A tracking prediction method for nonlinear friction torque of test mechanism under dynamic derivative long-term test

Abstract

The present invention belongs to the field of mechanism friction modeling, and discloses a tracking and prediction method for the nonlinear friction torque of a test mechanism under a long-term dynamic derivative test. The method is based on the friction test of the transmission part coating to obtain the time-varying history of the coating friction coefficient; a nonlinear function of the friction coefficient is constructed based on the cumulative sliding displacement to describe the change process of the friction coefficient in the long-term experiment; based on the force analysis of the dynamic derivative test mechanism, the support reaction force of each rotating pair is solved, and the contact pressure distribution of the rotating pair is calculated and solved through the elastic contact model; based on the obtained contact pressure distribution, a tangential stick-slip friction force model is constructed to solve the friction torque of the rotating pair and obtain the friction torque of the mechanism motion chain; based on the nonlinear function of the friction coefficient, the sliding displacement in the cumulative calculation test is adjusted to achieve tracking and prediction of the nonlinear friction torque of the test mechanism under the long-term dynamic derivative test.

Description

Technical Field

[0001] The invention belongs to the field of mechanism friction modeling. Aiming at the problem that the friction force is difficult to characterize and predict due to the wear of the test mechanism in a long-term dynamic derivative experiment, a tracking and prediction method for the nonlinear friction torque of the test mechanism in a long-term dynamic derivative experiment is designed. Background Art

[0002] Today's high-end aircraft are developing towards supersonic and hypersonic speeds. At the same time, they must have high maneuverability and be able to maneuver flexibly in highly dynamic environments. Therefore, higher requirements are placed on the aerodynamic stability of aircraft. The dynamic derivative test is a key link in aircraft design and performance evaluation. It simulates the aerodynamic conditions of the aircraft during service in a wind tunnel, controls the movement and attitude of the aircraft through the test mechanism, and simultaneously collects the force and position state data of the aircraft. The dynamic derivative is calculated to evaluate the aerodynamic stability of the aircraft under different flight conditions and optimize the design of the aircraft's aerodynamic shape. The dynamic derivative test has become an indispensable part of the development process of high-end aircraft.

[0003] In the dynamic derivative test, long-term high-frequency excitation will cause friction loss of the transmission parts, resulting in changes in the friction torque of the transmission pair, causing the dynamic characteristics of the system to drift, thereby reducing the motion control accuracy, thus affecting the accuracy and effectiveness of the dynamic derivative test results in long-term tests. The current wind tunnel test is constantly developing towards a continuous wind tunnel. The attenuation of the accuracy of long-term dynamic derivative tests restricts the progress of continuous tests and limits the efficiency of dynamic derivative experiments. In order to improve the accuracy of dynamic derivative tests, it is necessary to analyze and model the friction loss of the transmission parts under long-term tests, characterize and predict the friction of the transmission pair, and then achieve an improvement in motion control accuracy. Therefore, there is an urgent need for a tracking and prediction method for the nonlinear friction torque of the test mechanism under long-term dynamic derivative tests.

[0004] Professor Zhang Yongnian of Nanjing Agricultural University published a paper in 2022, "Dynamic Error Analysis and Optimal Design of Planar Flexible Multi-link Mechanisms with Angular Contact Ball Bearings and Rough Clearance Surface Sliding Bearing Joints", which aims at the analysis and calculation needs of friction on the contact surface of rough joints, and proposed a rough clearance surface rotation joint model, which can accurately simulate the actual contact pressure of rough clearance surface rotation joints with less calculation amount, and realize accurate calculation of friction force. However, it lacks analysis of long-term wear. Under long-term operation, the accuracy of the proposed model will decrease. The paper "The Effect of Flexibility on the Wear of the Coach in Multi-body Systems" published by Zhao Bo's team of Shanghai Jiaotong University in 2014 is aimed at the prediction method of wear on the gap hinged joint parts in flexible multi-body systems. It realizes accurate simulation of mechanism wear and friction force while taking into account the flexibility of components. However, its simulation method has large amount of calculation and long simulation time, and it is difficult to use it in the tracking prediction of dynamic derivative test mechanisms.

[0005] In the above-mentioned mechanism friction modeling methods, there is a lack of wear modeling in the mechanism movement in the rapid calculation, which leads to a decrease in the model accuracy under long-term operation. The modeling methods that take the mechanism wear into account have too much calculation and long simulation time, and cannot be directly used in the tracking and prediction of the mechanism friction force in the long-term dynamic derivative test. Therefore, a tracking and prediction method for the nonlinear friction torque of the test mechanism in the long-term dynamic derivative test with a simple calculation model and taking into account the long-term wear is needed. Summary of the invention

[0006] The present invention relates to the field of nonlinear friction modeling of mechanisms, and to a tracking and prediction method for the nonlinear friction torque of a test mechanism under a long-term dynamic derivative test, aiming to solve the technical problem that the wear of the rotating pair in the high-pressure long-term transmission under the continuous dynamic derivative excitation test increases the friction coefficient, resulting in the drift of the friction characteristics of the mechanism and the failure of the dynamic model. The method is based on the friction test of the transmission part coating to obtain the time-varying history of the coating friction coefficient; the nonlinear function of the friction coefficient is constructed based on the cumulative sliding displacement to describe the change process of the friction coefficient in the long-term experiment; the support reaction force of each rotating pair is solved based on the force analysis of the dynamic derivative test mechanism, and the contact pressure distribution of the rotating pair is calculated and solved through the elastic contact model; based on the contact pressure distribution, a tangential stick-slip friction force model is constructed to solve the friction torque of the rotating pair and the friction torque of the mechanism motion chain; based on the nonlinear function of the friction coefficient, the sliding displacement in the cumulative calculation test is adjusted to achieve the tracking prediction of the nonlinear friction torque of the test mechanism under the long-term dynamic derivative test. The invention can predict the friction torque of the mechanism in real time, has stronger adaptability to long-term tests, and can effectively suppress characteristic drift and model failure caused by wear and tear during long-term operation.

[0007] The technical solution of the present invention:

[0008] A tracking and prediction method for the nonlinear friction torque of a test mechanism under a dynamic derivative long-term test, firstly based on a reciprocating sliding friction test, the time-varying history of the friction coefficient of a transmission component coating is obtained; according to the accumulated sliding displacement, a nonlinear function of the friction coefficient is constructed to describe the variation law of the friction coefficient during the long-term experiment; based on the known dynamic derivative test mechanism force analysis, the support reaction force of each rotating pair is analyzed, an elastic contact model is constructed, and the contact pressure distribution of the rotating pair is calculated and solved; a tangential stick-slip friction force model is established to solve the friction torque of the rotating pair, and then the friction torque of the mechanism motion chain is obtained; according to the aforementioned nonlinear function of the friction coefficient, the friction coefficient of the tangential stick-slip friction force model is dynamically adjusted by accumulating the sliding displacement in the experiment, and finally the tracking and prediction of the nonlinear friction torque of the test mechanism in the long-term experiment is realized.

[0009] The specific steps are as follows:

[0010] (1) Based on the friction tester, a high-speed reciprocating sliding experiment between a small ball and a plane is selected, in which both the small ball and the plane are treated with the coating required for the dynamic derivative test. The contact force and friction force in the reciprocating sliding experiment are collected, and the friction coefficient of the coating is calculated. The experiment is carried out for a long time, and the time-varying history curve of the friction coefficient, the contact force, and the sliding displacement are recorded. The reciprocating motion function form and the friction coefficient calculation formula are shown in the following equations (1) and (2):

[0011] (1)

[0012] (2)

[0013] Among them, y represents the distance of round-trip sliding, A represents the round-trip amplitude, f represents the round-trip frequency, and t represents the time variable. is the friction coefficient, , are the contact force and friction force in the reciprocating sliding test.

[0014] (2) Because the coating will wear and fall off during the reciprocating motion, causing direct contact between parts of the surface of the components, the friction coefficient of the contact surface is uneven. Therefore, a layered friction model is proposed, and its function form is as follows:

[0015] (3)

[0016] in, is the friction coefficient, , They represent the friction coefficients of coating contact and component direct contact respectively, and S represents the relative value of coating contact area to the total contact area.

[0017] Due to wear and tear, S decreases continuously until it completely falls off to 0. According to the Archard wear model, the wear amount is proportional to the contact pressure and sliding displacement. A nonlinear function is constructed to describe the wear process, and its form is as follows:

[0018] (4)

[0019] Where k is the wear coefficient, which is related to the material properties. is the contact pressure, L is the friction formation, and a is the offset coefficient.

[0020] Combining formulas (3) and (4) yields a nonlinear function of the friction coefficient as the contact pressure and sliding displacement change, as shown below:

[0021] (5)

[0022] According to the friction coefficient, contact pressure and sliding displacement measured in the previous step of the high-speed reciprocating sliding experiment, substitute them into the above formula (5) to fit and determine the various parameters. The input and output of its nonlinear function are shown as follows: Figure 2 .

[0023] (3) Perform force analysis on the transmission structure of the dynamic derivative test mechanism and solve the support reaction force of each rotating pair. The mechanism consists of transmission rods AB, BC, CE, and driver BD. A is the base. AB and BC are hinged at the fulcrum B. BC and CE are hinged at C. E is the base. BD and BC are hinged at B, and D is the base. The external load of the dynamic derivative test mechanism is , after acting on the mechanism, there are large support reaction forces at the fulcrums A, B, C, D, and E, generating large friction forces. The analysis of the support reaction forces is shown in the following formula:

[0024] (6)

[0025] in, , , , , The pivot points are B, A, C, E, and D. , , , is the moment acting on the fulcrums B, A, C, and E, where For external load, , , is the friction torque, , are the angles between BC and the horizontal plane, and between AB and the vertical plane, respectively. , , , The rod lengths of AB, BC, BD, and CE are shown in the force analysis diagram of the transmission structure of the dynamic derivative test mechanism. Figure 3 shown.

[0026] Based on the obtained support reaction force, an elastic contact model of the revolving pair is constructed, in which the revolving pair is composed of a transmission rod and a support. By introducing n spring damping units to describe the influence of the deformation of the elastic layer between each revolving pair, the contact pressure distribution is solved. Since the hardness of the transmission rod is higher than that of the support, it is assumed that only the support is deformed in the elastic contact. Therefore, there is an elastic deformation arc segment in the contact area between the transmission rod and the elastic layer of the support. n spring damping units are evenly distributed in the arc segment to describe the deformation and force of the elastic deformation arc segment. The schematic diagram of the elastic contact model is shown in the figure. Figure 4 As shown. From this, the maximum contact angle function can be obtained:

[0027] (7)

[0028] in, is the maximum penetration depth between the transmission rod and the support, is the support radius, is the eccentricity difference between the cylindrical axial surface on the transmission rod and the circular hole of the support, is the radius of the cylindrical axis surface on the transmission rod.

[0029] The contact pressure of a single spring damping unit satisfies the following formula (8):

[0030] (8)

[0031] In the formula, is the elastic modulus of a single spring-damper unit, is the elastic modulus of the support, is the Poisson's ratio of the support, is the thickness of the elastic layer, is the penetration depth of the i-th spring-damper unit, is the unit area of ​​the i-th spring damping unit, and h is the depth dimension of the transmission rod and the support.

[0032] Since it is assumed that the transmission rod does not deform, the ends of each spring damping unit are on the cylindrical axis of the transmission rod, and the penetration depth satisfies the following formula:

[0033] (9)

[0034] Along the normal direction of the contact surface, n The total contact force is obtained by adding the forces of the spring damping units, and the support reaction force of this support is shown in the following formula:

[0035] (10)

[0036] The magnitude of the support reaction force can be obtained by the above formula (6), and the contact pressure of each spring damping unit can be determined by the combined formula (7), (8), (9), and (10), and the contact pressure distribution of the revolving pair can be obtained by solving the above formula.

[0037] (4) The tangential stick-slip friction model between the support and the transmission rod is constructed, and the LuGre friction calculation method is used. The formula is as follows:

[0038] (11)

[0039] In the formula, is the relative sliding speed, , , , All are empirical values, 100000 N / m, 400Ns / m, 0, 2, respectively. is the Stribeck speed, which determines the transition speed range of friction from static friction to dynamic friction. Its empirical value is 0.01 mm / s. and are the dynamic and static friction coefficients, is the tangential friction force of the i-th spring-damper unit, is the total friction between the support and the transmission rod.

[0040] Based on the above-obtained distribution of the contact pressure of the rotating pair, the distribution of the friction coefficient in the rotating pair can be obtained by substituting it into equation (5), and it changes with the sliding displacement history. The contact pressure of the single spring damping unit can be obtained through the previous equation (8). Substituting the friction coefficient and the contact pressure of the single spring damping unit into equation (11), the friction force of the single spring damping unit and the total friction force of the rotating pair can be obtained. The friction torque of the rotating pair can be obtained as shown in the following equation:

[0041] (12)

[0042] in, , , The friction torque of the jth revolving pair, the friction force and the radius of the cylindrical axis surface on the transmission rod are solved in turn by solving the friction torque of each revolving pair of the transmission structure in the dynamic derivative test mechanism, and the friction torque of the mechanism motion chain can be obtained.

[0043] (5) In the long-term dynamic derivative test, the above method is used to substitute the external load and sliding displacement of each rotating pair measured in real time, and the support reaction force, friction coefficient, friction force, and friction torque of each rotating pair are calculated in real time to achieve the tracking prediction of the nonlinear friction torque of the test mechanism. The tracking prediction results of the nonlinear friction torque of each rotating pair are shown in the figure below. Figures 5 to 8 shown.

[0044] Beneficial effects of the invention: The invention proposes a tracking prediction method for the nonlinear friction torque of a test mechanism under a dynamic derivative long-term test. Compared with the traditional method, this method can predict the friction torque of the mechanism in real time, has stronger adaptability to long-term tests, and can effectively suppress characteristic drift and model failure caused by wear caused by long-term operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 The present invention is a flow chart of a method for tracking and predicting the nonlinear friction torque of a test mechanism under a long-term dynamic derivative test.

[0046] Figure 2 It is a schematic diagram of the change of the friction coefficient with the sliding displacement of the present invention.

[0047] Figure 3 It is a force analysis diagram of the transmission structure in the dynamic derivative test mechanism of the present invention.

[0048] Figure 4 It is a schematic diagram of the elastic contact model of the present invention.

[0049] Figure 5 This is a diagram showing the predicted results of the friction torque of the rotating pair at the fulcrum A of the present invention.

[0050] Figure 6 This is a diagram showing the predicted results of the friction torque of the rotating pair at the fulcrum B of the present invention.

[0051] Figure 7 This is a diagram showing the predicted results of the friction torque of the rotating pair at the fulcrum C of the present invention.

[0052] Figure 8 This is a diagram showing the predicted results of the friction torque of the rotating pair at the fulcrum E of the present invention. DETAILED DESCRIPTION

[0053] The specific implementation of the present invention is described in detail below in combination with the technical scheme and the accompanying drawings.

[0054] (1) Based on a friction tester, a high-speed reciprocating sliding experiment between a ball and a plane was carried out to study the tribological properties of a specific coating material under dynamic derivative experimental conditions. In the experiment, a coating that meets the requirements of the dynamic derivative test was selected to treat the contact surface between the ball and the plane, and the contact force and friction force during the reciprocating sliding process were collected in real time. By measuring the friction force between the contact surfaces during the experiment, the friction coefficient of the coating was calculated, and the changing trend of the coefficient was tracked and recorded for a long time. The experiment also simultaneously monitored the time-varying data of the contact force and sliding displacement, forming a time-varying curve of the coating friction coefficient and its dynamic response relationship with the contact conditions, which provided an experimental basis for further analyzing the durability and stability of the coating material under high-speed friction conditions. The reciprocating motion function form and the friction coefficient calculation formula are shown in the following equations (1) and (2).

[0055] (2) In the proposed layered friction model, the change in the friction coefficient is affected by the wear of the coating, and the functional form is shown in formula (3). As the wear progresses, the coating layer thickness S gradually decreases until the coating is completely detached and S=0. According to the Archard wear model, the wear amount is proportional to the contact pressure and sliding displacement. In order to more accurately describe the wear process of the coating, a nonlinear function is constructed, as shown in formula (4), which is used to describe the dynamic change process of the wear amount with time or sliding distance. By combining formula (3) and formula (4), the nonlinear relationship between the friction coefficient and the contact pressure and sliding displacement can be obtained, as shown in formula (5).

[0056] Next, the experimental data of friction coefficient, contact pressure and sliding displacement obtained from the high-speed reciprocating sliding experiment are substituted into formula (5), and the parameters in the nonlinear function are fitted using the least squares method to determine the specific model parameters. This can be used to predict the wear and friction coefficient changes of the coating under long-term service conditions.

[0057] (3) The force analysis of the transmission structure of the dynamic derivative test mechanism is carried out to solve the support reaction force of each rotating pair. The mechanism consists of transmission rods AB, BC, CE and driver BD. Point A is fixed to the base, and the transmission rods AB and BC are connected by hinges at the fulcrum B. BC and CE are hinged at the fulcrum C. Point E is also fixed to the base. The BD driver is hinged to the transmission rod BC at point B, and point D is also fixed to the base. When the system is subjected to external loads, large support reaction forces are generated at the fulcrums A, B, C, D and E, which in turn leads to significant friction.

[0058] In order to accurately analyze the mechanical behavior of the mechanism, it is necessary to carry out systematic mechanical modeling and calculation of the reaction forces at each support point. By balancing the force and moment conditions, the relevant mechanical equations can be established, and the support reaction forces at each support point can be further solved. Combined with the actual external load and the structural geometric characteristics of the transmission mechanism, the specific expression and action form of the support reaction force are shown in the following formula (6).

[0059] Based on the obtained support reaction force, the elastic contact model of the revolving pair is further constructed to describe the contact behavior between the transmission rod and the support in the revolving pair. The revolving pair consists of a transmission rod and a support. It is assumed that in actual work, since the material hardness of the transmission rod is higher than that of the support, only the support undergoes elastic deformation during the contact process, and the transmission rod can be regarded as a rigid body. In this model, n spring-damper units are introduced to characterize the influence of the elastic layer deformation of the support under stress on the contact mechanical properties. Figure 4 As shown, the maximum contact angle between the two can be expressed by formula (7). From this, the contact pressure of a single spring damping unit and the corresponding penetration depth can be written, which are expressed by formulas (8) and (9) respectively. The support reaction force has been obtained through the above steps. The sum of the contact pressures of the spring damping units is the total contact force, which is equal to the support reaction force. Therefore, the contact pressure of a single spring damping unit can be calculated by combining the above formulas (7), (8) and (9), thereby determining the contact pressure distribution.

[0060] (4) The LuGre friction calculation method is used to construct a tangential stick-slip friction model between the support and the transmission rod, and its specific form is shown in formula (11). Based on the contact pressure distribution of the rotating pair derived above, it is substituted into formula (5) to obtain the distribution characteristics of the friction coefficient in the rotating pair, and it is dynamically adjusted with the change of sliding displacement. According to formula (8), the contact pressure of a single spring-damper unit is further calculated, and the friction coefficient and the contact pressure of the unit are substituted into formula (11) to solve the friction force of a single spring-damper unit and the total friction torque of the rotating pair. In this way, the overall friction torque of the rotating pair can be obtained, and the specific expression is shown in formula (12).

[0061] (5) In the long-term test of dynamic derivative, based on the above method, the real-time measured external load and the sliding displacement of each rotating pair are used as input parameters to calculate the support reaction force, friction coefficient, friction force and friction torque of each rotating pair in real time. Through this process, the nonlinear friction torque in the dynamic derivative test mechanism can be dynamically tracked and predicted. In the calculation process, the real-time load is first substituted into the mechanical model of the overall test mechanism to obtain the support reaction force of each rotating pair. The friction coefficient of each rotating pair is solved by the constructed layered friction model, and the instantaneous friction force and the torque generated are calculated in combination with the contact pressure distribution and displacement history, so as to realize the real-time tracking and dynamic prediction of its nonlinear friction torque. Figures 5 to 8 These are the nonlinear friction torque tracking prediction results for each rotating pair.

[0062] Compared with traditional methods, this method can realize real-time prediction of the friction torque of the mechanism, effectively suppress the system characteristic drift and model failure caused by wear due to long-term operation, have stronger adaptability to long-term tests, and ensure the stability and accuracy of the prediction model during the test.

Claims

1. A tracking and prediction method for nonlinear friction torque of a test mechanism under a long-term dynamic derivative test, characterized in that: Here are the steps: (1) Based on a friction tester, a high-speed reciprocating sliding experiment between a small ball and a plane is selected, in which both the small ball and the plane are treated with the coating required for the dynamic derivative test. The contact force and friction force in the reciprocating sliding experiment are collected, and the friction coefficient of the coating is calculated. The experiment is carried out for a long time, and the time-varying history curve of the friction coefficient and the contact force and sliding displacement are recorded. The reciprocating motion function form and the friction coefficient calculation formula are shown in the following equations (1) and (2): y=Asin(2πft) (1) Among them, y represents the distance of the round-trip sliding, A represents the round-trip amplitude, f represents the round-trip frequency, t represents the time variable, μ represents the friction coefficient, and F N 、F f are the contact force and friction force in the reciprocating sliding test; (2) Because the coating will wear and fall off during the reciprocating motion, causing direct contact between parts of the surface of the components, the friction coefficient of the contact surface is uneven, so the layered friction model is proposed. Its function form is as follows: μ=μ1S+μ2(1-S) (3) Wherein, μ is the friction coefficient, μ1 and μ2 represent the friction coefficients of coating contact and component direct contact, respectively, and S represents the relative value of coating contact area to total contact area; Due to wear and tear, S decreases continuously until it completely falls off to 0. According to the Archard wear model, The wear amount is proportional to the contact pressure and sliding displacement; a nonlinear function is constructed to describe the wear history, and its form is as follows: Among them, k is the wear coefficient, which is related to the material properties, L is the friction formation, and a is the offset coefficient; Combining equations (3) and (4), we can obtain the nonlinear function of the friction coefficient as the contact pressure and sliding displacement change, as shown in the following equation: According to the friction coefficient, contact pressure and sliding displacement measured by the high-speed reciprocating sliding experiment, substitute them into formula (5) and fit and determine the various parameters therein; (3) The transmission structure of the dynamic derivative test mechanism is subjected to force analysis to solve the support reaction force of each rotating pair. The dynamic derivative test mechanism is composed of transmission rods AB, BC, CE and driver BD. A is the base. AB and BC are hinged at the fulcrum B. BC is hinged with CE at C. E is the base. BD is hinged with BC at B, and D is the base. The external load of the dynamic derivative test mechanism is M4, which acts on the dynamic derivative test mechanism. The analysis of its support reaction force is shown in the following formula: Among them, F1, F2, F3, F4, F5 are the fulcrums B, A, C, E, D, M1, M2, M3, M4 are the moments acting on the fulcrums B, A, C, E, among which M4 is the external load, M1, M2, M3 are the friction moments, α and β are the angles between BC and the horizontal plane, and between AB and the vertical plane, respectively, l AB , l BC , l BD , l CE The rod lengths are AB, BC, BD, and CE; Based on the obtained support reaction force, the elastic contact model of the revolving pair is constructed, in which the revolving pair is composed of a transmission rod and a support. By introducing n spring damping units to describe the influence of the deformation of the elastic layer between each revolving pair, the contact pressure distribution is solved. Since the hardness of the transmission rod is higher than that of the support, it is assumed that only the support is deformed in the elastic contact. Therefore, there is an elastic deformation arc segment in the contact area between the transmission rod and the elastic layer of the support. n spring damping units are evenly distributed in the arc segment to describe the deformation and force of the elastic deformation arc segment, thereby obtaining the maximum contact angle function: Among them, δ max is the maximum penetration depth between the transmission rod and the support, R B is the support radius, e b R is the eccentricity difference between the cylindrical axial surface on the transmission rod and the circular hole of the support. P is the radius of the cylindrical axial surface on the transmission rod; The contact pressure of a single spring damping unit satisfies the following formula (8): In the formula, E w is the elastic modulus of a single spring damping unit, E B is the elastic modulus of the support, v B is the Poisson's ratio of the support, d k is the thickness of the elastic layer, δ i is the penetration depth of the i-th spring-damper unit, A i is the unit area of ​​the i-th spring damping unit, h is the depth dimension of the transmission rod and the support, and n is the number of spring damping units; Since it is assumed that the transmission rod does not deform, the ends of each spring damping unit are on the cylindrical axis of the transmission rod, and the penetration depth satisfies the following formula: Along the normal direction of the contact surface, the forces of n spring damping units are added together to obtain the total contact force, and the support reaction force of this support is shown in the following formula: Through the above formula (6), the magnitude of the support reaction force is obtained, and the contact pressure of each spring damping unit is determined by the combined formula (7)(8)(9)(10), and the contact pressure distribution of the revolving pair is obtained by solving the formula; (4) The tangential stick-slip friction model between the support and the transmission rod is constructed, and the LuGre friction calculation method is used. The formula is as follows: In the formula, v t is the relative sliding velocity, σ0, σ1, σ2, and γ are all empirical values, which are 100000 N / m, 400 Ns / m, 0, and 2, respectively. s is the Stribeck speed, which determines the transition speed range of friction from static friction to dynamic friction. Its empirical value is 0.01 mm / s. k and μ s are the dynamic and static friction coefficients, p fi is the tangential friction force of the i-th spring damping unit, F f is the total friction between the support and the transmission rod; Based on the obtained contact pressure distribution of the rotating pair, the distribution of the friction coefficient in the rotating pair is obtained by substituting it into equation (5): And it changes with the sliding displacement process. The contact pressure of the single spring damping unit is obtained by formula (8). Substituting the friction coefficient and the contact pressure of the single spring damping unit into formula (11), the friction force of the single spring damping unit and the total friction force of the revolving pair are obtained. The friction torque of the revolving pair is obtained as shown in the following formula: M fj =F fj R pj (12) Among them, M fj 、F fj , R pj The friction torque of the jth revolving pair, the friction force and the radius of the cylindrical axis surface on the transmission rod are solved in sequence for each revolving pair friction torque of the transmission structure in the dynamic derivative test mechanism to obtain the friction torque of the mechanism kinematic chain; (5) In a long-term dynamic derivative test, the above method is used to substitute the external load and the sliding displacement of each rotating pair measured in real time, and the support reaction force, friction coefficient, friction force, and friction torque of each rotating pair are calculated in real time to achieve tracking and prediction of the nonlinear friction torque of the test mechanism.

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