A method for constructing damper force-displacement curve considering displacement slip

Abstract

The present invention discloses a method for constructing a damper force-displacement curve that takes displacement slip into account, comprising the following steps: S1. Constructing a function expression for the damper force-displacement curve that takes displacement slip into account; S2. Constructing a function expression for the upper branch curve of the damper force-displacement curve that takes displacement slip into account; S3. Constructing a complete function expression that takes displacement slip into account; S4. Establishing a function expression for the damper force-displacement curve that takes displacement slip into account for a specific damper; and S5. Performing parameter identification on all unknown parameters in the function expression for the force-displacement curve in step S4, thereby obtaining the damper force-displacement curve. The present invention addresses the slippage phenomenon that can occur with different types of dampers during testing or operation, providing a valuable computational basis for pseudo-static mechanical performance analysis of dampers and their application in structural seismic resistance.

Description

Technical Field

[0001] The present invention relates to the fields of mechanical properties of dampers and structural seismic resistance, and in particular to a method for constructing a damper force-displacement curve taking displacement slip into consideration. Background Art

[0002] With the rapid development of building seismic resistance theory, significant breakthroughs and applications have been made in building vibration control methods. For building structures, installing dampers is a simple and effective vibration reduction measure. Currently, dampers suitable for building vibration reduction include magnetorheological dampers, oil dampers, friction dampers, mild steel dampers, and restrained buckling braces. Oil dampers, friction dampers, and restrained buckling braces are widely used in vibration reduction structures.

[0003] A simple and accurate mechanical model of a damper is fundamental for predicting its mechanical properties and a prerequisite for seismic calculations or optimized designs of damper structures. However, because the damper's ends are typically connected to the test fixture or engineering structure using pins, and the fluid inside the fluid damper is difficult to completely fill, during damper testing or operation, when the damping force is unloaded to near 0 kN, the damper's force-displacement curve slips. This occurs when the displacement changes significantly while the damping force remains virtually unchanged near 0 kN. This phenomenon is common in tests of magnetorheological dampers, friction dampers, and restrained buckling braces. Although there are many different mechanical models for different types of dampers, to date, there is no single computational method or mechanical model that can describe the displacement slip phenomenon in the force-displacement curves of various dampers. Summary of the Invention

[0004] The present invention provides a method for constructing a damper force-displacement curve taking displacement slip into account, which solves the slip phenomenon that exists in different types of dampers during experimental testing or operation, fills the technical gap in this field, and provides a valuable calculation basis for the pseudo-static mechanical performance analysis of the damper and its application in structural seismic resistance.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is: the method for constructing the force-displacement curve of the present invention comprises the following steps:

[0006] S1. Construct the functional expression (1) of the damper force-displacement curve considering displacement slip;

[0007] S2. Based on the function expression (1) in step S1, construct the function expression (2) of the upper branch curve of the damper force-displacement curve considering displacement slip;

[0008] S3. Introduce the parameters of the lower branch curve and construct the complete function expression (3) considering displacement slip;

[0009] S4. Introducing parameters that affect the damping force amplitude, thereby establishing a function expression (4) of the damper force-displacement curve considering displacement slip for a specific damper;

[0010] S5. Perform parameter identification on all unknown parameters in the function expression (4) of the force-displacement curve in step S4, thereby obtaining the force-displacement curve of the damper.

[0011] Preferably, in step S1, the parameters of displacement slip width and curve slope control are introduced, and the constructed function expression (1) is:

[0012]

[0013] Where U is the displacement loading amplitude of the damper, D is the displacement slip width of the damper, x is the real-time displacement value of the damper during loading, y is the calculated value of the ordinate corresponding to x, and n is the parameter controlling the slope of the curve, where n is an odd number greater than 1.

[0014] Preferably, in step S2, the function expression (2) is:

[0015]

[0016] Where: the amplitude of y in the interval [-U, U] is ±1.

[0017] Preferably, in step S3, considering the central symmetry between the upper branch curve and the lower branch curve of the damper force-displacement curve, the parameters of the lower branch curve are introduced to construct the function expression (3):

[0018]

[0019] Where λ is the sign function considering the branch of the curve, is the real-time loading velocity of the damper piston rod, which is greater than 0 when positive loading occurs and less than 0 when negative loading occurs.

[0020] Preferably, in step S4, according to the specific type and working principle of the damper, parameters affecting the damping force amplitude are introduced to construct the function expression (4) of the force-displacement curve as follows:

[0021]

[0022] Where λ is the sign function of the branch of the curve, and f is the parameter that affects the amplitude of the damping force of the damper. For example, for a magnetorheological damper, f is the damping force when the magnetorheological damper is not powered. and the yield force f when energized τ For metal yield dampers, f is the yield force f of the metal yield damper.y ; For friction dampers, f is the friction force f of the friction damper f ; F is the damping force corresponding to the damper at x, the amplitude of F in the interval [-U, U] is ±f, x is the real-time displacement of the damper piston rod, and sgn() represents the sign function.

[0023] Preferably, in step S5, all unknown parameters f, U, D, n, etc. in the function expression (4) are identified based on the design parameters or test data of a specific damper, so as to finally determine the force-displacement curve of the damper.

[0024] The method for identifying the parameter f is: under normal circumstances, based on the test loading conditions or test variables of the damper, representative test data measured under multiple test conditions are selected, and the least squares method is used to fit the functional relationship between the damper damping force amplitude parameter f and the test loading conditions or test variables.

[0025] The parameter U is identified as follows: usually, U is equal to the maximum displacement amplitude under the test loading conditions.

[0026] The method for identifying the parameter D is as follows: generally, based on the test loading conditions or test variables of the damper, representative test data measured under multiple test conditions are selected, and the functional relationship between the displacement slip width D of the damper and the test loading conditions or test variables is obtained by using the least squares method for fitting.

[0027] The identification method of the parameter n is as follows: after the parameters f, U, and D are determined, only the parameter n of the curve slope control in expression (4) is not identified. Then, the calculation results of expression (4) at different n values ​​are compared with the determination coefficient R obtained by fitting the test curve using the nonlinear least squares method. 2 , select R 2 The n that is closest to 1 is sufficient, and n is an odd number greater than 1.

[0028] The beneficial effects of adopting the above technical solution are: the present invention proposes a method for constructing a damper force-displacement curve taking into account displacement slip by gradually introducing parameters that consider the displacement slip width, introducing curve slope control parameters, introducing parameters that consider the lower branch curve, introducing parameters that consider the impact on the damping force amplitude, establishing a method for identifying unknown parameters, etc., which solves the slip phenomenon that exists in different types of dampers during experimental testing or operation, fills the technical gap in this field, and provides a valuable calculation basis for the pseudo-static mechanical performance analysis of the damper and its application in structural seismic resistance. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] 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 embodiments.

[0030] Figure 1 The force-displacement curves of the magnetorheological damper under different current and displacement loading levels are measured experimentally.

[0031] Figure 2 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;

[0032] Figure 3 The figure is a comparison diagram of the force-displacement test curve of the magnetorheological damper under different current and displacement loading levels and the force-displacement curve calculation results of the present invention. DETAILED DESCRIPTION

[0033] Taking the test results of a magnetorheological damper as an example, the method for constructing a force-displacement curve of a magnetorheological damper considering displacement slip in the present invention includes the following steps:

[0034] S1. Construct the functional expression (1) of the force-displacement curve of the magnetorheological damper considering displacement slip.

[0035] 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;

[0036] S3. Introduce the parameters of the lower branch curve and construct the complete function expression (3) considering displacement slip;

[0037] S4. Introduce the damping force amplitude parameter considering the influence of current, so as to establish the function expression (4) of the damper force-displacement curve of the magnetorheological damper considering displacement slip under different currents;

[0038] S5. Perform parameter identification on all unknown parameters in the function expression (4) of the force-displacement curve in step S4, thereby obtaining a force-displacement curve calculation method for the magnetorheological damper.

[0039] In step S1, the parameters of displacement slip width and curve slope control are introduced, and the constructed function expression (1) is:

[0040]

[0041] 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, and n is the parameter controlling the slope of the curve, where n is an odd number greater than 1.

[0042] In step S2, the function expression (2) is:

[0043]

[0044] Where: the amplitude of y in the interval [-U, U] is ±1.

[0045] In step S3, considering the central symmetry 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 and the constructed function expression (3) is:

[0046]

[0047] Where λ is the sign function considering the branch of the curve, is the real-time loading velocity of the piston rod of the magnetorheological damper, which is greater than 0 when positive loading occurs and less than 0 when negative loading occurs.

[0048] In step S4, according to the working principle of the magnetorheological damper, the parameters that affect the damping force amplitude are introduced to construct the function expression (4) of the output force-displacement curve:

[0049]

[0050] Where: λ is the sign function considering the branch of the curve, f τ is the damper yield force, is the damping force when the damper is not energized, 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, n is the parameter controlled by the slope of the curve, and n is an odd number greater than 1. sgn() represents the sign function.

[0051] In step S5, all unknown parameters f, U, D, n, etc. in the function expression (4) are identified according to the design parameters or test data of a specific damper, so as to finally determine the force-displacement curve of the damper.

[0052] Preferably, the parameter The acquisition and calculation method 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. Perform fitting, The fitting data are shown in Table 1:

[0053] Table 1. Parameters Fitting data

[0054]

[0055] The fitting formula is:

[0056]

[0057] 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;

[0058] 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 Perform fitting, f τ The fitting data are shown in Table 2:

[0059] Table 2. Parameter f τ Fitting data

[0060]

[0061] f t The fitting formula is:

[0062] f τ =f τ0 e bI -f τ0 (6)

[0063] 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;

[0064] 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:

[0065] Table 3. Parameter D fitting data

[0066]

[0067] The fitting formula is:

[0068] D=D0-D1e -cI (7)

[0069] 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.

[0070] 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 curve slope control 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.

[0071] Substitute the obtained parameters into expression (4):

[0072]

[0073] 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.

[0074] The above description is only provided 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 method for constructing a damper force-displacement curve considering displacement slip, characterized in that: The following steps are involved: S1. Construct the function expression (1) considering displacement slip in the damper force-displacement curve; introduce the parameters considering displacement slip width and curve slope control, and the constructed function expression (1) is Where U is the displacement loading amplitude of the damper, D is the displacement slip width of the damper, x is the real-time displacement value of the damper during loading, y is the calculated value of the ordinate corresponding to x, and n is the parameter for controlling the slope of the curve, and n is an odd number greater than 1. S2. Based on the function expression (1) in step S1, construct the function expression (2) of the upper branch curve of the damper force-displacement curve considering displacement slip; the function expression (2) is: Where: the amplitude of y in the interval [-U, U] is ±1; S3. Introducing the parameters of the lower branch curve to construct the complete function expression (3) considering the displacement slip; In view of the central symmetry between the upper branch curve and the lower branch curve of the damper force-displacement curve, introducing the parameters of the lower branch curve to construct the function expression (3) is Where λ is the sign function considering the branch of the curve, is the real-time loading velocity of the damper piston rod, which is greater than 0 when positively loaded and less than 0 when negatively loaded; S4. Introducing parameters that affect the damping force amplitude, a function expression (4) of the damper force-displacement curve considering displacement slip is established for a specific damper; Based on the specific type and working principle of the damper, parameters that affect the damping force amplitude are introduced to construct the function expression (4) of the force-displacement curve as follows: Where: λ is the sign function of the curve branch, f is the parameter that affects the damping force amplitude of the damper, and for the magnetorheological damper, f is the damping force when the magnetorheological damper is not powered. and the yield force f when energized τ For metal yield dampers, f is the yield force f of the metal yield damper. y ; For friction dampers, f is the friction force f of the friction damper f ; F is the damping force corresponding to the damper at x, the amplitude of F in the interval [-U, U] is ±f, x is the real-time displacement of the damper piston rod, and sgn() represents the sign function; S5. Perform parameter identification on all unknown parameters in the function expression (4) of the force-displacement curve in step S4, thereby obtaining the force-displacement curve of the damper.

2. The construction method according to claim 1, wherein: In step S5, all unknown parameters f, U, D, and n in the function expression (4) are identified based on the design parameters or test data of a specific damper, thereby ultimately determining the force-displacement curve of the damper.

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