The Damper Spring Unit of the Sentinel 1 Solar Array

The Damper Spring Unit (DSU, see Figure 1) has been designed to provide the damping required to control the deployment speed of the spring driven solar array deployment in an ARA Mk3 or FRED based Solar Array in situations where the standard application of a damper at the root-hinge is not feasible. The unit consists of four major parts: a main bracket, an eddy current damper, a spring unit, an actuation pulley which is coupled via Kevlar cables to a synchro-pulley of a hinge. The damper slows down the deployment speed and prevents deployment shocks at deployment completion. The spring unit includes 4 springs which overcome the resistances of the damper and the specific DSU control cable loop. This means it can be added to any spring driven deployment system without major modifications of that system. Engineering models of the Sentinel 1 solar array wing have been built to identify the deployment behavior, and to help to determine the optimal pulley ratios of the solar array and to finalize the DSU design. During the functional tests, the behavior proved to be very sensitive for the alignment of the DSU. This was therefore monitored carefully during the qualification program, especially prior to the TV cold testing. During TV "Cold" testing the measured retarding torque exceeded the max. required value: 284 N-mm versus the required 247 N-mm. Although this requirement was not met, the torque balance analysis shows that the 284 N-mm can be accepted, because the spring unit can provide 1.5 times more torque than required. Some functional tests of the DSU have been performed without the eddy current damper attached. It provided input data for the ADAMS solar array wing model. Simulation of the Sentinel-1 deployment (including DSU) in ADAMS allowed the actual wing deployment tests to be limited in both complexity and number of tests. The DSU for the Sentinel-1 solar array was successfully qualified and the flight models are in production

Kinematically started efficient position analysis of deformed compliant mechanisms utilizing data of standard joints

Topology optimization of a flexure-based mechanism requires the properties of the mechanism in several deformed configurations. This paper presents a fast and accurate method to compute these configurations. It is generally applicable on mechanisms with complex standard flexure joints. First kinematic equations of the mechanism are derived by allowing the mechanism to move only in the directions for which it is designed. Secondly the configurations of the joints are approximated based on the rotations of the elements by which the joints are modeled. These orientations are obtained by a parameterization based on a priori knowledge of standard flexure joints. Finally, the resulting approximation is used as initial guess to obtain the configuration accurately, after which relevant properties like stiffness can be derived. For a manipulator with three complex joints the computation time was reduced up to a factor of 65 compared to a conventional method. When for optimization purposes an approximation is acceptable, the computation time can be reduced by a factor of 600, using a linear description of the deformation that remains in the first part of the method

Derivation of a superelement with deformable interfaces – applied to model flexure joint

Design and optimization, as well as real time control, of flexure mechanisms require efficient but accurate models. The flexures can be modelled using beam elements and the frame parts can be modelled using superelements. Such a superelement efficiently models arbitrarily shaped bodies by few coordinates, using models obtained by model order reduction. The interfaces between the frame parts and the flexures often experience considerable deformation which affects the stiffness. To define the interface deformation in a reduced order model, this paper derives a multipoint constraint formulation, which relates the nodes on the deformable interface surface of a finite element model to a few coordinates. The multipoint constraints are imposed using a combination of the Lagrange multiplier method and master–slave elimination for efficient model order reduction. The resulting reduced order models are used in the generalized-strain multi-node superelement (GMS) that was defined in (Dwarshuis et al. in Multibody Syst. Dyn. 56(4):367–399, 2022). The interface deformations can be coupled to the cross-sectional deformation of higher order beam elements (i.e. beam elements of which the deformation of the cross-sections is explicitly taken into account). This paper applies this technique to model flexure joints, where the flexures are modelled with beam elements, and the frame components and critical connections using the GMS. This approach gives generally over 94% accurate stiffness, compared to nonlinear finite element models. The errors were often more than 50% lower than errors of models which only contain beam elements

Beams with a Varying Cross Section in the Generalized Strain Formulation for Flexure Modeling

Flexure joints are rapidly gaining ground in precision engineering because of their predictable behavior. However, their range of motion is limited due to a stress limitation and a loss of support stiffness in deformed configurations. The support stiffness can be significantly increased by using leafsprings of which the width and thickness vary over the length of the leafspring. This paper presents formulations for two beam elements with a varying cross section that can be used for the efficient modeling of these types of leafsprings. One of these beam-formulations includes the modeling of the warping due to torsion, which is shown to be essential for accurate modeling. The 90% accuracy in stiffness results and 80% accuracy in stress results, in comparison with results of finite element analyses, are sufficient for the evaluation of concept-designs. Optimizations show that the support stiffness of two typical flexure joints can be increased by a factor of up to 4.0 keeping the same range of motion, by allowing the cross section to vary over the length of the leafspring. In these two flexure joints, 98% of this improvement can already be obtained by only varying the thickness, and keeping a constant width

A multinode superelement in the generalized strain formulation

Design and optimization of flexure mechanisms and real time high bandwidth control of flexure based mechanisms require efficient but accurate models. The flexures can be modeled using sophisticated beam elements that are implemented in the generalized strain formulation. However, complex shaped frame parts of the flexure mechanisms could not be modeled in this formulation. The generalized strain formulation for flexible multibody analysis defines the configuration of elements using a combination of absolute nodal coordinates and deformation modes. This paper defines a multinode superelement in this formulation, i.e., an element having its properties derived from a reduced linear finite element model. This is accomplished by defining a local element frame with the coordinates depending on the absolute nodal coordinates. The linear elastic deformation is defined with respect to this frame, where rotational displacements are defined using the off-diagonal terms of local rotation matrices. The element frame can be defined in multiple ways; the most accurate results are obtained if the resulting elastic rotations are as small as possible. The inertia is defined in two different ways: the so-called "full approach" gives more accurate results than the so-called "corotational approach" but requires a special term that is not available from standard finite element models. Simulations show that (flexure based) mechanisms can be modeled accurately using smart combinations of superelements and beam elements