Integrated Motional Measurement for a Flexible Structure

Integrated navigation systems based on gyros and accelerometers are well established devices for vehicle guidance. The system design is traditionally based on the assumption that the vehicle is a rigid body. However, generalizing such integrated systems to flexible structures is possible. The example of the motion of a simple beam being considered here is meant to be a first approach to obtain sophisticated motional measurements of a wing of a large airplane during flight. The principle of integrated navigation systems consists of combining different measuring methods by using their specific advantages. Gyros and accelerometers are used to obtain reliable signals within a short period of time. On the other hand, aiding sensors like radar units and strain gauges are used because of their long-term accuracy. The kernel of the integrated system consists, however, of an extended Kalman filter that estimates the motion state of the structure. Besides the sensor signals, the basis for the filter is an additional kinematical model of the structure. By means of a model reduction, a kinematical model of the beam was developed. Based on simulation the paper presents this approach, the appropriate sensor set, and first estimated motion results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integrated motion measurement of rigid multibody systems

During the last years, integrated navigation systems based on gyros, accelerometers, and GPS receivers became powerful devices for the guidance of aircraft and ships. Comparable equipment using especially wheel sensors exists for cars. The kernel of such systems is a Kalman filter estimating the relevant vehicle motion. The filter design in turn requires a kinematical model to settle on the motion components considered and to describe the mechanical meaning of the measurements employed. Until now, usual models consider only one to six degrees of freedom of a single rigid body. The assumption of a solitary rigid body is not a consequence of the basic concept of integrated navigation; it reflects merely classical navigation requirements. In principle, determining the motion of multibody systems, representing certain vehicle types of varying shape, is possible if appropriate kinematical models and sensor arrangements are available. Based on the theory of integrated navigation systems, the paper outlines the fundamentals of designing integrated motion measurement systems for rigid multibody structures. The example of a double pendulum with a movable inertial support and with equipment of microelectromechanical inertial sensors and of small radar units illustrates this approach. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An elastic beam approach to predictive vehicle motion planning

Vehicle guidance systems are among the latest automotive developments. Examples are A daptive C ruise C ontrol (ACC), lane departure warning and active lane keeping. However, the rapid development of environmental sensor systems such as radar, lidar and video technologies in combination with data fusion of the single sensor signals enables further applications as for example lane changing assistance, collision avoidance or even autonomous driving. For all of these functions, trajectories have to be planned and, depending on the application, to be communicated to the driver. Recently, methods originally developed in robotics as for example so-called elastic bands are adapted for road vehicle applications. Here an virtual elastic beam is proposed to guide the vehicle. The beam is deflected by virtual potential fields generated by obstacles in the traffic space. In doing so, the elastic beam avoids obstacles and provides collision-free trajectories, while its bending stiffness counteracts the curvature of the trajectory. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of three-dimensional mechanical systems using point coordinates with a recursive approach

In this paper, the dynamic simulation of constrained mechanical systems that are interconnected of rigid bodies is studied using projection recursive algorithm. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. Closed-chain system is transformed to open-chain by cutting suitable kinematical joints and introducing cut-joint constraints. For the resulting open-chain system, the equations of motion are generated recursively along the serial chains. An example is chosen to demonstrate the generality and simplicity of the developed formulation.     

Design of continuous strain-type sensors for systems of structural mechanics

In this paper, we present a general approach for designing continuous strain-type sensors to measure specific kinematical entities in systems of structural mechanics. We first discuss the case of three-dimensional bodies in the geometrically linear regime, for which the solution of the sensor design problem is found from a problem-oriented application of a work-based integral formulation to an auxiliary problem of statics; yet, the resulting sensor works for static and dynamic problems. The deduction of solutions for the sensor design problem on a structural mechanics level is straightforward, because the three-dimensional solution is work-based. Hence, for any theory of structural mechanics, for which a corresponding work-based integral formulation exists, we can easily find a solution of the sensor design problem. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

线性主动结构及模态(Ⅱ)——离散系统及梁

在“线性主动结构及模态(Ⅰ)”中给出了主动结构的基本概念及模态的若干属性的基础上,对主动离散系统及主动梁的属性做了进一步的讨论,包括稳定性和正交性,并用具体实例对模态做了解释．将伴随结构概念在梁结构中推广,具体讨论了两种配置的主动梁,它们分别代表离散传感和作动及分布传感和作动的配置,并给出了用主动梁振型和伴随主动梁振型表示的正交性条件．用实例给出了同位和非同位主动刚度梁的特征值随反馈大小的变化．     

The tangent stiffness matrix in rigid multibody vehicle dynamics

In the development of the equations of motion of a rigid multibody system, particularly vehicles, it is quite common to linearize the equations after they are derived, or even to ignore the non-linear terms from the outset. When doing so, the tangent stiffness matrix, i.e., the stiffness term that results from preload of the system rather than physical flexibility, is often ignored. The motion analysis of preloaded mechanical systems, e.g., the ride quality analysis of vehicle suspensions, may be significantly altered by this omission. Explicit expressions for the tangent stiffness matrix for a few of the common constraint types, including the revolute joint and the rolling wheel, are derived in this article. These expressions are coded into software and included in an open-source linear equation of motion generator for rigid multibody systems. A sample automotive suspension system is analysed, comparing the results with and without the tangent stiffness matrix effects; additionally, a benchmark solution is developed using a commercial multibody dynamics code. The results provide confirmation of the significance of the tangent stiffness effect on motion analysis and correlate well with non-linear transient solutions.     

基于模糊传感器的机器人动态障碍环境中的运动控制

对自主式机械手在动态和部分已知且存在运动障碍环境中的运动规划和控制进行了研究,解决了自由碰撞运动控制中具有普遍意义的问题。利用人工势能场的机器人导航控制技术由模糊控制实现,系统的稳定性由李雅普诺夫原理保证。模糊控制器为机器人伺服提供控制指令,使机器人在不可预知的环境中能实时地、自主地选择到达目标的路径和方向。在动态环境的实时控制中,基于传感器的运动控制是处理未知模型和障碍物的重要控制方式。     

A linear model for the static and dynamic analysis of non-homogeneous curved beams

A simple one-dimensional mechanical model is presented to analyse the static and dynamic feature of non-homogeneous curved beams and closed rings. Each cross-section is assumed to be symmetrical and the “resultant loads” are acted in the plane of symmetry. The internal forces in a cross-section are replaced by an equivalent force–couple system at the origin of the cylindrical coordinate system used. The equations of motion and the boundary conditions are expressed in terms of two kinematical variables. The first kinematical variable is the radial displacement of cross-sections and the second one is the rotation of the cross-sections. Each of them depends on the time and the polar angle. Assumed form of the displacement field assures the fulfillment of the classical Bernoulli–Euler beam theory. Rotary inertia is included in the equations of motion. Natural frequencies for simply supported laminated composite curved beams and non-homogeneous circular rings are obtained by exact solutions. The application of the model presented is illustrated by examples.     

弹性振动的闭环系统

细长体的飞行器在飞行中考虑了既有刚性运动又有弹性振动的运动,由于刚性运动对弹性振动的影响,通过安装在飞行器上面的仪表所测得的角速度作为反馈信号输入到控制器,由控制器输出端输出信号到执行机构来实现反馈控制,把刚性运动飞行器、弹性振动飞行器同时考虑作受控对象,这里我们研究了由刚性飞行器、弹性飞行器和控制器三者形成的闭环系统的弹性振动问题,得到了求闭环系统的频率和振型的公式,设计控制器使得闭环系统渐近稳定的条件和能控性、能观测性的条件。     

Unknown nonlinear chaotic gyros synchronization using adaptive fuzzy sliding mode control with unknown dead-zone input

In this paper, the problem of synchronizing two chaotic gyros in the presence of uncertainties, external disturbances and dead-zone nonlinearity in the control input is studied while the structure of the gyros, parameters of the dead-zone and the bounds of uncertainties and external disturbances are unknown. The dead-zone nonlinearity in the control input might cause the perturbed chaotic system to show unpredictable behavior. This is due to the high sensitivity of these systems to small changes in their parameters. Thereby, the effect of these issues should not be ignored in the control design for these systems. In order to eliminate the effects from the dead-zone nonlinearity, in this paper, a robust adaptive fuzzy sliding mode control scheme is proposed to overcome the synchronization problem for a class of unknown nonlinear chaotic gyros. The main contribution of our paper in comparison with other works that attempt to solve the problem of dead-zone in the synchronization of chaotic gyros is that we assume that the structure of the system, uncertainties, external disturbances, and dead-zone are fully unknown. Simulation results are provided to illustrate the effectiveness of the proposed method.     

Mechanical oscillators described by a system of differential-algebraic equations

The classical framework for studying the equations governing the motion of lumped parameter systems presumes one can provide expressions for the forces in terms of kinematical quantities for the individual constituents. This is not possible for a very large class of problems where one can only provide implicit relations between the forces and the kinematical quantities. In certain special cases, one can provide non-invertible expressions for a kinematical quantity in terms of the force, which then reduces the problem to a system of differential-algebraic equations.     

Vibro-acoustic method for estimating a liquid level and viscosity

The goal of this work has been to examine a possibility to measure a liquid level and its viscosity by the vibro-acoustic methods. Preliminary laboratory investigations were completed on a glass vessel filled with solutions of various viscosity and level, excited by a hammer. A microphone and four accelerometers were used as sensors. Few criteria symptoms were checked. For the level and viscosity estimation there were used the placement and values of the Fourier's spectra maximum of the acoustic signal, and of the vibration signals from sensors. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamics of a two-layer beam with layer slip

A possible type of structural damping in mechanical systems when there is a distinct dependence of the oscillation decrement on the amplitude is investigated, using the example of the solution of a model problem on the oscillations of a two-layer beam. It is assumed that layer slip only occurs along the beam axis and that the layers together in the transverse direction. The interaction between the layers is of an elastic-friction form. The equations of motion of the beam in Timoshenko's form are numerically integrated using Godunov's difference scheme.     

Piezoelectric control of flexible vibrations in rotating beams: An experimental study

Active control of flexible vibrations by distributed piezoelectric actuators and sensors plays an increasing role in engineering, especially in light-weight structures. Exemplarily, in this contribution a rotating beam is studied which can be found in many practical applications, e.g. as robot arms or flexible manipulators in production processes. It has been intensively shown in the literature that it is possible to completely suppress the flexible vibrations by an appropriate distribution of piezoelectric actuation strains. In order to compensate the inertial forces in the considered rotating beam, a complex distribution is obtained, such that a practical realisation would be very extensive. To overcome the problem, a discrete approximation by piezoelectric patches is applied. In order to find an optimal configuration for an experimental setup, and to investigate several control strategies, a numerical simulation model has been implemented based on Bernoulli-Euler beam theory. The numerical results are verified by an experimental set-up, in which 48 piezoelectric patches have been attached on a beam with rectangular hollow cross-section. Each patch can be used either as an actuator or a sensor. Additionally, strain gauges can be used as sensors. For monitoring, acceleration sensors are used. The control system is implemented within a dSpace environment. The results show a significant reduction of the flexible vibrations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An approach to benchmarking of loosely coupled low-cost navigation systems

New solutions to the navigation problem related to low-cost integrated navigation systems (INS) are often published. Since these new solutions are generally compared with ad hoc mathematical models that are not fully exposed, one cannot be sure of the relative improvements. In this work, complete mathematical model for a low-cost INS is suggested to be used as a benchmarking. As far as the authors’ knowledge, a benchmarking for low-cost INS has not been previously reported. Shown INS comprises a strapdown inertial navigation system, loosely coupled to a GPS receiver. The INS mathematical model is based upon classical navigation equations and classical sensor models, both from recognized authors. The algorithm that details the INS operation is also presented. The benchmarking is provided as an open-source toolbox for MATLAB. Additionally, this work can be taken as a starting point for new practitioners in the INS field. To validate the INS mathematical model, real-world data sets from three different Micro Electro-Mechanical Systems (MEMS) inertial measurement units (IMU) and a GPS receiver are processed. It is observed that obtained RMS errors from the three INS are coherent with the quality of corresponding MEMS IMU. This confirms that the proposed benchmarking is a suitable tool to evaluate objectively new solutions to low-cost INS.     

Novel three-piston pump design for a slipper test rig

Slipper's micro motions including the squeezing motion, spinning motion, and tilting motion have a significant impact on its lubricating condition and dynamic behavior. However, few experimental studies are on these micro motions within a real axial piston pump, especially the slipper's spinning motion. The experimental investigations on the slipper in the past mainly focused on the parameters of the oil film such as pressure, thickness, and temperature. The sensors were often installed in the fixed swash plate when the cylinder block was chosen to rotate. Alternatively, the sensors were mounted in the fixed modified slipper when the swash plate rotated. The biggest challenge of the direct measurements of these micro motions is the space limitation for the sensor installation due to the compact structure of axial piston pumps as well as the slipper's macro motion. This paper presents a new three-piston pump for the slipper test rig which can provide enough installation space for the sensor. To realize the cylinder block balance, a hold-down plate is first introduced into this three-piston pump. In addition, a detailed set of relevant equations is derived to evaluate the functionality of the hold-down plate. Finally, the slipper's spinning motion was measured directly and continuously using this three-piston pump, which confirmed the capability of the slipper test rig.     

Use of the elastic-and-rigid-combined beam element for dynamic analysis of a two-dimensional frame with arbitrarily distributed rigid beam segments

This paper presents an elastic-and-rigid-combined beam element such that the dynamic characteristics of a hybrid beam and a two-dimensional frame composed of any number of elastic and rigid beam segments can be easily determined. First of all, the displacements for the two nodes of a rigid beam segment are determined in terms of the displacements of its centre of gravity (c.g.). Next, the mass and stiffness matrices for the elastic-and-rigid-combined beam element are derived using the above-mentioned nodal displacements of the rigid beam segment and those of the two adjacent elastic beam elements. Furthermore, for the transformation of state variables of last elastic-and-rigid-combined (or three-node) beam element between the local and global co-ordinate systems, a new transformation matrix is also presented. Finally, the overall property matrices of the entire vibrating system are determined with the conventional assembly technique of finite element method (FEM) and its natural frequencies and associated mode shapes are determined with the standard approach. Some important factors, such as length of rigid beam segment, position for the centre of gravity (c.g.) of rigid beam segment, and total number of rigid beam segments in the entire vibrating system, are investigated. Numerical results reveal that the above-mentioned parameters have significant influence on the dynamic characteristics of the structure with arbitrarily distributed rigid beam segments.     

Planar motion and stability for a rigid body with a beam in a field of central gravitational force

Planar motion for a rigid body with an elastic beam in a field of central gravitational force was investigated, and both of the orbital motion and attitude motion were under consideration. The equations of motion of the system were derived by the variational principle, and on view point of generalized Hamiltonian dynamics, the sufficient conditions for the stability of one class of relative equilibria were given by the energymomentum method.     

The variability of dynamic responses of beams resting on elastic foundation subjected to vehicle with random system parameters

This paper investigates the variability of dynamic responses of a beam resting on an elastic foundation, which is subjected to a vehicle with uncertain parameters, such as random mass, stiffness, damping of the vehicle and random fields of mass density, and the elastic modulus of the beam and stiffness of elastic foundation. The vehicle is modeled as a two-degree-of-freedom spring-damper-mass system. The equations of motion of the beam was constructed using a finite element method. The mass and elastic properties of the beam, and the stiffness of foundation are assumed to be Gaussian random fields and were simulated by the spectral represent method. Masses, stiffness of the spring, and the damping coefficient of the vehicle are assumed as Gaussian random variables. The numerical analyses were performed using the finite element method (FEM) in conjunction with the Monte Carlo simulation (MCS). The variability of dynamic responses of the beam were investigated with various cases of random parameters. For each sample, the equations of motions were solved with the Wilson-q integral method to find dynamic responses. The influence of random system parameters and their correlation on the response variability is discussed in detail.