Abstract
Electrohydraulic Stewart platform is a multi-input and multi-output mechanical-hydraulic coupling system, which has the advantages of large power-to-weight ratio and high accuracy. It has been widely used in construction machinery, aerospace, and other fields. In the actual working process, especially in the high-speed motion, the Stewart platform movement process will produce a large impact and vibration and then affect the stability, accuracy, and service life of the platform. When the frequency of the external excitation coincides with the natural frequency of the electrohydraulic Stewart platform, it may cause the failure of the platform. Therefore, based on the relationship between the volumetric elastic modulus of the gas-bearing oil and the hydraulic stiffness of the leg, a mechanical-hydraulic coupling dynamic model of the electrohydraulic Stewart platform was established, and the natural frequencies and modal shapes of the platform were analyzed under typical conditions. The sensitivity calculation formula of the natural frequency of the system on the upper platform mass and the hydraulic stiffness of the outer leg is given by an analytical method, and the influence law of the upper platform mass and the outer leg stiffness on the natural frequency and the sensitivity of the electrohydraulic Stewart platform under typical conditions is discussed. This study can provide theoretical support for dynamic optimization of the electrohydraulic Stewart platform.
Highlights
Electrohydraulic Stewart platform is a multi-input and multi-output mechanical-hydraulic coupling system, which has the advantages of large power-to-weight ratio and high accuracy
Compared with the series simulator platform, the electrohydraulic Stewart platform has the advantages of large power-to-weight ratio, large stiffness, small inertia, and high precision [1,2,3] and is currently widely used in various fields such as machine tool [4], medical equipment [5], vehicle [6, 7], spacecraft [8, 9], and telescope [10, 11]. e design and development of the electrohydraulic Stewart platform involve multiple disciplinary fields such as machinery [12], fluid transmission and control [13, 14], computer [15], and sensor [16]. e electrohydraulic Stewart platform is a multi-input multi-output system with strong coupling because its legs cooperate with each other to achieve the corresponding position and attitude in the design space
By subbing pose parameters of pose 2, data in Table 1, and hydraulic stiffness of six legs into (15), the modal frequency and mode shapes of the platform transmission system can be obtained, as shown in Tables 4 and 5, which correspond to Cases (c) and (d), respectively: According to Tables 2–5, the Stewart 6-DOF platform has the following characteristics: (1) When the pose of the platform is changed, the Jacobian matrix of the upper platform and the outer leg changes, leading to the change of the stiffness matrix in the system dynamics equation, so the sixth-order natural frequency and the corresponding mode shapes of the system change, but the influence range is small
Summary
E positions of the six supporting legs of the platform can be expressed as li Ra × Ai + E − ai,. Pose 1 represents that the electrohydraulic Stewart platform is in the positive position, as shown, and the platform has symmetry. E pose 2 represents the general position of the electrohydraulic Stewart platform; that is, the shape and position parameters of the platform vary and the platform is not symmetrical. Dynamic Equation of the Electrohydraulic Stewart Platform Drive System. Because the mass and inertia of each leg are relatively small on the upper and lower platforms, it is unnecessary to consider. Because the working space of the electrohydraulic Stewart platform is very small, Coriolis and centrifugal forces can be ignored. K diag k1 k2 k3 k4 k5 k6 , c diag c1 c2 c3 c4 c5 c6 , fa fa fa2 fa fa4 fa fa6 T
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