Stiffness and Damping Formulations for Jointed Deployable Space Truss Structure

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.

The existence of many different dynamic large eddy simulation (LES) methods leads to questions about the theoretical foundation of dynamic LES methods. It was shown recently that the use of stochastic analysis enables a theoretically well based systematic derivation of a realizable linear dynamic model (LDM) and a realizable nonlinear dynamic model (NDM). A priori and a posteriori analyses of turbulent channel flow are used here to study the characteristic properties of these dynamic models. The LDM and NDM are compared with other dynamic models: the non-stabilized and stabilized dynamic Smagorinsky model (DSM), which is used in many applications of LES, and Wang-Bergstrom's dynamic model (WBDM), which represents an extension of the DSM. The DSM and WBDM do not represent realizable models because they are not derived as consequences of a realizable stochastic process. The comparisons reported here show that the LDM and NDM are based on a dynamic model formulation that avoids shortcomings of existing concepts. The LDM and NDM account for backscatter, and they are computationally stable without any modification. The LDM and NDM represent the instantaneous small scale structure of turbulence very well. Compared to the DSM and WBDM, respectively, the LDM and NDM are computationally more efficient.

In order to further reduce the incisions of laparoscopic surgery and the possibility of infection, the organic combination of single-incision laparoscopic surgery (SILS) and robotics has made the degree of minimally invasive surgery further improved. A new 5-DOF single-incision laparoscopic surgery robot was designed based on Axiomatic Design Theory, whose structure consisting of the movement mechanism, the endoscope and the position and pose adjustment mechanism. The robot parts are connected in series and parallel, allowing a pivotal motion of the endoscope in the center of the robot for realizing the incision. In order to achieve a performance optimization and a dynamic control of the single-incision laparoscopic surgical robot, the kinematics and dynamic modeling and dynamic stiffness analysis of the robot are especially important. The forward kinematics equation, inverse kinematics equation and Jacobian matrix of the SILS robot are derived based on D-H method and geometric method, and the kinematics numerical simulation is carried out by Matlab. The dynamic equation of the robot is derived by Kane method. Subsequently, a numerical simulation of the robot dynamics equation is performed, with its virtual prototype utilized to set the motion plan of the robot mechanism. After robot’s dynamic simulation, the numerical changes of the driving force and torque for each robot’s moving mechanism are obtained. The performed simulation results further verify the correctness of the established robot’s dynamic model. Finally, utilizing the above methods, the dynamic stiffness model and evaluation index of the robot are determined, and the dynamic stiffness of the robot is analyzed and evaluated. The results of the kinematics, dynamic and stiffness analysis of the SILS robot further validate that the 5-DOF SILS robot has a reasonable structure, motion and sufficient stability to meet the needs of single-incision laparoscopic surgery.

In the aeroelastic analysis of flight vehicles with electromechanical actuators (EMAs), an accurate prediction of flutter requires dynamic stiffness characteristics of the EMA. The dynamic stiffness transfer function of the EMA with brushless direct current (BLDC) motor can be obtained by conducting complicated mathematical calculations of control algorithms and mechanical/electrical nonlinearities using linearization techniques. Thus, system identification approaches using experimental data, as an alternative, have considerable advantages. However, the test setup for system identification is expensive and complex, and experimental procedures for data collection are time-consuming tasks. To obtain the dynamic stiffness transfer function, this paper proposes a linear system identification method that uses information obtained from a reliable dynamic stiffness model with a control algorithm and nonlinearities. The results of this study show that the system identification procedure is compact, and the transfer function is able to describe the dynamic stiffness characteristics of the EMA. In addition, to verify the validity of the system identification method, the simulation results of the dynamic stiffness transfer function and the dynamic stiffness model were compared with the experimental data for various external loads.

Nonlinear dynamic modeling and model reduction strategy are studied in this paper for a rotating thin cylindrical shell. The nonlinear dynamic model is first established in terms of ordinary differential equations, in which the effects of Coriolis and centrifugal forces are considered, as well as the initial hoop tension due to rotation. This model describes both the in‐plane vibrations and the flexural vibration and reflects the coupling effects of those deformations. Based on this original model, a novel model reduction strategy is proposed to reduce the degrees of freedom by neglecting vibration modes predominated by in‐plane vibrations. Meanwhile, for the reduced‐order model, the in‐plane vibrations’ contributions to the rotating shell’s response are still preserved. To validate the dynamic model and the model reduction strategy, comparisons and simulations are carried out. Subsequently, nonlinear dynamic behaviors are investigated preliminarily by analyzing the rotating cylindrical shell’s amplitude‐frequency responses under different excitation levels.

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.

Current and displacement stiffness are important parameters of axial magnetic bearing (AMB) and are usually considered as constants for the control system. However, in actual dynamic work situations, time-varying force leads to time-varying currents and air gap with a specific frequency, which makes the stiffness of appear decrease and even worsens control performance for the whole system. In this paper, an AMB dynamic stiffness model considering the flux variation across the air gap due to frequency is established to obtain the accurate dynamic stiffness. The dynamic stiffness characteristics are analyzed by means of the dynamic equivalent magnetic circuit method. The analytical results show that the amplitude of current and displacement stiffness decreases with frequency increasing. Moreover, compared with the stiffness model without considering the variation of flux density across the air gap, the improved dynamic stiffness results are closer to the actual results. Through the dynamic stiffness measurement method of AMB, experiments of AMB in magnetically suspended molecular pump (MSMP) are carried out and the experimental results are consistent with theoretical analysis results. This paper proposes the dynamic stiffness model of axial magnetic bearing considering the variation of flux density across the air gap, which improves the accuracy of the AMB stiffness analysis.

An extension to the LuGre dynamic friction model from longitudinal to longitudinal/lateral motion is developed in this paper. Application of this model to a tyre yields a pair of partial differential equations that model the tyre-road contact forces and aligning moment. A comparison of the steady-state behaviour of the dynamic model with existing static tyre friction models is presented. This comparison allows one to determine realistic values of the parameters for the new dynamic model. Via the introduction of a set of mean states we reduce the partial differential equations to a lumped model governed by a set of three ordinary differential equations. Such a lumped form describes the aggregate effect of the friction forces and moments and it can be useful for control design and online estimation. A method to incorporate wheel rim rotation is also proposed. The proposed model is evaluated by comparing both its steady-state as well as its dynamic characteristics via numerical simulations. The results of the simulations corroborate steady-state and dynamic/transient tyre characteristics found in the literature.

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

Hybrid pump-controlled asymmetric cylinder drive systems are implemented for energy saving purposes in applications that do not require fast responses. Under low-velocity and low-pressure conditions, the friction influence in the hybrid pump-controlled system is evident. Researchers have developed various models to describe friction. These friction models are implemented based on the relative motion of the contact surfaces, and they can be categorized into static friction and dynamic friction models. For example, dynamic friction models are suitable for simulating the friction in hydraulic cylinder seals under lubrication conditions. Among the dynamic models, the LuGre model can capture almost all static and dynamic friction behaviors at the macroscopic level; for example, stiction, the Stribeck effect, and hysteresis. Thus, the LuGre model is suitable for describing the friction in hydraulic cylinders. Because the friction force in the hydraulic cylinder is mainly from the cylinder seal and seal deformation occurs under pressure due to its flexibility, the friction in a hybrid pump-controlled hydraulic system is affected by the relative motion of the contact surfaces. Therefore, to investigate factors that affect the friction other than the relative motion of the contact surfaces, the friction behaviors of a hybrid pump-controlled hydraulic system are studied. Pressure difference and acceleration terms are introduced in the LuGre friction model, and the simulated friction results of the updated LuGre model are compared with the measured experimental results to validate the new friction model.

Friction-based dampers have gained attention as a cost-effective way to provide structural control during natural hazards. However, the dry friction interfaces in these systems result in a highly nonlinear damping response during the reversal of damper travel, termed damper backlash. Moreover, the stick-slip phenomena intrinsic to the sliding response of dry friction interfaces make the accurate modeling of friction-based structural dampers challenging. Dynamic friction modeling for structural dampers currently relies on analytical models to approximate the damper’s response at a current location given the damper’s state and average out the complex system responses during travel reversal or stick-slip movement to obtain a model of the system’s performance. In this chapter, we propose the use of a deep learning model to capture the temporal dynamics of the system that when combined with the LuGre friction model provides a physics-informed machine learning approach for inferring the damping force of a dry friction interface given the state of the model. Specifically, this chapter uses a long short-term memory model to infer the LuGre friction model’s parameters. A methodology for parameter identification using truncated backpropagation through time is given, which allows for real-time updating. Model validation is performed using a 9 kip rotary friction damper designed for high damping performance and mechanical simplicity. The model is validated with data from real natural hazard events and used in a real-time hybrid simulation. The performance, reliability, and accuracy of the deep-learning-based friction model are discussed.

The dynamic characteristics of machine tools vary significantly depending on operating conditions, such as load magnitude and feed velocity. One of the primary factors contributing to this variability is the change in frictional force within feed drive components. Since frictional behavior is highly sensitive to operating conditions, accurately predicting the dynamic characteristics becomes challenging. The friction force within rolling guide elements, such as the feed drive components for machine tools, changes drastically during the transition from a stopped state to a rolling state. In the pre-rolling region, the frictional force is dominated by displacement, while in the rolling region, it is dominated by velocity due to the influence of lubrication. Additionally, the frictional behavior is expected to be affected by the component temperature and the machine position. Therefore, to predict the dynamic characteristics of machine tools under various operating conditions, it is critical to comprehensively investigate and model friction characteristics, including temperature and position dependencies, in addition to general dependencies of displacement and velocity. In this study, the friction characteristics of the feed drive components were analyzed experimentally, and a friction model was constructed. Using a vertical machining center, frictional behavior was investigated with respect to velocity dependence, displacement dependence, positional dependence, and temperature dependence. Based on the experimental data, model parameters were identified, and the friction model was developed based on the LuGre model with adjustments to account for all factors. Finally, the validity of the proposed model was verified to ensure it can accurately represent the influence of various operating conditions as compared to the conventional friction model.

There have not been any suitable friction models to properly solve plasticity problems yet. Most recently, a new dynamic friction model merging the definition expression of the viscosity with the Amontons-Coulomb friction model suggested by the author has been successfully applied in axisymmetric upsetting to predict the contact stresses. In this paper, the dynamic friction model is further used for resolving the problem of plane-strain compression. With element-equilibrium approach, contact stresses in plane-strain compression have been derived. The mathematical expressions of these contact stresses are verified by the previous experimental data with various ratios of instant length to instant height of workpiece and different lubrications. The curves obtained from the dynamic friction model agree with these experimental results very well, not only for contribution of the normal pressure, mean normal pressure, but also for contribution of the friction stress. Comparisons of results of the dynamic friction model, the Amontons-Coulomb friction model, and the constant friction model with the experimental data are also made. It is seen that the predictions by the dynamic friction model show much better solutions to the practical plasticity problems. It is believed that the dynamic friction model could extensively be used to plasticity problems of solids.

Clamping effects on the dynamic characteristics of composite machine tool structures

Due to the uncontrollable dragging force and velocity of the drilling robot, the weight on bit (WOB) and rate of penetration (ROP) can not be controlled. So, there is not an application of in the drilling engineering even through downhole robots have been developed for many years. Dynamic characteristics are the theoretical basis for controlling WOB and ROP. In this paper, the power source of the driving force of the drilling robot is found, which is the pressure difference between inside and outside of the drilling robot. The calculation model of the dragging force of the drilling robot is obtained. On the basis, a fluid–solid coupling nonlinear dynamic model (CT-drilling robot-hydraulic motor-bit-rock-drilling fluid) is established. The nonlinear dynamic characterization is simulated by Runge–Kutta method. The nonlinear dynamic model of the coiled tubing drilling system introduces the characteristics of drilling fluid, rock mechanics and ROP for the first time. The effects of robot position, friction coefficient, displacement fluctuation of drilling fluid and WOB fluctuation on the dynamic characteristics of drilling system are studied. It is found that the displacement of drilling fluid, position of drilling robot and friction coefficient are the main factors affecting the dynamics of the CT drilling system based on drilling robot. This paper finds out power source of the drilling robot, which is the pressure difference between the internal and external of the drilling robot. The acquisition of dynamic characteristics will provide a theoretical basis for the control method of downhole robot, rock breaking mechanism based on drilling robot, bit selection and design of bottom hole assembly, etc. It will also promote the development of downhole robots and solve the bottleneck problem of coiled tubing “buckling” and “locking”.