. The cyclic relationship of clonk with the shuffle response of the driveline system is also established for transient decay of the clonk phenomenon. In particular, the multi-body model is used to ascertain the effect of vehicle laden state on the propensity of driveline clonk, an approach not hitherto reported in literature.
A heavy-haul train–track coupled dynamic model is developed based on the vehicle–track coupled theory. The numerical model is verified in two typical cases. For the calculation, the different lines are considered, which are composed by the plane curve with 400 m radius and the vertical convex (concave) curves with the 8 grade difference. Taking the freight wagons in the 10,000 t and 20,000 t trains as the research objects, their curing performances, the corresponding coupler behaviors, and rail displacements in the emergency and full service braking conditions are analyzed and compared. The results indicate that the alignment of horizontal curve section will cause a distinct tilt angle of wagon coupler, and the tilt amplitudes are almost unchanged for different coupler compression forces. It can be attributed to the stronger coupler stabilizing ability of the freight wagon system. However, under the influence of coupler angle, the coupler longitudinal force produces a large lateral component, which significantly deteriorates the curving performances of wagons bearing the maximum coupler compression forces. Generally, when the 10,000 t and 20,000 t trains brake in the sharp curve, the maximum values of wheelset lateral force and rail lateral displacement increase by 33% and 28%, respectively, with respect to the results calculated in the idle condition. For the dynamics evaluation of freight wagons, the train marshalling modes, the idle condition, and braking condition should be considered comprehensively according to the actual situations.
Condition-based maintenance is a maintenance strategy which can be employed for monitoring the condition of rolling element bearings (REBs). For that purpose, the physics-based modelling of these machine elements is an interesting approach. There is a wide range of REBs regarding their internal configuration, dimensions and operating conditions. In this paper, a methodology to create a physics-based mathematical model to reproduce the dynamics of multiple kinds of REB is presented. Following a multi-body modelling, the proposed methodology takes advantage of the reusability of models to cover a wide range of bearing configurations, as well as to generalise the dimensioning of the bearing and the application of the operating conditions. The methodology is proved to be valid by its application to two case studies. Simulations of a deep-groove ball bearing and a cylindrical roller bearing are carried out, analysing their dynamic response as well as analysing the effects of damage in their parts. Results of the two case studies show good agreement with experimental data and results of other models in literature.
In previous research, a set of nonlinear algebraic kinematic constraint equations were developed that describe the configuration of a wheelset in contact with a track at two distinct points. In such a case of two points of contact, a simplified wheelset model that has the lateral displacement and angle of attack as the independent variables can be developed. In the current investigation, this approach is extended to the new case of a wheelset in contact with a tangent track at three distinct points. The solution of this three-point contact problem requires specifying the wheelset angle of attack only. This wheelset configuration is significant in derailment investigations because it is a possible configuration at the initiation of a wheel climb derailment. In order to study this wheel climb initiation configuration, a set of nonlinear kinematic constraint equations is developed as a function of the wheelset angle of attack and solved for the unknown system coordinates and contact surface parameters using an iterative Newton–Raphson algorithm. The wheelset angle of attack during wheel climb derailments can be determined forensically at the derailment site, making this approach of practical significance. It is shown in this investigation that the system configuration can be fully defined for wheel climb derailment initiation, which allows for the investigation of various derailment parameters such as the wheel–rail contact angle. It is then reinforced in this study that the wheelset flange angle, which is the angle between the tangent to the wheel surface at the contact point and the wheelset axle, is not representative of the wheel–rail contact angle, which is the angle between the tangent to the contact surfaces and the lateral common tangent to the two railheads; this distinction can only be demonstrated through full definition of the system configuration that accounts for the wheelset roll angle. This investigation therefore calls into question the Nadal
This paper addresses three-dimensional dynamic modeling of an elevator traveling cable with bending and torsional stiffnesses and arbitrarily moving ends. Two different types of elements are introduced to model the traveling cable: one is based on Rayleigh beam theory and the other Kirchhoff plate theory. Dynamic equations of motion, which are presented as differential algebraic equations, are solved by the backward differentiation formula. Equilibria of a traveling cable with different cable parameters and car positions are first calculated. Motions of cable ends are prescribed next to simulate the free response of the traveling cable due to motion of the car. Finally, effects of different types of building sways on dynamic responses of the traveling cable are examined.
Tilt rotor supported by rolling bearings is often used in mechanical equipment. In the past, researches on dynamic performance of bearing-rotor were mainly carried out for horizontal rotor, but there is insufficient reported research on the tilting rotors. In this paper, the dynamic performance of a tilt rotor supported by spherical roller bearings is studied. Through the dynamics analysis of the rotor, a transfer matrix dynamics model for the tilt rotor is established. The stiffness and damping calculation model of spherical roller bearings is built. With a calculation example, the effects of tilting angles and some rotor structure parameters on the system’s dynamic performance are studied numerically. The results obtained show that with the increase in the tilt angle, the critical speed of the rotor decreases, and the amplitude increases in the vertical direction of the shaft. With the same tilting angle, the smaller the distance from the disc to the middle point of the rotating shaft, the larger the amplitude of the vibration mode and the amplitude difference compared to that of the rotor without inclination. The unbalanced response amplitude curves of the rotor distribute asymmetrically because of the rotor’s inclination. The bigger the inclination angle, the more obvious is the asymmetry distribution.
The chaotic dynamics along with the control of chaos in a half-car model with semi-active suspension system is considered in this paper. The time series responses, phase space trajectories, Poincaré sections, and Lyapunov exponent methods are used to analyze the chaotic behavior in the open-loop system. In order to suppress the chaotic responses in the system, a chaos controller is applied based on the development of Ott–Grebogi–Yorke algorithm. In this new control strategy, the Poincaré map of the system is estimated using the support vector machine innovatively. After linearization of the Poincaré map, the optimal discrete-time linear quadratic regulator is designed for the linear map as a main contribution. The discrete optimal Ott–Grebogi–Yorke controller improves the performance of the system along with the rejection of chaos in the responses. This improvement involves the reduction in settling time, control effort, and energy consumption in the suspension system.
Establishing a precise system level model for transmission system is quite necessary and feasible for today’s computer technology. Taking into account of the exact parameters and actual working condition, an accurate model for a new deep hybrid transmission with compound planetary gear set is constructed, which in consideration of the gravity and centrifugal effect. The system level model contains the gears, shafts, bearings, clutches, electric motors and the housings. Few studies are found to investigate structure influence in system level for noise, vibration and harshness performance. Validation for the simulation results with test in three typical working conditions is carried out, which shows a quite well agreement. Furthermore, some parameters for this compound planetary gear set are investigated. The results show that for radial clearance between the ratchet and ring gear the smaller the better, while the axial clearance between the ratchet and ring gear requires cautious consideration to realize a better vibration performance for different planetary gear set. In the case of carrier, the radius of the connection pawl and the thickness of the carrier input shaft have remarkable influence on vibration characteristics. The vibration amplitude is the lowest when these two values equaling to 55 and 7 mm, respectively. Other than that, it is interesting to notice that the carrier position has a significant influence on the system vibration in pure electric drive mode. It is shown that if the planet carrier is fixed and sun gear rotates as input, the position of carrier should keep planet gears at high gravity center and symmetrical distribution on both sides of carrier centerline in the gravitational direction. The vibrational magnitude is the smallest as the carrier rotating 50° along z axis for this compound planetary gear set.
In the development and layout of timing chain drives for internal combustion engines, multi-body simulation is used to evaluate the chain drive in terms of both the acoustic and the dynamic behaviour. Owing to the complex structure of chain drives and surrounding components, the system cannot be described by analytical equations. The elastic behaviour of the single components can influence the dynamic and acoustic behaviour of the chain drive system and the timing system. This paper describes a new methodology for chain drive simulation with a full 3D representation of the chain drive and the option of a fully elastic consideration of the surrounding structures. The surrounding structures and components can be included in a fully elastic manner as finite element components in an arbitrary range. The described method allows the combination of typical multi-body components, such as chain links, with finite element structures. After presenting the strategy of modelling the chain drive as a combination of multi-body simulation and the finite element method, simulations are compared with conducted experiments for a simple two-sprocket chain drive. The simulation results show good agreement with the measurements.
In this paper, a controller for an automated steering articulated vehicle with the special capability to reduce off-tracking in low-speed maneuvers is proposed. Conventional tractor–trailers have a large off-tracking in low-speed maneuvers. In the proposed vehicle, all wheels of the tractor and trailer are steerable (all wheel steering). The controllers of the tractor and trailer work independently, and each one consists of two layers. A fuzzy controller and a PID controller are designed in the upper and lower layer, respectively, to control the actuators. The aim of the controller is to ensure that the end points of both the tractor and the trailer exactly follow the path of tractor’s first point. To assess the performance of proposed controller as well as steerability effect of all wheels in low speeds, the TruckSim simulation software is used. The simulation results confirm that the proposed approach improves the maneuverability and accuracy of path tracking not only compared to conventional vehicles but also to the conventional tractor–active trailer scheme, which was previously proposed by a number of studies. Additionally, it reduces lateral tire forces to enhance the working life.
In this paper, an unbalanced Jeffcott rotor supported by the roller bearings is modelled, and the dynamic differential equations are obtained by the Lagrange’s equations. The fourth order Runge–Kutta method is employed to simulate this system in two cases. Simulation results show the combined effect of the coupled lateral and torsional vibrations and the variable compliance vibration of the rotor. In the case of that only a large and constant radial force is applied, the sum and difference between variable compliance and rotational frequency components of the torsional vibrations of the disk are induced because of the roller bearings’ rotation. And when they are near to the natural frequency of the torsional vibration, the resonance peaks appear. In the case of that a large and constant radial force and a harmonic torque are simultaneously applied, the two components, the sum and difference between rotational frequency and the frequency of the external torque, of the lateral vibrations of the disk are induced. When the frequency of the external harmonic torque approximatively equal to a special value, the two frequency band lines, variable compliance and the sum of rotational frequency and the frequency of external torque, intersect near the natural frequency of the lateral vibration, and the vibration may aggravate.
The expression of the centrifugal forces resulting from a flexible body negotiating a curve differs significantly from the expression of the centrifugal forces used in rigid body dynamics. In rigid body railroad vehicle dynamics, the balance speed does not depend on the body inertia; it depends on the vehicle speed, super elevation, track gauge, and gravity constant. This is not, however, the case when the structural flexibility is considered. In this paper, a general multibody system (MBS) approach that accounts for the nonlinear dynamic coupling between the wheel–rail contact forces and the tank car structural flexibility is used to examine the effect of increasing the tank car thickness on the nonlinear dynamics of railroad vehicles. The flexible tank cars are modelled in this investigation using the nonlinear finite element (FE) floating frame of reference (FFR) formulation. The tank car FE model is integrated with a computational railroad vehicle algorithm in which a three-dimensional elastic contact formulation is used to describe the rail–wheel interaction in order to allow for wheel–rail separations. A complete expression for the centrifugal and Coriolis forces is used with triangular shell finite elements to develop the tank car models with different thicknesses. The effect of the coupling between different modes of displacements is examined by comparing the results of the simulations of the flexible and rigid tank car models. A parametric study is performed in order to explain the effect of the thickness increase on the tank car natural frequencies. Furthermore, the effect of increasing the tank car thickness on the critical speed as well as on the nonlinear dynamics of the railroad vehicle during curve negotiation is examined. The FE/FFR formulation allows for accurately capturing the effect of the change of the tank car thickness on the centrifugal and Coriolis inertia forces that define the balance speed during curve negotiations. The analysis presented in this paper shows that there is a strong dynamic coupling between different modes of displacements of the tank car, the plate thickness, and the wheel–rail contact parameters. The effect of increasing the tank car thickness on the wheel wear is also examined in this paper.
Good design for the piston skirt can improve efficiency without harming emissions, while it simultaneously reduces wear and improves the reliability of the engine. In this paper, the finite element method is applied to solve the Reynolds equation to analyze the piston skirt-liner system lubrication, and the side motion of piston skirt solved with Runge–Kutta is coupled with lubrication. Some factors that have an effect on the lubrication and dynamic characteristics are selected as variables, such as the clearance, offset distance of the piston pin, bump position, curvature, the length of piston skirt, and the ellipticity of the piston skirt. The orthogonal experimental design which includes six factors with five levels is used to analyze the dominance of these structure factors, and the effects of all the responses for the structural parameters to the friction loss are also identified, and the orthogonal samples simulated by the experiment are conducted to do the regression for the piston skirt. Some regression models are introduced to predict the friction loss, the precise comparison of all the models are compared, and the larger error appears in these prediction models, and then the particle swarm optimization-support vector regression is also used to predict the friction loss, and the results agree well with each other. All the analyses are very useful to provide guidance for the design of the piston skirt-liner during the development of the engine.
In this paper, two different model order reduction approaches for elastic multibody systems with moving loads are considered. The first approach is based on a parametric formulation of the input and output matrices and application of parametric model order reduction. Therefore, a quasi-static description without considering the time dependency of the parameter is proposed. In the second approach, the time-varying input matrix is approximated in a low-dimensional subspace and model order reduction of a time-invariant system is performed. To investigate the applicability of these methods for the generation of reduced elastic multibody systems, for the first time, both approaches are compared for a thin-walled cylinder model with a rotating force.
This article focuses on inverse kinematic formulation and dynamic modeling of the Nao biped robot's lower body, accompanied by verification with the joints' angles as experimental data. Dynamic modeling in two different planes is discussed and joint angles for the given positions, nominal conditions, and trajectory computations are simulated and graphically illustrated. A new approach for development of the inverse dynamics on the aforementioned robot's lower body is proposed in this paper, analytically studied, and compared with MSC Adams for two various scenarios of fixed supporting leg and ground contact implementation.
Journal bearings are generally used to comprise a revolute joint in mechanical systems. Noncircularity and clearance in journal bearing are obvious due to a long time of nonuniform wear. In this regard, a method of analyzing the contact in revolute joints with noncircular clearances in a multibody system is proposed. The revolute joint with noncircular clearance is assumed to be constituted by an elliptic bore and a pin. The method described is not representative of an elliptic bore journal bearing in a detailed manner. This method involves discretizing the geometric profile of the bushing of the revolute joint. By analyzing the relative separations between the discrete points and the geometric center of the pin, the contact area between the bushing and the pin can be judged and the maximum contact depth obtained. Compared with traditional methods, the proposed method has the advantage that it can be used to analyze noncircular contact problems in revolute joints with a clearance. A slider–crank mechanism is used as an example to compare the effects of the geometrical properties of circular and noncircular (elliptical) revolute joints with clearance on the dynamic response of the mechanisms. The results show that clearance joints with noncircular geometry predominantly affect the dynamic stability of a high-speed mechanism. Moreover, the efficiency of the contact analysis and model solving precision are strongly dependent on the number of discrete points in the geometric profile of the joint elements. The size of the joint clearance has a small effect on the solving efficiency of the model.
This study aimed to examine the dynamic response of large converters to the braking process. Based on the rigid–flexible coupling theory of the multi-body dynamics, and by adopting the finite element method and multi-body dynamics software Recurdyn, this work constructed a variety of rigid–flexible coupling dynamic models of converter transmission systems. With torsional vibration of the converter furnace during braking as the object of analysis, this research studied the pattern of the impact of speed change of driving motors, braking time, and rotational damping of the system on the torsional vibration characteristics of converters during the braking process. Comparison of the simulation results indicated that the rigid–flexible coupling mode had a greater impact on the simulation results and simulation efficiency. In particular, the analysis model using elastic units in the coupling between rigid and flexible bodies could effectively simulate the torsional and vibrational response of the converter braking process. Dynamic simulation results showed that increasing the braking time and rotational damping of the driving motor could effectively reduce the torsional vibration of the furnace under certain conditions. Within the same braking time, the maximum value and the continuity of the driving motor acceleration had the greatest impact on the torsional vibration amplitude of the furnace, and optimal control of furnace torsional vibration could be achieved when the acceleration was a second-order curve.
Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is becoming an important issue in human–machine interaction. Anticipating the dynamic behavior of variable topology mechanisms requires solving a nonsmooth dynamic problem. The core challenge is a physically meaningful transition condition at the topology switching events. Such a condition is presented in this article. Two versions are reported, one using projected motion equations in terms of redundant coordinates, and another one using the Voronets equations in terms of minimal coordinates. Their computational properties are discussed. Results are shown for joint locking of a planar 3R mechanisms and a 6DOF industrial manipulator.
The paper investigates the role of radial load and rotating speed on the high frequency vibration of a deep groove ball bearing. Firstly, a bearing dynamic model with 6-DOF balls was established, considering the interactions between balls, races and the cage. The dynamic model was solved by fourth order varying steps Runge-Kutta integration. The frequency spectrums of dynamic response of races were analyzed with yule-walker and FFT. Secondly, a verification experiment was done with different radial loads and speeds. Finally, compared with the numerical and experimental results, the similar trend of the high frequency vibration was emerged. Higher vibration frequencies result with increasing bearing load; higher vibration amplitude cause by more quickly rotating speed. That is because the nature frequencies of the races are excited by the contact and shock between balls and races when balls leave from the non-load to the load zone. The frequency spectrums were also affected by the interaction between the balls and cage.
Lyapunov characteristic exponents are indicators of the nature and of the stability properties of solutions of differential equations. The estimation of Lyapunov exponents of algebraic multiplicity greater than 1 is troublesome. In this work, we intuitively derive an interpretation of higher multiplicity Lyapunov exponents in forms that occur in simple linear time invariant problems of engineering relevance. We propose a method to determine them from the real Schur decomposition of the state transition matrix of the linear, nonautonomous problem associated with the fiducial trajectory. So far, no practical way has been found to formulate the method as an algorithm capable of mitigating over- or underflow in the numerical computation of the state transition matrix. However, this interesting approach in some practical cases is shown to provide quicker convergence than usual methods like the discrete QR and the continuous QR and Singular Value Decomposition (SVD)methods when Lyapunov exponents with multiplicity greater than one are present.
One of the reasons for frequent vibrations of coaches and hunting instability are hollow worn wheels. The main purpose of this paper is to investigate the effect of the wheel surface hollowing on the inconstancy and vibrations of a wagon. Considering the nonlinearity of the hollow surface, as well as both single and double point wheel-rail contacts are the significant points of this study. In order to do this, 800 wheel profiles of 100 coaches were measured in a controlled manner in a period of six months as an infield study. Statistical methods were used to categorize the measured hollow wheel profiles and select eight of the most observed ones. Then, a nonlinear mathematical model of a high-speed railway vehicle with 21 degrees of freedom was used for dynamic analysis of a wagon equipped by the hollow worn wheels on a tangent track. In order to model the effect of hollowing on the dynamic behaviour of the vehicle, the nonlinearity of wheel profile was taken into account. Also, both single and double point wheel-rail contacts were considered for accurate modelling of the wheel-rail interaction forces. Based on the results of the study, the tread hollowing must be considered as an independent dimensional parameter in periodic inspections. Also, it was concluded that worn wheels should be inspected regularly and re-profiled before their false flanges exceed a limit of 2 mm, in order to prevent the hunting phenomenon, and ensure being away from derailment of a passenger railway vehicle. Validation of the mathematical modelling was performed through the modelling of vehicle in ADAMS/Rail and comparing the results.
The use of modern multibody simulation techniques enables the description of complex products, such as mobile machinery, with a high level of detail while still solving the equations of motion in real time. Using the appropriate modelling and implementation techniques, the accuracy of real-time simulation can be improved considerably. Conventionally, in multibody system dynamics, equations of motion are implemented using the full matrices approach that does not consider the sparsity feature of matrices. With this implementation approach, numerical efficiency decreases when sparsity increases. In this study, a numerical procedure based on semi-recursive and augmented Lagrangian methods for real-time dynamic simulation is introduced. To enhance computing efficiency, an equation of motion is implemented by employing the sparse matrix technique.
We examined energy harvesting using a vertical composite laminate beam with an additional moving mass subjected to kinematic harmonic excitation. The gravity effect and the moving tip mass applied to the system cause considerable changes in effective spring-mass characteristics of the bending beam. Simultaneously, we observed dynamical beam damping by an additional degree of freedom and non-linear effects including friction between the moving mass and the beam structure. The experiments were performed on the beam excited kinematically by a shaker, while beam velocity measurements were made by a scanning laser vibrometer. We applied modal analysis in the limit of a fairly low excitation level. The selected modal vibrations are illustrated by corresponding output time series.
The main goal of this investigation is to integrate an electronically controlled pneumatic (ECP) brake model with efficient longitudinal train force algorithms based on the trajectory coordinate formulations. The ECP brake model, developed in this investigation consists of the train line (cable), locomotive automatic brake valve, air brake pipe, and ECP manifold. The train line, which covers the entire length of the train, allows the brake commands to be received by the car simultaneously. While pneumatic pressure is used to generate the braking forces, the brake pipe is no longer used to provide the brake level commands. Instead, the brake pipes are used to provide a continuous supply of compressed air stored in a reservoir mounted on each railcar. Using the ECP system to apply the brakes uniformly and instantaneously gives better train control, shortens the stopping distances, and leads to a lower risk of derailment. In this investigation, the fluid continuity and momentum equations are used to develop the governing air pressure flow equations. These partial differential equations are converted to a set of ordinary differential equations using the finite element method leading to an air brake force model that accounts for the effect of the air flow in long train pipes as well as the effect of leakage and branch pipe flows. The car brake forces are applied to the wheels using the ECP manifold located in each car. The ECP manifold used in this investigation has four valves: cut-off valve, vent valve, auxiliary valve, and emergency valve. The ECP manifold is connected to three main pneumatic components: the auxiliary reservoir, the emergency reservoir, and the brake cylinder. The reservoirs serve as the main storage of the pressurized air, while the brake cylinder and other mechanical components such as the rigging and the brake shoes transmit the brake force to the wheels. In this investigation, a mathematical model of the ECP manifold and its components is developed. The relationship between the main components of the ECP brake system and the train dynamics is discussed, and the final set of differential equations that integrates the ECP brake and train dynamics is presented. Different simulation scenarios are considered in this study in order to investigate the effect of the brake forces on the train longitudinal dynamics in the case of different braking scenarios. The performance of the developed ECP brake system is compared with the Association of American Railroads safety and operation standards, and with experimental results published in the literature.
In this paper, an analytical reduced dynamic model of a rail vehicle system is developed. This model considers only 38 degrees of freedom of the rail vehicle system. This reduced model can predict the dynamic behaviour of the rail vehicle while being simpler than existing dynamic models. The developed model is validated using experimental results found in the bibliography and its results are compared with existing more complex models from the literature. The developed model is used for the passenger comfort evaluation, which is based on the value of the weighted root mean square acceleration according to the ISO 2631 standard. Several parameters of the system, i.e., passenger position, loading of the railway vehicle and its speed, and their effect on the passenger comfort are investigated. It was shown that the level of comfort is mostly affected by the speed of the railway vehicle and the position of the seat. The load, however, did not have a significant effect on the level of comfort of the passenger.
In this paper, a comparison is made on different torque vectoring strategies to find the best strategy in terms of improving handling, fuel consumption, stability and ride comfort performances. The torque vectoring differential strategies include superposition clutch, stationary clutch, four-wheel drive and electronic stability control. The torque vectoring differentials are implemented on an eight-DOF vehicle model and controlled using optimized fuzzy-based controllers. The vehicle model assisted with the Pacejka tyre model, an eight-cylinder dynamic model for engine, and a five-speed transmission system. Bee’s Algorithm is employed to optimize the fuzzy controller to ensure each torque vectoring differential works in its best state. The controller actuates the electronic clutches of the torque vectoring differential to minimize the yaw rate error and limiting the side-slip angle in stability region. To estimate side-slip angle and cornering stiffness, a combined observer is designed based on full order observer and recursive least square method. To validate the results, a realistic car model is built in Carsim package. The final model is tested using a co-simulation between Matlab and Carsim. According to the results, the torque vectoring differential shows better handling compared to electronic stability control, while electronic stability control is more effective in improving the stability in critical situation. Among the torque vectoring differential strategies, stationary clutch in handling and four-wheel drive in fuel consumption as well as ride comfort have better operation and more enhancements.
The mechanical operation of a biologically inspired robot hopper is presented. This design is based on the hind leg dynamics and jumping gait of a desert locust (Schistocerca gregaria). The biological mechanism is represented as a lumped mass system. This emulates the muscle activation sequence and gait responsible for the long, coordinated jump of locusts, whilst providing an engineering equivalent for the design of a biological inspired hopper for planetary exploration. Despite the crude simplification, performance compares well against biological data found in the literature and scaling towards size more typical of robotic realisation are considered from an engineering point of view. This aspect makes an important contribution to knowledge as it quantifies the balance between biological similarity and efficiency of the biomimetic hopping mechanism. Further, this work provides useful information towards the biomimetic design of a hopper vehicle whilst the analysis uncover the range maximisation conditions for powered flight at constant thrust by analytic means. The proposed design bridges concepts looking at the gait dynamics and designs oriented to extended, full powered trajectories.
The present investigation is an attempt to evaluate the dynamic behaviours of multi-cracked cantilever rotor shaft with an additional mass attached at the tip of the shaft, which is partially submerged in the viscous fluid. In this work, theoretical expressions are developed to find the fundamental natural frequency and amplitude of the multi-cracked rotor shaft with attached mass, using influence coefficient method. Navier–Stoke’s equations are used for the analysis of external fluid forces acting on the rotor. Viscosities of the fluid and relative crack locations are taken as main variable parameters. For the analysis, suitable theoretical expressions are considered, and the Matlab programming is made to obtain the results. Experimental verifications are also performed to prove the validity of the theory developed.
Minimizing working time of the internal combustion engine is an important method for hybrid electric vehicles to save energy and reduce emissions. However, vibrations caused by frequent engine starts and stops deteriorate driveability and ride comfort. Especially in power split hybrid vehicles, there is no kinematically decoupled device between the engine and transmission, so that vibrations transfer from the powertrain to the car body through not only engine mounts but also the driveline system. Hardware test results show that the longitudinal vibration of seat track is the most severe with a maximum peak-to-peak acceleration of 1.8 m/s2. In this study, dynamic models of the driveline system and the powertrain mounting system are respectively established in detail. The natural characteristic analyses of the two dynamic models reveal that engine order vibrations can stimulate a series of low-frequency resonances during the engine starts, which is finally embodied in the car body vibrations. Then, two dynamic models are coupled together to analyze the transient dynamic characteristics associated with engine starts. It is evident by simulations that the longitudinal vibration of car body is mainly transferred by the driveline, whereas the vertical vibration of car body is mainly transferred by the powertrain mounting system. Besides, the initial crankshaft position of the gasoline engine has an obvious effect on the engine order vibration, and further results in different transient responses of the full vehicle system.
Shorter stopping distance and less deviation from the straight line are two requirements of vehicle safe braking on split-µ roads. The first one is achieved by controlling the longitudinal slip of each wheel at its optimum value calculated by road conditions. However, in order to directly control the vehicle directional stability, a new multivariable controller is optimally developed for integrated active front steering (AFS) and direct yaw moment control. In an efficient way to manage two control inputs, the weights of the integrated optimal control law are online determined by fuzzy logics. These logics are defined using the stability index obtained by the phase plane analysis of nonlinear vehicle model. In this way, the required external yaw moment can be calculated for different driving conditions to only compensate the drawback of AFS for stabilising the vehicle system. The minimum usage of stabilising external yaw moment leads to the less reduction of maximum achievable braking forces of one side wheels and results the shorter stopping distance. By determination of the weighs in limit conditions, the integrated control law easily leads to the stand-alone braking control law. The simulation results carried out using a validated vehicle model demonstrate that the integrated control system has a better braking performance compared with the stand-alone braking system, reported in literature, to attain the shorter stopping distance with less lateral deviation on split-µ roads.
The main functions of suspension system are to provide ride comfort for the passengers and vehicle handling (road holding). But, in many studies, full attention to the ride comfort leads to the determination of incorrect suspension system parameters as well as other problems such as rollover and reducing road-holding ability in the vehicle. The aim of this study is to present a method for the optimized design of the vehicle suspension system in order to improve the ride comfort, road holding, workspace and preventing rollover, considering a full vehicle model with 11-DOF. The most important feature of this study is that the prevention of rollover factor and all of suspension functions are considered simultaneously. In this research, in order to assess the ride comfort, the vertical acceleration values of seats that are caused by random road roughness are calculated by power spectral density of road in frequency domain. In the context of prevention of rollover, Fishhook manoeuvre is performed using a mathematical model for the roll motion, and then the dynamic behaviour of the variables is considered in rollover threshold. Then, the optimization problem is solved to minimize the vertical acceleration values and vehicle roll angle by considering the physical limitation and safety of the model. The results of the optimization show that the vertical acceleration, in frequency domain at the desired boundary values (as defined in ISO 2631), decreases and rollover resistance of the vehicle increases.
This work is concerned with the numerical solution of the equations of the dynamics of flexible multibody systems with dissipative physical mechanisms. Specifically, we consider systems composed of rigid and deformable bodies made of a viscoelastic continuum, that may experience large displacements and strains, connected by joints. Within this framework, we present a novel integration scheme for these types of systems that intrinsically satisfies the laws of thermodynamics and existing symmetries. The resulting solutions are physically accurate since they preserve the fundamental physical properties of the model. Furthermore, the method gives excellent performance with respect to robustness and stability. Justification of these claims as well as numerical examples that illustrate the performance of the scheme are provided.
Vibration characteristics of a roller bearing caused by a roller passing over the defect on the races are determined by the contact forces between the roller and races of the bearing. The vibration characteristics and contact forces are determined by the sizes and edge discontinuities of the defect. Therefore, it is very useful to investigate the relationships between defect edge discontinuities and the contact forces, and those between defect edge discontinuities and the vibrations for diagnosing the defects with different edge discontinuities in the roller bearings. A dynamic nonlinear finite element model for a roller bearing with a localized surface defect considering different edge discontinuities on its outer race is developed using an explicit dynamics finite element software package in this work. The effects of the defect edge discontinuities, radial load, and shaft speed on the contact force between the roller and outer race of the roller bearing are investigated, as well as the vibrations of the bearing. In-depth analyses of the contact forces between the roller and localized surface defect with different edge discontinuities are presented, which did not study in the previous literatures. The numerical results show that the number of the impacts between the roller and end edge of the defect caused by the re-stressing is more than that between the roller and beginning edge of the defect caused by the de-stressing, which is also affected by the defect edge discontinuities.
Input torque balancing through addition of an auxiliary mechanism is a well-known way to improve the dynamic behavior of mechanisms. One of the more efficient methods used to solve this problem is creating a cam-spring mechanism. However, the use of a cam mechanism is not always possible or desirable because of the wear effect due to the contact stresses and high friction between the roller and the cam. The Scotch yoke mechanism is most commonly used in control valve actuators in high-pressure oil and gas pipelines, as well as in various internal combustion engines, such as the Bourke engine, SyTech engine and many hot air engines and steam engines. This mechanism does not create lateral forces on the piston. Therefore, the main advantages of applications include reducing friction, vibration and piston wear, as well as smaller engine dimensions. However, the input torque of the Scotch yoke mechanism is variable and can be balanced. This paper proposes to balance the input torque of Scotch yoke mechanisms without any auxiliary linkage just by adding linear springs to the output slider. It is shown that after cancellation of inertial effects the input torque due to friction in joints becomes constant, which facilitates the control of the mechanism. An optimal control is considered to improve the operation of balanced Scotch yoke mechanisms. The efficiency of the suggested technique is illustrated via simulations carried out by using ADAMS software.
The absolute nodal coordinate formulation (ANCF) is a finite-element-based formulation developed for large deformation analysis in multibody applications. During the course of progress of the ANCF, a number of beam, plate and shell elements are introduced. Numerous different kinematic and strain energy definitions have been considered. However, the convergence behavior of ANCF-based beam elements has been investigated in the past primarily only with uniform mesh refinement. The objective of this paper is to study numerically the effects of different mesh refinement strategies within an Euler–Bernoulli beam-type problem solved with two-dimensional ANCF-based beam elements. To this end, h- and p-refinement meshing strategies are implemented for two-dimensional ANCF beam elements. The p-refinement is achieved by adding internal degrees of freedom to the elements. In addition, another p-refinement strategy is studied that employs higher-order derivatives as nodal coordinates. The rates of convergence for the different meshing strategies are calculated based on the known iteratively solved extensible elastica analytical solution. The numerical results indicate that the p-refinement strategy, with increasing number of higher-order derivatives at the element interfaces, in conjunction with h-refinement improves the rate of convergence. For the studied numerical example, this mesh strategy leads to better absolute error of displacement convergence than the uniform h-refinement or the p-refinement with internal nodes. The improvement in rate of convergence results from the use of higher-order derivatives that impose continuity to the bending and axial deformations across the elements, which may smooth the oscillations of bending and the axial strain fields.
The dynamic characteristics and optimization of a cutting mechanism about aluminum electrolytic capacitor casing machine were investigated with a lumped mass-spring damper model in this paper. In the lumped mass-spring damper model, compliance of the links and effects of mechanism position on deformable transfer relationship are taken into account. Besides, torsional and bending vibrations of camshaft are also considered. Cam profile is an important input excitation of the cutting mechanism and has important influence on the dynamic performance. Therefore, optimization of cam profile was also studied based on the dynamic model and B-spline. Acceleration fluctuations were significantly reduced after the optimization.
The majority of biomechanical analyses of human motions, including those with musculoskeletal models, use inverse dynamic approaches due to its ability to deal with experimentally acquired kinematic and kinetic data. Yet, a forward dynamic approach can be more powerful and provide better insights on the transmission of forces in the internal biomechanical systems and structures of the human body. Although both approaches may use the same biomechanical model the results achieved do not necessarily correlate with each other. The aim of this study is to demonstrate the source of the lack of correlation between inverse and forward dynamics methodologies providing, in the process, insights on how to overcome such differences. Two types of problems involving the biomechanics of the spatial human motion are used to evaluate the correlation between the forward and inverse dynamic approaches: a gait analysis of a deterministic biomechanical model of the lower limbs, and, a full musculoskeletal model of the upper limb, which is characterised by the solution of a redundant muscle force sharing problem. For that purpose, an inverse dynamic model is applied to estimate the forces responsible for two experimentally acquired motions that are, afterwards, given as input to the forward dynamics model, which is used, in turn, to compute the kinematics of the biomechanical model. The comparison between the reference kinematics, acquired experimentally, and that resulting from the forward dynamic analysis supports that a lack of correlation between the inverse and forward dynamic analysis is always observed. It is proposed here, and demonstrated, that a controller implemented in a feedback loop is able to enhance numerical stability of the forward dynamics solution, leading to the ability of the forward dynamics approach to successfully simulate the acquired motions.
Railway vehicle homologation with respect to running dynamics is addressed via dedicated norms that require the knowledge of the accelerations and wheel–rail contact forces obtained from experimental computational testing. Multibody dynamics allows the modelling of railway vehicles and their simulation on realistic operations conditions. However, the representativeness of the multibody models, and the results of their use in railway dynamics are greatly influenced by the modelling assumptions and their ability to represent the operational conditions. In this paper, two alternative multibody models of a railway vehicle are presented and simulated in a realistic railway track scenarios to appraise the consequences of different modelling assumptions on the railway dynamic analysis outcome. A vehicle–track interaction compatibility analysis is performed afterwards according to norm EN 14363. The analysis consists of two stages: the use of a simplified method, described in the norm for the identification of the different performance indexes from the railway vehicle dynamic analysis outcome; and the visual inspection of the vehicle motion with respect to the track via dedicated visualization tools. The results of the virtual vehicle homologation tests are presented and discussed in face of the modelling assumptions used, being significant differences identified between the railway vehicle modelled with cylindrical joints with clearances or with equivalent force elements. It is also concluded that the use of clearance joints prevents the need to use modelling assumptions on the equivalent force elements that have limited or no physical meaning, thus reducing the number of modelling parameters for which a high level of abstraction has to be exercised.
This paper presents a model to study the effect of piston ring dynamics on basic tribological parameters that affect the performance of internal combustion engines by using dynamics analysis software (AVL Excite Designer). The paramount tribological parameters include friction force, frictional power losses, and oil film thickness of piston ring assembly. The piston and rings assembly is one of the highest mechanically loaded components in engines. Relevant literature reports that the piston ring assembly accounts for 40% to 50% of the frictional losses, making it imperative for the piston ring dynamics to be understood thoroughly. This analytical study of the piston ring dynamics describes the significant correlation between the tribological parameters of piston and rings assembly and the performance of engines. The model was able to predict the effects of engine speed and oil viscosity on asperity and hydrodynamic friction forces, power losses, oil film thickness and lube oil consumption. This model of mixed film lubrication of piston rings is based on the hydrodynamic action described by Reynolds equation and dry contact action as described by the Greenwood–Tripp rough surface asperity contact model. The results in the current analysis demonstrated that engine speed and oil viscosity had a remarkable effect on oil film thickness and hydrodynamic friction between the rings and cylinder liner. Hence, the mixed lubrication model, which unifies the lubricant flow under different ring–liner gaps, is needed via the balance between the hydrodynamic and boundary lubrication modes to obtain minimum friction between rings and liner and to ultimately help in improving the performance of engines.
Taking the off-sized balls and raceway error into account, the effects of axial preloading displacement on the mechanical performance of angular contact ball bearings are investigated in this paper. Through the geometric analysis of the angular contact ball bearing and the force balance, the contact load-deformation expressions of ball-to-raceway, the expression of load zone and their relation to axial preloading displacement are derived. By numerical calculation for a concrete example, we found the influences of preloading on the loading zone and maximum ball load and found the influences of off-sized balls and raceway error on the minimum preloading displacement, ball load distribution, inner ring centre trajectory and inner ring vibration frequency. Some curves about these influences are obtained and discussed.
In this paper, a new continuum-based pantograph/catenary model based on the absolute nodal coordinate formulation (ANCF) is proposed and used to develop an effective method to control the contact force which arises from the pantograph/catenary interaction. In the proposed new model, only one ANCF gradient vector is used in the formulation of the pantograph/catenary contact conditions, thereby allowing for using the proposed approach for both fully parameterized and gradient-deficient ANCF finite elements. The proposed contact formulation can also be considered as a more general sliding joint formulation that allows for the use of the more efficient gradient-deficient ANCF finite elements in modeling very flexible cables. A three-dimensional multibody system (MBS) model of a pantograph mounted on a train is developed using a nonlinear augmented MBS formulation. In order to take into account the catenary large deformation, ANCF finite elements are used. The contact between the pantograph and the catenary system is ensured using a sliding joint constraint whereas the contact between the rail vehicle wheels and the train track is modelled using an elastic contact formulation. In addition to the use of the new MBS approach to model the pantograph/catenary interaction, the contact force between the pantograph and the catenary is computed using a simpler lumped parameter model which describes the pan-head and the plunger subsystem dynamics. In order to reduce the standard deviation of the contact force without affecting its mean value, a control actuator is used between the pan-head and the plunger. To this end, three types of control laws for the control action are designed to improve the contact quality both in the transient phase and in the steady state phase of the pantograph/catenary interaction. The first control law proposed features a feedback structure whereas the second and the third control strategies employ a feedback plus feed-forward architecture. In order to demonstrate the effectiveness of the proposed method, the results of a set of numerical simulations with and without the controllers are presented.
Alternative propulsion architecture systems are described and evaluated from the standpoint of efficiency and potential for use as mechanical energy storage systems in automobiles. Air hybrids are studied and modeling/simulation results are presented along with experimental data from a test bed to assess round-trip efficiencies of such storage systems. A possible architectural scheme is proposed for the use of compressed air for rapid energy recharge. This is followed by an assessment of hydraulic hybrids and flywheel hybrids. These systems are sized for comparable applications. Simulations are then used to objectively compare losses in these systems and to estimate operating round-trip efficiencies in energy storage applications.
In this paper, a type of planetary gear system in the wind turbine was studied by taking into account the actual conditions where the planetary gear system works. A nonlinear multi-gap planetary gear system finite element method model was established, and the engagement stress, the displacement, and the velocity curve with time of nodes of the planetary gear system were obtained by using explicit dynamic solution method. Under different speeds and different load, the variation of planetary gear system dynamic transmission error was then studied combined with the theory of gearing. The results showed that it is different from the dynamic transmission error of planetary gear system and planetary gear. Time-varying mesh stiffness of sun gear and the ring gear are also different along with their speed change. There are some correlation among time-varying mesh stiffness, meshing impact stress, and dynamic transmission errors. Therefore, it is suggested that the meshing stiffness and impact stress effect on the dynamic transmission error should be considered in the study of transmission error of wind turbine planetary gear system.
This paper presents an approach to predict and evaluate the dynamic characteristics of the transmission system in conveying equipment under various working conditions. To solve the problems of varying mass and load, the space, which the transmission system locates, is divided into multiple space-fixed finite control volumes according to the material distribution as well as motion pattern. Each volume is further discretized into a series of finite elements. System-governing equations are obtained by the assembly of all the individual elements’ dynamic equations and the topological structure of the transmission system. Karnopp model is utilized as the basis to render the duty resistance induced by friction. As an illustrative example, the present method is applied to model a large-scale armoured face conveyor, and the corresponding simulation code is developed based on Matlab/Simulink. Simulation results show that the start-up and stop processes with empty load are relatively smooth, which is beneficial to protect the components of the system, especially the chains. Furthermore, the resulted chain-steady velocity, chain-load spectrum and minimum tension force can be directly used to predict the conveying capacity, evaluate chain strength and optimise the pretension force.
This work presents a new framework by integrating some recent methods in the fields of road and vehicle modeling and optimization for multi-objective optimization of a passive vehicle model capable of estimating vehicle performance in facing random road excitation. To achieve this purpose, simulation of an actual random road power spectral density is employed, and a five-degree of freedom half-car model, capable of approximating vehicle performance, is developed. Furthermore, with the aid of stochastic theory, criteria of vehicle performance, including ride comfort (acceleration of seat) and road holding (working space and vertical tyre velocity), are calculated in terms of root mean square. These criteria are applied as objective functions in multi-objective uniform-diversity genetic algorithm optimization of the vehicle model. Based on different performance criteria, several design points are chosen from Pareto front, and frequency responses of those designs are depicted. Comparison between results of current work and those reported in a single-objective optimization study delineates a considerable improvement in the performance of the vehicle-vibration model. It is concluded from the obtained results that the proposed framework enables designers to select proper primary designs as a basis of later design stages with regard to the priority of desired performance criteria.
Seat transmissibility is used to evaluate the vibration attenuation performance of seats. Because the seat and the driver interact with each other, the seat transmissibility is affected by the dynamic characteristics of the driver. The constraint on the movement of the driver caused by the safety belt results in the change of the seat–driver dynamics and the seat transmissibility. Vibration accelerations were measured on the seat cushion and at the seat base on a medium size wheel loader when the driver wore a lap belt or a four-point seat harness. The seat effective amplitude transmissibility value and the seat transmissibility derived from the cross spectral density method were analysed to investigate the effect of safety belt on the seat transmissibility. Two multi-body models of the seat–driver system were built in MATLAB and their parameters were identified in cases where the driver wore the lap belt or the four-point seat harness. Based on the analysis of these parameters, the way how the safety belt affects the seat–driver dynamics and the seat transmissibility is studied.
This paper deals with the electromagnetic damper, which is composed of a permanent-magnet DC motor, a ball screw and a nut, as the passive, semi-active and active actuator in the vehicle suspension system. The main objective pursued in the paper is to study the dependences of the performance and energy regeneration of the electromagnetic suspension system on the road unevenness and the travel speed. For this purpose, the nonlinear equations of the electromagnetic damper electric circuit in the three mentioned suspension systems are developed. For the vehicle passing over the road unevenness, a seven degrees of freedom model is considered, and the simplest point-follower model is used for the tyre representation. To investigate the electromagnetic suspension system performance and energy regeneration, two types of road unevenness including a road section with a standard pure random profile and a bump modelled by cosine wave of variable height and length are applied. The simulation results demonstrate that an increase in the travel speed leads to the power spectral density increment of the road profile and in turn causes the negative effects on the performance and growth in the energy regeneration. Furthermore, when the bump height gets larger, maximum body acceleration, maximum suspension travel and energy regeneration will increase. There will be a peak on the maximum body acceleration response course when the bump length is equal to 1.1 m because of exciting the sprung mass frequencies. On the maximum suspension travel and energy regeneration response course, there is a peak when the travel speed is equal to 30 km/h, which excites the unsprung mass frequencies.
The human body is an over-actuated multi-body system, as each joint degree of freedom can be controlled by more than one muscle. Solving the force-sharing problem (i.e. finding out how the resultant joint torque is shared among the muscles actuating that joint) calls for an optimization process where a cost function, representing the strategy followed by the central nervous system to activate muscles, is minimized. The main contribution of the present study has been the particular formulation of that cost function for the case of the pathological gait of a single subject suffering from anterior cruciate ligament rupture. Our hypothesis was that the central nervous system does not weight equally the muscles when trying to compensate for a lower limb injury during gait (in contrast to what is the usual practice for healthy gait where all muscles are weighted equally). This hypothesis is supported by the fact that muscle activity in injured individuals differs from that of healthy subjects. Different functions were tested until we finally came out with a cost function that was consistent with experimental electromyography measurements and inverse dynamics results for a subject suffering this particular pathology.
This paper describes and evaluates the use of the Absolute Nodal Coordinate Formulation (ANCF) in modeling large size wind turbine blades. Modern blade model can be divided into two regions classified by aerodynamic and structural function. The aerodynamic region, blade-span, is utilizing the thinnest possible airfoil section. On the other hand, the transition between the circular mount and the first airfoil profile is referred as blade-root region, which carries highest loads along the blade. In this investigation, an efficient procedure is developed for mapping NACA airfoil wind-turbine blades into ANCF thin plate models. The procedure concerns a complete wind turbine blade structure, blade-root as well as the blade-span regions with non-uniform and twisted nature. As a result, the slope discontinuity problem arises in both chord-wise and span-wise directions, and consequently presents numerical errors in dynamic simulation. The paper investigates the methods of modeling slope discontinuity resulting from the variations of the cross-sectional layouts across the blade. The developed method is applied for the gradient-deficient thin plate element in order to account for structural discontinuity. In addition, the aerodynamic loads are precisely expressed and the aerodynamic characteristics of such blades are examined with the ANCF and with the classical finite element method. The static and dynamic solutions of different operating conditions are obtained and results are compared with those obtained using ANSYS code. Both the limitations and advantages of using the ANCF in modeling large size wind turbine blades are concluded and discussed. A Dynamics for Design (DFD) procedure is presented with numerical example concerning large-rotation, large deformation wind turbine blades.
Analysis of tyre transient dynamics is an important aspect in the study of vehicle ride comfort and handling performance. A three-dimensional finite element excavator tyre model considering intricate tread patterns and reinforced inner layers was developed in this paper. For the validation of the finite element tyre model, simulation and experimental results of tyre stiffness and contact pressure on the tyre–road interaction interface were studied and compared. The validated tyre model was further applied to simulate the tyre–speed bump impact, and transient dynamic responses of the excavator tyre such as tyre acceleration were analysed in the time and frequency domain. The influences of the inflation pressure, the translational velocity and the axle load on the tyre transient dynamics were studied and analysed based on the simulation results.
The inverse dynamics of human gait from motion capture data is an already mature discipline. The present work addresses the problems that arise when assistive devices such as crutches and active orthoses are added to the analysis. The objective is to provide an analysis tool for the gait of spinal cord-injured subjects, since these patients always require the help of assistive devices to walk. A gait analysis system for subjects walking with the aid of crutches and active knee–ankle–foot orthoses is presented. The assistive devices are introduced both at the experimental and computational levels. The required sensors and actuators are incorporated to the system, and the measurements are used to solve the inverse dynamics problem in order to calculate the joint motor torques produced by the subject during gait. Such analysis can be greatly helpful for comparing the performance of passive and active orthoses, evaluating and improving the controllers in the latter, monitoring the adaptation of the patients to the orthoses and their rehabilitation level, and improving the understanding of the interaction between active orthoses and the muscular system.
The four-caster manually manoeuvred vehicle is a crucial device for goods movement and disability transport. While there are manual handling related health and safety concerns, no dynamical theoretical-empirical investigation exists. Theoretical examination demonstrates that, in loose terms, the motion resistance effects are affected by vehicle-frame translational velocity direction: the proportion of the moment effect to translational effect produced by motion resistance varies in a highly non-linear way depending on the vehicle-frame velocity direction. An empirical study is devised from the theory. As the intention was to investigate the presence of this phenomenon in real use, human operators were used: they made planar manoeuvres from static equilibrium with a self-selected load while attempting to maintain 11 (maximum) different centres of zero velocity which related to the velocity directions. Results demonstrate that (1) the proportion of moment motion resistance effect to translational motion resistance effect does vary and (2) it is motion resistance rather than inertial forces which are the first-order effect. These results are an essential first step in understanding the manoeuvring difficulties and health and safety issues which arise with these vehicles.
The involuntary interaction of pilots with vehicles is often an undesired consequence of the biodynamic feedthrough of cockpit vibrations into the control system in relation with the characteristics of the man–machine interface. This work presents a numerical study of how the estimated muscular activation patterns associated with performing basic helicopter piloting tasks may affect the variability of the pilot’s biodynamic feedthrough and admittance. The limbs’ motion is predicted using an inverse kinematics formulation for redundant manipulators imposing the motion of the hand from measurements. Articulation torques are then estimated by inverse dynamics. Activation of the involved muscles is estimated according to the ‘total activation’ paradigm. Equivalent pilot feedthrough is obtained by consistent linearization of the constitutive model of the muscles about the reference activation. The effect on equivalent feedthrough of non-optimal activation, resulting from the addition of torque-less activation modes to the optimal activation, is evaluated and discussed. The multibody model of the pilot’s biodynamic feedthrough is incorporated in a detailed multibody model of a helicopter, to perform coupled bioaeroservoelastic simulations.
Chaos control of an apparent-type gyrostat satellite (GS) is investigated in this work. The GS under study consists of a main platform along with the three reaction wheels. The mathematical model of the GS is first derived using the quaternion-based kinematic and Euler-based kinetic equations of motion under the gravity gradient perturbation. Chaotic dynamics of the open-loop system without a feedback is then analyzed by the use of the numerical simulation in the phase portrait trajectories, Poincare' section, and time series responses. The existence of chaos is also demonstrated using the Lyapunov exponent criterion. In order to suppress chaos in the GS, a quaternion feedback controller is designed by the modification of Ott–Grebogi–Yorke (OGY) algorithm based on the linearisation of Poincare' map. In the controller strategy, the Poincare' map is estimated by the least square-support vector machine technique. Then, the discrete-time proportional-integral-derivative (PID) controller is applied on the linearised Poincare' map. The discrete-time PID-OGY control system rejects the chaotic behaviours in the attitude orientation of GS with the generation of a small control input leading to a decrease in the control effort and energy consumption.
A multiple point source model is developed in this research for studying both shear and compressional spherical wave propagation in a non-viscous fluid-saturated elastic porous medium. Relative displacement between the fluid and solid of the medium is quantified by the spherical wave governing equations, such that the waves described are more representative to that in engineering practices. The shear wave has shown significant influences on the characteristics of superposed shear and compressional waves generated by multiple point sources. Utilization of multiple point sources shows higher efficiency and effectiveness in generating desired waves, in comparing with that of single source. Specifically, the multiple sources model is more energy effective in comparing with the single source model by always producing larger magnitudes of relative displacement than a single source with the same energy, which becomes more significant when the distance between the source and the considered geological particles increases. Multiple point sources also show advantages on duration, direction control and magnitude adjustment for the waves generated. Numerical analyses are performed for comparing different shear, compressional and the superposed wave responses under single and multiple sources.
As both ordinary and well-trained human motion is mostly planned and controlled unconsciously by the central nervous system (CNS), human control mechanisms remain relatively obscure. Despite, they are an interesting topic, for example, with regard to improve protheses or athletic motion. To learn and understand more about the control of human motion, we use rigid multibody systems to represent bones and joints and formulate an optimal control problem (OCP) with the goal to minimise a physiologically motivated cost function, while the equations of motion and further nonlinear constraints have to be fulfilled. The investigated biomechanical movements are induced either via joint torques or via Hill-type muscle forces. We compare several cost functions known from literature to another one concerning the impact on the joints by involving the constraint forces. A direct transcription method called DMOCC (discrete mechanics and optimal control for constraint systems) is used to solve the OCP, whereby we benefit from its structure preserving formulation, as the resulting optimal discrete trajectories are symplectic-momentum preserving.
A formulation using dual-number coordinate transformations is developed to calculate the accelerations within the plane joint, a complex joint where the displacements are naturally expressed in different coordinate frames. The calculation of the accelerations in the Tracta constant-velocity shaft coupling is presented as an example of how the methodology can be applied in an automatic-computation scheme applicable to many types of mechanisms including those with a plane joint.
This paper discusses an application of dual algebra to the analysis of human knee joint stiffness matrix. According to the proposed methodology, the general stiffness matrix characterizing the elasticity properties of the knee ligaments is reduced to a dual diagonal stiffness matrix. For this purpose, the similarity transform was extended to the field of dual numbers. The theoretical framework proposed seems particularly useful when comparing stiffness matrices obtained from different experimental setup and within different Cartesian coordinate systems.
Soil compaction, as a form of soil degradation, accounts for the increase of soil strength and the reduction of soil production capability. Two finite element tire models were developed based on the real geometry and structure of a Bridgestone bias tire. With a single wheel tester, field experiments were performed to validate the finite element tire–soil interaction models. The influence of axle load and inflation pressure on the soil compaction was studied with a finite element tire model using coarse meshes, which improves the computation efficiency without degrading the simulation accuracy. Tire mobility such as drawbar pull, rolling resistance and lateral force generated inside the tire–soil contact patch is an important index for the performance of off-road vehicles. The relationship between the slip ratio, the slip angle and the tire mobility was investigated through the simulations carried out with the other finite element tire model using fine meshes.
Ball bearings, one of the most widely used components in rotating machinery, play a critical role in system performance. Localized defects such as pit and spall may develop in ball bearings during service. The vibration waveform of the impulse generated by a ball passing over a defect on the races is determined by the shape and size of the localized defect. Hence, it is important to study the relationship between the localized defect shape and its pulse waveform characteristics in order to diagnose the types of defect in bearings. This study examines the effects of the defect shape, radial load and shaft speed on the pulse waveform characteristics generated by localized defects using the method of explicit dynamic finite element analysis. To validate the proposed model, the results obtained from the experiments have also been provided, and the waveform and the duration of the pulse generated by the defect on the outer race are in good agreement with the simulation results, which shows validation of the proposed model. Both the experimental results and the simulation results have confirmed that the impulse shape generated by the defect on the raceway will be influenced by the contact deformations at the edges of the defect. The results obtained also demonstrate that the explicit dynamic finite element analysis approach can be used to analyze the pulse waveform characteristic generated by localized defects in ball bearings.
The launcher models used in most of the previous studies have few degrees of freedom that cannot possibly capture many important motion characteristics. In this work, a flexible multibody model of a missile launcher system is built. The fixed, azimuth and elevation platforms and the launching pod are modeled as flexible bodies. Both the normal vibration modes and constraint modes are considered. Modes that do not contribute significantly to the total strain energy are eliminated to reduce simulation time. The joint flexibility effects are also included to the model by spring-damper elements. For the plume force and the motor thrust, experimental data are utilized. The forces transmitted to the base of the launcher system and the azimuth platform displacements during the launch are determined. Launching tests show good conformity with the simulation results, thus revealing that the developed model provides a realistic representation of the system.
In this article the multibody simulation software package MADYMO for analysing and optimizing occupant safety design was used to model crash tests for Normal Containment barriers in accordance with EN 1317. The verification process was carried out by simulating a TB31 and a TB32 crash test performed on vertical portable concrete barriers and by comparing the numerical results to those obtained experimentally. The same modelling approach was applied to both tests to evaluate the predictive capacity of the modelling at two different impact speeds. A sensitivity analysis of the vehicle stiffness was also carried out. The capacity to predict all of the principal EN1317 criteria was assessed for the first time: the acceleration severity index, the theoretical head impact velocity, the barrier working width and the vehicle exit box. Results showed a maximum error of 6% for the acceleration severity index and 21% for theoretical head impact velocity for the numerical simulation in comparison to the recorded data. The exit box position was predicted with a maximum error of 4°. For the working width, a large percentage difference was observed for test TB31 due to the small absolute value of the barrier deflection but the results were well within the limit value from the standard for both tests. The sensitivity analysis showed the robustness of the modelling with respect to contact stiffness increase of ±20% and ±40%. This is the first multibody model of portable concrete barriers that can reproduce not only the acceleration severity index but all the test criteria of EN 1317 and is therefore a valuable tool for new product development and for injury biomechanics research.
This article studies the problem of wirl vibrations of a rotating drill string bit under conditions of its friction interaction with the bore-hole bottom surface at the wandering contact point. The mechanism of the bit spinning and rolling without sliding on the rigid surface has been analyzed. To study the wirl vibrations, the methods of nonholonomic mechanics are used. As an example, spherical bit whirling on spherical bore-hole bottom is considered. The kinematic inducement of the rotating bit motion without sliding is shown to be the main cause of its stability loss. The detailed study of the bit whirling revealed three types of its stable and unstable motions associated with direct and inverse rolling as well as pure spinning. It is found that the most detectable influence on dynamics of the system and its stability is exerted by the overall stiffness of the drill string tube, which depends on parameters of compressive axial force and torque and diminishes as their critical values are approached.
The goal of this study is to expand the combination of the arbitrary Lagrange–Euler (ALE) and absolute nodal coordinate formulation (ANCF) to plate elements. In the ALE–ANCF method, nodal coordinates are not associated with any specific material points. This means that nodal positions in a finite element mesh can be varied during simulations forward in time. This article contains a description of the kinematics and equation of motion of a thin ALE–ANCF plate element. The element kinematics is described using C1 continuous shape functions and elastic forces are evaluated using a combined membrane and curvature approach. The presented plate element formulation is validated by comparison with a conventional ANCF plate element.
This article combines the three-order harmonic balance method and eight-order Taylor expansion technique to give the qualitative analysis of responses for the spindle-ball bearing system. The effects of the bearing clearance and initial position of rotor on the frequency–response curves are investigated. As the number of contact balls alters due to the combining actions of the bearing clearance and initial position of rotor, the grazing phenomenon occurs and the frequency–response curve undergoes a major change. The system’s characteristic coefficients are also found to sharply grow at the point the number of contact balls alters. They therefore can be treated as the signs to indicate the occurrence of the grazing phenomenon, which is helpful for the researchers to study the non-linear and non-smooth properties of the spindle-ball bearing system.
Dynamic response of mechanical systems containing rigid links connected by joints is affected by the velocity and mass of the systems components as well as by the presence of clearance or impact between components. Accurate simulations of such systems are increasingly important due to their wide application in engine design, knitting machinery or single and dual-arm robotic systems, as well as for their initial and optimised design. A virtual prototype of a newly developed extensible crank mechanism (applied to the design development of a bicycle crank) is presented in this article and its dynamical behaviour is analysed. The equations of motion of the extensible crank, constrained to either a circular or an elliptical path, are considered. Accurate simulation of the constrained extensible crank mechanism explores its performance and behaviour under the combined effect of different parameters such as clearance and impact. A three-dimensional finite element model is used to study the flexural behaviour of the extensible crank under the maximal loads that causes its motion.