A parameter optimization design method of a nonlinear damping track system

Abstract

The application discloses a parameter optimization design method of a nonlinear damping track system, and comprises the following steps: defining five key load positions of a vibration isolator according to the quasi-static component of a response signal of the vibration isolator when a train passes; solving vibration energy of the five key load positions by using a preset energy definition formula, analyzing energy distribution characteristics, and sorting vibration isolation demand priorities at different key load positions; constructing an optimal nonlinear restoring force curve of a floating slab vibration isolator by using reverse design according to the vibration isolation demand priorities and displacement suppression demand of the key load positions; and performing nonlinear damping design on a vibration isolator with a stiffness first gradually hard and then gradually soft characteristic (HFTS), and obtaining a design parameter rule. The method provides a new solution for the design of a high-performance floating slab passive vibration isolator with displacement suppression and low-frequency vibration isolation demand, and can meet the track displacement suppression demand while ensuring vertical low dynamic action.

Description

Technical Field

[0001] This invention relates to the field of rail transportation technology, and in particular to a parameter optimization design method for a nonlinear vibration reduction track system. Background Technology

[0002] In the field of rail transportation, there is a significant demand for railway vibration-damping track designs that can achieve low-frequency vibration control to avoid harmful vibrations jeopardizing the safety and reliability of engineering projects. With the rapid development of rail transportation, the requirements for low-frequency vibration control performance are becoming increasingly stringent. Traditional steel spring floating slab systems struggle to meet displacement suppression requirements while simultaneously improving the system's low-frequency vibration isolation performance. Therefore, there is an urgent need to develop a design method for low-frequency track vibration isolators that can suppress displacement. Summary of the Invention

[0003] The purpose of this invention is to provide a parameter optimization design method for a nonlinear vibration reduction track system, which solves the problem of active vibration isolation for track systems with displacement restriction requirements; the proposed variable stiffness vibration isolation scheme can meet the track displacement suppression requirements while ensuring low vertical dynamic action.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] This invention provides a parameter optimization design method for a nonlinear vibration reduction track system, comprising the following steps:

[0006] S1. Based on the quasi-static components of the vibration isolator's response signal when a train passes, define the five key load positions of the vibration isolator: P0, P1, P2, P3, and P4.

[0007] S2. Using a preset energy definition formula, calculate the vibration energy at the five key load locations, analyze the energy distribution characteristics, and prioritize the vibration isolation requirements at different key load locations.

[0008] S3. Based on the priority of vibration isolation requirements and displacement suppression requirements at key load locations, construct the optimal nonlinear restoring force curve of the floating plate vibration isolator using reverse design.

[0009] S4. Based on the optimal nonlinear restoring force curve of the floating plate vibration isolator, perform nonlinear damping design on the stiffness characteristics of the HFTS vibration isolator to obtain the design parameter rules.

[0010] Further, step S1 includes:

[0011] S11. The typical response curve of the vibration isolator when a train passes by is obtained through simulation;

[0012] S12. Based on the typical response curve, the displacement and support reaction force response signals of the vibration isolator are decomposed into quasi-static and dynamic components based on frequency thresholds, respectively; wherein, the quasi-static component is caused by the loading of the train passing directly above the vibration isolator; the dynamic component is caused by the unevenness of the wheel and rail, and is a vibration signal;

[0013] S13. Based on the peak amplitude of the response curve of the quasi-static component of the vibration isolator, determine the key load positions P0, P1, P2, P3 and P4 of the railcar.

[0014] Further, in step S13:

[0015] P0 represents the static equilibrium position of the floating plate when the vibration isolator only bears the weight of the floating plate, rails, and fasteners.

[0016] P1 represents the minimum position of the floating plate when the adjacent bogies of two adjacent cars move away from the vibration isolator;

[0017] P2 represents the minimum position of the floating plate when the first or last bogie leaves the vibration isolator;

[0018] P3 represents the maximum value of the floating plate position when the first or last bogie approaches the vibration isolator;

[0019] P4 represents the maximum position of the floating plate when adjacent bogies of two adjacent cars approach the vibration isolator.

[0020] Furthermore, the preset energy definition formula in step S2 is as follows:

[0021]

[0022] Where i represents the load position P0, P1, P2, P3, P4, or other positions; W i N represents the vibrational energy near the critical load location i; i This indicates the number of times the vibration signal has occurred near the critical load location i; t i，j and T i，j Let f represent the start and end times of the j-th vibration signal occurring near the critical load location i, respectively; dyn (t) and Let x represent the dynamic components of the support reaction force response function and the dynamic components of the velocity response function, respectively; dyn (t) represents the displacement response function.

[0023] Furthermore, in step S3, constructing the optimal nonlinear restoring force curve of the floating slab vibration isolator using reverse design includes:

[0024] S31. Based on the load characteristics of the floating slab system, the vibration isolation requirements of the vibration isolator, and the displacement suppression requirements, the restoring force curve of the stiffness characteristics of HFTS is introduced, and displacement constraints, minimum stiffness constraints, and maximum stiffness constraints are constructed.

[0025] S32. Set the system restoring force function corresponding to the restoring force curve of the stiffness characteristics of the HFTS;

[0026] S33. Using the maximum displacement constraint, minimum stiffness constraint and maximum stiffness constraint conditions, solve for the three undetermined coefficients in the system's restoring force function to construct the optimal nonlinear restoring force curve of the floating plate vibration isolator.

[0027] Furthermore, in step S31:

[0028] The displacement constraint is to suppress the quasi-static displacement response of the floating slab system by improving the overall energy storage capacity of the vibration isolator.

[0029] The minimum stiffness constraint is: improve the broadband vibration isolation performance near the two critical locations, P4 and P0, by reducing the dynamic stiffness of the vibration isolators.

[0030] The maximum stiffness constraint is: by limiting the maximum stiffness of the vibration isolator over the entire range, the vibration isolation performance of the floating plate system is prevented from being excessively deteriorated locally.

[0031] Furthermore, in step S32, the system restoring force function is as follows:

[0032]

[0033] Where f(X) and g(X) intersect at P(d0,f0), and g(X) and The system exhibits rotational symmetry about point P; where X represents the system displacement and r represents the function. The magnification factor between f(X) and d m The design value represents the peak value of the quasi-static displacement response of the HFTS vibration isolator, where a, b, and n are all undetermined coefficients.

[0034] Further, step S33 includes:

[0035] 1) Quantitative analysis of the displacement constraints, minimum stiffness constraints, and maximum stiffness constraints:

[0036] Displacement constraint: Throughout the entire operation of the vehicle, the peak value of the quasi-static component of the displacement response of the floating platform system shall not exceed d. m ;

[0037] Minimum stiffness constraint: The equivalent stiffness of the system is defined if and only if the floating slab system is at either critical load position P0 or P4. To obtain the minimum value k0, which satisfies K(X). min =K(0)=K(d) m ) = k0, where k0 represents the minimum equivalent stiffness of the floating slab system;

[0038] Maximum stiffness constraint: The floating plate system is constrained throughout the entire effective formation interval X∈[0,d] m The upper limit of stiffness within [ ] does not exceed k m That is, satisfying K(X)≤k m , where k m This represents the maximum value of the equivalent stiffness of the floating slab system;

[0039] 2) Solve for the three undetermined coefficients a, b, and n in the restoring force function of the system using the following formula:

[0040]

[0041] Where d represents the maximum displacement generated by the existing linear vibration isolator, and k represents the stiffness value of the existing steel spring floating plate vibration isolator.

[0042] Furthermore, in step S4, the design parameter rules include:

[0043] 1) When the equivalent stiffness of the HFTS system reaches its maximum value, the damping ratio of the floating slab system is selected as 25%;

[0044] 2) When the equivalent stiffness of the HFTS system is equal to that of the existing linear floating slab system, the damping coefficient of the floating slab system shall be the same as that of the existing steel spring floating slab vibration isolator.

[0045] 3) When the equivalent stiffness of the HFTS system reaches its minimum value, the damping ratio of the floating slab system is selected as 5%.

[0046] 4) The damping coefficients at other locations are determined by fitting the data using a cubic polynomial interpolation method based on the five key load locations in the displacement-damping coefficient plane mentioned above.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] This invention provides a parameter optimization design method for a nonlinear vibration-damping track system. For a floating slab vibration-damping track system, based on its load characteristics and mechanism, it proposes benchmark values ​​for each level of parameters and optimized design schemes for nonlinear characteristic parameters, achieving active vibration isolation with displacement suppression requirements. This method, based on the requirements of vibration control objectives and complex load characteristics on the system's energy storage capacity and equivalent stiffness distribution, performs inverse analytical construction of the system's restoring force function. This provides a novel solution for the design of high-performance floating slab passive vibration isolators that simultaneously meet displacement suppression and low-frequency vibration isolation requirements, satisfying track displacement suppression requirements while ensuring low vertical dynamic effects. Attached Figure Description

[0049] Figure 1 Simulation diagram of the generation mechanism of the vibration isolator response characteristics provided by the present invention;

[0050] Figure 2a This is a quasi-static component signal decomposition diagram of the displacement response of the vibration isolator provided by the present invention.

[0051] Figure 2b The dynamic signal decomposition diagram of the displacement response of the vibration isolator provided by the present invention;

[0052] Figure 2c A quasi-static component signal decomposition diagram of the support reaction force response provided by the present invention;

[0053] Figure 2d The dynamic component signal decomposition diagram of the support reaction force response provided by the present invention;

[0054] Figure 3 A schematic diagram of the restoring force curve with "first hardening then softening (HFTS)" stiffness characteristics provided for this invention;

[0055] Figure 4 The energy distribution diagram of the dynamic components of the vibration response provided by the present invention near different key load locations. Detailed Implementation

[0056] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0057] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front end," "rear end," "both ends," "one end," and "the other end," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0058] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installed," "equipped with," "connected," etc., should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be a connection within two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0059] The present invention will be further described below with reference to specific embodiments, but the present invention is not limited to the embodiments.

[0060] Step 1: Based on the quasi-static components of the vibration isolator's response signal when a train passes, define the five key load positions of the vibration isolator: P0, P1, P2, P3, and P4.

[0061] Furthermore, the method for determining the location of critical loads includes the following steps:

[0062] Step 1.1: Obtain the typical response curve of the vibration isolator when a train passes by through simulation, as shown below. Figure 1 As shown, the control objective is given according to the "Technical Specification for Floating Slab Track" (CJJ / T191-2012), and the basic simulation conditions are shown in Table 1 below:

[0063]

[0064]

[0065] Table 1

[0066] Step 1.2: Decompose the displacement and support reaction force response signals of the vibration isolator into quasi-static and dynamic components based on a frequency threshold (e.g., 4Hz), such as... Figures 2a-2d As shown; the quasi-static component is caused by the loading directly above the vibration isolator when the train passes; the dynamic component is the vibration signal, which is caused by the unevenness of the wheel and rail.

[0067] Step 1.3: Determine the critical load locations P0, P1, P2, P3, and P4 of the railcar based on the peaks and troughs of the quasi-static component response curve of the vibration isolator. The definitions of each critical load location are shown in Table 2 below:

[0068]

[0069] Table 2

[0070] Step 2: Use the energy definition formula to solve for the vibration energy near each key load location, and obtain the energy distribution of the dynamic components of the vibration response as follows: Figure 4 As shown, the energy distribution characteristics are analyzed, and the priority of vibration isolation requirements at different load locations is ranked as follows: P4≈P3>P0>P1≈P2>Other

[0071] The energy definition formula is as follows:

[0072]

[0073] Where i represents the load position P0, P1, P2, P3, P4, or other positions; W i N represents the vibrational energy near the critical load location i; i This indicates the number of times the vibration signal has occurred near the critical load location i; t i,j and T i,j Let f represent the start and end times of the j-th vibration signal occurring near the critical load location i, respectively; dyn (t) and Let x represent the dynamic components of the support reaction force response function and the dynamic components of the velocity response function, respectively; dyn (t) represents the displacement response function.

[0074] Step 3: Based on the priority of vibration isolation requirements and displacement suppression requirements at key load locations, construct the optimal nonlinear restoring force curve for the floating slab vibration isolator using a reverse design method. The curve adopts a restoring force curve with "first gradually stiffening then gradually softening (HFTS)" stiffness characteristics, such as... Figure 3 As shown;

[0075] Furthermore, the method for optimizing the nonlinear restoring force curve design includes the following steps:

[0076] Step 3.1: Based on the load characteristics of the floating slab system, the vibration isolation requirements of the vibration isolators, and the displacement suppression requirements, a restoring force curve with "gradually stiffening followed by gradual softening (HFTS)" stiffness characteristics is introduced, and the following design is performed:

[0077] 1) The displacement constraint condition is: to suppress the quasi-static displacement response of the floating slab system by improving the overall energy storage capacity of the vibration isolator;

[0078] 2) The minimum stiffness constraint is: by reducing the dynamic stiffness of the vibration isolators near the two critical locations P4 and P0, the broadband vibration isolation performance near the critical locations is improved.

[0079] 3) The maximum stiffness constraint is: by limiting the maximum stiffness of the vibration isolator over the entire range, the vibration isolation performance of the floating plate system is prevented from being excessively deteriorated locally.

[0080] Step 3.2: Define the basic form of the system's restoring force function as follows, and the curve is shown in the figure. Figure 3 As shown:

[0081]

[0082] d m This represents the design value of the peak value of the quasi-static displacement response of the HFTS vibration isolator, where a, b, and n are all undetermined coefficients; where X represents the system displacement, and r represents the function... The magnification factor between f(X) and d m The design value represents the peak value of the quasi-static displacement response of the HFTS vibration isolator, where a, b, and n are all undetermined coefficients.

[0083] Step 3.3: Solve for the three undetermined coefficients in the system's restoring force function using the three constraints: displacement constraint, minimum stiffness constraint, and maximum stiffness constraint.

[0084] Furthermore, the method for solving for the undetermined coefficients includes the following steps:

[0085] Step 3.3.1: To ensure that the HFTS vibration isolator meets the vibration isolation requirements of the floating slab system, the following three constraints are quantitatively analyzed:

[0086] 1) Displacement constraint: During the entire operation of the vehicle, the peak value of the quasi-static component of the displacement response of the floating platform system does not exceed d. m ;

[0087] 2) Minimum stiffness constraint: The equivalent stiffness of the system is defined if and only if the system is at either of the two critical load locations, P0 or P4. To obtain the minimum value k0, which satisfies K(X). min =K(0)=K(d) m ) = k0, where k0 represents the minimum equivalent stiffness of the floating slab system;

[0088] 3) Maximum stiffness constraint: The floating slab system is constrained throughout the entire effective formation interval X∈[0, d]. m The upper limit of stiffness within [ ] does not exceed k m That is, satisfying K(X)≤k m , where k mThis represents the maximum value of the equivalent stiffness of the floating slab system.

[0089] The three constraints in this embodiment are set as follows:

[0090] Step 3.3.2: Solve for the undetermined coefficients a, b, and n in the restoring force curve function using the following formula:

[0091]

[0092] Where d represents the maximum displacement (m) generated by the existing linear vibration isolator, and k represents the stiffness value (N / m) of the existing steel spring floating plate vibration isolator.

[0093] The obtained parameters to be determined can be determined as follows:

[0094] Step 4: Based on the optimal nonlinear restoring force curve of the floating plate isolator, perform nonlinear damping design on the stiffness characteristics of the HFTS isolator to obtain the design parameter rules.

[0095] For the nonlinear damping design of the stiffness characteristics of HFTS isolators, the damping ratio of floating slab isolators should be limited to a range of not less than 5% and not more than 25%. Therefore, the design rules for the damping coefficient variation of the HFTS system are as follows:

[0096] 1) When the equivalent stiffness of the HFTS system reaches its maximum value (approximately x2 = 0.438 mm), the damping ratio of the system is selected as 25% (the corresponding damping coefficient is approximately 49371 N·s / m); the HFTS system refers to a floating plate system equipped with a vibration isolator with a gradually hardening and then softening stiffness characteristic.

[0097] 2) When the equivalent stiffness of the HFTS system is equal to that of the existing linear system (approximately at x1 = 0.171 mm and x3 = 2.19 mm), the damping coefficient of the system is selected to be the same as that of the existing steel spring floating plate vibration isolator, 16000 N·s / m.

[0098] 3) When the equivalent stiffness of the HFTS system reaches its minimum value (approximately at x0 = 0 mm and x4 = 3.3 mm), the damping ratio of the system is selected as 5% (the corresponding damping coefficient is approximately 9874.21 N·s / m);

[0099] 4) The damping coefficients at other locations are determined by fitting the five key points in the displacement-damping coefficient plane mentioned above, as shown in Table 3 below, using the cubic polynomial interpolation method.

[0100] Key Point 1 0 9874.21 Key Point 2 0.035 16000 Key Point 3 0.087 49371 Key Point 4 1.9 16000 Key Point 5 3 9874.21

[0101] Table 3

[0102] Based on the requirements of vibration control objectives and complex load characteristics on the system's energy storage capacity and equivalent stiffness distribution, this method analytically constructs the system's restoring force function in reverse, providing a novel solution for the design of high-performance floating slab passive vibration isolators that simultaneously meet the requirements of displacement suppression and low-frequency vibration isolation.

[0103] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for parameter optimization design of a nonlinear damping track system, characterized in that, Includes the following steps: S1. Based on the quasi-static components of the vibration isolator's response signal when a train passes, define five key load locations for the vibration isolator. , , , and ; S2. Using a preset energy definition formula, calculate the vibration energy at the five key load locations, analyze the energy distribution characteristics, and prioritize the vibration isolation requirements at different key load locations. The preset energy definition formula is as follows: ；（1） Where i represents the load position , , , and Or other locations; This represents the vibrational energy near the critical load location i; This indicates the number of times the vibration signal has occurred near the critical load position i; and These represent the start and end times of the j-th vibration signal that appears near the critical load location i, respectively. and These represent the dynamic components of the support reaction force response function and the dynamic components of the velocity response function, respectively. Represents the displacement response function; S3. Based on the priority of vibration isolation requirements and displacement suppression requirements at key load locations, construct the optimal nonlinear restoring force curve of the floating plate vibration isolator using reverse design. S4. Based on the optimal nonlinear restoring force curve of the floating plate vibration isolator, perform nonlinear damping design on the stiffness characteristics of the HFTS vibration isolator to obtain the design parameter rules. In step S3, constructing the optimal nonlinear restoring force curve of the floating slab vibration isolator using reverse design includes: S31. Based on the load characteristics of the floating slab system, the vibration isolation requirements of the vibration isolator, and the displacement suppression requirements, the restoring force curve of the stiffness characteristics of HFTS is introduced, and the maximum displacement constraint, minimum stiffness constraint, and maximum stiffness constraint conditions are constructed. S32. Set the system restoring force function corresponding to the restoring force curve of the stiffness characteristics of the HFTS; S33. Using displacement constraints, minimum stiffness constraints, and maximum stiffness constraints, solve for the three undetermined coefficients in the system's restoring force function to construct the optimal nonlinear restoring force curve of the floating plate vibration isolator.

2. The parameter optimization design method for a nonlinear vibration reduction track system according to claim 1, characterized in that, Step S1 includes: S11. The typical response curve of the vibration isolator when a train passes by is obtained through simulation; S12. Based on the typical response curve, the displacement and support reaction force response signals of the vibration isolator are decomposed into quasi-static and dynamic components based on frequency thresholds, respectively; wherein, the quasi-static component is caused by the loading of the train passing directly above the vibration isolator; the dynamic component is caused by the unevenness of the wheel and rail, and is a vibration signal; S13. Determine the critical load locations of the rail train based on the peak amplitude of the response curve of the quasi-static component of the vibration isolator. , , , and .

3. The parameter optimization design method for a nonlinear vibration reduction track system according to claim 2, characterized in that, In step S13: This indicates the static equilibrium position of the floating plate when the vibration isolator only bears the weight of the floating plate, rails, and fasteners. This indicates the minimum position of the floating plate when adjacent bogies of two adjacent cars move away from the vibration isolator; This indicates the minimum position of the floating plate when the first or last bogie leaves the vibration isolator; This indicates the maximum position of the floating plate when the first or last bogie approaches the vibration isolator; This indicates the maximum position of the floating plate when adjacent bogies of two adjacent cars approach the vibration isolator.

4. The parameter optimization design method for a nonlinear vibration reduction track system according to claim 1, characterized in that, In step S31: The displacement constraint is to suppress the quasi-static displacement response of the floating slab system by improving the overall energy storage capacity of the vibration isolator. The minimum stiffness constraint is: by reducing as well as Increase the dynamic stiffness of the vibration isolators near two key locations to improve the broadband vibration isolation performance near these key locations; The maximum stiffness constraint is: by limiting the maximum stiffness of the vibration isolator over the entire range, the vibration isolation performance of the floating plate system is prevented from being excessively deteriorated locally.

5. The parameter optimization design method for a nonlinear vibration reduction track system according to claim 4, characterized in that, In step S32, the system restoring force function is as follows: ；（2） Where f(X) intersects g(X) at g(X) and The system exhibits rotational symmetry about point P; where X represents the system displacement and r represents the function. The magnification factor between f(X) and f(X) The design value represents the peak value of the quasi-static displacement response of the HFTS vibration isolator, where a, b, and n are all undetermined coefficients.

6. The parameter optimization design method for a nonlinear vibration reduction track system according to claim 5, characterized in that, Step S33 includes: 1) Quantitative analysis of the displacement constraints, minimum stiffness constraints, and maximum stiffness constraints: Displacement constraint: Throughout the entire operation of the vehicle, the peak value of the quasi-static component of the displacement response of the floating platform system shall not exceed [a certain value]. ; Minimum stiffness constraint: if and only if the floating plate system is in or The equivalent stiffness of the system at two critical load locations ( (Achieve minimum value) That is, satisfy ,in, This represents the minimum equivalent stiffness of the floating slab system; Maximum stiffness constraint: The floating slab system throughout the entire effective formation range The upper limit of stiffness within does not exceed That is, satisfy ,in, This represents the maximum value of the equivalent stiffness of the floating slab system; 2) Solve for the three undetermined coefficients a, b, and n in the restoring force function of the system using the following formula: ；（3） Where d represents the maximum displacement generated by the existing linear vibration isolator, and k represents the stiffness value of the existing steel spring floating plate vibration isolator.

7. The parameter optimization design method for a nonlinear vibration reduction track system according to claim 6, characterized in that, In step S4, the design parameter rules include: 1) When the equivalent stiffness of the HFTS system reaches its maximum value, the damping ratio of the floating slab system is selected as 25%; 2) When the equivalent stiffness of the HFTS system is equal to that of the existing linear floating slab system, the damping coefficient of the floating slab system shall be selected to be the same as that of the existing steel spring floating slab vibration isolator. 3) When the equivalent stiffness of the HFTS system reaches its minimum value, the damping ratio of the floating slab system is selected as 5%; 4) The damping coefficients at other locations are determined by fitting the data using a cubic polynomial interpolation method based on the five key load locations in the displacement-damping coefficient plane mentioned above.

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