A method for calculating interface contact force considering bending effect

Abstract

The application discloses a method for calculating interface contact force by considering the influence of bending effect, and the method is realized by a curved interface force-electric contact model. The interface contact force of the curved interface is calculated by using parameters which are easy to obtain, and the convenience and accuracy of the measurement of the interface contact force of the curved interface are improved.

Description

Technical Field

[0001] This invention belongs to the field of contact force detection technology, specifically a method for calculating interface contact force considering the influence of bending effect. Background Technology

[0002] Bending interface contact structures are widely found in key parts of high-end equipment, such as annular sealing joints of aero engines, disc coils of superconducting magnets, and rotating pair components in precision instruments. The service performance of these structures largely depends on the mechanical behavior of the contact interface. The contact state of the interface directly affects key performance parameters such as structural sealing performance, system stiffness, force transmission path stability, and force-electric response.

[0003] However, due to the influence of random roughness and curvature changes at curved interfaces, the distribution of contact force and the contact area exhibit significant nonlinear evolution with load, making their contact behavior more complex and difficult to predict than that of conventional planar contact. Currently, there is a lack of theoretical models for curved interfaces based on contact mechanics, making it difficult to measure the contact force at curved interfaces. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating interfacial contact force that takes into account the influence of bending effects, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating interfacial contact force considering the influence of bending effects, characterized by comprising the following steps:

[0006] S1: Obtain the equivalent resistivity of the interfacial contact material by consulting material parameters or by measurement. Long contact interface Wide contact interface Central angle of the contact interface The elastic modulus of the two contacting materials and Poisson's ratio of the two contacting materials and And the initial maximum depth of the two contact surfaces when no load is applied. Observe the contact interface parameters using a profile observation instrument. C and ;

[0007] S2: Measure the contact resistance between the two contact surfaces. ;

[0008] S3: By formula: Calculate the equivalent elastic modulus of the materials at the two contact interfaces. The data obtained in step S1 and step S2 are substituted into a curved interface force-electric contact model to calculate the interface contact force, and the curved interface force-electric contact model is as follows:

[0009] ,

[0010] In the formula, is the interface contact force, is the ballast depth after the load is applied to the two contact interfaces, The expression for calculating the ballast depth

[0011] is obtained by simultaneously solving the following formulae: In the formula, is the equivalent radius of the spherical microconvex, is the radius of a single spherical microconvex on the two contact curved surfaces, and the average radius of the microconvex is obtained by observing the curved surface microconvex by means of a profilometer.

[0012] Preferably, in step S1, the central angle of the contact interface is obtained by calculation, and the specific steps are as follows:

[0013] S11: The radii of the two contact curved surfaces and are measured respectively, and the central angle

[0014] is obtained by simultaneous calculation by means of the formula: In the formula, is the radius of the contact arc surface of the two contact curved surfaces.

[0015] Further, in step S1, when the resistivities of the two contact interface materials are different, the equivalent thermal resistance method is adopted, and the equivalent resistivity of the interface contact material is calculated by means of the formula: In the formula, is the equivalent resistivity of the interface contact material, and are the resistivities of the two contact interface materials respectively, and the equivalent resistivity is substituted into the curved interface force-electric contact model to calculate the interface contact force.

[0016] Compared with the prior art, the present application has the following beneficial effects:

[0017] The present application creates a curved interface force-electric coupling model based on the Hertz contact theory, without considering the influence of the curved configuration in the existing model; the randomness in the contact interface is simplified by combining the volume contact theory, the influence of the curvature change on the contact parameters in the contact interface is analyzed, the unmeasurable contact stress in the contact interface is inverted according to the measurable contact resistance, and the convenience and accuracy of the curved interface contact force measurement are improved. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a curved surface contact schematic diagram provided by an embodiment of the present application;

[0019] Figure 2 is an initial maximum depth schematic diagram of curved surface contact provided by an embodiment of the present application;

[0020] Figure 3 is a detection experiment schematic diagram provided by an embodiment of the present application;

[0021] Figure 4 is a coil structure schematic diagram provided by an embodiment of the present application;

[0022] Figure 5 is a coil surface profile diagram provided by an embodiment of the present application;

[0023] Figure 6 is a coil experiment data statistical diagram provided by an embodiment of the present application;

[0024] Figure 7 is a plane interface contact experiment schematic diagram provided by an embodiment of the present application;

[0025] Figure 8 is a plane contact interface profile diagram provided by an embodiment of the present application;

[0026] Figure 9 is a plane interface contact experiment data statistical diagram provided by an embodiment of the present application. DETAILED DESCRIPTION

[0027] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0028] Please refer to Figures 1-9 , the present application provides a technical solution: a method for calculating interface contact force considering the influence of bending effect; the derivation process of the method is as follows:

[0029] Because the contact model of the bending interface is not directly given in the traditional contact model, and based on the contact theory of two curved surface elastic bodies in the Hertz contact theory, as shown in Figure 1 , when two cylinders are in contact, a theoretical model about the contact of the cylinders can be obtained, and the formula is as follows:

[0030] (1)

[0031] wherein R is the radius of the contact arc surface of the two cylinders, and are the radii of the two cylinders, respectively;

[0032] In the curved state, the contact arc surface radius can also be expressed as:

[0033] (2)

[0034] wherein is the arc length, is the central angle corresponding to the arc length;

[0035] In the Hertz contact theory, for the elastic bodies ignoring surface roughness, the relationship between the load and the deformation of the curved interface when the two cylinders are in parallel contact can be obtained as:

[0036] (3)

[0037] wherein is the load-induced pressure deformation, W is the width of the contact interface, F is the load applied to the contact interface, that is, the interface contact force between the two curved surfaces, is the equivalent elastic modulus, According to the two curved surface elastic body contact theory in the Hertz contact theory, the formula is:

[0038] (4)

[0039] wherein and are the elastic modulus and Poisson's ratio of one of the two cylinders, respectively, and are the elastic modulus and Poisson's ratio of the other cylinder, respectively;

[0040] In the Hertz contact theory, the expression of the contact area when the cylinders are in contact with each other is:

[0041] (5)

[0042] wherein is the contact surface radius in the Hertz contact theory, which can be calculated by formula (6):

[0043] (6)

[0044] The Hertz contact theory ignores the roughness of the elastomer surface, but in the actual contact state, the contact surface is not smooth, and the roughness cannot be ignored. Therefore, the contact area of the curved surface obtained by the Hertz contact theory is the nominal contact area. The nominal contact area of the two curved surfaces can be obtained by combining formulas (2)-(6):

[0045] (7)

[0046] Considering that the actual contact interface is composed of randomly distributed micro-convex bodies, and the volume of the micro-convex body approximately remains constant during the contact deformation process, a theoretical model for describing the real contact area of the curved surface contact interface can be established based on the volume conservation principle. However, the probability of contact between different micro-convex bodies is still random, so we need to calculate the number of micro-convex bodies in contact, i.e., the number of contact points, which can be calculated as follows:

[0047] When a macroscopically uniform load is applied to the curved interface, the force expression of a single pair of micro-convex bodies is:

[0048] (8)

[0049] where is the load borne by a single pair of micro-convex bodies, d is the indentation depth of a single micro-convex body, represents the equivalent radius of a single pair of micro-convex bodies in contact. In the calculation and application, it can be assumed that the micro-convex bodies in the contact interface are ideal spherical micro-convex bodies with consistent shape and size. The difference in the shape distribution of the micro-convex bodies is simplified as the difference in the contact probability distribution, and the equivalent radius can be expressed as:

[0050] (9)

[0051] where is the radius of a single spherical micro-convex body, which can be obtained by observing the curved surface micro-convex body and calculating the average radius of the micro-convex body using a profile observation instrument. Based on the actual applied load F and the load borne by a single micro-convex body , the number of micro-convex bodies in contact on the curved interface N can be calculated as:

[0052] (10)

[0053] At this time, the real contact area of the curved interface can be represented as the product of the number of all contact micro-convex bodies and the contact area of a single micro-convex body , and its expression is:

[0054] (11)

[0055] Under the action of pure normal load, the contact area of a single micro-asperity on the contact surface with the opposite surface can be calculated according to the model of two elastic spheres in contact in the Hertz contact theory. The expression of the contact area of two micro-asperities is:

[0056] (12)

[0057] By combining formulas (10) to (12), the relationship between the real contact area, load, micro-asperity radius, and contact depth is obtained as:

[0058] (13)

[0059] In the research paper: [Zhao, H., Ta, W. & Zhou, Y. The mechanical-thermal-electrical contact behaviors between rough surfaces under cyclic loading. Acta Mech. Sin. 39, 123212 (2023).], the contact model between interfaces was established by representing the contact process with probability, which gives another expression for the number of contact points on a rough interface :

[0060] (14)

[0061] where is the maximum number of contact points on the contact surface, C and are parameters in the expression of the profile support curve in the above paper, and the detailed derivation process is explicitly stated in the paper, is the normalized cross-sectional height expression between two contact surfaces, which is specifically:

[0062] (15)

[0063] where is the initial maximum depth, The measurement is shown in Figure 2 , is the pressure depth of the micro-asperity when the load is applied.

[0064] At this time, the number of micro-asperities in contact on the curved interface N is calculated as:

[0065] (16)

[0066] The two expressions of the number of contact points, formula (10) and formula (16), are combined to obtain the relationship between the radius of the micro-convex body and the load and the contact depth of the micro-convex body:

[0067] (17)

[0068] The formula shows that, under the premise that the macro load and the curved interface angle remain unchanged, when the depth of ballast is constant, the radius of the micro-convex body is constant, thereby ensuring that the number of contact micro-convex bodies is constant, i.e., the real contact area remains unchanged. In this way, the correlation between the macro curved interface and the micro contact behavior is realized. By combining formula (17) with formula (13), the expression of the real contact area is obtained as:

[0069] (18)

[0070] After obtaining the real contact area of the curved interface, the contact force, resistance, and bending angle of the contact interface can be coupled based on the resistance law. By substituting formula (18) into the expression of the resistance law, the curved interface force-electric contact model is obtained as:

[0071] (19)

[0072] In the formula, is the contact resistance, is the equivalent resistivity of the interface contact material, is the initial maximum depth, L is the arc length of the contact interface, is the width of the contact interface, is the central angle of the contact interface, , , , , , is easily obtained by instrument measurement, is calculated by formula (17), is the equivalent elastic modulus, which can be calculated by formula (4), so that the interface contact force F between the two curved surfaces is calculated by the easily obtained measurement parameters and material parameters; when the resistivities of the two contact interface materials are the same, the equivalent resistivity of the interface contact material is the resistivity of any one of the two contact interface materials, and when the resistivities of the two contact interface materials are different, the equivalent thermal resistance method is used to calculate the equivalent resistivity of the interface contact material, and the calculation formula is: is calculated, in which, and are the resistivities of the two contact interface materials, and the interface contact force is calculated by substituting the equivalent resistivity into the curved interface force-electric contact model.

[0073] Model validation

[0074] Experimental verification 1: Since it is difficult to apply a uniform load to the curved interface in actual operation, and it is also difficult to accurately measure the contact force between the interfaces, the model verification is carried out according to the calculation method recorded in the literature [Wurui Ta, Xiaoyu Tang, Youhe Zhou; An electrometric method for the interface stress and contact resistance of pancake coil under winding force. Rev. Sci. Instrum. 1 January 2023; 94 (1): 014711.], the inter-turn contact force of the multi-turn coil is simulated as the contact force between the curved interfaces in the 360° bending state, the theoretical inter-turn contact force of the coil is calculated by the calculation method in the literature, and the calculated contact force is substituted into the theoretical model of the application, the contact resistance is calculated by the curved interface force-electric contact model of the application, and the correctness of the theoretical model of the application is verified by comparing the contact resistance calculated by the curved interface force-electric contact model of the application with the actually measured contact resistance.

[0075] In this experiment, two coils with different number of turns are used for verification, and the coil parameters are shown in Table 1.

[0076] Table 1 Coil parameter table

[0077]

[0078] Wherein, △r is the thickness of a single turn of the coil, the detection schematic diagram is as shown in Figure 3 , and the experimental coil structure is as shown in Figure 4 , the test coil has a multi-turn curved geometric shape and a regular rectangular contact interface; the detection device includes a nanovoltmeter (KEITHLEY 2182A), a current source (KEITHLEY 6221), and a winding device; the winding material used for the coil is T2 copper strip (99.90% Cu) or N6 nickel strip (99.50% Ni+Co), which is closely related to the curved interface force-electric contact model proposed in the application, so that the theoretical value and the experimental contact resistance value can be directly compared; before starting the measurement, the profile observation instrument is used to observe the surface profile of the coil, as shown in Figure 5 , wherein, in this experiment, the contact interface parameters of the 10-turn coil are C = 8.95 x 10-5, = 150, and the contact interface parameters of the 62-turn coil are C = 1.00 x 10-4, = 0.028; during the experiment, the winding force was adjusted by a weight to accurately control the contact state between the coil layers, thereby generating a bending interface with different properties.

[0079] Finally, the comparison results are shown in Figure 6 Compared with the flat interface, the curved interface force-electric contact model of the application improves the contact resistance prediction accuracy by 70%, and the calculated data show that the proposed model can more accurately describe the force-electric coupling behavior of the curved interface contact under different coil turns and load conditions.

[0080] Experimental verification 2: The curved interface force-electric contact model of the application is simplified to a flat interface contact, and its applicability under certain boundary conditions is verified by comparison with experimental data.

[0081] The experimental design principle is as follows: when the length of the test piece (0.05 meters) is fixed, if the curvature radius is set to be large, the contact surface is approximately a flat interface contact state (set to 2000 meters in this experiment). Under this parameter setting, the central angle becomes very small, and the contact interface can be regarded as a plane. By comparing the calculation results of this approximate model with the experimental data of the flat contact, the accuracy of the model is verified.

[0082] As shown in Figure 7 , the four-wire method is used to measure the contact resistance to improve the measurement accuracy and eliminate the interference of the lead resistance; the sample size is 50 mm x 30 mm x 20 mm; in order to observe the initial surface state of the sample, a MicroXAM-800 non-contact optical profiler is used to measure the morphology and roughness of the rough surface, and the morphology observation results of different interfaces are shown in Figure 8 , the initial parameters of the flat interface contact state are C=6, x=13.4, and the experimental measurement results and the theoretical calculation results of the curved interface force-electric contact model of the application are shown in Figure 9 , the comparison of experimental results and theoretical results, with the central angle decreasing continuously, the contact state of the contact interface tends to be more and more close to the flat interface contact state; as shown in Figure 9 , it can be clearly observed that the theoretical results of 0.1° agree best with the experimental results, thereby verifying the effectiveness of the force-electric coupling contact model of the curved interface developed in this study.

[0083] Although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art can modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for part of the technical features, and any modification, equivalent substitution, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A method for calculating interface contact force considering the influence of bending effect, characterized in that, comprising the steps of: S1: Obtain the equivalent resistivity of the interface contact material by consulting material parameters or measurement , the length of the contact interface , the width of the contact interface , the central angle of the contact interface , the elastic modulus of the two contact materials and , the Poisson's ratio of the two contact materials and , and the initial maximum depth of the two contact surfaces without load Observe the contact interface parameters C and with a profilometer S2: measuring the contact resistance of the two contact surfaces ; S3: By formula: Calculate the equivalent elastic modulus of the materials at the two contact interfaces. Substitute the data obtained in steps S1 and S2 into the interface force-electrical contact model to calculate the interface contact force. The interface force-electrical contact model is as follows: wherein is the interfacial contact force, is the depth of ballast after loading of both contact interfaces, by solving the following equations simultaneously: resulting in the expression for the calculated depth of ballast wherein is the equivalent radius of the spherical microprotrusions, is the radius of a single spherical microprotrusion on both contact surfaces, which is obtained by observing the microprotrusions of the surfaces with a profilometer and calculating the average radius of the microprotrusions.

2. The method of claim 1, wherein, In step S1, the central angle of the contact interface The calculation is as follows: S11: Measure the radius of the two contact surfaces respectively and by the formula: , the center angle of the circle is calculated simultaneously , wherein, is the radius of the contact arc surface of the two contact curved surfaces.

3. The method of claim 1, wherein, In step S1, when the resistivities of the two contact interface materials are different, the equivalent thermal resistance method is used, and the equivalent resistivity of the interface contact material is calculated by the formula: The calculation result is as follows, wherein, is the equivalent resistivity of the interface contact material, and are the resistivities of the two contact interface materials, and the interface contact force is calculated by substituting the equivalent resistivity into the curve interface force-electric contact model.

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