In the model of mass B, the upper three input keys (potential variables) on the left and right sides represent the force of spring i and j on B, respectively. Divided into three parts by dashed lines: Ji, R, and Jj, where the upper part of R is Newton's equation and the lower part is Euler's equation, and the upper three 1-junction flow variables represent the translational speed of B in the static system, the lower part The three 1-node flow variables represent the angular velocity of B in the coupled system; Ji includes three 0-junctions and submodules Ai and ri. 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 transformer MTF whose adjustment signal (transformation ratio) is correspondingly equal to each element of the vector transformation matrix in equation (3).
The force transformation module Ai Figure 4 solves the torque module ri. To make the expression concise, only the mass model linking two springs (and damping) is given. A new port can be modeled on Ji or Jj and connected to R without changing Causality, so you can increase the port arbitrarily. It will be expanded into a model that can connect n springs (and dampers) and package it into sub-modules as shown. The mass model P-space spring and damping parallel model As shown, the left 1-node in the figure is a fixed point, so the stream signal at the 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 on the mass, and is adjusted by the three transducers MTF into the three directions of X, Y and Z components. . The three MTF adjustment signals are the direction cosines of the spring and damping axis.
The parallel-damping model of the space spring connects the mass model and the parallel model of the spring and damper to form a bond model of the entire spatial multi-degree-of-freedom system, as shown. The signal flow is also given: the position signal is generated by the P module's velocity signal V integral, and the angular velocity signal ω of the P module is transformed into the derivative of Euler angles through equation (4), and then integrated to obtain the attitude (ie Euler angle). Position and attitude signals are input to the kinematics inverse solution module to calculate the cosine output of each spring to each MTF for adjustment.
Model 2 simulation of a spatial multi-degree-of-freedom vibration system takes a hypothetical hydraulic Stewart platform as an example. When the platform is locked in a certain position by a hydraulic lock, it can be regarded as a parallel connection of 6 springs (with damping). Into a multi-degree-of-freedom vibration system. Its motion platform and load can be equivalent to a mass of 7t. The piston and piston rod diameters of the hydraulic cylinder are 110mm and 70mm, respectively. The hydraulic spring stiffness is calculated as 1.16×107N/m, and the viscous damping coefficient Bc is 8750Ns/m. According to the above method, the model is established so that the platform is locked in the initial neutral position. When the force along the Z-axis is slowly applied to 5.3165×105N in the positive direction, the heave displacement of the platform is 0.01m, and the stiffness of the platform in the heave degree of freedom is calculated. It is 5.3165×105/0.01=5.3165×107 N/m. Then the force is released. At this time, the initial displacement of the platform is 0.01m and there is no initial damping free movement. From the figure, the vibration frequency is 13.81313 Hz.
When the platform is locked in the initial neutral position and remains stationary for the 50 s, it is subjected to a pulse impact force with a width of 0.1 s and an amplitude of 25 t in the Z-axis direction. The simulation response curve is shown in (3). The figure shows that under the impact of 25t impact, the vibration amplitude reaches 0.011m, and the vibration response ends approximately 2s after the start of the action. The response of the platform under various conditions 3 Conclusion The established spatial spring damping parallel key map model is closer to the real system than the traditional theoretical analysis. The correctness of this model is verified by simulation calculation. This model has reference value for the study of complex spatial vibration system.
The force transformation module Ai Figure 4 solves the torque module ri. To make the expression concise, only the mass model linking two springs (and damping) is given. A new port can be modeled on Ji or Jj and connected to R without changing Causality, so you can increase the port arbitrarily. It will be expanded into a model that can connect n springs (and dampers) and package it into sub-modules as shown. The mass model P-space spring and damping parallel model As shown, the left 1-node in the figure is a fixed point, so the stream signal at the 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 on the mass, and is adjusted by the three transducers MTF into the three directions of X, Y and Z components. . The three MTF adjustment signals are the direction cosines of the spring and damping axis.
The parallel-damping model of the space spring connects the mass model and the parallel model of the spring and damper to form a bond model of the entire spatial multi-degree-of-freedom system, as shown. The signal flow is also given: the position signal is generated by the P module's velocity signal V integral, and the angular velocity signal ω of the P module is transformed into the derivative of Euler angles through equation (4), and then integrated to obtain the attitude (ie Euler angle). Position and attitude signals are input to the kinematics inverse solution module to calculate the cosine output of each spring to each MTF for adjustment.
Model 2 simulation of a spatial multi-degree-of-freedom vibration system takes a hypothetical hydraulic Stewart platform as an example. When the platform is locked in a certain position by a hydraulic lock, it can be regarded as a parallel connection of 6 springs (with damping). Into a multi-degree-of-freedom vibration system. Its motion platform and load can be equivalent to a mass of 7t. The piston and piston rod diameters of the hydraulic cylinder are 110mm and 70mm, respectively. The hydraulic spring stiffness is calculated as 1.16×107N/m, and the viscous damping coefficient Bc is 8750Ns/m. According to the above method, the model is established so that the platform is locked in the initial neutral position. When the force along the Z-axis is slowly applied to 5.3165×105N in the positive direction, the heave displacement of the platform is 0.01m, and the stiffness of the platform in the heave degree of freedom is calculated. It is 5.3165×105/0.01=5.3165×107 N/m. Then the force is released. At this time, the initial displacement of the platform is 0.01m and there is no initial damping free movement. From the figure, the vibration frequency is 13.81313 Hz.
When the platform is locked in the initial neutral position and remains stationary for the 50 s, it is subjected to a pulse impact force with a width of 0.1 s and an amplitude of 25 t in the Z-axis direction. The simulation response curve is shown in (3). The figure shows that under the impact of 25t impact, the vibration amplitude reaches 0.011m, and the vibration response ends approximately 2s after the start of the action. The response of the platform under various conditions 3 Conclusion The established spatial spring damping parallel key map model is closer to the real system than the traditional theoretical analysis. The correctness of this model is verified by simulation calculation. This model has reference value for the study of complex spatial vibration system.
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