Magnetorheological damper force-displacement curve considering displacement slip and application thereof

Abstract

The application discloses a force-displacement curve of a magneto-rheological damper considering displacement slip and application, the force-displacement curve introduces a displacement slip parameter, a curve slope control parameter, a parameter of a lower branch curve and a damping force amplitude parameter influenced by a current, and fills the technical blank in the field, can not only calculate the damping force size of the magneto-rheological damper under different currents and displacement loading levels, but also can express the mechanical properties of displacement slip in the force-displacement curve of the damper, and provides valuable reference for quasi-static mechanical performance analysis of the magneto-rheological damper and application of the magneto-rheological damper in structural seismic resistance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of magnetorheological damper mechanics characteristics and structure seismic resistance, and particularly relates to a magnetorheological damper force-displacement curve considering displacement slip and application. BACKGROUND

[0002] The magnetorheological damper is a semi-active vibration reduction device made of magnetorheological fluid, and has the advantages of simple structure, fast response, strong controllability, easy integration with a control system, etc., and has been applied in the field of vibration control in machinery, automobiles and civil engineering in recent years.

[0003] The mechanical model of the magnetorheological damper is the basis for predicting the mechanical properties of the damper, and is also a prerequisite for setting up a magnetorheological damper seismic structure for seismic calculation or optimization design. Due to the complexity of the magnetorheological effect, the mechanical model of the magnetorheological damper proposed by the current research is difficult to accurately and comprehensively describe various mechanical properties of the magnetorheological damper. Quasi-static test is an effective method for studying the seismic performance of a structure, and quasi-static test of the magnetorheological damper can understand the mechanical properties of the magnetorheological damper under quasi-static loading, and can provide a data basis for the mechanical property model research of the magnetorheological damper and its seismic design and optimization arrangement in engineering structures.

[0004] In the test or actual engineering application, the two ends of the magnetorheological damper are usually connected by a pin shaft, and the magnetorheological fluid in the damper is difficult to completely fill, the connecting part is loose during the reciprocating motion of the damper, and other reasons, when the damping force is unloaded to near 0kN, the force-displacement curve of the magnetorheological damper will slip, that is, the displacement changes significantly while the damping force remains almost unchanged near 0kN, and this phenomenon exists in a large number of test tests of the magnetorheological damper. However, so far, there is no calculation method or mechanical model that can describe the displacement slip phenomenon of the force-displacement curve of the magnetorheological damper. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a magnetorheological damper force-displacement curve considering displacement slip and application, which fills the technical gap in the field, can not only calculate the damping force of the magnetorheological damper under different current, displacement loading levels, but also express the mechanical properties of the displacement slip in the damper force-displacement curve, and provides valuable reference for the quasi-static mechanical property analysis of the magnetorheological damper and its application in structure seismic resistance.

[0006] In order to achieve the above object, the technical scheme adopted by the present application is: a force-displacement curve of a magneto-rheological damper considering displacement slip, the force-displacement curve considers a displacement slip width parameter, a curve slope control parameter, a curve branch parameter and a damping force amplitude parameter influenced by current size, and the expression of the force-displacement curve of the magneto-rheological damper is:

[0007] In the formula, λ is a parameter considering curve branch, f τ is the yield force of the damper under different currents, is the damping force when the current of the damper is 0, F is the corresponding damping force of the damper at x, the amplitude of F in the interval [-U, U] is x is the real-time displacement of the damper piston rod, U is the displacement loading amplitude, D is the displacement slip width parameter, n is the curve slope control parameter, and n is an odd number greater than 1, and sgn() represents a sign function.

[0008] Preferably, the parameters are obtained and calculated as follows: when the current is 0, f τ is 0, at this time the magneto-rheological damper only has the damping force Therefore, under the condition that the current is 0, the values of the damping force of the magneto-rheological damper measured under different displacement loading levels are selected to fit , and the fitting formula is:

[0009]

[0010] In formula (5), the parameters a, are obtained from the test data according to the nonlinear least square method to control the variation relationship of and U.

[0011] Preferably, the parameters f τ are obtained and calculated as follows: the yield force f τ of the magneto-rheological damper is only related to the current size, and f τ can be obtained by subtracting from the total damping force measured by the test, τ Therefore, the average value of f τ under different displacement loading levels at the same current level is selected as the f τ value corresponding to this current level, and f τ is fitted according to the values of f τ under different current levels, and the fitting formula is:

[0012] f τ0 e bI -f τ0 (6)

[0013] In formula (6), parameters b, f τ0 The parameters for controlling the change relationship between f and I are obtained by fitting the test data according to a nonlinear least square method; and I is a magneto-rheological damper current. τ The parameters for controlling the change relationship between f and I are obtained by fitting the test data according to a nonlinear least square method; and I is a magneto-rheological damper current.

[0014] The parameter D is obtained and calculated as follows: the value of the displacement slip width D changes with the change of the current, and is not affected by the displacement loading level, so the average value of D under different displacement loading levels at the same current level is selected as the D value corresponding to the current level; and D is fitted according to the values of D under different current levels, and the fitting formula is:

[0015] D=D0-D1e -cI (7)

[0016] In formula (7), parameters c, D0 and D1 are parameters for controlling the change relationship between D and I, which are obtained by fitting the test data according to a nonlinear least square method; and I is a magneto-rheological damper current.

[0017] The parameter n is obtained as follows: the parameters f τ , D are calculated, at this time, only the parameter n controlling the slope of the curve in expression (4) is not identified, so the determination coefficient R 2 of the slip model with different n values and the test curve is obtained by fitting using a nonlinear least square method, and n corresponding to the R 2 closest to 1 is selected, and n is an odd number greater than 1.

[0018] The construction method of the force-displacement curve function expression of the present application comprises the following steps:

[0019] S1. constructing a function expression (1) of the force-displacement curve of the magneto-rheological damper considering displacement slip;

[0020] S2. constructing a function expression (2) of the upper branch curve of the force-displacement curve of the magneto-rheological damper considering displacement slip on the basis of the function expression (1) in step S1;

[0021] S3. introducing a parameter considering the lower branch curve to construct a complete function expression (3) considering displacement slip;

[0022] S4. introducing a damping force amplitude parameter considering the influence of the current to establish a function expression (4) of the damper force-displacement curve of the magneto-rheological damper considering displacement slip under different currents.

[0023] Preferably, in step S1, a parameter considering the displacement slip width is introduced to construct the function expression (1) as follows: ​

[0024]

[0025] In the formula, U is the displacement loading amplitude of the magneto-rheological damper, D is the displacement slip width of the magneto-rheological damper, x is the real-time displacement value of the magneto-rheological damper in the loading process, y is the calculated value of the longitudinal coordinate corresponding to x, n is the parameter of the control curve slope, and n is an odd number greater than 1.

[0026] Preferably, in step S2, the function expression (2) is:

[0027]

[0028] In the formula, the amplitude of y in the interval [-U, U] is ±1.

[0029] Preferably, in step S3, in view of the center symmetry relationship of the upper branch curve and the lower branch curve of the force-displacement curve of the magneto-rheological damper, the parameter of the lower branch curve is introduced for consideration, and the function expression (3) constructed is

[0030]

[0031] In the formula, λ is the parameter considering the curve branch, sgn() represents the sign function, is the loading speed of the damper piston rod, which is greater than 0 when loading in the positive direction and less than 0 when loading in the negative direction.

[0032] Preferably, in step S4, according to the working principle of the magneto-rheological damper and the like, the parameter affecting the amplitude of the damping force is introduced for consideration, and the function expression (4) of the force-displacement curve constructed is:

[0033]

[0034] In the formula: f τ is the yield force of the damper under different currents, is the damping force when the current of the damper is 0, F is the damping force corresponding to x of the damper, and the amplitude of F in the interval [-U, U] is x is the real-time displacement of the damper piston rod.

[0035] The application of the force-displacement curve of the application: under the condition of any current and loading displacement combination, when the damping force of the magneto-rheological damper is unloaded to close to 0kN, it is used to express the mechanical properties of the displacement slip of the damper.

[0036] The beneficial effects produced by the above technical solutions are that: the force-displacement curve of the magneto-rheological damper considering displacement slip is constructed by introducing the displacement slip parameter, the curve slope control parameter, the parameter of the lower branch curve and the damping force amplitude parameter affected by the current, which fills the technical gap in the field, can not only calculate the damping force size of the magneto-rheological damper under different current and displacement loading levels, but also express the mechanical properties of displacement slip in the damper force-displacement curve, and provides valuable reference for the quasi-static mechanical performance analysis of the magneto-rheological damper and its application in structural seismic resistance. BRIEF DESCRIPTION OF DRAWINGS

[0037] The application will be further described in detail below with the test results of the magneto-rheological damper as an example, in combination with the drawings and specific embodiments.

[0038] Figure 1 is the force-displacement curve of the magneto-rheological damper under different current and displacement loading levels measured by test;

[0039] Figure 2 is the calculation result schematic diagram obtained by steps S1, S2, S3 and S4 in the damper force-displacement curve calculation method considering displacement slip of the application;

[0040] Figure 3 is the comparison diagram of the force-displacement test curve of the magneto-rheological damper and the calculation result of the force-displacement curve of the application under different current and displacement loading levels. DETAILED DESCRIPTION

[0041] The force-displacement curve of the magneto-rheological damper considering displacement slip of the application considers the displacement slip width parameter, the curve slope control parameter, the curve branch parameter and the damping force amplitude parameter affected by the current size, and the expression of the force-displacement curve is:

[0042]

[0043] In the formula, λ is the parameter considering the curve branch, f τ is the yield force of the damper under different current, is the damping force when the current of the damper is 0, F is the damping force of the damper corresponding to x, the amplitude of F in the interval [-U, U] is x is the real-time displacement of the damper piston rod, U is the displacement loading amplitude, D is the displacement slip width parameter, n is the curve slope control parameter, and n is an odd number greater than 1, and sgn() represents the sign function.

[0044] Preferably, the parameter is obtained and calculated as follows: when the current is 0, f τ is 0, at this time, the magneto-rheological damper only has damping force Therefore, under the condition that the current is 0, the value of the damping force of the magnetorheological damper at different displacement loading levels is selected. Perform fitting, The fitting data are shown in Table 1:

[0045] Table 1. Parameters Fitting data

[0046]

[0047] The fitting formula is:

[0048]

[0049] In formula (5), parameters a, The control method is obtained by fitting the experimental data according to the nonlinear least square method. Parameters related to the change of U;

[0050] Parameter f τ The acquisition and calculation method is as follows: The yield force f of the magnetorheological damper τ It is only related to the current, and the total damping force is subtracted You can get f τ Therefore, when the same current level is selected, f τ The average value of the current level is used as the f τ value, and then according to different current levels f τ The value of f τ Fitting, f τ The fitting data are shown in Table 2:

[0051] Table 2. Parameter f τ Fitting data

[0052]

[0053] f t The fitting formula is:

[0054] f τ =f τ0 e bI -f τ0 (6)

[0055] In the formula, parameters b and f τ0 The nonlinear least squares method is used to fit the experimental data to control f τ Parameters related to the change of I; I is the magnetorheological damper current;

[0056] The method for obtaining and calculating the parameter D is as follows: the value of the displacement slip width D changes with the change of current and is not affected by the displacement loading level. Therefore, the average value of D under different displacement loading levels at the same current level is selected as the D value corresponding to this current level; then, D is fitted based on the values ​​of D under different current levels. The fitting data of D are shown in Table 3:

[0057] Table 3. Parameter D fitting data

[0058]

[0059] The fitting formula is:

[0060] D=D0-D1e -cI (7)

[0061] Wherein, parameters c, D0, and D1 are obtained by fitting the experimental data and are used to control the changing relationship between D and I; I is the magnetorheological damper current. The nonlinear least squares method is used to fit the parameters c, D0, and D1, and the values ​​of each parameter are obtained as c = 0.0075, D0 = 11.888, and D1 = 7.783, respectively.

[0062] The method to obtain parameter n is: f τ On the basis of the calculation of D, at this time, only the parameter n of the control curve slope in expression (4) is not identified, so the determination coefficient R obtained by fitting the slip model with different n values ​​and the test curve using the nonlinear least squares method can be compared. 2 , select R 2 The n closest to 1 can be used, and n is an odd number greater than 1. In this embodiment, n is 5.

[0063] Substitute the obtained parameters into expression (4):

[0064]

[0065] like Figure 3 As shown, the simulated slip model curve is compared with the experimental curve, with the blue solid line representing the simulated curve and the black dashed line representing the experimental curve. The high overall agreement between the simulated and experimental curves demonstrates that the slip model provided by this invention can not only calculate the damping force of a magnetorheological damper under different current and displacement loading levels, but also describe the mechanical properties of displacement slip in the damper's force-displacement curve. This provides a valuable reference for the pseudo-static mechanical performance analysis of magnetorheological dampers and their application in structural seismic protection.

[0066] The method for constructing the above force-displacement curve includes the following steps:

[0067] S1. Construct a function expression (1) considering displacement slip in the force-displacement curve of the magneto-rheological damper;

[0068] S2. On the basis of the function expression (1) in step S1, construct a function expression (2) of the upper branch curve of the force-displacement curve of the magneto-rheological damper considering displacement slip;

[0069] S3. Introduce a parameter considering the lower branch curve to construct a complete function expression (3) considering displacement slip;

[0070] S4. Introduce a parameter considering the influence of the damping force amplitude to establish a function expression (4) of the force-displacement curve of the magneto-rheological damper considering displacement slip under different currents.

[0071] In step S1, a parameter considering the width of displacement slip is introduced, and the constructed function expression (1) is

[0072]

[0073] In the formula, U is the displacement loading amplitude of the magneto-rheological damper, D is the displacement slip width of the magneto-rheological damper, x is the real-time displacement value in the loading process of the magneto-rheological damper, y is the calculated value of the ordinate corresponding to x, n is a parameter controlling the slope of the curve, and n is an odd number greater than 1.

[0074] In step S2, the function expression (2) is

[0075]

[0076] In the formula: the amplitude of y in the interval [-U, U] is ±1.

[0077] In step S3, in view of the center symmetry relationship between the upper branch curve and the lower branch curve of the force-displacement curve of the magneto-rheological damper, a parameter considering the lower branch curve is introduced, and the constructed function expression (3) is

[0078]

[0079] In the formula, λ is a parameter considering the curve branch, sgn() represents a sign function, is the loading speed of the damper piston rod, which is greater than 0 when loading in the positive direction and less than 0 when loading in the negative direction.

[0080] In step S4, according to the working principle of the magneto-rheological damper and the like, a parameter considering the influence of the damping force amplitude is introduced, and the function expression (4) of the force-displacement curve is constructed:

[0081]

[0082] In the formula: fτ Fy is the yield force of the damper under different currents, Fy is the yield force of the damper under different currents, F is the damping force of the damper corresponding to x, and the amplitude of F in the interval [-U, U] is x is the real-time displacement of the damper piston rod.

[0083] The application of the force-displacement curve of the present application: under the condition of any current and loading displacement combination, the damping force of the magneto-rheological damper is unloaded to close to 0 kN, which is used to express the mechanical properties of the damper displacement slip.

[0084] The above description is only proposed as the technical scheme that the present application can be implemented, and is not a single limitation condition for the technical scheme itself.

Claims

1. A method for obtaining a force-displacement curve of a magneto-rheological damper considering displacement slip, characterized in that: The force-displacement curve considers a displacement slip width parameter, a curve slope control parameter, a curve branch parameter, and a damping force amplitude parameter influenced by current size, and an expression of the force-displacement curve is: where λ is a parameter considering curve branch, f τ is the yield force of damper under different current, is the damping force when the damper current is 0, F is the corresponding damping force of the damper at x, and the amplitude of F in the interval [-U, U] is x is the real-time displacement of the damper piston rod, U is the displacement loading amplitude, D is the displacement slip width parameter, n is the curve slope control parameter, and n is an odd number greater than 1, and sgn() represents the sign function, is the loading speed of the damper piston rod, which is greater than 0 when loading in the positive direction and less than 0 when loading in the negative direction.

2. The force-displacement curve acquisition method according to claim 1, characterized in that Parameter The acquisition and calculation method is that when the current is 0, f τ is 0, at this time, the magneto-rheological damper only exists damping force Therefore, under the condition that the current is 0, the values of the damping force of the magneto-rheological damper measured under different displacement loading levels are selected to fit The fitting formula is: In formula (2), the parameter a, The parameters for controlling the change relationship of U obtained by fitting the test data according to the nonlinear least square method are as follows: and U.

3. The force-displacement curve acquisition method of claim 1, wherein Parameter f τ The acquisition and calculation method is: the yield force f τ of the magnetorheological damper is only related to the current size, and the total damping force measured by the test is subtracted f τ Therefore, the average value of f τ at different displacement loading levels under the same current level is selected as the f τ value corresponding to this current level, and the f τ values under different current levels are fitted to obtain the fitting formula of f τ ​ f τ = f τ0 e bI -f τ0 (3) In formula (3), parameters b, f τ0 The parameter for controlling f τ The parameter for controlling the change relation of I; I is the current of the magneto-rheological damper.

4. The force-displacement curve acquisition method of claim 1, wherein The parameter D is obtained and calculated as follows: the value of the displacement slip width D changes with the change of the current, and is not affected by the displacement loading level, so the average value of D under different displacement loading levels at the same current level is selected as the D value corresponding to the current level; and D is fitted according to the values of D under different current levels, and a fitting formula is: D = D0- D1e -cI (4) In formula (4), the parameters c, D0 and D1 are parameters for controlling the change relationship between D and I, which are obtained from test data according to a nonlinear least square method; and I is a current of the magnetorheological damper.

5. The force-displacement curve acquisition method of claim 1, wherein The method for obtaining the parameter n is: in the parameter f τ On the basis of the calculation of D, only the parameter n controlling the slope of the control curve in the expression (1) is not identified at this time, so the determination coefficient R 2 of the slip model with different n values and the fitting curve obtained by using the nonlinear least square method can be compared 2 The n corresponding to the R 2 closest to 1 can be selected, and n is an odd number greater than 1.

6. Use of the force-displacement curve acquisition method according to any one of claims 1 to 5, characterized in that, Under any current and loading displacement combination condition, when the damping force of the magnetorheological damper is unloaded to close to 0 kN, a mechanical characteristic for expressing the displacement slip of the damper is obtained.

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