Damper force-displacement curve construction method considering displacement slippage

Abstract

The invention discloses a damper force-displacement curve construction method considering displacement slippage. The method comprises the steps that S1, a function expression considering displacement slippage in a damper force-displacement curve is constructed; s2, constructing a function expression of an upper branch curve considering displacement slippage in a damper force-displacement curve; s3, constructing a complete function expression considering displacement slippage; s4, establishing a function expression of a damper force-displacement curve considering displacement slippage of a certain specific damper; and S5, performing parameter identification on all unknown parameters in the function expression of the force-displacement curve in the step S4 so as to obtain the force-displacement curve of the damper. According to the method, the slippage phenomenon of different types of dampers in the experimental test or working process is avoided, and valuable calculation basis is provided for quasi-static mechanical property analysis of the dampers and application of the dampers to structural seismic resistance.

Description

Technical Field

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

[0002] With the rapid development of building seismic theory, building shock control methods have gradually made great breakthroughs and applications. For building structures, setting up dampers is one of the simple and effective shock reduction measures. At present, dampers suitable for building structure shock reduction include magnetorheological dampers, oil dampers, friction dampers, mild steel dampers, restrained buckling braces, etc., and oil dampers, friction dampers, restrained buckling braces, etc. are widely used in shock-absorbing structures.

[0003] A simple and accurate mechanical model of the damper is the basis for predicting the mechanical properties of the damper, and is also a prerequisite for setting up the damper shock-absorbing structure for seismic calculation or optimization design. However, due to the fact that the two ends of the damper are usually connected to the test device or engineering structure by pins, and the liquid inside the fluid damper is difficult to be completely filled, during the test or operation of the damper, when the damping force is unloaded to close to 0kN, the force-displacement curve of the 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 tests of magnetorheological dampers, friction dampers, and restrained buckling braces. Although there are many different mechanical models for different types of dampers, there is no calculation method or mechanical model that can describe the displacement slip phenomenon of the force-displacement curve 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 consideration, which solves the slip phenomenon existing in different types of dampers during experimental tests 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 function expression (1) considering displacement slip in the damper force-displacement curve;

[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 the displacement slip;

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

[0009] S4. Introduce the parameters that affect the damping force amplitude, so as to establish the function expression (4) of the damper force-displacement curve of a specific damper considering displacement slip;

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

[0011] Preferably, in step S1, the parameters of displacement sliding 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, n is the parameter controlled by the slope of the curve, and 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 relationship 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, It is the real-time loading speed 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:

[0021]

[0022] Where: λ is the sign function of the branch of the curve, f is the parameter that affects the damping force amplitude 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 the friction damper, 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 according to the design parameters or test data of a specific damper, so as to finally determine the force-displacement curve of the damper.

[0024] The identification method of the parameter f is: usually, according to 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 damping force amplitude parameter f of the damper and the test loading conditions or test variables.

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

[0026] The identification method of the parameter D is: usually, according to 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.

[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. Next, 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 scheme are: the present invention proposes a method for constructing a damper force-displacement curve taking displacement slip into consideration by gradually introducing parameters taking into consideration the displacement slip width, introducing curve slope control parameters, introducing parameters taking into consideration the lower branch curve, introducing parameters taking into consideration the influence of the damping force amplitude, establishing a method for identifying unknown parameters, etc., thereby solving the slip phenomenon existing in different types of dampers during experimental tests or working processes, filling the technical gap in this field, and providing 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 implementation methods.

[0030] Figure 1 It is the force-displacement curve of the magnetorheological damper under different current and displacement loading levels measured in the experiment;

[0031] 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;

[0032] 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

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

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

[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 a 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 magnetorheological damper, D is the displacement slip width of the magnetorheological damper, x is the real-time displacement value of the magnetorheological damper during loading, y is the calculated value of the ordinate corresponding to x, and n is the parameter controlled by the slope of the curve, and 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 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):

[0046]

[0047] Where λ is the sign function considering the branch of the curve, is the real-time loading speed 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 affecting the damping force amplitude are introduced to construct the function expression (4) of the force-displacement curve:

[0049]

[0050] Where: λ is the sign function of 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, and sgn() represents the sign function.

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

[0052] 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:

[0053] Table 1. Parameters Fitting data

[0054]

[0055] The fitting formula is:

[0056]

[0057] 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;

[0058] 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:

[0059] Table 2. Parameters 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 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;

[0064] 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:

[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 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.

[0070] The method for obtaining parameter n is as follows: 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) has not been 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 may 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 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.

[0074] 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 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; 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 the displacement slip; S3. Introduce the parameters of the lower branch curve and construct the complete function expression (3) considering displacement slip; S4. Introduce the parameters that affect the damping force amplitude and establish the function expression (4) of the damper force-displacement curve of a specific damper considering displacement slip; S5. Perform parameter identification on all unknown parameters in the function expression (4) of the force-displacement curve in step S4, so as to obtain the force-displacement curve of the damper.

2. The construction method according to claim 1, characterized in that: In step S1, the parameters of displacement slip width and curve slope control are introduced, 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, n is the parameter controlled by the slope of the curve, and n is an odd number greater than 1.

3. The construction method according to claim 1, characterized in that: In step S2, the function expression (2) is: Where: the amplitude of y in the interval [-U, U] is ±1.

4. The construction method according to claim 1, characterized in that: In step S3, considering the central symmetry relationship 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 and the constructed function expression (3) is: Where λ is the sign function considering the branch of the curve, It is the real-time loading speed of the damper piston rod, which is greater than 0 when positive loading occurs and less than 0 when negative loading occurs.

5. The construction method according to claim 1, characterized in that: In step S4, according to the specific type and working principle of the damper, the parameters affecting the damping force amplitude are introduced to construct the function expression (4) of the force-displacement curve: Where: λ is the sign function of the branch of the curve, f is the parameter that affects the damping force amplitude 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 the friction damper, 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.

6. The construction method according to claim 1, characterized in that: 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.

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