Study on the use of space spring tremor simulation

The three input keys (potential variables) on the left and right sides of the model of the mass B represent the forces of the springs i and j to B, respectively. According to the dotted line, it is divided into three parts: Ji, R and Jj, where the upper part of R is Newton's equation, the lower part is Euler's equation, and the upper three 1-junction flow variables represent the translational velocity of B in the static system. The three 1-junction flow variables represent the angular velocity of B in the connected system; Ji includes three 0-junctions, sub-modules Ai and ri, and Ai is used to convert the force in the static system into the connected system. In the figure, each rij in the figure represents a modulation converter MTF whose adjustment signal (transform ratio) is correspondingly equal to each element of the vector transformation matrix in equation (3).

Force transformation module Ai Figure 4 Solving the torque module ri For the sake of simplicity, only the mass model connecting two springs (and damping) is given. It is possible to generate a new port and connect to R according to Ji or Jj, without changing. Causality, so you can add ports arbitrarily. It will be expanded to a model that can connect n springs (and damping) and package it into a sub-module as shown. The model of the mass P-space spring and the damped parallel model are as shown, the 1-node on the left side of the figure is a fixed fixed point, so the flow signal of the flow source Sf is always zero. In the figure, the C element represents the spring, the R element represents the damping, and the potential signal of the right “0” junction is the resultant force of the spring and the damping to the mass, and is adjusted by the three converters MTF into components in the three directions of X, Y and Z. . The adjustment signals of the three MTFs are the cosine of the direction of the spring and the damping axis.

The space spring damped parallel model connects the mass model with the spring and damped parallel model to form a key map model for the entire spatial multi-degree of freedom system, as shown. The signal flow is also given: the position signal is generated by the V signal integral of the P module, and the angular velocity signal ω of the P module is transformed into the derivative of the Euler angle by the equation (4), and then the attitude is obtained (ie, the Euler angle). The position and attitude signals are input into the kinematics inverse solution module, and the direction cosine output of each spring is calculated to be adjusted to each MTF.

The model 2 simulation study of the spatial multi-degree-of-freedom vibration system is based on a hypothetical hydraulic Stewart platform. When the platform is locked by a hydraulic lock at a certain position, it can be regarded as 6 springs (plus damping) in parallel. Space multi-degree of freedom vibration system. Its motion platform and load can be equivalent to 7t mass, the piston and piston rod diameter of hydraulic cylinder are 110mm and 70mm respectively, the hydraulic spring stiffness is calculated to be 1.16×107N/m, and the viscous damping coefficient Bc is 8750Ns/m. The model is established as described above to lock the platform in the initial neutral position. When the force of 5.3165×105 N is slowly applied along the Z-axis, the platform's heave displacement is 0.01 m, thereby calculating the stiffness of the platform in the heave freedom. It is 5.3165×105/0.01=5.3165×107 N/m. Then the force is released, at which time the platform has an initial displacement of 0.01 m and no damping of the initial velocity. The vibration frequency is 13.38313 Hz.

When the platform lock is in the initial neutral position and remains stationary until the 50th, it is subjected to the pulse impact force of 0.1s width and 25t amplitude in the Z-axis direction, and the simulation response curve is as shown in -(3). It can be seen from the figure that under the action of 25t impact force, the vibration amplitude reaches 0.011m, and the vibration response ends about 2s after the start of the action. The response of the platform under various conditions 3 conclusions of the space spring damping parallel key map model, compared with the traditional theoretical analysis, closer to the real system. The correctness of the model is verified by simulation calculation. The model has reference value for studying complex vibration system in space.

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