The relative movement of the tool and the table completes the machining and cutting of the workpiece. Due to the large size of the workpiece machined by the heavy-duty CNC machine tool, that is, the stroke of the table is long, the axial dimension of the feed screw shaft is large, and the elasticity of the feed screw shaft is considered.
QYLC10 machine feed drive system simplified model When considering the elasticity of the screw shaft, the rotation angle m of the motor shaft is not equal to the rotation angle L/i of the gear pair after deceleration of the gear pair with the reduction ratio i, and the rotation angle L of the load shaft end. The angular difference that exists is related to the driving torque acting on the screw shaft. The driving torque, the friction torque and the reaction torque of the large gear are applied to the motor shaft, and the driving torque, the friction torque and the elastic torque applied by the pinion to the large gear are applied to the screw shaft. According to the D'Alembert principle of the mechanical system, the equation of motion of the motor shaft and the load shaft can be listed as: Tm-Bm-T1=Jm(1)k(mi-L)-BL=JL(2)
Combining equations (1), (2), and (3), eliminating the intermediate variable T1,m, the transfer function between the motor drive torque Tm and the load angle L is: G(s)=k/iJLJms4+ (JLBm+JmBL)s3+(JLk/i2+Jmk)s2+(Bmk+BLk/i2)s(4) When the elasticity of the feed screw shaft is not considered, when it is regarded as a rigid axis, the transfer function of the system is: G(s)=1/i(Jm+JL/i2)s2+(Bm+BL/i2)s(5)
Where: s is the Laplace transform operator. Comparing equations (4) and (5), it can be seen that when considering the elasticity of the feed screw shaft, the order of the feed drive system is increased from second order to fourth order. Due to the higher order of the system, the more serious the phase lag, the more difficult the system is to stabilize. Therefore, the elasticity of the screw shaft affects the stability of the feed system.
Using the pole-arbitrary configuration compensation method of the state space can overcome the limitations of the system correction design in the classical control theory and obtain the ideal design result <7>. Therefore, it is necessary to know the state space model of the feed drive system. Define the state variable x1=m, x2=m, x3=L, x4=L of the feed system, then substitute equation (3) into equations (1) and (2) to obtain: m=-kJmi2x1-BmJmx2+ kJmix3+TmJm(6)
L=kJLix1-kJLx3-BLJLx4(7)
According to the definitions of equation (6), equation (7) and state variables, the state space expression of the system can be written as: x1x2x3x4=010-kJmi2-BmJmkJmi01kJLi0-kJL-BLJLx1x2x3x4+01Jm0Tm(8)y=<0010>x1x2x3x4( 9)
When the parameter in formula (8) is: Jm=00001Nms2/rad, JL=0001Nms2/rad, Bm=BL=001Nms/rad, k=100, 10, 1Nm/rad, i=5, draw with MATLAB software An open-loop Bode diagram with different stiffness coefficients taking different values, as shown. It can be seen that as the stiffness coefficient decreases, the amplitude-frequency characteristic of the Bode diagram shifts to the left through the frequency, and the phase lag of the phase-frequency characteristic is severe, resulting in a decrease in the stability of the system. From the stability performance index of the system, when the stiffness coefficient k=100Nm/rad, the amplitude margin of the system is calculated as Kg=266dB, the phase margin is 758, and the system is stable.
When k=10Nm/rad, the amplitude margin of the system is Kg=664dB, the phase margin is 752, the system is stable, but the stability margin decreases. When k=1Nm/rad, the amplitude margin of the system is Kg=-134dB, the phase margin is -911, and the system is unstable. It can be seen that as the stiffness coefficient of the system decreases, the stability of the system decreases, and the system is re-manufactured until the system is unstable. Shown are the step characteristics of the stiffness coefficients k = 100 Nm / rad and k = 10 Nm / rad. It is also apparent that the stiffness of the system has an effect on stability, and the lower the stiffness, the worse the stability. When the stiffness coefficient k is less than 5 Nm/rad, the system will oscillate violently and begin to become unstable.
The open-loop frequency characteristics of the system with different stiffness coefficients The step response curve of the system with different stiffness coefficients. 2 Feeding system design and simulation When taking k=100Nm/rad, the coefficient matrix A and output coefficient of equation (8) are obtained. Matrix B, calculated controllable matrix In order to verify the feasibility of the pole configuration, based on Simulink, the state variable simulation model of the feed drive system is established according to equations (6), (7) and (8). As shown in the figure <9>. Add the step input to the simulation model. Signal, measure the output response and status response of the system. In order to ensure that the static error of the system is 0, the compensation gain Z<7> is introduced. When Z=1/50, the input is a unit step, and the final steady state value of the output is also 1, that is, the static error of the system is 0. The state variable simulation model of the feed drive system inputs the parameter values ​​of the inertia and damping of the system in the MATLAB command window, as well as the values ​​of the state feedback vector K and the compensation gain Z, and simulates the system to obtain the state response of the system. As shown, the output response of the system is shown as a solid line in the middle. The middle dashed line is the step input signal. It can be seen that the system tracks the step input signal quickly and steadily, and the adjustment time is about 02s. After the pole configuration, the state response pole of the feed system is configured. The output response of the feed system is k=10Nm/rad. When the closed-loop pole vector is set to P=, the state feedback vector K and the compensation gain Z are also obtained. The simulation results shown by the mid-dot line indicate that the system output response is different in speed due to the difference in the settings of the closed-loop poles. Therefore, the Ackerman pole configuration method can be used to set the closed-loop pole of the system at any desired position, so that the system can obtain faster and more stable dynamic performance, thereby effectively overcoming the adverse effect of stability due to insufficient stiffness of the feed system. . (Finish)
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