Method Of Multibody Systems Research Articles

Dynamics modelling and Layout optimization of CFRP in-situ machining system

The multi-support reconfigurable compliant tooling and robotic in-situ processing method provide a new technical direction for CFRP milling edge processing. Aiming at the layout optimization of CFRP in-situ machining system (CFRPIMS), the dynamics characteristics of the whole system were studied. A rigid-flexible coupling dynamics model of the CFRPIMS was proposed by applying transfer matrix method for multibody systems (MSTMM), treating CFRP as a thin-walled flexible plate and supporting fixtures as rigid bodies. And then the natural frequency and dynamics responses under the different support layout are simulated, which are verified by modal tests and excitation tests. To improve the support rigidity of CFRP workpieces, the optimization model of overall layout of the compliant tooling was established combined with genetic algorithm. Based on the milling test results, compared with the original scheme, the optimization method can effectively reduce the vibration response of the workpiece in the y-direction (along the milling edge direction) and the z-direction (perpendicular to milling edge direction) by more than 60 %.

Evaluation and implementation of Lie group integration methods for rigid multibody systems

AbstractAs commonly known, standard time integration of the kinematic equations of rigid bodies modeled with three rotation parameters is infeasible due to singular points. Common workarounds are reparameterization strategies or Euler parameters. Both approaches typically vary in accuracy depending on the choice of rotation parameters. To efficiently compute different kinds of multibody systems, one aims at simulation results and performance that are independent of the type of rotation parameters. As a clear advantage, Lie group integration methods are rotation parameter independent. However, few studies have addressed whether Lie group integration methods are more accurate and efficient compared to conventional formulations based on Euler parameters or Euler angles. In this paper, we close this gap using the $\mathbb{R}^{3}\times SO(3)$ R 3 × S O ( 3 ) Lie group formulation and several typical rigid multibody systems. It is shown that explicit Lie group integration methods outperform the conventional formulations in terms of accuracy. However, it turns out that the conventional Euler parameter-based formulation is the most accurate one in the case of implicit integration, while the Lie group integration method is computationally the more efficient one. It also turns out that Lie group integration methods can be implemented at almost no extra cost in an existing multibody simulation code if the Lie group method used to describe the configuration of a body is chosen accordingly.

Orbit-attitude-structure coupled modelling method in local translational coordinate frame for multibody systems

The absolute coordinate-based (ACB) method, including absolute nodal coordinate formulation and natural coordinate formulation, is a widely-used dynamic modelling method for multibody systems. However, the problem of accuracy loss would arise when multi-scale motions are described in the same global coordinate system, such as large-scale orbital motions, small-scale attitude motions and structural vibrations, and micro-scale contact/collision. To address this problem, an ACB method in local translational coordinate system is proposed such that the large-scale orbital motions can be separated from other smaller-scale motions. The dynamic equations are derived by the Hamilton's equations and the Kronecker product. The validity of the proposed method is studied using an orbit-attitude coupled model of an orbiting rigid plate. It is found that the attitude errors of the original ACB method increase as time step size decreases. The reason for this counterintuitive phenomenon is that more serious accuracy loss is encountered for smaller time step size. In addition, more iterations are required for the original ACB method to obtain the prescribed tolerable error in each time step due to accuracy loss. In comparison, the proposed method is more accurate and efficient in numerical simulations. Finally, the proposed method is applied to the orbit-attitude-structure coupled simulation of a space robotic system.

A novel method for studying fluid-solid interaction problems of the rotor system in air bearings with manufacturing errors

A novel method for studying fluid–solid interaction problems of the rotor system in air bearings is proposed. The overall transfer equation of the rotor system is established based on the new version of transfer matrix method for multibody systems (NV-MSTMM), coupling with the extended transient Reynold equation, which achieves the two-way fluid–solid interaction analysis of the rotor system. The transfer matrix of the spatial flexible Timoshenko beam is first derived based on NV-MSTMM. The accuracy of the proposed approach is verified by an experiment and published literature. The influence of manufacturing errors including roundness, convexity, concavity and tapers on the dynamic performance of the rotor system is investigated comprehensively. The results show that the types and amplitude of manufacturing errors have complex effects on dynamic performance. Roundness with spatial numbers of 3 to 6, concavity and taper1 errors decrease the error motion amplitude, while convexity and taper2 errors increase it. Especially, roundness errors with spatial numbers of 1 and 2 notably increase the error motion amplitude, which should be avoided strictly.

Dynamics modelling and influencing factor analysis of a rocket-launcher coupling system considering uncertain parameters

Vibration characteristic is an important factor affecting the motion of rocket in the launcher and its firing performance. In this paper, a rocket-launcher coupling dynamics model is proposed by applying the transfer matrix method for multibody systems. Considering manufacturing error and nonlinear contact force, the dynamics equations of the rocket-launcher coupling system during the whole process of firing are deduced. Combined with the dynamics model and equations, a dynamics simulation system is developed with uncertain parameters. The uncertain parameter description scheme and probability sampling scheme are proposed to obtain dynamics characteristic and firing performance of the system. The relevant tests are carried out to verify simulation results. Then, the factors affecting the firing performance are discussed. In view of the analysis results, the influence weight of initial disturbance on firing precision is 85% under the condition of full-loading continuous firing, and the swing angular velocity of rocket at muzzle is the main influence factor.

Development of a constraint stabilization method of multibody systems based on fuzzy logic control

The numerical solution of multibody systems is not a straightforward problem. The formulation of the equations of motion is augmented with the constraint equations that lead to a set of differential algebraic equations (DAEs). These constraints govern the relative motion between the system’s components at the position level (geometric constraints) and may restrict the velocity of particular components (rolling constraints). There are several factors that determine the effectiveness of numerical integration methods and the extent of their applicability owing to the various motion circumstances. These factors include numerical stability throughout the integration and computation time, as well as allowable error percentage and the length of simulation time. In this regard, this research examines existing approaches for constraint stabilization during numerical integration and introduces a new methodology based on fuzzy control algorithm, whose coefficients are independent of the dynamic characteristics of different systems. Schematics of the new methodology are presented; two examples of spatial multibody systems with holonomic and nonholonomic constraints are solved to evaluate the effectiveness of the proposed method. It can be concluded that fuzzy control contributes an excellent solution for generic system configuration and is suitable for lengthy simulations with minimal computation time.

Vibration Modeling and Analysis of a Flexible 3-PRR Planar Parallel Manipulator Based on Transfer Matrix Method for Multibody System

This paper presents the vibration model of a 3-prismatic–revolute–revolute (PRR) planar parallel manipulator (PPM) with three flexible intermedia links, utilizing the linear transfer matrix method for multibody systems (MSTMM). The dynamic characteristics of the PRR PPM are also investigated. The dynamic model of the 3-PRR PPM is derived, and the transfer matrix and transfer equation of each component in the system, as well as the overall transfer equation and transfer matrix of the system are obtained. The vibration characteristics of the whole system are determined using the MSTMM and verified through ANSYS simulation. Furthermore, the relationship between the natural frequencies and the flexible PPM configurations is analyzed under a specific circular trajectory. The results demonstrate that the natural frequency of the system changes constantly with the configurations, and the trends of the first six orders are similar. This novel modeling approach does not require global dynamic equations and is both efficient and accurate. Moreover, it can be easily extended to other parallel manipulators with flexible components.

On shift selection for Krylov subspace based model order reduction

Mechanical systems are often modeled with the multibody system method or the finite element method and numerically described with systems of differential equations. Increasing demands on detail and the resulting high complexity of these systems make the use of model order reduction inevitable. Frequently, moment matching based on Krylov subspaces is used for the reduction. There, the transfer functions of the full system and of the reduced system are matched at distinct frequency shifts. The selection of these shifts, however, is not trivial. In this contribution we suggest an algorithm that evaluates an increasing number of shifts iteratively until a reduced model that approximates the full model in a subspace with very low approximation error is found. Thereafter, the projection matrix that spans this subspace is decomposed with singular value decomposition and only most important directions are retained. In this way, small reduced models with good approximation properties that do not exceed a predefined error bound can be found or low-error models for a given reduced order can be generated. The evaluation of more shifts than necessary and further reduction by means of singular value decomposition is the novelty of this contribution. In this paper, this novel approach is extensively studied and, furthermore, applied to the numerical example of an industrial helicopter model.

Parameter identification method for multibody systems incorporating the adjoint method and feature extraction based on the proper orthogonal decomposition

Parameter identification method for multibody systems incorporating the adjoint method and feature extraction based on the proper orthogonal decomposition

Generation mechanism and control of high‐frequency vibration for tracked vehicles

AbstractA crawler system provides much larger ground contact, leading to excellent terrain adaptability. Due to its structural characteristics, high‐frequency vibration proportional to the vehicle speed is generated during the driving process. This is a result of the polygon and rolling effects between the track and the wheels. A field test of a tracked vehicle is performed to monitor movement signals of the chassis and a rocker arm. Their corresponding power spectral density distributions confirm the correctness of the frequency‐calculation equation. Then, a novel elastic track tensioning device with a damper is designed as a cushion between the idler and the chassis. Depending on its geometry, the equivalent damping coefficient for a dynamic model is evaluated. Subsequently, the damping is altered in response to different operating conditions by a hybrid damping fuzzy semiactive control system. The controller accounts for both chassis and track vibration. Based on the transfer matrix method for multibody systems, a dynamical model of the track system is developed. Control performances are evaluated using two numerical simulations of obstacle crossing and off‐road driving operations. Results indicate that the proposed semiactive tensioner is substantially better than the conventional one. This paper provides a novel feasible scheme for vibration reduction of tracked vehicles.

Sensitivity analysis method for frequency response function based on extended transfer matrix method for linear multibody systems

The sensitivity analysis for frequency response function is of great importance in the areas of system identification, model updating, dynamic optimization, vibration control and structural damage detection, et al. In allusion to the problems resulting from the prohibitive computational cost using the direct method and the modal truncated errors using the modal superposition method, a novel sensitivity analysis method for frequency response function based on the extended transfer matrix method for linear multibody systems is proposed. The sensitivity transfer equations of elements and system are established utilizing the direct differentiation method, from which the frequency response function sensitivity can be accordingly obtained. The results are also used to the sensitivity analysis for random vibration response. The proposed strategy is analytically and numerically validated by examples, indicating that it not only inherits the advantages of transfer matrix method for multibody systems that the system global dynamics equations are not needed, the system matrix order is low, the solution procedure is highly stylized, and the computational speed is high, but also achieves accurate computation of frequency response function sensitivity without modal truncation and the assumption of proportional damping.

Dynamics control for complex mechanical systems with nonlinear actuators using the transfer matrix method for linear multibody systems

Smart actuators, such as magnetorheological dampers, piezoelectric actuators et al., are increasingly being explored for various nano-positioning and vibration control applications. However, those actuators reduce control performance due to the existence of inherent hysteresis nonlinearities between the input and the output. The nonlinearities may cause undesirable inaccuracies, oscillations, poor control performance even leading to instabilities of the closed-loop system. In order to accurately model complex mechanical systems with such nonlinear actuators, a comprehensive mathematical model, which uses the transfer matrix method for linear multibody systems (linear MSTMM) to model the linear dynamics properties and the hysteresis model to describe the hysteresis nonlinearities, is presented. And then a hysteresis observer based on the hysteresis model is established to compensate the hysteresis nonlinearity of actuators. Then, a hybrid controller combining the proposed linearization and PID control for complex mechanical systems based on the comprehensive model is proposed and explored. The experimental results show that the proposed hybrid control method can achieve precise control of the complex mechanical systems with nonlinear actuators.

Analysis of submarine mast vibration response by transfer matrix method for multibody systems

The submarine mast will bend and vibrate under the impact of the current, and the serious vibration will affect the mast performance and even damage the mast. Therefore, the dynamic characteristics of submarine masts are critical in their design. In this paper, the multi-supported mast of a submarine is modeled using transfer matrix method for multibody systems (MSTMM). The element transfer equations are derived for rigid body sheet, spring, beam and rigid body sheet coupled spring, respectively. Considering the rigid body sheet and spring as one element or two independent elements, two modeling ways are proposed, and the system overall transfer equation is deduced separately. The modal superposition method is used to calculate the forced vibration response by establishing the body dynamic equations and augmented eigenvectors. Without deducing system global dynamics equation and with simplicity, efficiency and versatility. Two numerical examples are used to demonstrate MSTMM's modeling flexibility. It provided a theoretical basis for the structural analysis and optimization design of the submarine mast.

Modified reduced transfer equations for linear multibody system dynamics

The transfer matrix method for multibody systems (MSTMM) has been extensively applied in various engineering practices, pursuing a high computational efficiency. Partitioning the state vector of each connecting point into two complementary reduced state vectors and relating them by a point-wise linear formulation leads to a reduced form of the MSTMM. In this way, sequential multiplications of the transfer matrices of the components will be avoided, and the numerical stability of the MSTMM gets better. According to existing manners, the original transfer matrices of all the body components should be obtained first in the context of the reduced MSTMM. Modified reduced transfer equations for linear multibody systems independent from the original transfer equations are proposed in this paper to eliminate useless operations relating to zero operands in the transfer matrices and consistence matrices for multi-input body components. The modified reduced transfer equations for linear multibody systems is verified by comparing the computational results with those obtained by using the original reduced transfer equations as well as finite element method.

Sensitivity analysis of multiple launch rocket system based on the response surface method

With the advantages of fast firing speed, sudden and fierce firepower, low cost, strong mobility and quick response, multiple launch rocket system (MLRS) has become one of the main weapons in modern war. The optimization design is an important method to improve the performance of MLRS, and the sensitivity analysis of MLRS dynamics is an important way to improve the efficiency of optimization design. With the linear transfer matrix method for multibody systems (the linear MSTMM), the launch dynamics response of MLRS was simulated. The modeling and simulation results were validated by the test results. Due to the collision between the rocket and the launch tube, the response simulation is not differentiable. Analytic method for sensitivity analysis, such as the direct differentiation method, can not be used directly. The responce surface method is a combination of mathematical method and statistical method. Its basis idea is establishing an agent function to replace the orignal objective function for fast calculation. Based on the responce surface method, an agent function of initial disturbance of MLRS were established, and the agent function were validated by the test group data. By differentiation of the agent function, the sensitivity analysis results of initial disturbance of MLRS were obtained. The proposed method is easy to implement for engineering. The main factors affecting the initial disturbance of MLRS are pointed out. This paper provides theorectical basis and technical support for the design, development, and improvement of firing density of MLRS.

Calculation and analysis of vibration characteristics of IMU isolation system with MRE isolators

To improve the dynamical test accuracy of an inertial measurement unit (IMU), the magnetorheological elastomer (MRE) isolators were applied to suppress its vibration. In this paper, the dynamics model of a laser gyro strapdown IMU was developed based on the Riccati transfer matrix method for multibody systems. Combining with different control algorithms, the acceleration of the IMU shell was taken as the control object and the vibration characteristics of system was calculated and analysed. By comparing the root mean square values of the IMU components, it predicts that the effect of vibration reduction by adding control is better than that by passive control. Moreover, different control methods are suitable for different excitations.

Research on vehicle engine dynamics simulation based on transfer matrix method for multibody systems

The engine is the core component of a vehicle, its dynamical characteristics are directly related to the performance of the vehicle. In order to simulate the dynamical characteristics, engine can be modelled as a shell and a crank-connecting rodpiston mechanism. Transfer matrix method for multibody systems is used to deduce the mathematical equations and develop the simulation program code. The time history curves of displacement, velocity and acceleration of the engine mechanism are plotted. Compared with the results by the ADAMS software, the agreeable datum show that this method can accurately calculate the motion characteristics of the engine. It provides a reference for the optimal design of various engines.

Research on dynamics software of transfer matrix method for multibody systems

The general and fast programmed dynamics modeling, computation and design method of complex mechanical multibody system have become the theoretical and technical problems that must be solved in the development of modern industry. The transfer matrix method for multibody systems (MSTMM) has become a powerful tool for dynamics modeling and simulation of multibody systems by virtue of its flexible modeling, such as no need for global dynamics equation, low matrix order, fast computational speed, automatic derivation of overall transfer equation and high degree of programming. In order to apply MSTMM to practical engineering problems quickly, the MSTMM is taken as the core theory of dynamics modeling and computation, and the visualization dynamics software of MSTMM is established by combining OpenCascade, Qt and other open source software. The software realizes the automatic derivation of the overall transfer equation and the fast computation of system dynamics. The engineering example of a tracked vehicle verifies the effectiveness of the software.

Dynamic analysis of flexible pendulums based on modal neutral file and Riccati transfer matrix method for multibody systems

The Modal Neutral File (MNF) is a binary file used to transfer the information of a flexible body from the finite element software to ADAMS, which contains wealthy information of flexible body. The flexible pendulums is composed of the flexible beams with large motion and small deformation and pin hinges. In this paper, the finite element information of the beam is obtained by analyzing the Modal Neutral File of the beam. The floating frame method and the modal synthesis method are used to study the flexible beam with large motion and small deformation. The Riccati transfer equations of the flexible beam with large motion and small deformation and the pin hinge moving in space are derived according to the kinematic equations and the dynamics equations. The flexible pendulums with three bodies are numerically simulated by using the transfer equations and the results are compared and verified with results of ADAMS software.

Vibration characteristics analysis of the complex structure system based on the transfer matrix method for multibody system

In order to meet the particular environment and requirements of launch, the model and vibration characteristics of a complex launch structure system need to be analyzed. In this paper, the complex structure system is regarded as a multi-rigid-flexiblebody system using the transfer matrix method for multibody systems (MSTMM). By establishing the transfer relationship between various components, the overall transfer matrix and overall transfer equation of this system are obtained, and then the natural frequencies are computed. Compared with the finite element computed results, the effectiveness of the model is verified. By putting the transient load on the bottom of a cylinder during the projectile moving, the dynamics responses of the cylinder under a single fire are yielded, which provides influential research means for dynamics model and vibration characteristic analysis of the complex structure system.