Magnetorheological damper force-displacement curve considering displacement slippage and application

Abstract

The invention discloses a magnetorheological damper force-displacement curve considering displacement slippage and application, displacement slippage parameters, curve slope control parameters, lower branch curve parameters, damping force amplitude parameters influenced by current and the like are introduced into the force-displacement curve, and the technical blank in the field is filled. According to the method, the damping force of the magneto-rheological damper under different currents and displacement loading grades can be calculated, the mechanical property of displacement slippage in a damper force-displacement curve can be expressed, and valuable reference is provided for quasi-static mechanical property analysis of the magneto-rheological damper and application of the magneto-rheological damper to structural seismic resistance.

Description

Technical Field

[0001] The invention relates to the field of mechanical characteristics of magnetorheological dampers and structural seismic resistance, and in particular to a magnetorheological damper force-displacement curve considering displacement slip and its application. Background Art

[0002] Magnetorheological damper is a semi-active vibration reduction device made by using the rheological effect of magnetorheological fluid. It has excellent characteristics such as simple structure, fast response, strong controllability, and easy control system integration. In recent years, it has been used in vibration control in the fields of machinery, automobiles, and civil engineering.

[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 the magnetorheological damper shock-absorbing structure for seismic calculation or optimization design. Due to the complexity of the magnetorheological effect, the mechanical model of the magnetorheological damper proposed in current research is difficult to accurately and comprehensively describe the various mechanical properties of the magnetorheological damper. Quasi-static test is an effective method to study the seismic performance of structures. Conducting quasi-static tests on magnetorheological dampers to understand their mechanical properties under quasi-static loading can provide a data basis for the study of the mechanical performance model of magnetorheological dampers and their seismic design and optimal layout in engineering structures.

[0004] In experimental tests or actual engineering applications, the two ends of the magnetorheological damper are usually connected by pins. In addition, the magnetorheological fluid inside the damper is difficult to be completely filled, and the connectors are loose during the reciprocating motion of the damper. When the damping force is unloaded to close to 0kN, the force-displacement curve of the magnetorheological damper will slip, that is, the displacement changes significantly while the damping force is almost unchanged near 0kN. This phenomenon exists in large numbers in the experimental tests of magnetorheological dampers. However, up to now, 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 of the invention

[0005] The technical problem to be solved by the present invention is to provide a magnetorheological damper force-displacement curve and application taking displacement slip into consideration, which fills the technical gap in this field. It can not only calculate the damping force of the magnetorheological damper under different current and displacement loading levels, but also express the mechanical characteristics of displacement slip in the damper force-displacement curve, providing a valuable reference for the pseudo-static mechanical performance analysis of the magnetorheological damper and its application in structural seismic resistance.

[0006] In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a force-displacement curve of a magnetorheological damper considering displacement slip, wherein the force-displacement curve 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 of the magnetorheological damper is:

[0007] Where: λ is the parameter for considering the branch of the curve, f τ is the yield stress of the damper under different currents, is the damping force when the damper current is 0, F is the damping force corresponding to 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.

[0008] Preferably, the parameter The method of obtaining and calculating is: when the current is 0, f τ is 0, at this time the magnetorheological damper only has damping force Therefore, under the condition of zero current, the damping force values ​​of the magnetorheological damper measured under different displacement loading levels are selected. Perform fitting, the fitting formula is:

[0009]

[0010] In formula (5), the parameters a, The control method is obtained by fitting the test data according to the nonlinear least squares method. Parameters that vary with U.

[0011] Preferably, parameter f τ The acquisition and calculation method of is: The yield force f of the magnetorheological damper τ It is only related to the current size, and the total damping force measured by the test is subtracted from You can get f τ Therefore, when the same current level is selected, f τ The average value is used as the f corresponding to this current level. τ value, and then according to different current levels f τ The value of f τ Perform fitting, the fitting formula is:

[0012] f τ =f τ0 e bI -f τ0 (6)

[0013] In formula (6), parameters b and f τ0 The control function f is obtained by fitting the test data according to the nonlinear least squares method. τ Parameter that changes with I; I is the magnetorheological damper current.

[0014] The acquisition and calculation method of the parameter D is as follows: the value of the displacement slip width D changes with the change of the current, but 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 according to the value of D under different current levels, and the fitting formula is:

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

[0016] In formula (7), the parameters c, D0, and D1 are obtained by fitting the test data according to the nonlinear least square method and are used to control the changing relationship between D and I; I is the current of the magnetorheological damper.

[0017] The method for obtaining the parameter n is as follows: f τ , D are calculated. At this time, only the parameter n controlling the slope of the curve in expression (4) is not identified. Therefore, the determination coefficient R obtained by fitting the slip model with different n values ​​to the test curve using the nonlinear least squares method can be compared. 2 , select R 2 The n that is closest to 1 is sufficient, and n is an odd number greater than 1.

[0018] The method for constructing the force-displacement curve function expression of the present invention comprises the following steps:

[0019] S1. Construct the functional expression of displacement slip in the force-displacement curve of magnetorheological damper (1);

[0020] S2. Based on the function expression (1) in step S1, construct the function expression (2) of the upper branch curve of the magnetorheological damper force-displacement curve considering displacement slip;

[0021] S3. Introduce the parameters of the lower branch curve and construct the complete function expression (3) considering displacement slip;

[0022] S4. The damping force amplitude parameter considering the influence of current is introduced to establish the function expression (4) of the damper force-displacement curve of the magnetorheological damper considering displacement slip under different currents.

[0023] Preferably, in step S1, a parameter considering the displacement slip width is introduced, and the constructed function expression (1) is:

[0024]

[0025] Where U is the displacement loading amplitude of the MR damper, D is the displacement slip width of the MR damper, x is the real-time displacement value of the MR damper during loading, y is the calculated value of the ordinate corresponding to x, n is the parameter controlling the slope of the curve, and n is an odd number greater than 1.

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

[0027]

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

[0029] Preferably, in step S3, considering the central symmetry relationship between the upper branch curve and the lower branch curve of the magnetorheological damper force-displacement curve, the parameters of the lower branch curve are introduced to construct the function expression (3):

[0030]

[0031] Where λ is the parameter for considering the branch of the curve, sgn() represents the sign function, is the loading speed of the damper piston rod, which is greater than 0 when positively loaded and less than 0 when negatively loaded.

[0032] Preferably, in step S4, according to the working principle of the magnetorheological damper, etc., parameters affecting the damping force amplitude are introduced to construct the function expression (4) of the force-displacement curve:

[0033]

[0034] Where: f τ is the yield stress of the damper under different currents, is the damping force when the damper current is 0, F is the damping force corresponding to 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.

[0035] The force-displacement curve of the present invention is used to express the mechanical characteristics of the damper displacement slipping when the damping force of the magnetorheological damper is unloaded to close to 0 kN under any combination of current and loading displacement.

[0036] The beneficial effect of adopting the above technical scheme is that: the present invention constructs a force-displacement curve of a magnetorheological damper taking displacement slip into consideration by introducing displacement slip parameters, curve slope control parameters, parameters of the lower branch curve and damping force amplitude parameters affected by current, etc., which fills the technical gap in this field. It can not only calculate the damping force of the magnetorheological damper under different current and displacement loading levels, but also express the mechanical characteristics of displacement slip in the damper force-displacement curve, providing a valuable reference for the pseudo-static mechanical performance analysis of the magnetorheological damper and its application in structural seismic resistance. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present invention will be further described in detail below by taking the test results of the magnetorheological damper as an example in combination with the accompanying drawings and specific implementation methods.

[0038] Figure 1 It is the force-displacement curve of the magnetorheological damper under different current and displacement loading levels measured in the experiment;

[0039] Figure 2 It is a schematic diagram of calculation results obtained in steps S1, S2, S3, and S4 of the damper force-displacement curve calculation method considering displacement slip in the present invention;

[0040] Figure 3 It is a comparison diagram of the force-displacement test curve of the magnetorheological damper and the calculation result of the force-displacement curve of the present invention under different current and displacement loading levels. DETAILED DESCRIPTION

[0041] The force-displacement curve of the magnetorheological damper considering displacement slip of the present invention, wherein the force-displacement curve 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 magnitude, and the expression of the force-displacement curve is:

[0042]

[0043] Where: λ is the parameter for considering the branch of the curve, f τ is the yield stress of the damper under different currents, is the damping force when the damper current is 0, F is the damping force corresponding to 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.

[0044] Preferably, the parameter The method of obtaining and calculating is: when the current is 0, f τ is 0, at this time the magnetorheological 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. To fit, The fitting data of is shown in Table 1:

[0045] Table 1. Parameters Fitting data

[0046]

[0047] The fitting formula is:

[0048]

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

[0050] Parameter f τ The acquisition and calculation method of is: The yield force f of the magnetorheological damper τ It is only related to the current size, and is subtracted from the total damping force You can get f τ Therefore, when the same current level is selected, f τ The average value is used as the f corresponding to this current level. τ value, and then according to different current levels f τ The value of f τ Fitting, f τ The fitting data is 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 control function f is obtained by fitting the test data according to the nonlinear least squares method. τ Parameters related to the change of I; I is the magnetorheological damper current;

[0056] The acquisition and calculation method of the parameter D is as follows: the value of the displacement slip width D changes with the change of the current, but 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 according to the value of D under different current levels. The fitting data of D is 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 test data and are used to control the changing relationship between D and I; I is the current of the magnetorheological damper; the parameters c, D0, and D1 are fitted by the nonlinear least squares method, and the values ​​of each parameter are obtained as c=0.0075, D0=11.888, and D1=7.783, respectively.

[0062] The method for obtaining parameter n is as follows: f τ , D are calculated. At this time, only the parameter n controlling the slope of the curve in expression (4) is not identified. Therefore, the determination coefficient R obtained by fitting the slip model with different n values ​​to the test curve using the nonlinear least squares method can be compared. 2 , select R 2 The n closest to 1 may 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 simulation curve of the slip model is compared with the test curve, the blue solid line is the simulation curve, and the black dotted line is the test curve. The overall agreement between the simulation curve and the test curve is high, indicating that the slip model provided by the present invention can not only calculate the damping force of the magnetorheological damper under different current and displacement loading levels, but also describe the mechanical characteristics of displacement slip in the damper force-displacement curve, providing a valuable reference for the pseudo-static mechanical performance analysis of the magnetorheological damper and its application in structural seismic resistance.

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

[0067] S1. Construct the functional expression of displacement slip in the force-displacement curve of magnetorheological damper (1);

[0068] S2. Based on the function expression (1) in step S1, construct the function expression (2) of the upper branch curve of the magnetorheological damper force-displacement curve considering displacement slip;

[0069] S3. Introduce the parameters of the lower branch curve and construct the complete function expression (3) considering displacement slip;

[0070] S4. The damping force amplitude parameter considering the influence of current is introduced to establish the function expression (4) of the damper force-displacement curve of the magnetorheological damper considering displacement slip under different currents.

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

[0072]

[0073] Where U is the displacement loading amplitude of the MR damper, D is the displacement slip width of the MR damper, x is the real-time displacement value of the MR damper during loading, y is the calculated value of the ordinate corresponding to x, n is the 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] Where: the amplitude of y in the interval [-U, U] is ±1.

[0077] In step S3, considering the central symmetry relationship between the upper branch curve and the lower branch curve of the magnetorheological damper force-displacement curve, the parameters of the lower branch curve are introduced to construct the function expression (3):

[0078]

[0079] Where λ is the parameter for considering the branch of the curve, sgn() represents the sign function, is the loading speed of the damper piston rod, which is greater than 0 when positively loaded and less than 0 when negatively loaded.

[0080] In step S4, according to the working principle of the magnetorheological damper, etc., the parameters affecting the damping force amplitude are introduced to construct the function expression (4) of the force-displacement curve:

[0081]

[0082] Where: fτ is the yield stress of the damper under different currents, is the damping force when the damper current is 0, F is the damping force corresponding to 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.

[0083] The force-displacement curve of the present invention is used to express the mechanical characteristics of the damper displacement slipping when the damping force of the magnetorheological damper is unloaded to close to 0 kN under any combination of current and loading displacement.

[0084] The above description is only proposed as an implementable technical solution of the present invention, and is not intended to be a single limitation on the technical solution itself.

Claims

1. A force-displacement curve of a magnetorheological damper considering displacement slip, characterized in that: The force-displacement curve takes into account 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. The expression of the force-displacement curve is: Where: λ is the parameter for considering the branch of the curve, f τ is the yield stress of the damper under different currents, is the damping force when the damper current is 0, F is the damping force corresponding to 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.

2. The force-displacement curve according to claim 1, characterized in that: The parameters The method of obtaining and calculating is: when the current is 0, f τ is 0, at this time the magnetorheological damper only has damping force Therefore, under the condition of zero current, the damping force values ​​of the magnetorheological damper measured under different displacement loading levels are selected. Perform fitting, the fitting formula is: In formula (5), the parameters a, The control method is obtained by fitting the test data according to the nonlinear least squares method. Parameters that vary with U.

3. The force-displacement curve according to claim 1, characterized in that: Parameter f τ The acquisition and calculation method of is: The yield force f of the magnetorheological damper τ It is only related to the current size, and the total damping force measured by the test is subtracted from You can get f τ Therefore, when the same current level is selected, f τ The average value is used as the f corresponding to this current level. τ value, and then according to different current levels f τ The value of f τ Perform fitting, the fitting formula is: f τ =f τ0 e bI -f τ0 (6) In formula (6), parameters b and f τ0 The control function f is obtained by fitting the test data according to the nonlinear least squares method. τ Parameter that changes with I; I is the magnetorheological damper current.

4. The force-displacement curve according to claim 1, characterized in that: The acquisition and calculation method of the parameter D is as follows: the value of the displacement slip width D changes with the change of the current, but 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 according to the value of D under different current levels, and the fitting formula is: D=D0-D1e -cI (7) In formula (7), the parameters c, D0, and D1 are obtained by fitting the test data according to the nonlinear least square method and are used to control the changing relationship between D and I; I is the current of the magnetorheological damper.

5. The force-displacement curve according to claim 1, characterized in that: The method for obtaining parameter n is as follows: f τ , D are calculated. At this time, only the parameter n controlling the slope of the curve in expression (4) is not identified. Therefore, the determination coefficient R obtained by fitting the slip model with different n values ​​to the test curve using the nonlinear least squares method can be compared. 2 , select R 2 The n that is closest to 1 is sufficient, and n is an odd number greater than 1.

6. Application of the force-displacement curve according to any one of claims 1 to 5, characterized in that: Under any combination of current and loading displacement, when the damping force of the MR damper is unloaded to close to 0 kN, it is used to express the mechanical characteristics of the damper displacement slipping.

Images