Method and device for determining the friction resistance and tangent stiffness of a friction support

Abstract

The application discloses a kind of friction support friction resistance and tangent rigidity determination method and device, it is related to structural nonlinear analysis technical field, the method includes: obtaining the maximum friction resistance of support and the sliding speed of support in set time period;According to the trigonometric function type relation among support friction resistance, support tangent rigidity and support sliding speed, the trigonometric function type iteration model that support friction resistance and support tangent rigidity change with support sliding speed is established;Based on trigonometric function type iteration model, according to the change of support sliding speed in set time period, the support friction resistance and support tangent rigidity in set time period are obtained.Solved in prior art, using WEN plastic unit adds unit mechanics formula to nonlinear dynamic equation for numerical calculation, there is need to carry out step-by-step integration, calculation workload is large, when integral step is large, friction resistance calculation result fluctuation is large, and the problem that tangent rigidity cannot be determined.

Description

Technical Field

[0001] This invention relates to the field of structural nonlinear analysis technology, specifically to a method and apparatus for determining the frictional resistance and tangential stiffness of friction supports. Background Technology

[0002] Bearings, as components for supporting and fixing equipment, are widely used in structures such as bridges, buildings, and machinery. Commonly used bearings include spherical steel bearings, pot bearings, and plate bearings. When these bearings move horizontally, they all generate frictional resistance. Frictional resistance affects structural deformation, especially under dynamic loads, where it significantly impacts the structural response. Therefore, accurate calculation of frictional resistance is crucial for the rational design and safety of structures.

[0003] In existing technologies, WEN plastic elements are generally used to incorporate element mechanics formulas into nonlinear dynamic equations for numerical calculation. This method has several drawbacks, including the need for step-by-step integration, large computational workload, large fluctuations in frictional resistance calculation results when the integration step is large, and inability to determine tangential stiffness. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method and apparatus for determining the frictional resistance and tangential stiffness of friction supports. This method solves the problems of existing technologies that use WEN plastic elements to incorporate element mechanics formulas into nonlinear dynamic equations for numerical calculations, which require step-by-step integration, resulting in a large computational workload. When the integration step is large, the frictional resistance calculation results fluctuate greatly, and the tangential stiffness cannot be determined.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] On the one hand, this solution provides a method for determining the frictional resistance and tangential stiffness of a friction support, including:

[0007] Obtain the maximum frictional resistance of the support and the sliding speed of the support within a set time period;

[0008] Based on the trigonometric function relationship between support friction, support tangential stiffness and support sliding velocity, a trigonometric function iterative model is established to show the variation of support friction and support tangential stiffness with support sliding velocity.

[0009] Based on a trigonometric function iterative model, the bearing friction and bearing tangential stiffness are obtained within a set time period according to the change in bearing sliding speed within a set time period.

[0010] In some optional solutions, the method based on a trigonometric function iterative model, which obtains the support friction and support tangential stiffness within a set time period according to the change in support sliding velocity within that time period, includes:

[0011] Based on the current support sliding velocity and the next support sliding velocity, determine the friction coefficient and the tangential stiffness coefficient at the next moment;

[0012] Based on the friction coefficient, tangential stiffness coefficient, and maximum friction coefficient of the support at the next moment, determine the friction coefficient and tangential stiffness of the support at the next moment.

[0013] Repeat the above steps until the support friction and support tangential stiffness within the set time period are obtained.

[0014] In some alternative solutions, according to the formula:

[0015] Determine the friction coefficient at the next moment;

[0016] Among them, z t+1 Let v be the friction coefficient at the next moment. t v is the current sliding velocity of the support. t+1 Let Δt be the sliding velocity of the support at the next moment, Δt be the time interval between the next moment and the current moment, w0 be the velocity coefficient of the time interval, w0 = w / Δt, and w be the velocity coefficient, w = π / 2v. s v s This is the threshold value for the dynamic friction velocity of the support.

[0017] In some alternative solutions, according to the formula: F t+1 =F y ·z t+1 Determine the bearing friction resistance at the next moment;

[0018] Among them, F t+1 For the support friction resistance at the next moment, F y For the maximum frictional resistance of the support, z t+1 This represents the friction coefficient at the next moment.

[0019] In some alternative solutions, according to the formula:

[0020] Determine the tangent stiffness coefficient at the next moment;

[0021] Where, z′ t+1 v is the tangent stiffness coefficient at the next moment. t v is the current sliding velocity of the support. t+1 Let Δt be the sliding velocity of the support at the next moment, Δt be the time interval between the next moment and the current moment, w0 be the velocity coefficient of the time interval, w0 = w / Δt, and w be the velocity coefficient, w = π / 2v. s v s This is the threshold value for the dynamic friction velocity of the support.

[0022] In some alternative solutions, according to the formula: K t+1 =F y ·z′ t+1 Determine the tangential stiffness of the support at the next moment;

[0023] Among them, K t+1 F is the tangential stiffness of the support at the next moment. y For the maximum frictional resistance of the support, z′ t+1 This represents the tangent stiffness coefficient at the next moment.

[0024] In some alternative schemes, the time interval between the next moment and the current moment is 0.01s.

[0025] In some alternative schemes, the sliding velocity of the support within a set time period is obtained according to the formula: v = sin(2πt);

[0026] Where v is the sliding velocity of the support and t is time.

[0027] In some alternative solutions, the maximum frictional resistance of the support is determined based on frictional resistance test data.

[0028] On the other hand, this solution also provides a device for determining the frictional resistance and tangential stiffness of a friction support, comprising:

[0029] The parameter acquisition module is used to obtain the maximum frictional resistance of the support and the sliding speed of the support within a set time period.

[0030] The model building module is used to establish a trigonometric function iterative model of the variation of support friction and support tangential stiffness with support sliding speed based on the trigonometric function relationship between support friction, support tangential stiffness and support sliding speed.

[0031] The frictional resistance and tangential stiffness determination module is used to obtain the bearing frictional resistance and bearing tangential stiffness within a set time period based on the bearing sliding velocity change within a set time period using a trigonometric function iterative model.

[0032] Compared with existing technologies, the advantages of this invention are as follows: This solution obtains the maximum frictional resistance of the support and the sliding velocity of the support within a set time period; based on the trigonometric function relationship between the support frictional resistance, the support tangential stiffness, and the support sliding velocity, it establishes a trigonometric function iterative model showing the variation of the support frictional resistance and the support tangential stiffness with the support sliding velocity; based on the trigonometric function iterative model, it obtains the support frictional resistance and the support tangential stiffness within a set time period according to the change in the support sliding velocity within that time period. This solves the problems in existing technologies where WEN plastic elements are used to incorporate element mechanics formulas into nonlinear dynamic equations for numerical calculation, which requires step-by-step integration, resulting in a large computational workload; when the integration step size is large, the frictional resistance calculation results fluctuate greatly; and the tangential stiffness cannot be determined. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a flowchart illustrating the method for determining the frictional resistance and tangential stiffness of a friction support in an embodiment of the present invention.

[0035] Figure 2 This is a schematic diagram of the friction support unit in an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of the support friction resistance within a set time period in an embodiment of the present invention;

[0037] In the diagram: 1. First node; 2. Second node; 3. Threshold for dynamic friction velocity of the support. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0039] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0040] like Figure 1 As shown, in one aspect, the present invention provides a method for determining the frictional resistance and tangential stiffness of a friction support, comprising:

[0041] S1: Obtain the maximum frictional resistance of the support and the sliding speed of the support within a set time period.

[0042] S2: Based on the trigonometric function relationship between support friction, support tangential stiffness and support sliding velocity, establish a trigonometric function iterative model of the variation of support friction and support tangential stiffness with support sliding velocity.

[0043] S3: Based on a trigonometric function iterative model, the bearing friction and bearing tangential stiffness are obtained within a set time period according to the change in bearing sliding speed within a set time period.

[0044] Step S3 specifically includes:

[0045] S31: Determine the friction coefficient and tangential stiffness coefficient at the next moment based on the current support sliding velocity and the next support sliding velocity.

[0046] S32: Determine the support friction coefficient and the support tangential stiffness at the next moment based on the friction coefficient, the tangential stiffness coefficient, and the maximum friction coefficient of the support at the next moment.

[0047] S33: Repeat the above steps until the bearing friction and bearing tangential stiffness within the set time period are obtained.

[0048] In some alternative embodiments, according to the formula:

[0049] Determine the friction coefficient at the next moment;

[0050] Among them, z t+1 Let v be the friction coefficient at the next moment. t v is the current sliding velocity of the support. t+1 Let Δt be the sliding velocity of the support at the next moment, Δt be the time interval between the next moment and the current moment, w0 be the velocity coefficient of the time interval, w0 = w / Δt, and w be the velocity coefficient, w = π / 2v. s v s This is the threshold value for the dynamic friction velocity of the support.

[0051] In some alternative embodiments, according to formula: F t+1 =F y ·z t+1 Determine the bearing friction resistance at the next moment;

[0052] Among them, F t+1 For the support friction resistance at the next moment, F y For the maximum frictional resistance of the support, z t+1 This represents the friction coefficient at the next moment.

[0053] In some alternative embodiments, according to the formula:

[0054] Determine the tangent stiffness coefficient at the next moment;

[0055] Where, z′ t+1 v is the tangent stiffness coefficient at the next moment. t v is the current sliding velocity of the support. t+1 Let Δt be the sliding velocity of the support at the next moment, Δt be the time interval between the next moment and the current moment, w0 be the velocity coefficient of the time interval, w0 = w / Δt, and w be the velocity coefficient, w = π / 2v. s v s This is the threshold value for the dynamic friction velocity of the support.

[0056] In some alternative embodiments, according to formula: K t+1 =F y ·z′ t+1 Determine the tangential stiffness of the support at the next moment;

[0057] Among them, K t+1 F is the tangential stiffness of the support at the next moment. y For the maximum frictional resistance of the support, z′ t+1 This represents the tangent stiffness coefficient at the next moment.

[0058] In some optional embodiments, the time interval between the next moment and the current moment is 0.01s.

[0059] In some optional embodiments, the support sliding speed within a set time period is obtained according to the formula: v = sin(2πt);

[0060] Where v is the sliding velocity of the support and t is time.

[0061] In some alternative embodiments, the maximum frictional resistance of the support is determined based on frictional resistance test data.

[0062] On the other hand, the present invention also provides a device for determining the frictional resistance and tangential stiffness of a friction support, comprising:

[0063] The parameter acquisition module is used to obtain the maximum frictional resistance of the support and the sliding speed of the support within a set time period.

[0064] The model building module is used to establish a trigonometric function iterative model of the variation of support friction and support tangential stiffness with support sliding speed based on the trigonometric function relationship between support friction, support tangential stiffness and support sliding speed.

[0065] The frictional resistance and tangential stiffness determination module is used to obtain the bearing frictional resistance and bearing tangential stiffness within a set time period based on the bearing sliding velocity change within a set time period using a trigonometric function iterative model.

[0066] In summary, this invention obtains the maximum frictional resistance of the support and the support sliding velocity within a set time period. Based on the trigonometric function relationship between the support frictional resistance, support tangential stiffness, and support sliding velocity, a trigonometric function iterative model is established to show the variation of support frictional resistance and support tangential stiffness with support sliding velocity. Based on this iterative model, the support frictional resistance and support tangential stiffness within the set time period are obtained according to the change in support sliding velocity. After obtaining the support tangential stiffness, the Jacobian matrix of the support frictional resistance element can be constructed to analyze the mechanical behavior of the overall structure. By determining the frictional resistance of the frictional supports, the deformation of the system structure caused by frictional vibration can be further determined, and the support sliding velocity can be corrected, providing support for subsequent system structure design and development.

[0067] This invention establishes a trigonometric function-based iterative model of the variation of support friction and tangential stiffness with support sliding velocity based on the trigonometric function relationship between support friction, support tangential stiffness, and support sliding velocity. This solves the problems of existing technologies that use WEN plastic elements to incorporate element mechanics formulas into nonlinear dynamic equations for numerical calculations, which require step-by-step integration, resulting in a large computational workload. Furthermore, with large integration steps, the calculated friction results fluctuate significantly, and the tangential stiffness cannot be determined. This invention promotes rapid convergence of the boundary nonlinear dynamic equations and improves the efficiency of time-history analysis. The calculation of the tangential stiffness of the support friction element is simplified, making the static and dynamic calculations of the overall structure containing friction supports simpler and more efficient.

[0068] The following specific examples will help to facilitate understanding of the present invention.

[0069] like Figure 2 As shown, the friction support unit includes: a first node 1, a second node 2, and a support dynamic friction velocity threshold 3. The first node 1 and the second node 2 represent two nodes in the friction support that slide relative to each other, and the frictional resistance between them is affected by the maximum frictional resistance of the support and the support dynamic friction velocity threshold 3.

[0070] In this example, the support is a single support element with no vertical force, and the maximum frictional resistance F of the support is... y =200kN, the sliding velocity of the support between the first and second nodes of the support element is v = sin(2πt) m / s, the time t starts at 0s and ends at 1s, and the time interval Δt = 0.01s. The threshold velocity of the support dynamic friction is v. s =10 -6 m / s, velocity coefficient The time interval velocity coefficient w0 = w / Δt = 1.57 × 10 8 .

[0071] Step 0 is the initial step, with initial velocity v0 = 0 m / s, initial friction coefficient z0 = 0, and initial tangent stiffness coefficient z′0 = 1.57 × 10⁻⁶. 6 At this point, the initial support frictional resistance F0 = 0 kN, and the initial support tangential stiffness K0 = 3.14 × 10⁻⁶ kN. 8 .

[0072] Based on the parameters of the initial step, calculate the support friction and support tangential stiffness at subsequent time steps. In the first step, time t1 = 0.01s, the support sliding velocity v1 = sin(2πt1) = 0.063m / s. v1 + v0 > v s z1 = 1, z′1 = 0, and correspondingly, F1 = 200kN, K1 = 0.

[0073] By repeating this iterative process, the frictional resistance and tangential stiffness of the friction support within the 0-1s time interval can be obtained. The frictional resistance values ​​are as follows: Figure 3 As shown, the frictional resistance of the friction support obtained by the present invention is stable and without fluctuation.

[0074] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and 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, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0075] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0076] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for determining the frictional resistance and tangential stiffness of a friction support, characterized in that, include: Obtain the maximum frictional resistance of the support and the sliding speed of the support within a set time period; Based on the trigonometric function relationship between support friction, support tangential stiffness and support sliding velocity, a trigonometric function iterative model is established to show the variation of support friction and support tangential stiffness with support sliding velocity. Based on the trigonometric function iterative model, the bearing friction and bearing tangential stiffness within a set time period are obtained according to the change in bearing sliding speed within a set time period. The aforementioned trigonometric function-based iterative model obtains the support friction and support tangential stiffness within a set time period based on the change in support sliding velocity over that time period, including: Based on the current support sliding velocity and the next support sliding velocity, determine the friction coefficient and the tangential stiffness coefficient at the next moment; Based on the friction coefficient, tangential stiffness coefficient, and maximum friction coefficient of the support at the next moment, determine the friction coefficient and tangential stiffness of the support at the next moment. Repeat the above steps until the support friction and support tangential stiffness within the set time period are obtained; According to the formula: Determine the friction coefficient at the next moment; in, The friction coefficient at the next moment. The current sliding speed of the support. The next moment is the support sliding speed. The time interval between the next moment and the current moment. The velocity coefficient for the time interval. , For speed coefficient, , The threshold value for dynamic friction velocity of the support; According to the formula: Determine the bearing friction resistance at the next moment; in, For the support friction resistance at the next moment, For the maximum frictional resistance of the support, The friction coefficient at the next moment; According to the formula: Determine the tangent stiffness coefficient at the next moment; in, The tangent stiffness coefficient for the next moment. The current sliding speed of the support. The next moment is the support sliding speed. The time interval between the next moment and the current moment. The velocity coefficient for the time interval. , For speed coefficient, , The threshold value for dynamic friction velocity of the support; According to the formula: Determine the tangential stiffness of the support at the next moment; in, For the support tangential stiffness at the next moment, For the maximum frictional resistance of the support, This represents the tangent stiffness coefficient at the next moment.

2. The method for determining the frictional resistance and tangential stiffness of a friction support as described in claim 1, characterized in that, The time interval between the next moment and the current moment is 0.01s.

3. The method for determining the frictional resistance and tangential stiffness of a friction support as described in claim 1, characterized in that, According to the formula: Get the support sliding speed within a set time period; in, The sliding speed of the support, For time.

4. The method for determining the frictional resistance and tangential stiffness of a friction support as described in claim 1, characterized in that, The maximum frictional resistance of the support is determined based on frictional resistance test data.

5. A device for determining the frictional resistance and tangential stiffness of a friction support, characterized in that, include: The parameter acquisition module is used to obtain the maximum frictional resistance of the support and the sliding speed of the support within a set time period. The model building module is used to establish a trigonometric function iterative model of the variation of support friction and support tangential stiffness with support sliding speed based on the trigonometric function relationship between support friction, support tangential stiffness and support sliding speed. The frictional resistance and tangential stiffness determination module is used to obtain the frictional resistance and tangential stiffness of the support within a set time period based on the change of the support sliding speed within a set time period using a trigonometric function iterative model. The aforementioned trigonometric function-based iterative model obtains the support friction and support tangential stiffness within a set time period based on the change in support sliding velocity over that time period, including: Based on the current support sliding velocity and the next support sliding velocity, determine the friction coefficient and the tangential stiffness coefficient at the next moment; Based on the friction coefficient, tangential stiffness coefficient, and maximum friction coefficient of the support at the next moment, determine the friction coefficient and tangential stiffness of the support at the next moment. Repeat the above steps until the support friction and support tangential stiffness within the set time period are obtained; According to the formula: Determine the friction coefficient at the next moment; in, The friction coefficient at the next moment. The current sliding speed of the support. The next moment is the support sliding speed. The time interval between the next moment and the current moment. The velocity coefficient for the time interval. , For speed coefficient, , The threshold value for dynamic friction velocity of the support; According to the formula: Determine the bearing friction resistance at the next moment; in, For the support friction resistance at the next moment, For the maximum frictional resistance of the support, The friction coefficient at the next moment; According to the formula: Determine the tangent stiffness coefficient at the next moment; in, The tangent stiffness coefficient for the next moment. The current sliding speed of the support. The next moment is the support sliding speed. The time interval between the next moment and the current moment. The velocity coefficient for the time interval. , For speed coefficient, , The threshold value for dynamic friction velocity of the support; According to the formula: Determine the tangential stiffness of the support at the next moment; in, For the support tangential stiffness at the next moment, For the maximum frictional resistance of the support, This represents the tangent stiffness coefficient at the next moment.

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