A passive control device and design method for dead-zone operation precision of a reciprocating mechanism

Abstract

The application provides a passive control device and design method for dead-zone operation precision of a reciprocating mechanism. The device is installed on a sliding block of the mechanism, and comprises a vibrator, an amplitude limiting device and a nonlinear energy sink (NES). The distance between the amplitude limiting device and the vibrator is continuously adjustable. The mass ratio of the vibrator to the sliding block is between 1% and 5%. The application can generate a larger control force under a smaller vibrator mass by using the amplitude limiting device, and solves the problem of poor positioning precision of the mechanism caused by the gap between mechanisms by combining the nonlinear control force generated by the NES. The application does not depend on the state observation of the controlled mechanism, and effectively reduces the complexity of the control structure without increasing the connecting structure between the controlled mechanism and the fixed frame.

Description

TECHNICAL FIELD

[0001] The application belongs to a damping energy consumption device, and particularly relates to a passive control device and design method for dead-zone operation precision of a reciprocating mechanism. BACKGROUND

[0002] A nonlinear energy sink (NES) is a kind of nonlinear passive vibration absorber. When a main structure is subjected to external excitation, vibration energy is unidirectionally transferred to the NES through nonlinear stiffness and dissipated through damping. The NES has good application prospects in various fields due to its light weight, strong robustness, and wide vibration reduction frequency band.

[0003] Clearances inevitably exist in the kinematic pairs of a mechanism, thereby affecting the dynamic characteristics and operation precision of the mechanism. When a reciprocating mechanism reaches a dead-zone position, the repeated positioning precision of a slider will be degraded due to the existence of the clearance in the kinematic pair. A literature (A. Azimi Olyaei, M. R. Ghazavi, Stabilizing slider-crank mechanism with clearance joints, Mech. Mach. Theory. 53 (2012) 17-29.) proposes an active control strategy for improving the precision degradation caused by the clearance in the kinematic pair. The strategy stabilizes the dynamic characteristics of the kinematic pair with clearance by using an extended delayed feedback method. However, the method depends on real-time measurement of the operation state of the mechanism, and a control structure between the slider and the rack needs to be constructed, which increases the implementation difficulty of the scheme. SUMMARY

[0004] The application provides a passive control device and design method for dead-zone operation precision of a reciprocating mechanism, aiming to improve the repeated positioning precision of the reciprocating mechanism in the dead zone.

[0005] The application is implemented by the following technical scheme: a passive control device for dead-zone operation precision of a reciprocating mechanism, comprising one nonlinear energy sink (NES), a guide rail, two supports, and two amplitude limiting devices; the nonlinear energy sink comprises a vibrator, a damping device, and a nonlinear spring; the vibrator is installed on a reciprocating slider (hereinafter referred to as a slider) of a controlled mechanism through the guide rail, and the installation direction is parallel to the running direction of the slider; the slider is located on the main guide rail of the controlled mechanism and performs reciprocating motion; the two amplitude limiting devices are symmetrically installed at both ends of the running direction of the vibrator and are respectively fixed to the slider; the two nonlinear energy sinks are installed in the vertical direction of the running direction of the vibrator; one end of the nonlinear energy sink is connected to the slider through the support, and the other end is connected to the vibrator.

[0006] A design method for a passive control device for dead-zone operation precision of a reciprocating mechanism, and the specific steps include:

[0007] Step S1: according to the specific structure of the controlled mechanism, the dead zone operation precision passive control device of the reciprocating mechanism is arranged on the slider.

[0008] Step S2: adjust the distance between the stopper and the vibrator, so that the vibrator stroke is equal to the comprehensive gap of the controlled mechanism.

[0009] Step S3: determine the damping and stiffness values of the nonlinear energy sink; based on the materials of the collision block and the stopper, the end face curvature radius of the stopper, the Hertz contact stiffness is calculated.

[0010] Step S4: set the initial mass of the vibrator to be 1% to 5% of the total mass of the slider; establish the dynamic equation set of the controlled mechanism and the control device.

[0011] Step S5: solve the dynamic equation set, calculate the dead zone repeat positioning precision value of the controlled mechanism; if the precision is unacceptable and the vibrator mass is within the given interval, return to step S4 to select the vibrator mass again; if the precision is unacceptable and the vibrator mass exceeds the given interval, go to step S6; if the precision is acceptable, end the process.

[0012] Step S6: redesign the damping and stiffness values of the nonlinear energy sink, and return to step S3.

[0013] Compared with the prior art, the present application has the following advantages:

[0014] (1) The present application does not rely on the state observation of the controlled mechanism, and effectively reduces the complexity of the control structure without increasing the connection structure between the controlled mechanism and the fixed frame.

[0015] (2) The present application combines the nonlinear energy sink and the limiting device, which can generate larger control force with smaller vibrator mass by using the limiting device, and can suppress high-frequency vibration of the slider in a wide frequency band by combining the nonlinear spring structure of the NES, thereby solving the problem of poor dead zone repeat positioning precision of the motion mechanism caused by the mechanism gap. BRIEF DESCRIPTION OF DRAWINGS

[0016] The present application will be further described in detail below with reference to the accompanying drawings. The drawings described herein form a part of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0017] Figure 1 It is a structure schematic diagram of a reciprocating mechanism dead zone operation precision passive control device of the present application.

[0018] Figure 2 It is a principle diagram of a reciprocating mechanism dead zone operation precision passive control device of the present application.

[0019] Figure 3 Structure diagram of the crank slider system with control mechanism in the embodiment of the present application.

[0020] Figure 4 Comparison diagram of the front and rear repeat positioning accuracy of the mechanism controlled in the embodiment of the present application. DETAILED DESCRIPTION

[0021] The technical solutions of the present application will be described in detail below in combination with embodiments. The illustrative embodiments and descriptions of the present application are only used to explain the present application and do not limit the present application.

[0022] The present application is realized by the following technical solutions:

[0023] In combination with Figure 1 and Figure 2 , a passive control device for dead zone operation accuracy of a reciprocating mechanism, comprising a nonlinear energy sink (NES) 3, a guide rail 7, two supports 6, and two limiting devices 2; the nonlinear energy sink 3 comprises a vibrator 1, a damping device 301, and a nonlinear spring 302; the vibrator 1 is installed on a reciprocating slider 5 (hereinafter referred to as slider) of a controlled mechanism through the guide rail 7, and the installation direction is parallel to the running direction of the slider 5; the slider 5 is located on the main guide rail 4 of the controlled mechanism and performs reciprocating motion; the two limiting devices 2 are symmetrically installed at both ends of the running direction of the vibrator 1 and are respectively fixed to the slider 5; the two nonlinear energy sinks 3 are installed in the vertical direction of the running direction of the vibrator 1; one end of the nonlinear energy sink 3 is connected to the slider 5 through the support 6, and the other end is connected to the vibrator 1.

[0024] The vibrator 1 is symmetrically provided with a collision block 101 at both ends of the running direction, and the material of the collision block 101 is selected from any one of brass, rubber, or copper-aluminum alloy; the vibrator 1 is pre-provided with a bolt hole for installing a counterweight structure, so as to adjust the mass of the vibrator 1.

[0025] The limiting device 2 comprises a mounting support 201, a locking nut 202, and a stopper 203; the mounting support 201 is fixed to the slider 5 through a bolt; the end face of the stopper 203 is a spherical surface, which is in contact with the collision block 101 of the vibrator 1 during the operation of the mechanism; the surface of the stopper 203 is processed with threads matched with the inner hole of the mounting support 201, so as to adjust the axial position of the stopper 203 to control the distance between the vibrator 1 and the stopper 203; the locking nut 202 is coaxial with the stopper 203 and is used to lock the axial position of the stopper 203.

[0026] The nonlinear spring 302 is connected in parallel with the damping device 301, and the damping device 301 is connected with the vibrator 1 and the support 6 through hinges at two ends; the support 6 is fixed on the sliding block 5 through bolts; the specific structure of the nonlinear energy sink 3 is realized by selecting one of the nonlinear spring damping device, elastic string or metal rubber.

[0027] Preferably, the sliding block 5 is reserved with a sliding groove and a bolt hole for mounting the guide rail 7, so as to facilitate accurate positioning of the guide rail 7.

[0028] Preferably, the mass of the vibrator 1 is 1% to 5% of the total mass of the sliding block 5.

[0029] Preferably, the Rockwell hardness of the material of the impact block 101 is less than that of the material of the stopper 203.

[0030] A design method of a passive control device for dead zone operation precision of a reciprocating mechanism, the specific steps comprising:

[0031] Step S1: According to the specific structure of the controlled mechanism, the passive control device for dead zone operation precision of the reciprocating mechanism is arranged on the sliding block 5.

[0032] Step S2: Adjust the distance between the stopper 203 and the vibrator 1, so that the stroke of the vibrator 1 is equal to the comprehensive gap of the controlled mechanism.

[0033] Step S3: Determine the damping and stiffness values of the nonlinear energy sink 3; based on the materials of the impact block 101 and the stopper 203, and the end face curvature radius of the stopper 203, calculate the Hertz contact stiffness.

[0034] Step S4: Set the initial mass of the vibrator 1 to be 1% to 5% of the total mass of the sliding block 5; establish the dynamic equation set of the controlled mechanism and the control device.

[0035] Step S5: Solve the dynamic equation set to calculate the dead zone repeatability precision value of the controlled mechanism; if the precision is not acceptable and the vibrator mass is within the given interval, return to step S4 to select the vibrator mass again; if the precision is not acceptable and the vibrator mass exceeds the given interval, go to step S6; if the precision is acceptable, end the process.

[0036] Step S6: Redesign the damping and stiffness values of the nonlinear energy sink, and return to step S3.

[0037] The working principle of the present application is that the existence of the mechanism comprehensive gap causes the bearing and shaft diameter of the pair of movements to continuously collide-contact-separate, thereby generating local high-frequency vibration. When the slider reaches the dead zone position, the force of the pair of movements on the slider continuously decreases, resulting in the high-frequency vibration phenomenon becoming particularly obvious; the non-linear energy sink dissipates the vibration of the slider by the inertial force caused by the relative movement of the vibrator and the slider, and realizes vibration absorption on a wide frequency band through the non-linear spring; the limiting device ensures that the stroke of the vibrator is the same as the mechanism comprehensive gap, ensures that the collision block and the position limiter are in contact when the slider reaches the dead zone position, increases the reaction force of the vibrator on the slider, thereby further weakening the high-frequency vibration and reducing the influence of the gap on the positioning accuracy of the mechanism.

[0038] Embodiment

[0039] In combination Figure 3 And Figure 4 The present embodiment provides a crank slider system applying the dead zone operation precision passive control device of the reciprocating mechanism, and the main moving parts of the system include: a main shaft, a crank, a connecting rod, a slider and a controller. The slider performs linear reciprocating motion under the drive of the crank; the rotational pair between the connecting rod and the slider is provided with a radial gap of 0.2 mm; and the gaps in other pairs of movements are ignored.

[0040] According to the control device provided in the above specific embodiment, assuming that the crank speed is constant, the dynamic equation set of the system is:

[0041]

[0042] Among them,

[0043]

[0044] Among them: m3, m4, M vi respectively correspond to the mass of the connecting rod, the mass of the slider and the mass of the vibrator; L2 and L3 respectively correspond to the length of the crank and the length of the connecting rod; b3 is the ratio of the length from the mass center of the connecting rod to the rotational pair between the crank and the connecting rod to the length of the connecting rod; I G3 is the moment of inertia of the connecting rod about the mass center in the running plane; ω is the crank speed; g is the gravity acceleration; R i and R j respectively correspond to the bearing radius and the shaft diameter radius; θ2 is the rotation angle of the crank; θ3, respectively correspond to the rotation angle, angular velocity and angular acceleration of the connecting rod; x4, respectively correspond to the displacement, velocity and acceleration of the mass center of the slider; x5, respectively correspond to the displacement, velocity and acceleration of the mass center of the vibrator; δ r and respectively correspond to the penetration distance and penetration speed of the rotational pair; δv and These correspond to the penetration distance and penetration speed of the oscillator relative to the limiter, respectively; These correspond to the initial contact velocity of the shaft diameter relative to the bearing and the initial contact velocity of the oscillator relative to the limiter, respectively; α is the eccentricity angle of the rotating pair. Q is the eccentric angular velocity of the rotating joint; c The resultant force of the collision between the rotating pairs; ψ is the angle between the normal contact force and the resultant force of the revolute joint; ψ is the angle between Q and Q. c Angle with the global X-axis; F ext and F NES These correspond to the resultant force of the control device acting on the slider and the resultant force of the nonlinear spring damping acting on the oscillator, respectively; c r and c v These correspond to the clearance of the rotating joint and the clearance between the oscillator and the limiter, respectively; K r K a C a These correspond to the contact stiffness of the rotating pair, the stiffness of the nonlinear energy trap, and the damping of the nonlinear energy trap, respectively; e is the eccentricity; μ is the friction coefficient of the rotating pair; and sign is the sign function.

[0045] The initial conditions at time t0 are set as follows:

[0046]

[0047] System parameters are set as follows: m3 = 0.103 kg, m4 = 3.3 kg, L2 = 0.032 m, L3 = 0.12 m, b3 = 0.5, I G3 =1.6×10 -4 kg·m 2 ω = 200 rpm, R i =9mm, R j =9.2mm, c r =0.2mm, c v =0.2mm, K r =1×10 11 N / m 1.5 K c =1×10 10 N / m 1.5 C a =1×10 4 N / m·s, μ=0.02.

[0048] Adjusting the oscillator mass M vi =0.105kg, the positioning accuracy of the system controlling the front and rear sliders at the bottom dead center is as follows: Figure 4 As shown. From Figure 4It can be seen that the positioning accuracy of the slider lower dead point is effectively improved, and the accuracy is improved from 49 μm before control to 0.9 μm (after 50 slider running periods), and the accuracy control effect is obvious.

[0049] The above specific embodiments explain the purpose, technical solutions and beneficial effects of the present application in detail. It should be understood that the above description is only a specific embodiment of the present application and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A passive control device for dead-zone operation accuracy of a reciprocating motion mechanism, characterized in that; It includes a nonlinear energy trap, a guide rail (7), two supports (6), and two limiting devices (2); the nonlinear energy trap includes an oscillator (1) and a nonlinear spring damping device (3); the oscillator (1) is mounted on the slider (5) of the controlled mechanism via the guide rail (7), and the running direction of the oscillator (1) is parallel to the running direction of the slider (5); the slider (5) is located on the main guide rail (4) of the controlled mechanism and performs reciprocating motion; the two limiting devices (2) are symmetrically installed at both ends of the running direction of the oscillator (1) and are respectively fixed to the slider (5); the two nonlinear spring damping devices (3) are symmetrically installed on both sides of the running direction of the oscillator (1); the two ends of the nonlinear spring damping device (3) are respectively connected to the support (6) and the oscillator (1) via rotating hinges; the support (6) is fixed to the slider (5).

2. The passive control device for dead zone operation accuracy of a reciprocating motion mechanism according to claim 1, characterized in that: The oscillator (1) has a collision block (101) symmetrically installed at both ends of the running direction. The collision block (101) is made of brass, rubber or copper-aluminum alloy.

3. The passive control device for dead zone operation accuracy of a reciprocating motion mechanism according to claim 2, characterized in that: The limiting device (2) includes a mounting bracket (201), a locking nut (202), and a limiter (203). The mounting bracket (201) is fixedly connected to the slider (5). The end face of the limiter (203) is a spherical curved surface, which contacts the collision block (101) of the vibrator (1) during the operation of the mechanism. The surface of the limiter (203) is machined with a thread that matches the inner hole of the mounting bracket (201). The axial position of the limiter (203) is adjusted by the thread to control the distance between the vibrator (1) and the limiter (203). The locking nut (202) is coaxial with the limiter (203) and is used to lock the axial position of the limiter (203).

4. The passive control device for dead zone operation accuracy of a reciprocating motion mechanism according to claim 3, characterized in that: The nonlinear spring damping device (3) includes a damping device (301) and a nonlinear spring (302); the damping device (301) and the nonlinear spring (302) are coaxially connected in parallel.

5. The passive control device for dead zone operation accuracy of a reciprocating motion mechanism according to claim 4, characterized in that: The mass of the oscillator (1) is 1% to 5% of the total mass of the slider (5).

6. The passive control device for dead zone operation accuracy of a reciprocating motion mechanism according to claim 5, characterized in that: The Rockwell hardness of the material of the collision block (101) is less than that of the Rockwell hardness of the material of the limiter (203).

7. A design method for a passive control device for dead-zone operation accuracy of a reciprocating motion mechanism according to claim 3, characterized in that, The specific steps include: Step S1: According to the specific structure of the controlled mechanism, set the passive control device for the dead zone running accuracy of the reciprocating motion mechanism on the slider (5); Step S2: Adjust the distance between the limit switch (203) and the oscillator (1) so that the stroke of the oscillator (1) is equal to the overall clearance of the controlled mechanism; Step S3: Determine the damping and stiffness values ​​of the nonlinear spring damping device (3); calculate the Hertzian contact stiffness based on the materials of the collision block (101) and the limiter (203) and the end face curvature radius of the limiter (203); Step S4: Set the initial mass of the oscillator (1) to 1%~5% of the total mass of the slider (5); establish the dynamic equations of the controlled mechanism and control device; Step S5: Solve the dynamic equations and calculate the dead zone repeatability accuracy of the controlled mechanism; if the accuracy is unacceptable and the oscillator mass is within the given range, return to step S4 to reselect the oscillator mass; if the accuracy is unacceptable and the oscillator mass exceeds the given range, proceed to step S6; if the accuracy is acceptable, end the process. Step S6: Redesign the damping and stiffness values ​​of the nonlinear energy trap, and return to step S3.

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