Deployment analysis of large space antenna using flexible multibody dynamics simulation

A technique is introduced for the kinematic synthesis of deployable cable-stiffened truss structures. This technique, which is an extension of a prior procedure [l-21 for generating deployable truss structures, can be applied to generate all concepts of cable-stiffened truss structures as well as all their deployable derivatives. Examples illustrating the implementation of this new technique, along with a discussion of the results achieved. are included in this article. The primary function of a deployable structure is to maintain a stable configuration in its deployed state. This is reflected in current design practices of trading off decreased deployment or retraction performance for increased structural performance. As a result, various designs of deployable truss structures (with, and without cables) have been introduced that are over-constrained during deployment/retraction, i.e. deployment/retraction of these structures can only be achieved through the deformation of individual links or by exploiting symmetric features of the structure. The number of different conceptual designs of deployable structures that are based on a given structural configuration is unlimited, if deployable structures are permitted to be overconstrained during deploymenthetraction. For this reason, researchers in the area of deployable structures have given little attention to the systematic design of deployable truss structures and have instead devoted much of their attention to the introduction and discussion of novel concepts of deployable truss structures [3-171. If, on the other hand, it is assumed that the primary function of a deployable structure is to serve as a mechanism with a minimum number (i.e. at least one) of degrees-of-freedom, then the number of different conceptual designs that are based on a given structural configuration is finite. Hence, it is then possible to generate all possible designs for a given structural configuration. The assumption that a deployable structure is not constrained during deployment/retraction has enabled the development of a technique for the generation of all conceptual designs of deployable truss structures that can be used as building blocks (modules) of much larger structures [I-21. It should be noted that this technique, referred to as kinematic synthesis of * Sr. Mechanical Engineer, Member AIAA deployable structures, does not assume that the structural configuration is known but instead uses the characteristics of a given class of structures (i.e. truss modules) to generate all possible configurations of structures in this class. The limitation of this technique to truss modules has been avoided in the Explosion-Implosion technique [19], developed by the same authors, for the generation of allconceptual designs of deployable truss structures of which the locations of the nodes are known. Both techniques have been shown to result in the generation of an enormous, yet finite, number of novel conceptual designs as well as those that have been reported in the literature. Furthermore, by limiting the degrees-of-freedom available at individual joints, conceptual designs can be generated of deployable structures that are overconstrained during deployment/retraction. Although the kinematic synthesis technique and the explosionimplosion technique result in the generation of an enormous number of conceptual designs of deployable truss structures, they are not applicable to truss structures with cables. Yet, cable-stiffened truss structures have important advantages such as the reduction in mass and/or reduction in joints that can be achieved by replacing links in truss structures with cables. The objective of this article is to modify the technique introduced in [I-21 such that the new technique is also applicable to cablestiffened truss structures. This new approach can then be applied to generate novel concepts of deployablecable-stiffened truss structures as well as those that have been reported in the literature.

There has been increasing demand for larger space structures to satisfy the requirements of astrophysics missions. However, storage space for payloads in satellites is limited, so deployable structures are used in most space missions to minimize storage space and consequently, to reduce launch costs. This work proposes a deployable truss structure which can improve the packaging efficiency of the existing truss structure. The main feature of the proposed structure is that it can be stored in a flat form. Each unit consists of Scissor-like Elements (SLEs) and the whole structure is deployed in a three-dimensional form with a simple mechanism. The detailed configurations and mechanism of the proposed structure are discussed. The geometric constraints for folding the proposed structure into a planar form were analyzed. A kinematic analysis to describe the motion of the structure was also performed. Then the packaging efficiency with respect to length, which is an important performance index of such deployable structures, was analyzed and compared with a typical truss structure.

The inter-connectivity and type selection of joints in a mechanism can be represented by a graph. In this article a technique is presented for the generation of such a graph for a (spatial) deployable truss structure. First a fundamental graph is constructed which reveals all possible joint connections in a deployable structure. This graph, which can be derived from the geometry of a deployable structure, is then reduced to the graph of the kinematic structure (revealing the joint inter-connectivity) by applying a set of rules. The process of joint specification is completed by assigning joint types to edges in the graph such that the required mobility of the deployable structure it represents is ensured. Procedures are provided that incorperate the techniques introduced in this article and which can be used to generate all possible joint assignments for a given deployable structure.

The representation and manipulation of finite rotations and the modelling of flexible bodies are at the heart of flexible multi-body systems dynamics simulations. When dealing with finite element formulations, the interpolation of finite-rotation fields becomes a critical issue. Objectivity, i.e. the invariance of interpolated strain fields to the addition of a rigid body motion, has been an important problem. Furthermore, the manipulation of finite rotations and the unavoidable associated singularities must be dealt in a rational manner. The various approaches to these two problems are reviewed in this article. Simple algorithms that achieve objectivity are proposed. Furthermore, these algorithms can deal with finite rotations of arbitrary large magnitude through a simple rescaling operation. The choice of unknowns, total versus incremental, is also discussed as it affects the performance of the computational process. Numerical examples are presented, which demonstrate the ability of the proposed approach to handle finite rotations of arbitrary magnitudes in complex, flexible multi-body systems.

Vibration isolation and precision pointing control will be essential to the success of future space science missions such as Next Generation Space Telescope (NGST). This research investigated the use of actively controlled piezoelectric stack actuators to reduce the transmission of mechanical disturbances to the optics and to coarsely point the telescope. Initial actuator requirements were based on approximate expected motions on the spacecraft side (due to unbalanced reaction wheel assemblies), the structural dynamic properties of the flexible, deployable truss structure that supports the active optics, and the allowable motions on the telescope side. Piezoelectric actuator design was based on flextensional motion amplification, with sizing details determined using results from finite element analysis. A compressive pre-load was maintained on the fragile piezoceramic stacks via a mechanical interference (center block) fit into the actuator frame. Device performance characteristics, including blocked force, passive stiffness, free displacement, motion amplification factor, natural vibration frequencies, and electromechanical coupling coefficient were determined numerically and experimentally, with good agreement. An initial controlled isolation test of the entire system reduced the transmissibility by more than 80% over the frequency range from 4-20 Hz. Finally, an active isolation system with dual sensor feedback was implemented and shown to successfully reduce telescope motion by a factor of 10 (from 4-40 Hz) and to provide lower-frequency pointing capability. Introduction As space systems continue to grow in complexity and require greater precision, piezoelectric materials will be investigated for an increasing number of actuator applications, including precision pointing and vibration isolation and control. There are several approaches to vibration isolation, which have been successful in the past. Vibration isolation can be achieved through passive or active techniques or a combination of the two. The chosen method of isolation depends primarily on the application and requirements of the system. Precision pointing, on the other hand, is achieved solely by active control systems, which combine the necessary structural and mechanical components with a control design. Pointing systems are primarily limited by the quality of the mechanical system as well as the drive system, which is actuating movement. The structure (holding the pay load) to be controlled can be a rigid body, quasi-static flexible body, or a dynamic flexible body. With the classical arrangements of sensors and actuators in these control systems, only the rigid body configuration is commonly controlled. NGST (Next Generation Space Telescope) is the successor to the Hubble Space Telescope (HST) mission. NGST is a deployable 8-meter diameter truss structure holding the telescope and instruments such as cameras and spectrometers that are required by the scientific goals of the mission. In order to meet the scientific goals or projects such as the Origins of Galaxies studies [Mather, et al] along with independent science projects dealing with current scientific interests, positioning the optics and minimizing vibratory loads are very important. Positioning control for the HST was done as a rigid structure pointed as a unit to a precision of a small fraction of an arcsecond, but NGST is a dynamic flexible structure with sub-micron positioning performance. For NGST, the isolation system is to be used to reduce the ultrafine pointing requirements on the fine pointing system (fast steering mirror and adjusters distributed across the mirror) by as much as 1 2 orders of magnitude. This isolation system is aimed to reduce the estimated 30-nm peak disturbances at the mast to 6-nm or less in a range of 4 4 0 Hz, with most concern on the 15 20 Hz region. By substantially reducing these axial disturbances, the dynamic, wavefront error correction requirements will also be reduced, and the fine pointing system will have less of a burden. In order to achieve these requirements, piezoelectric stack actuators are ideal because they can provide sufficiently high output forces with large bandwidths. Individually, piezoelectric stack displacements are extremely small, on the order of approximately 2000 jiie; therefore, multiple stacks can be used in series to produce the desired output. In addition to this, mechanical amplification devices can be used to increase actuation displacement by reducing the actuation force. Compliant mechanisms, flexurehinged mechanisms and flextensional mechanisms Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. are commonly used for motion amplification, depending on the application. The flextensional actuator used in this research is shown in Figure I and consists of four stacks of piezoceramics connected in parallel to a flextensional mechanism that amplifies and converts the output

Assessing a glove for its ability to reduce vibration transmitted to the hand can be improved if the transmissibility of the glove to the hand can be predicted. This study proposes a simple lumped parameter model of the hand and the glove for predicting the transmissibility of a glove to the hand. The model of the hand consists of three main body segments: the palm, the fingers, and the palm tissues, connected via translational and rotational springs and dampers. The glove material was represented by translational spring and damper. The results showed that the glove transmissibility predicted using the model overestimated the glove transmissibility measured experimentally at frequencies greater than 62 Hz, implying that a simple three degree-of-freedom model of the hand and the glove may not be able to provide a reasonable prediction of glove transmissibility.

In this paper, the dynamic behaviors of a elastic rod connected by a joint with clearance of deployable truss structures are investigated. A one-dimensional cantilever with joint support is examined in the deployable truss structure. These formulations consist of the nonlinear joint dynamic stiffness model and damping models are formulated and the dynamic characteristics of free-vibrating structures are estimated. The natural frequency transitions are investigated by considering the contact and noncontact conditions of the clearances, then the formulation of dynamic stiffness model is obtained. The friction models are mathematically formulated and simplified to make them easy to calculate. The impact damping models are formulated using the linear envelope of the time response and it can be negligible when the speed is small. The dynamic characteristics can be estimated by integrating these models and formulations using the energy loss factors. Experimental evaluations show the dynamic characteristics and demonstrate the validity of the formulations.

Temperature-induced responses, such as strains and displacements, are related to the boundary conditions. Therefore, it is required to determine the boundary conditions to establish a reliable bridge model for temperature-induced responses analysis. Particularly, bridge bearings usually present nonlinear behavior with an increase in load, and the nonlinear boundary conditions cause significant effect on temperature-induced responses. In this paper, the bridge nonlinear boundary conditions were simulated as bilinear translational or rotational springs, and the boundary parameters of the bilinear springs were identified based on the measured temperature-induced responses. First of all, the temperature-induced responses of a simply support beam with nonlinear translational and rotational springs subjected to various temperature loads were analyzed. The simulated temperature-induced strains and displacements were assumed as measured data. To identify the nonlinear translational and rotational boundary parameters of the bridge, the objective function based on the temperature-induced responses is then created, and the nonlinear boundary parameters were further identified by using the nonlinear least squares optimization algorithm. Then, a beam structure with nonlinear translational and rotational springs was simulated as a numerical example, and the nonlinear boundary parameters were identified based on the proposed method. The numerical results show that the proposed method can effectively identify the parameters of the nonlinear boundary conditions. Finally, the boundary parameters of a real arch bridge were identified based on the measured strain data and the proposed method. Since the bearings of the real bridge do not perform nonlinear behavior, only the linear boundary parameters of the bridge model were identified. Based on the bridge model and the identified boundary conditions, the temperature-induced strains were recalculated to compare with the measured strain data. The recalculated temperature-induced strains are in a good agreement with the real measured data.

Elastic instability of beams subjected to a partially tangential force

A hydraulic cylinder subjected to Euler's load in aspect of the stability and free vibrations taking into account discrete elastic elements

[Abstract] In the past decades, Synthetic Aperture Radar (SAR) antennas have attracted much attention for its advantages over other optical based antennas in earth observation because of their all-weather and daylight independent capabilities. The large size membrane SAR antennas has the advantages of achieving large gain and good resolution with ultra light mass. In this paper, we have developed a foldable deployable structure to deploy a membrane antenna in two directions, longitudinal and lateral directions. The longitudinal deployment is driven by two symmetrically arranged deployable structures. Each of them has a six-bar linkage mechanism and two closed-cable-loops. Several motion controllable hinges fulfill the lateral deployment. The hinge is composed of a SMA actuator, tape springs and a motion control mechanism. In this paper, the six-bar linkage has been designed with an optimal method to meet the demand of simultaneous deployment of all frames and keeping in a common plane after they are fully deployed. To analyze the dynamic performance of the driving mechanism, the multibody dynamic analysis software ADAMS has been used. For large size antennas, the effect of the frame flexibility on the dynamic performance of the system cannot be ignored. Using ADAMS/Flex, we studied the effect of frame flexibility on the dynamic properties of the support structure. Also, the natural frequencies and mode shapes of the deployed structure have been analyzed using finite element method. In this paper, the structure of the motion controllable hinge is introduced and the relationship between the joint output torque with respect to its parameters is studied.

The numerical prediction of spiral bevel gear contact dynamics is often hampered by the complexity of the gear tooth geometry and the three-dimensional (3D) nature of the motion transfer, which forms a major challenge for efficient contact detection and accurate contact force calculation. This works proposes a novel spiral bevel gear contact force element that enables the accurate prediction of 3D bevel gear contact force distributions in flexible multibody system dynamics simulations (MBDS). An efficient contact detection strategy, based on the surface of action, is used, while the accurate contact force calculation is obtained by inclusion of a new semi-analytical bevel gear contact stiffness model. This stiffness model relies on model order reduction (MOR) of finite element method (FEM)-based models to describe the bevel gear tooth and blank deformation, and analytical modeling to predict the tooth contact deformation. The solution can be used to model and analyze lightweight bevel gear dynamics. The method is validated against high-fidelity nonlinear finite element analysis-based contact simulations to evaluate the predicted transmission error, contact pattern, and contact pressure distribution. Finally, a use case is presented to demonstrate how the methodology enables detailed insights in spiral bevel gearbox dynamics, and noise and vibration (NVH) performance.

Coupling effects on a cantilever subjected to a follower force

In the article theoretical basis of flexible bodies’ large displacement within a multibody system as well as practical experience of flexible multibody dynamics simulation with integrated computer-aided design software systems EULER and Fydesis are considered. The hypothesis of flexible body undergoing both small elastic deformations and large motion within a multibody system is used [2]. The derivation of dynamic equations of motion of flexible bodies was first published in [3]. The derivation uses classical (linear) finite element method (FEM) and the Craig–Bampton method [1] of FE model’s matrices reduction. No additional approximations are involved, thus obtaining the most general equations in given problem definition. In the Craig–Bampton method a finite element model of a flexible body is reduced approximating small elastic deformation with a set of modes: static modes where the bound nodes’ displacements equal one unit, and normal modes where the bound nodes are fixed. The full finite element model and the reduced model are prepared in Fidesys software [4] and are transferred to EULER software to be used in a dynamics simulation as a part of a multibody system. For the flexible body’s spatial motion representation a floating frame of reference is used. A floating frame of reference defines the motion of a rigid body, related to which flexible body’s motion is considered as small deformations. The dynamic equation for flexible bodies are derived from Lagrange equations of the second kind. As generalized coordinates the floating frame of reference’s position and the modal coordinates vector are used. The expressions for the inertial forces vector and the generalized mass matrix are derived from the expression for the kinetic energy of the body. The article also contains all the other terms of the dynamic equation and the expressions for constraint equations’ components calculation. In the article an example of real practical motion simulation for KAMAZ-5308 vehicle with taking into consideration the flexibility of the vehicle’s frame is given. A finite element model of the frame with the load platform was developed to consider it’s flexible deformations. The following assumptions have been adopted for simulating the vehicle: additional attachments to the frame and platform, load platform’s wooden flooring are considered significantly less rigid than the basic structure; brackets for attaching the suspension and the cabin are considered very rigid in comparison with the structure itself; roundings and technological apertures are not considered. As the interface for dynamic reduction, there are 26 nodes corresponding to the places of attachment to the frame of the rest of the car - suspension, load and cabin. After the development of the finite element model in the Fidesys software, four files are created, containing the stiffness and mass matrices, model geometry, normal and static modes. The obtained model of the frame is used in the EULER software as part of a multibody system motion simulation. The model of a car with a flexible frame is used to take into account the effect of the dynamics of the car as a whole on the stress-strain state of the frame in the lane change maneuver.

We analyze the dynamics of an electrostatic comb drive model with one translational and one rotational degree of freedom, and show that an oscillatory voltage profile can significantly delay the onset of the rotational side pull-in instability. The result is facilitated by a simplified capacitance model that restricts the rotation to be small, but allows the translation to be large. The model further assumes that mechanical restoring forces are provided by linear springs, with the rotational spring much stiffer than the translational spring. Under these assumptions, translation and rotation are coupled only by the common input. Choosing the drive voltage to be a periodic puts the rotational dynamics in the form of Hill's equation. The input is restricted to be a piecewise constant bilevel signal, and Floquet theory is applied to compute a map of stabilizing input parameters. The results are validated against hybrid finite-element/lumped parameter simulations, with excellent agreement.