The stiffness analysis of the system influences the presence of the interference force F on the output y. The output displacement caused by the unit load disturbance is called the positional flexibility, the reciprocal of the positional flexibility is called the positional stiffness, and the positional stiffness is further divided into the dynamic positional stiffness and Static position stiffness. The dynamic position stiffness is the stiffness in the dynamic process, which is related to the frequency of change of the load resistance F, and the static stiffness is the stiffness in the case of ω=0. According to the definition of dynamic positional stiffness expression can be obtained by the formula (1): FY (s) = s3ωn2 + 2ξnωns2 + s + kqd2Dm - VtsA2E + kcA2 + (2) by the expression of ωn and ξn 2ωnξn = kcEVt, so by formula (2) available: FY (s) ) = - A2kcs3ωn2+2ξnωns2+s++1s2ωnξn+1 (3) Therefore, the dynamic positional stiffness is an inertial link whose inflection point frequency is 2ωnξn. The differential link is composed of a second-order differential link with a natural frequency ωn and a damping ratio ξn. The negative sign indicates that the influence of the load disturbance force reduces the output. Enter the parameters of the load-sensing steering system with the BZZ5E-1000 steering gear according to equation (3) (num=[3462611];den=[0.0541];bode(num,den)) to the MATLAB software to draw a diagram as shown in Figure 1. The load stiffness frequency characteristics shown in the Bird frequency plot.
Since ξn<0.5, the inflection point 2惯性nξn of the inertial link is smaller than æ¿n. From the Bode plot of load stiffness frequency characteristics, it can be seen that: (1) When ωn<2ωnξn, the second order differential link and inertial link do not work, and due to the addition of a priority valve in the load sensing system, when the interference force When F changes the load, the size of the opening of the priority valve spool can be controlled by the pressure change, so that the change of F has no effect on the output Y, and its value is FY=A2EVt.
The stiffness of the dynamic position of the system at this frequency does not change.
(2) When the frequency changes between 2ωnξn and ωn, the synthesis of the differential and inertial links is a straight line parallel to the horizontal axis, which shows that the change of F has no effect on the output Y, and the dynamic position of the system at this frequency is also basically not Change, its value is FYω=2æ¿nξn=A2EVt, expressed as hydraulic spring stiffness. Between 2ωnξn and ωn, due to the high frequency of F, there is not enough time for the leakage flow to pass. The steering cylinder can be regarded as a simple closed hydraulic cylinder whose rigidity is the hydraulic spring stiffness.
(3) When ω>ωn, the inertia load force at high frequencies is large, damping the piston movement, and the dynamic position stiffness increases quadratically with frequency. However, systems rarely work in this frequency range.
(4) The static position stiffness refers to the stiffness of ω = 0. It can be seen from formula (3) that when ω = 0, the static position stiffness is zero. This is because the static load disturbance force F will cause a continuous leak, causing the piston to move all the time.
(5) The higher the closed-loop stiffness, the smaller the error caused by the disturbance. In situations where the load torque is large and the accuracy is high, it is very important to improve the closed-loop stiffness of the system.
Conclusion (1) When the system frequency works between ωn<2ωnξn and 2ωnξn and ωn, the disturbance force does not change the stiffness of the steering system. The dynamic hydraulic spring stiffness value is FY=A2EVt, and the hydraulic spring stiffness and hydraulic pressure The square of the cylinder's total working area A is proportional to the elastic modulus of the fluid E and inversely proportional to the total volume of the cylinder Vt. When the system frequency is operated at ω>ωn, the dynamic position stiffness is proportional to the system frequency.
(2) When ω = 0, the static position stiffness is zero.
(3) Because the system seldom works in the state of ω>ωn, the greater the total working area A of the hydraulic cylinder and the elastic modulus of oil E, the smaller the systematic error caused by the disturbance and the greater the total volume Vt of the cylinder, The greater the error caused by system interference.
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