A device and method for measuring the tangential stiffness of a cosine wave regular morphology joint surface

Abstract

A device and method for measuring the tangential stiffness of a cosine wave regular morphology bonding surface, belonging to the field of bonding surface mechanical analysis and dynamics research, specifically relates to a method for measuring the tangential stiffness of a cosine wave regular morphology bonding surface based on theoretical formulas and device measurements. The device is composed of a workbench (1), a normal force device (2) fixed on the workbench, a tangential laser micro-displacement sensor (3), a normal force sensor (4), an upper test piece (5), a lower test piece (6), a tangential force sensor (7), a two-axis movable slide rail (8), a tangential loading screw (9), a shock-absorbing pad (10), and a signal acquisition system for calculating the mechanical properties of the bonding surface. The present invention is aimed at the regularity and periodicity of the machined surface, has the advantages of simple processing and easy operation, and can realize the analysis of the mechanical properties of the bonding surface when a tangential positive load and an offset load are applied to the bonding surface with a cosine wave regular morphology.

Description

Technical Field

[0001] The invention belongs to the field of mechanical analysis and dynamics research of bonding surfaces, and in particular relates to a method for measuring the tangential stiffness of a bonding surface with a cosine wave regular morphology based on a theoretical formula and device measurement. Background Art

[0002] According to reliable data, the stiffness of the machine tool joint surface accounts for 40%-50% of its total stiffness. Therefore, the performance of the joint surface directly affects the performance of the machine tool. Insufficient machine tool stiffness will cause deformation and vibration during the machine tool processing, which will not only affect the various precisions of the machine tool processing and the surface quality of the workpiece, but also reduce production efficiency and tool durability, and even reduce the service life of the machine tool. Therefore, if the stiffness of the joint surface can be improved, it will be of great significance to the improvement of the overall stiffness of the machine tool.

[0003] In the current analysis of the joint surface problem, most scholars try to solve the problem of contact mechanical properties of arbitrary rough surfaces based on irregular rough joint surfaces, targeting characteristic parameters such as the degree of roughness of the joint surface, machining methods, statistics and fractals. In fact, in most machining processes, there are often regular machining methods, so regular machining surfaces will be formed. In view of the regularity and periodicity of the machined surface, the establishment of a joint surface contact mechanical model provides a new idea for exploring mechanical properties such as joint surface contact stiffness. Summary of the invention

[0004] In order to solve the problem of the research gap of the above-mentioned processing surface with regular characteristics, the present invention discloses a method for measuring the tangential stiffness of the cosine wave regular morphology bonding surface and an experimental bench device.

[0005] Step 1: Theoretically derive the corresponding cosine wave regular morphology bonding surface tangential stiffness

[0006] Assume that the amplitude of the two cosine waves is A, the wavelength is f, the materials are the same, and there is only point contact before loading. After the normal load P acts, according to Hertz theory, the contact surface is an ellipse, and the cosine wave produces deformation in the normal direction. After the tangential load F acts, the contact surface is still an ellipse, and the cosine wave produces deformation in the tangential direction. The contact surface of the two cosine waves has friction, and the load input and displacement output of the two cosine waves are as follows: Figure 1a As shown, the displacement directions of the two cosine waves are Figure 1b shown.

[0007] According to Hertz's theory, the displacement of the contact surface of two cosine waves is:

[0008]

[0009] Where: G is the cosine wave equivalent shear modulus, E is the equivalent elastic modulus of the two cosine waves, E1 and E2 are the elastic moduli of the two cosine waves, υ is the Poisson's ratio, υ1 and υ2 are the Poisson's ratios of the two cosine waves, and R1 is the distance from any point (x', y') on the contact ellipse to the specified point (x, y).

[0010] R1 2 =(x-x') 2 +(y-y') 2 (2)

[0011] A normal load P is applied in the normal direction, and a tangential load F is applied in the tangential direction. The contact surface is usually divided into Figure 2 A no-slip zone and a slip zone are shown.

[0012] In the tangential contact process, the cosine waves that are completely consistent from top to bottom are used. A tangential load F is applied to one of the cosine waves to produce a constant tangential contact deformation. Then, according to the interaction force, the tangential contact deformation produced by the other cosine wave is -U, so that the two cosine waves can be balanced, and the relative displacement between the two cosine waves is 2U. Therefore, the analytical expression of the cosine tangential displacement is:

[0013]

[0014]

[0015] Where μ is the friction coefficient, P is the normal load, F is the tangential load, and G is the equivalent shear modulus. υ is Poisson's ratio, the first elliptic integral φ is the contact surface angle, The second elliptic integral e is the eccentricity of the contact ellipse: θ is the axis crossing angle,

[0016] Then the tangential stiffness is:

[0017]

[0018]

[0019] Step 2: Measure and obtain the tangential load and tangential displacement data of the joint surface

[0020] The purpose of the present invention is to provide a device for measuring the tangential stiffness of a cosine wave regular morphology bonding surface, to achieve the measurement of the tangential stiffness of a cosine wave regular morphology bonding surface, and to propose an identification method for the tangential stiffness of a cosine wave regular morphology bonding surface.

[0021] In order to achieve the above object, the present invention adopts the following technical solution:

[0022] A device for measuring the tangential stiffness of a cosine wave regular morphology bonding surface is designed, comprising a workbench (1), a normal loading device (2) fixed on the workbench, a tangential laser micro-displacement sensor (3), a normal force sensor (4), an upper test piece (5), a lower test piece (6), a tangential force sensor (7), a two-axis movable slide rail (8), a tangential loading device (9), a shock-absorbing pad (10), and a signal acquisition system for calculating the mechanical properties of the bonding surface. The device is characterized in that: the workbench (1) is arranged at the bottom of an overall mechanical frame, and the table top of the workbench (1) is a working surface with evenly distributed T-slots; shock-absorbing pads (2) are arranged under the four corners of the T-slot workbench, and a detachable positioning T-block is arranged on the bottom surface of the lower test piece (6), and the lower test piece (6) is fixed to the T-slot workbench (1) by means of the T-block and bolts. The bottom surface of the upper test piece (5) and the top surface of the lower test piece (6) are in contact with each other. A normal force sensor (4) is arranged on the top surface of the upper test piece (5). The normal loading device (2) is located directly above the center of the normal force sensor (4), the upper test piece (5) and the lower test piece (6). A tangential force sensor (7), a two-axis movable slide rail (8) and a tangential loading device (9) are arranged on the side of the lower test piece (6) along the T-slot direction. The two-axis movable slide rail (8) is fixed on the workbench (1) and can move in the Y and Z directions to meet the demand for applying a biased tangential force. The tangential loading device (9) can load the lower test piece (6) along the X direction. A tangential laser micro-displacement sensor (3) is arranged on the other side of the lower test piece (6). Each sensor is connected to a signal acquisition system.

[0023] The normal loading device is a hand-wheel type manual adjuster.

[0024] The tangential loading device (9) is a hand wheel type regulator.

[0025] One side of the lower specimen is located under the tangential force sensor, and the tangential laser micro-displacement sensor is arranged on the other side of the lower specimen, and the lasers emitted by the two tangential laser micro-displacement sensors act on the center of the upper specimen and the lower specimen.

[0026] The present invention aims at the regularity and periodicity characteristics of the machined surface, has the advantages of simple processing and easy operation, and can realize the mechanical property analysis of the bonding surface when tangential normal load and offset load are applied to the bonding surface with cosine wave regular morphology. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1a This is a diagram showing load input and displacement output.

[0028] Figure 1b This is a diagram showing the displacement direction of a single cosine wave.

[0029] Figure 2 Schematic diagram of the no-slip zone and sliding zone in tangential contact.

[0030] Figure 3 The device diagram for measuring the tangential stiffness of the cosine wave regular morphology bonding surface. In the figure: 1-workbench, 2-normal loading device, 3-tangential laser micro displacement sensor, 4-normal force sensor, 5-upper specimen, 6-lower specimen, 7-tangential force sensor, 8-two-axis moving slide rail, 9-tangential loading device, 10-shock-absorbing pad.

[0031] Figure 4 This is the main view of the upper specimen.

[0032] Figure 5 This is a top view of the upper specimen.

[0033] Figure 6 This is the front view of the lower specimen.

[0034] Figure 7 This is a top view of the lower specimen.

[0035] Figure 8 Schematic diagram of the forces acting on the upper and lower specimens. DETAILED DESCRIPTION

[0036] From the above, we can know that the theoretical tangential stiffness of the joint surface is:

[0037]

[0038] The device of the present invention is described in detail below in conjunction with the accompanying drawings.

[0039] like Figure 3As shown, a device for measuring the tangential stiffness of a cosine wave regular morphology bonding surface comprises a workbench (1), a normal loading device (2) fixed on the workbench, a tangential laser micro-displacement sensor (3), a normal force sensor (4), an upper test piece (5), a lower test piece (6), a tangential force sensor (7), a two-axis movable slide rail (8), a tangential loading device (9), a shock-absorbing pad (10), and a signal acquisition system for calculating the mechanical properties of the bonding surface. The device is characterized in that: the workbench (1) is arranged at the bottom of the overall mechanical frame, and the table top of the workbench (1) is a working surface with evenly distributed T-slots; shock-absorbing pads (2) are arranged under the four corners of the T-slot workbench, and a detachable positioning T-block is arranged on the bottom surface of the lower test piece (6), and the lower test piece (6) is fixed to the T-slot workbench (1) by T-blocks and bolts. The bottom surface of the upper test piece (5) and the top surface of the lower test piece (6) are in contact with each other. A normal force sensor (4) is arranged on the top surface of the upper test piece (5). The normal loading device (2) is located directly above the center of the normal force sensor (4), the upper test piece (5) and the lower test piece (6). A tangential force sensor (7), a two-axis movable slide rail (8) and a tangential loading device (9) are arranged on the side of the lower test piece (6) along the T-slot direction. The two-axis movable slide rail (8) is fixed on the workbench (1) and can move in the Y and Z directions to meet the demand for applying a biased tangential force. The tangential loading device (9) can load the lower test piece (6) along the X direction. A tangential laser micro-displacement sensor (3) is arranged on the other side of the lower test piece (6). Each sensor is connected to a signal acquisition system.

[0040] like Figure 4 As shown in FIG. 7 , the bonding surface of the upper and lower specimens is a bonding surface with a regular cosine wave morphology, and the intersection angle of the two cosine wave axes is 0°.

[0041] The measurement of the static tangential contact stiffness of the joint surface includes the following steps:

[0042] 1. Assemble all parts into a whole according to the above assembly relationship;

[0043] 2. By adjusting the hand wheel regulator of the normal loading device (2), the normal force is uniformly increased until a predetermined pressure is reached, and the normal force is measured by the normal force sensor (4). By adjusting the two-axis movable slide rail (8), the center of the tangential loading device (9) and the center of the side of the lower test piece (6) are on the same horizontal line. By adjusting the hand wheel regulator of the tangential loading device (9), the tangential force is uniformly increased until a predetermined tangential force is reached. The tangential force of the tangential joint surface of the upper test piece (5) and the lower test piece (6) is measured by the tangential force sensor (7), and the tangential displacement of the tangential joint surface of the upper test piece (5) and the lower test piece (6) is measured by the tangential laser micro displacement sensor (3);

[0044] 3. After one set of experiments is completed, the next set of test pieces is replaced and the above steps are repeated to obtain multiple sets of different types of tangential contact stiffness measurement data of the bonding surface; the tangential force sensor (7) and the tangential laser micro-displacement sensor (3) are processed by the signal acquisition system to obtain the tangential force-tangential displacement curve, and the tangential stiffness of the bonding surface can be obtained by taking its derivative.

[0045] Compared with the existing technology, the beneficial effects of the present invention are:

[0046] The present invention proposes a method for measuring the tangential stiffness of a cosine wave regular morphology bonding surface, and combines theory with experiment by deriving a theoretical model. The cosine wave contact model in the present invention is different from other cosine wave contact models in that the cosine wave contact model in the present invention includes an axis crossing angle, that is, a cosine wave contact model under different axis crossing angles. Compared with other regular contact models, this model is more universal. It can be applied to gear contact, roller bearings, and machined regular contact surfaces, and has more engineering practical value.

[0047] At the same time, this measurement method requires simple equipment, is easy to carry out, and is more likely to obtain accurate results. In addition to being applicable to cosine wave regular morphology surfaces, it is also applicable to other regular morphology characteristics and random morphology features, making it more universal.

[0048] The method for measuring the tangential stiffness of a cosine wave regular morphology bonding surface of the present invention can accurately obtain the tangential stiffness of the cosine wave regular morphology bonding surface, and the method is simple and easy to measure.

Claims

1. An application method of a device for measuring the tangential stiffness of a cosine wave regular morphology bonding surface, the device comprising a workbench (1), a normal loading device (2) fixed on the workbench, a tangential laser micro-displacement sensor (3), a normal force sensor (4), an upper test piece (5), a lower test piece (6), a tangential force sensor (7), a two-axis movable slide rail (8), a tangential loading device (9), a shock-absorbing pad (10), and a signal acquisition system for calculating the mechanical properties of the bonding surface, wherein the workbench (1) is arranged at the bottom of an overall mechanical frame, and the table top of the workbench (1) is a working surface with evenly distributed T-slots; shock-absorbing pads (10) are arranged under the four corners of the T-slot workbench, and a detachable positioning T-block is arranged on the bottom surface of the lower test piece (6); the lower test piece (6) is fixed to the T-slot workbench (1) by means of the T-block and bolts; the bottom surface of the upper test piece (5) and the top surface of the lower test piece (6) are in contact with each other, and the top of the upper test piece (5) is A normal force sensor (4) is arranged on the surface, a normal loading device (2) is located directly above the center of the normal force sensor (4), the upper test piece (5) and the lower test piece (6), a tangential force sensor (7), a two-axis movable slide rail (8) and a tangential loading device (9) are arranged on the side of the lower test piece (6) along the T-slot direction, the two-axis movable slide rail (8) is fixed on the workbench (1) and can move in the Y and Z directions to meet the demand for applying a biased tangential force, the tangential loading device (9) can load the lower test piece (6) along the X direction, and a tangential laser micro-displacement sensor (3) is arranged on the other side of the lower test piece (6); each sensor is connected to a signal acquisition system; one side of the lower test piece is located below the tangential force sensor, the tangential laser micro-displacement sensor is arranged on the other side of the lower test piece, and the lasers emitted by the two tangential laser micro-displacement sensors act on the center of the upper test piece and the lower test piece; Features: According to Hertz's theory, the displacement of the contact surface of two cosine waves is: Where: G is the cosine wave equivalent shear modulus, E is the equivalent elastic modulus of the two cosine waves, E1 and E2 are the elastic moduli of the two cosine waves, υ is the Poisson's ratio, υ1 and υ2 are the Poisson's ratios of the two cosine waves, and R1 is the distance from any point (x', y') on the contact ellipse to the specified point (x, y); R1 2 =(x-x') 2 +(y-y') 2 (2) A normal load P is applied along the normal direction, and a tangential load F is applied along the tangential direction. The contact surface is divided into a non-slip zone and a sliding zone. In the tangential contact process, the cosine waves that are completely consistent up and down are used. A tangential load F is applied to one of the cosine waves to produce a constant tangential contact deformation. Then, according to the interaction force, the tangential contact deformation produced by the other cosine wave is -U. Only in this way can the two cosine waves be balanced, and the relative displacement between the two cosine waves is 2U. Therefore, the analytical expression of cosine tangential displacement is: Where μ is the friction coefficient, P is the normal load, F is the tangential load, and G is the equivalent shear modulus. υ is Poisson's ratio, the first elliptic integral φ is the contact surface angle, The second elliptic integral e is the eccentricity of the contact ellipse: θ is the axis crossing angle, Then the tangential stiffness is: When measuring the static tangential contact stiffness of the joint surface, the normal force is uniformly increased by adjusting the hand wheel regulator of the normal loading device (2) until a predetermined pressure is reached. The normal force is measured by the normal force sensor (4). The center of the tangential loading device (9) and the center of the side of the lower test piece (6) are placed on the same horizontal line by adjusting the two-axis movable slide rail (8). The tangential force is uniformly increased by adjusting the hand wheel regulator of the tangential loading device (9) until a predetermined tangential force is reached. The tangential forces of the upper test piece (5) and the lower test piece (6) are uniformly increased. The tangential force on the bonding surface is measured by a tangential force sensor (7), and the tangential displacement of the tangential bonding surfaces of the upper test piece (5) and the lower test piece (6) is measured by a tangential laser micro-displacement sensor (3); after a set of experiments are completed, the next set of test pieces is replaced, and the above steps are repeated to obtain multiple sets of different types of bonding surface tangential contact stiffness measurement data; the tangential force-tangential displacement curve can be obtained by the tangential force sensor (7) and the tangential laser micro-displacement sensor (3) through signal acquisition system processing, and the tangential stiffness of the bonding surface can be obtained by taking the derivative thereof.

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