Flexure Support Research Articles

An adaptive frequency disturbance rejection control for an inertial reference unit under unknown disturbance

The inertial reference unit (IRU) can provide a reference beam for the line-of-sight stabilization system to achieve precise pointing and tracking. The reference beam leaves the IRU with minimal jitter and determines the accuracy of acquiring, tracking and pointing system. When the vehicle is moving, the disturbance usually gathers around one frequency. Meanwhile, the resonance introduced by the flexure support of the IRU seriously affects the stabilization accuracy. In this paper, an extended state observer with frequency adaptation is proposed to improve the performance of disturbance rejection. An auxiliary filter is used to optimize the disturbance frequency estimation and improve the control bandwidth. Simulation results and experimental data verify the effectiveness of the proposed method.

The Optimization of a Convex Aspheric Lightweight SiC Mirror and Its Optical Metrology

Space telescopes with large diameters or with wide fields require convex secondary mirrors which are mounted at the front of telescope. In this paper, a convex aspheric lightweight SiC mirror and Hindle detection method are presented. A parameter optimization method is utilized in the mirror design process in which the mirror surface accuracy is taken as the objective. As the mirror has a relative high diameter-to-thickness ratio, an S-type flexure support is proposed to maintain the surface figure under gravity, thermal change and assembly error. To minimize the surface figure under these loads, the design principle is studied separately. The optical metrology is performed by the Hindle ball supported by a gravity offloading system. The tested surface had an accuracy of λ/100 root mean square (λ = 632.8 nm). In addition, the mechanical design was validated by dynamic testing.

Numerical and experimental study on CFS spherically-hinged equal-leg angle columns: stability, strength and DSM design

This paper reports a numerical and experimental investigation on the stability/buckling, elastic and elastic-plastic behaviour and strength, and Direct Strength Method (DSM) design of cold-formed steel (CFS) spherically-hinged short-to-intermediate equal-leg angle columns. It extends the scope of similar studies recently carried out for CFS fixed-ended and pin-ended (cylindrically-hinged) columns with the same characteristics. Initially, the paper addresses the stability/buckling behaviour of spherically-hinged columns − the results presented and discussed, which include the selection of the column geometries to be analysed (numerically and experimentally), are obtained by means of Generalised Beam Theory (GBT). Then, the post-buckling behaviour and strength of columns containing initial geometrical imperfections is investigated, by means of Ansys shell finite element analyses, and an experimental study, carried out at UFRJ (Federal University of Rio de Janeiro) and whose results are subsequently used to validate the previously developed numerical model, intended to perform a parametric study to obtain numerical failure load data covering a wide slenderness range for the columns considered. Such results comprise (i) initial imperfection measurements, (ii) load-displacement equilibrium paths, (iii) deformed configurations (including the collapse modes) and (iv) failure loads. The experimental and numerical failure loads obtained are then used to develop, validate and assess the merits of a DSM-based rational design approach that adopts the same concepts and procedures that were previously employed for cylindrically-hinged columns. The need for modifications arises from the new major-axis flexure support conditions, which affect the column flexural-torsional behaviour significantly. It is shown that the proposed/modified DSM strength curves lead to safe and reliable failure load estimates for spherically-hinged short-to-intermediate equal-leg angle columns exhibiting a wide slenderness range, thus making it possible to extend the scope of the existing DSM-based design approach to cover also columns with these end support conditions. The very high prediction quality achieved is attested by the fact that the LRFD resistance factors obtained are well above ϕc = 0.85 (value prescribed by the North American Specification for compression members).

Space-qualified fast steering mirror for an image stabilization system of space astronomical telescopes.

A space-qualified fast steering mirror (SQ-FSM) was designed, built, and tested at the National Astronomical Observatories of the Chinese Academy of Sciences for an image stabilization system of space astronomical telescopes, which is used for the tip-tilt correction of small jitter of the satellite platform; this achieved image stability in a closed-loop manner. Its design primarily faces four challenges involving (1)sustaining the specified sine and random vibration without launch lock, as well as shock response spectrum experiments; (2)surface form error of a clear aperture of ϕ120 mm less than 1/50λ root mean square (RMS, λ=632.8 nm) with a relatively rigid mirror support; (3)resonance frequency of at least 800Hz and as high as possible; (4)minimum reaction force and torque in order to decrease its unfavorable influence on the satellite platform. To achieve these goals, the global optimizations and compromises have to be made throughout the design process. The study reviews the detailed design of the SQ-FSM with respect to the four challenges, mainly by keeping the mirror and its support lightweight, mirror bonding and solidification, actuator and its stiffness, flexure support of the mirror and its holder, material optimization for weight, stiffness, and coefficient of thermal expansion, as well as finite element analysis on statics and dynamics. The performances are also measured and expatiated, including the surface form, resonant frequency, tip-tilt stroke, vibration and shock response spectrum experiments, etc., which validate the performances of the SQ-FSM.

Design of flexure support of space compact reflector subassembly and dynamic analysis

The mirror assembly of an electro-optical tracking and pointing system for a space borne laser communication system is studied, three flexible supports are contrasted, according to practical applications of space load, the structural stiffness advantage and surface figure of the three flexible support scheme have been evaluated. The analysis results show that the surface figure RMS of neck side grooving flexible support scheme resisting microgravity and thermal environment change can reach 2.05 nm and 8.88 nm, the fundamental frequency mode is 926.1 Hz, in the balance between the surface figure RMS and the higher stiffness resisting hevibration damage, the flexible design is most reasonable. On this basis, the parameterized design of the flexible support structure of the reflector is completed and dynamic analysis have been done. The maximum stress of the frequency response is 96 Mpa, which is less than the material's tensile strength limit. The results of random vibration analysis show that root mean square of acceleration response is 11.14 g RMS, meeting 3σ law. Finally, a 0.2 g sine sweeptest proves that the relative error of the modal analysis is 2%, the experimental result show that the analysis results are basically accurate and reliable, that is, flexible support design is reliable to meet the requirements of use.

Investigation on the critical parameters affecting the working design dynamics of a torque motor employed in an electro-hydraulic servovalve

The torque motor is an intricate assembly in electro-hydraulic technology and plays a crucial role in converting the electrical signal into controlled mechanical output signal. It involves many precise components, such as the feedback spring, armature and its coil, permanent magnet, feed pipe, flexure shaft, jetpipe, and flexure support. The components are embedded together as a single operating component. Each component contributes to the effective dynamics of the system. The present paper proposes a novel approach to investigate the effect of critical parameters on the working design dynamics of the torque motor employed in the jetpipe electro-hydraulic servovalve. Based on the principles of mechatronics, a mathematical model is developed. The model-based design approach is employed to investigate the dynamics of the system. The required simulation parameters of the critical and precision components were obtained from solid and finite element (FE) models. The solid and FE models of the critical and precision components were first analyzed with suitable boundary and loading conditions to establish the stiffness. To validate the obtained FE results, experiments were carried out with a specially designed and fabricated test set-up. Based on the basic principle of electromagnetics, a nonlinear FE model of torque motor is analyzed for magnetic field distribution, the torque developed, and armature and jetpipe deflection for varied input current. From the results obtained, good agreement was observed between FE, simulated, and experimental values. The present novel approach enables one to improve the working design dynamics of the torque motor.

Optomechanical analysis of the flexure mounting configuration of large-aperture laser transport mirror

Motivated by the demand to minimize the mount-induced wavefront aberration of the large-aperture laser transport mirror, a low-stress flexure mounting configuration is proposed. Specific optomechanical analyses, including theoretical modeling, numerical analysis and field experiment, are presented. The mechanical properties of the flexure support were studied specifically. Besides, the relation between the mounting forces and the root-mean-square of the gradients (GRMS) value of the mirror surface is studied. Then, the appropriate value of the bolt preload is set to 500N, with which the GRMS value is just 5.35 nm/cm. The results indicate that the flexure mounting configuration is indeed a feasible and promising method to solve the mount-induced distortion problem of large-aperture optics.

Kinematic evaluation of the whiffletree lateral support setup and its application for the mirror support of the TMT tertiary mirror

With increasing size of the reflecting mirror apertures in telescopes, the lateral support is becoming more and more important. In order to find a setup satisfying the requirements for the TMT tertiary mirror, based on the classic three-point flexure support setup, a twelve-point lateral support setup was investigated its basic internal relations and properties were investigated. The virtual equivalent circle concept is then proposed to evaluate different potential setups. By studying the relationship between the virtual equivalent circle radius and the thermal deformation and resonant frequency, it can be concluded that a larger virtual equivalent circle radius results in a smaller the thermal deformation and a higher resonant frequency. Preliminary research results suggested that the TMT tertiary mirror surface figure error and thermal deformation requirements can easily be met. However, it was more difficult to obtain resonant frequencies higher than 15 Hz. Based on the virtual equivalent circle concept, the TMT tertiary mirror support setup was optimized, resulting in a resonant frequency of 17.7 Hz, which satisfies the requirements. The whiffletree lateral support setup can be applied to similar reflecting mirror support structures.

大口径空间反射镜Cartwheel型柔性支撑设计

The large aperture primary mirror assembly (PMA) mounted in space remote sensor should have the extraordinary virtues as high stiffness, high strength, high thermal stability etc.. A novel three-point flexural support configuration based on Cartwheel flexural hinge for large aperture PMA is presented in this paper. Firstly, the stiffness characteristic of the support structure is approached using the dimensionless design method. Then, static and dynamic analysis based on finite element method are performed on the PMA to find the optimal dimension parameters of the support flexure. Finally, optical test on a mirror with /40 root mean square (RMS) surface figure and vibration experiment on an equivalently spherical mirror are performed to validate the design configuration. The simulation and experiment results indicate that when the thickness of flexure t=8 mm, beam height h=4 mm, beam length L=8 mm, the surface figure of PMA can keep below RMS 12 nm under the load of 1 G gravity and 15C temperature change. The first natural frequency reaches 296 Hz, only deviating 6% from the analysis result. The Cartwheel flexure support can satisfy the extraordinary design requirements.

单轴柔性铰链柔度系数试验装置的设计

To obtain the test data from the experimental research on the compliance factors of the flexure support structure of a large scale reflector used in an airborne image sensor,a compact single-axis flexure hinge experimental setup was proposed and designed.By using this experimental setup,end-bending and pure moment bending experiments of the single-axis flexure hinge could be achieved on a common single-axis Material Testing System(MTS).This setup utilizes the leverage principle to realize the pure moment loading on the single-axis MTS and takes the side constraint configuration which is composed of several sets of rigid rollers to constrain the pure moment loading sub-assembly.By these ways,the effect of the friction on the load transmission was reduced greatly.Furthermore,the virtual simulation of the pure moment bending process was performed.It indicates that the side force stemmed from the constraint of L pushing component is the main influence factor on the bending processing,and the maximum side force can be controlled at 4.783 N.In order to verify the test data,Finite Element Analysis(FEA) and theoretical calculation were employed.The comparison shows that the test results are concident with FEA results and theoretical results well,and test results and theoretical results are slightly smaller than FEA results.Compared with FEA,the maximum relative error of the test data is only 3.87%,which indicates that this experimental setup is a good solution for study of flexure support structures used in optical reflectors.

Vibration apparatus with flexure means

A torsionally stiff flexure support for the slip plate in a vibration apparatus is provided permitting predetermined linear motion along the axis of vibration by longitudinal bending of the flexure, but by virtue of its torsional stiffness blocking pivoting movement about the center axis of the slip plate.