Frequency tuning scheme optimization method, system and equipment for variable stiffness vibration absorber

Abstract

The invention discloses a frequency tuning scheme optimization method, system and equipment of a variable stiffness vibration absorber, and relates to the field of mechanical system vibration reduction. The method comprises the following steps: establishing a main vibration system dynamic model containing a variable-stiffness vibration absorber; analyzing an influence rule of a ratio of the inherent frequency of the variable stiffness vibration absorber to the external excitation dominant frequency on a main vibration system response dynamic amplification coefficient based on a main vibration system dynamic model; based on the analyzed influence rule, segmenting and intercepting the ratio of the external excitation dominant frequency to the inherent frequency of the main vibration system between 0 and 2.0 to obtain a plurality of cut-off intervals; a quadratic linear programming optimization method is adopted, the dynamic amplification coefficient serves as an optimization target, and the optimal frequency ratio of each cut-off interval is calculated to form an optimized frequency tuning scheme of the variable stiffness vibration absorber; the optimized frequency tuning scheme is adopted to carry out dynamic tuning vibration elimination on the main vibration system, and the optimal vibration reduction effect can be achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical system vibration reduction, and in particular to a frequency tuning scheme optimization method, system and equipment for a variable stiffness vibration absorber. Background Art

[0002] The vibration absorber is the most widely used vibration reduction device in engineering. Its working principle is to attach a special device to the vibration-damped body to generate a force on the vibration-damped body to absorb vibration energy and reduce the vibration intensity of the vibration-damped body. The dynamic tuning vibration absorber is a specially designed type of vibration reduction device. Its main components are the mass elastic element that generates inertial force and the spring that generates restoring force. Its natural frequency needs to be close to the dominant frequency of the external excitation that follows the main vibration system to suppress the resonance of the main vibration system that is subjected to simple harmonic excitation.

[0003] The variable stiffness dynamic tuning vibration absorber (variable stiffness vibration absorber for short) adjusts the stiffness of the dynamic mass elastic element of the additional vibration absorber, controls the natural frequency of the vibration absorber in real time to be equal to (100% following) the dominant frequency of the external excitation, absorbs the vibration energy to the additional vibration absorber, and achieves the purpose of reducing the vibration amplitude of the main component. However, it is found in actual engineering practice that when the natural frequency of the vibration absorber 100% follows the dominant frequency of the external excitation, the vibration reduction effect is not optimal. Therefore, it is necessary to propose a frequency tuning scheme optimization method to optimize and improve the vibration reduction performance of the variable stiffness dynamic tuning vibration absorber. Summary of the invention

[0004] In response to the problems raised in the above background technology, the present invention provides a method, system and device for optimizing the frequency tuning scheme of a variable stiffness vibration absorber, so as to optimize the frequency tuning scheme of the variable stiffness dynamic tuning vibration absorber and achieve the best vibration reduction effect.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] In one aspect, the present invention provides a method for optimizing a frequency tuning scheme of a variable stiffness vibration absorber, comprising:

[0007] Establish the dynamic model of the main vibration system including variable stiffness vibration absorber;

[0008] Based on the dynamic model of the main vibration system, the influence of the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation on the dynamic amplification coefficient of the main vibration system response is analyzed;

[0009] Based on the analyzed influence law, the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system is segmented between 0 and 2.0 to obtain multiple truncation intervals;

[0010] The quadratic linear programming optimization method is used to take the dynamic amplification factor as the optimization target, and the optimal frequency ratio of each truncation interval is calculated to form the optimized frequency tuning scheme of the variable stiffness vibration absorber.

[0011] The optimized frequency tuning scheme is used to perform dynamic tuning and vibration elimination of the main vibration system.

[0012] Optionally, the establishing of the dynamic model of the main vibration system including the variable stiffness vibration absorber specifically includes:

[0013] Using the momentum theorem of classical mechanics, the dynamic model of the single-degree-of-freedom master vibration system for dynamic tuning and vibration elimination is established as follows:

[0014] ; Wherein m1 is the mass of the main vibration system, m2 is the mass of the variable stiffness vibration absorber; x1 is the displacement of the main vibration system, x2 is the displacement of the dynamic mass of the variable stiffness vibration absorber; c2 is the damping; k1 is the stiffness of the spring, k2 is the variable stiffness of the spring; the simple harmonic excitation applied to the main vibration system is F(t) = Fsinωt, F is the amplitude, and ω is the dominant frequency of the external excitation.

[0015] Optionally, the influencing rules include:

[0016] When the dominant frequency ω of external excitation is less than 0.8 times the natural frequency ω1 of the main vibration system, the natural frequency ω2 of the variable stiffness vibration absorber does not have to follow the dominant frequency of external excitation 100%. The ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of external excitation f=ω2 / ω is less than 1, and the dynamic amplification coefficient A1 / A0 of the main vibration system is less than 1, the vibration is weakened, and the vibration reduction effect is enhanced; where A1 is the amplitude of the vibration displacement of the main vibration system; A0 is the equivalent static displacement of the main vibration system.

[0017] Optionally, based on the analyzed influence law, the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system is segmented between 0 and 2.0 to obtain multiple truncation intervals, specifically including:

[0018] The ratio of the dominant frequency of external excitation to the natural frequency of the main vibration system, r = ω / ω1, is divided into 11 truncation intervals, including (0.0-0.1), (0.1-0.2), (0.2-0.3), (0.3-0.4), (0.4-0.5), (0.5-0.6), (0.6-0.7), (0.7-0.8), (0.8-0.9), (0.9-1.0) and (1.0-2.0).

[0019] Optionally, the quadratic linear programming optimization method is used to take the power amplification factor as the optimization target, and the optimal frequency ratio of each truncation interval is calculated to form an optimized frequency tuning scheme of the variable stiffness vibration absorber, which specifically includes:

[0020] For each truncation interval, the ratio of the natural frequency of the variable stiffness absorber to the dominant frequency of the external excitation f = ω2 / ω is taken as the independent variable, the dynamic amplification coefficient A1 / A0 is taken as the optimization target, and the sequential quadratic programming algorithm is used to search for the optimal solution of f = ω2 / ω as the optimal frequency ratio of the truncation interval;

[0021] Each truncation interval and the optimal frequency ratio corresponding to each truncation interval constitute an optimized frequency tuning scheme.

[0022] On the other hand, the present invention also provides a frequency tuning scheme optimization system for a variable stiffness vibration absorber, comprising:

[0023] Dynamic model building module, used to build the dynamic model of the main vibration system containing variable stiffness vibration absorber;

[0024] The influence law analysis module is used to analyze the influence of the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation on the dynamic amplification factor of the main vibration system response based on the dynamic model of the main vibration system;

[0025] The frequency ratio segmentation interception module is used to segmentally intercept the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system between 0 and 2.0 based on the analyzed influence law, and obtain multiple truncation intervals;

[0026] The optimal frequency ratio calculation module is used to adopt a quadratic linear programming optimization method, take the power amplification factor as the optimization target, calculate the optimal frequency ratio of each truncation interval to form an optimized frequency tuning scheme of the variable stiffness vibration absorber;

[0027] The dynamic tuning and vibration elimination module is used to perform dynamic tuning and vibration elimination of the main vibration system by adopting an optimized frequency tuning scheme.

[0028] On the other hand, the present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the frequency tuning scheme optimization method of the variable stiffness vibration absorber when executing the computer program.

[0029] Optionally, the memory is a non-transitory computer-readable storage medium.

[0030] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0031] The present invention provides a method, system and equipment for optimizing the frequency tuning scheme of a variable stiffness vibration absorber, by establishing a dynamic model of a main vibration system containing a variable stiffness vibration absorber; analyzing the influence of the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of an external excitation on the dynamic amplification factor of the main vibration system response based on the dynamic model of the main vibration system; based on the analyzed influence law, segmenting the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system between 0 and 2.0 to obtain a plurality of truncation intervals; using a quadratic linear programming optimization method, taking the dynamic amplification factor as the optimization target, calculating the optimal frequency ratio of each truncation interval to form an optimized frequency tuning scheme of the variable stiffness vibration absorber; using the optimized frequency tuning scheme to perform dynamic tuning and vibration elimination of the main vibration system, the optimal vibration reduction effect can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0033] Figure 1 It is a flow chart of a frequency tuning scheme optimization method of a variable stiffness vibration absorber of the present invention;

[0034] Figure 2 A schematic diagram of a dynamic model of a main vibration system including a variable stiffness vibration absorber constructed in the present invention;

[0035] Figure 3 It is a schematic diagram of the amplitude-frequency response of the dynamic amplification factor of the main vibration system under different conditions;

[0036] Figure 4 It is a schematic diagram of the amplitude-frequency response curve of the dynamic amplification factor of the main vibration system containing a variable stiffness vibration absorber;

[0037] Figure 5 It is a schematic diagram for comparing the amplitude-frequency characteristic curves of the main vibration system response dynamic amplification factor with continuously increasing frequency ratio;

[0038] Figure 6 A schematic diagram showing the comparison of the amplitude-frequency characteristic curves of the main vibration system response dynamic amplification factor with continuously decreasing frequency ratio;

[0039] Figure 7 Schematic diagram of the amplitude-frequency characteristic curve of the main vibration system response dynamic amplification factor when the optimal frequency tuning scheme is used;

[0040] Figure 8 It is a schematic diagram of the curve of the optimization target changing with the number of iterations;

[0041] Fig. 9 A schematic diagram of the amplitude power amplification factor of the improved frequency tuning solution of the present invention;

[0042] Fig.10 It is a schematic diagram of a dynamic model of a torsional vibration system including a vibration absorber according to an embodiment of the present invention;

[0043] Fig.11 It is a schematic diagram of the curve of the amplitude and frequency of the external excitation changing with time in an embodiment of the present invention;

[0044] Fig.12 Schematic diagram of variable torsional stiffness of vibration absorbers with two frequency tuning schemes according to an embodiment of the present invention;

[0045] Fig.13 Schematic diagram of vibration response displacement of the main vibration system according to an embodiment of the present invention;

[0046] Fig.14 It is a schematic diagram of the time-frequency comprehensive analysis result of the external excitation according to the embodiment of the present invention;

[0047] Fig.15 It is a schematic diagram of the vibration response result without a vibration absorber according to an embodiment of the present invention;

[0048] Fig.16 A schematic diagram of vibration response results of a passive vibration absorber according to an embodiment of the present invention;

[0049] Fig.17 This is a schematic diagram of the vibration response results of the variable stiffness vibration absorber of the 100% frequency tuning scheme according to an embodiment of the present invention;

[0050] Fig.18 This is a schematic diagram of the vibration response results of a variable stiffness vibration absorber with an improved frequency tuning scheme according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] The purpose of the present invention is to provide a method, system and device for optimizing the frequency tuning scheme of a variable stiffness vibration absorber, so as to optimize the frequency tuning scheme of the variable stiffness dynamic tuning vibration absorber and achieve the best vibration reduction effect.

[0053] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] Figure 1 This is a flow chart of a frequency tuning scheme optimization method for a variable stiffness vibration absorber of the present invention. Figure 1 The present invention provides a frequency tuning scheme optimization method for a variable stiffness vibration absorber, comprising the following steps 1 to 5.

[0055] Step 1: Establish the dynamic model of the main vibration system including the variable stiffness vibration absorber.

[0056] The dynamic model of the main vibration system with variable stiffness vibration absorber is established, such as Figure 2 As shown. For the main vibration system and the variable stiffness vibration absorber, let the mass of the main vibration system (referred to as the main mass) be m1, and the stiffness of the spring be k1. The mass of the variable stiffness dynamic tuning vibration absorber is m2, the variable stiffness of the spring is k2, and the damping is c2. The displacement of the main vibration system is x1, and the displacement of the dynamic mass of the variable stiffness vibration absorber is x2. A simple harmonic excitation F(t) = Fsinωt is applied to the main vibration system, with an amplitude of F and a frequency of ω.

[0057] Using the momentum theorem of classical mechanics, when a single-degree-of-freedom main vibration system is established for dynamic tuning and vibration elimination, the dynamic model of the main vibration system is:

[0058]

[0059] Assumptions

[0060]

[0061] In the formula, and are the vibration amplitudes of the main vibration system and the vibration absorber, respectively.

[0062] Substituting formula (2) into formula (1), we get:

[0063]

[0064] Assumptions

[0065] Δ(ω)={[(k1-m1ω 2 )(k2-ω 2 )-k2m2ω 2 ]+[c2ω(k1-m1ω 2 -m2ω 2 )] 2} 1 / 2 (4)

[0066] The amplitudes of the main vibration system and the vibration absorber are obtained as follows:

[0067]

[0068] Where φ1 and φ2 are the phase differences of the vibration displacement of the main vibration system and the vibration absorber, respectively.

[0069] The amplitude of the vibration displacement of the main vibration system can be converted into:

[0070]

[0071] Assume that the natural frequency of the main vibration system is The natural frequency of the vibration absorber is The equivalent static displacement of the main vibration system is A0=F / k1. The ratio of the dynamic mass of the vibration absorber to the mass of the main vibration system is μ=m2 / m1. The ratio of the natural frequency of the vibration absorber to the natural frequency of the main vibration system is b=ω2 / ω1. The ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system is r=ω / ω1. The damping ratio of the vibration absorber is ζ=c2 / 2m2ω2. Substituting the above parameters into formula (7), the displacement dynamic amplification coefficient A1 / A0 of the main vibration system is calculated, and the dimensionless result is:

[0072]

[0073] Step 2: Based on the dynamic model of the main vibration system, analyze the influence of the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation on the dynamic amplification coefficient of the main vibration system response.

[0074] Figure 2 The dynamic model shown can simulate the undamped main vibration system of the undamped passive vibration absorber. Assuming μ = 0.25, ω1 = ω2 and ζ = 0, the amplitude-frequency response of the main vibration system can be obtained, that is, the change of the response dynamic amplification factor A1 / A0 with the frequency ratio r = ω / ω1, as shown in Figure 3 As shown in the ξ=0 curve.

[0075] Assuming μ = 0.25, b = 1 and ζ = 0.1, the undamped main vibration system with a damped passive vibration absorber can be simulated, and the change of the dynamic amplification coefficient A1 / A0 of the main vibration system response with the frequency ratio r = ω / ω1 can be obtained, as shown in Figure 3 As shown in the curve of ξ=0.1.

[0076] By comparing the two curves of ξ=0 and ξ=0.1, it is found that the optimized m2, k2 and ζ can significantly and effectively reduce the power amplification coefficient A1 / A0, expand the vibration reduction frequency band, and improve the vibration reduction performance of the vibration absorber.

[0077] According to the theory of dynamic tuning vibration absorption, the optimal frequency ratio b of the undamped main vibration system with passive vibration absorber is determined. opt =ω2 / ω1=1 / μ+1, the optimal damping ratio is Substituting the above parameters into equation (8), we can obtain the amplitude-frequency response of the dynamic amplification factor of the main vibration system response, as follows: Figure 3 Middle opt 、b opt As shown in the curve.

[0078] Figure 2 The dynamic model shown can also simulate the undamped main vibration system of the variable stiffness vibration absorber. Assuming that the ratio of the natural frequency of the vibration absorber to the natural frequency of the main vibration system is b = ω2 / ω1, which is equal to the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system r = ω / ω1, that is, b = ω2 / ω1 = r = ω / ω1. At this time, the ratio of the natural frequency of the vibration absorber to the dominant frequency of the external excitation is f = ω2 / ω = 1, which satisfies the dynamic tuning condition. The amplitude-frequency response of the dynamic amplification coefficient of the main vibration system containing the variable stiffness vibration absorber is obtained, as shown in Figure 3 As shown in the curve where ξ=0.1, f=1.

[0079] Depend on Figure 3 It can be seen that the vibration reduction effect of the variable stiffness vibration absorber is better than that of the passive vibration absorber matching the optimal parameters. Therefore, the research focus of the present invention is the vibration reduction performance of the variable stiffness vibration absorber.

[0080] The following is an analysis of the influence of the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation on the dynamic amplification factor of the main vibration system response. The amplitude-frequency response curve of the dynamic amplification factor of the main vibration system containing the variable stiffness vibration absorber is as follows: Figure 4 shown.

[0081] Depend on Figure 4 It can be seen that when the dominant frequency of external excitation is much smaller than 0.8 times the natural frequency of the main vibration system, even if the main vibration system containing the variable stiffness vibration absorber meets the dynamic tuning conditions, the dynamic amplification factor of the main vibration system is still greater than 1, that is, vibration deterioration occurs. Therefore, when the dominant frequency of the external excitation changes transiently, the tuning scheme in which the natural frequency of the variable stiffness vibration absorber follows the dominant frequency of the external excitation 100% is not the optimal scheme and needs to be improved. The key parameters of the frequency tuning scheme are set, and the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation is f = ω2 / ω = 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, and the amplitude-frequency characteristic curve of the dynamic amplification factor of the main vibration system response from the magnified perspective is obtained, as shown in Figure 5 shown.

[0082] Depend on Figure 5 It can be seen that when the natural frequency of the variable stiffness vibration absorber is greater than the dominant frequency of the external excitation, the dynamic amplification factor of the main vibration system response is always greater than 1, and the vibration is further aggravated. It can be seen that it is wrong to optimize the frequency tuning scheme from this direction. Consider optimizing the adjustment from the opposite direction, that is, setting the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation to f = ω2 / ω = 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, and obtain the amplitude-frequency characteristic curve of the dynamic amplification factor of the main vibration system response from the magnified perspective, as shown in Figure 6 shown.

[0083] Depend on Figure 6 It can be seen that when the dominant frequency of external excitation is less than 0.8 times the natural frequency of the main vibration system, the natural frequency of the variable stiffness vibration absorber does not have to follow the dominant frequency of external excitation 100%, and its frequency ratio is less than 1. The power amplification factor of the main vibration system is less than 1, and the vibration is significantly weakened, which can achieve a better vibration reduction effect. Figure 6 Zoom in Figure 7 It can be seen that the smaller the dominant frequency of the external excitation is than the natural frequency of the main vibration system, that is, the smaller the key parameter of the frequency tuning scheme (the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation) is than 1, the better the vibration reduction effect can be achieved, indicating that when the dominant frequency of the external excitation increases from 0 to the natural frequency of the main vibration system, the improved and optimized frequency tuning scheme will have greater advantages. In the first stage, the ratio of the variable stiffness vibration absorber to the dominant frequency of the external excitation is set to f = ω2 / ω = 0.5. As the dominant frequency of the external excitation increases, the frequency ratio changes to f = ω2 / ω = 0.6, f = ω2 / ω = 0.7, f = ω2 / ω = 0.8 and f = ω2 / ω = 0.9 in stages. When the dominant frequency of the external excitation increases to more than 0.8 times the natural frequency of the main vibration system, the frequency ratio is set to f = ω2 / ω = 1.0, that is, the natural frequency of the variable stiffness vibration absorber 100% follows the dominant frequency of the external excitation, and the 100% frequency following scheme will be used afterwards. By integrating the above schemes at various stages, we can obtain an optimized frequency tuning scheme. The amplitude-frequency characteristic curve of the main vibration system in response to the dynamic amplification factor is compared as follows: Figure 7 shown.

[0084] Based on the above analysis, for external excitation with transient frequency changes, the frequency tuning scheme of the variable stiffness vibration absorber can be modified by a rough segmented interception method of the frequency ratio. By optimizing and improving this method more carefully and adopting a more detailed segmented interception optimization method, the theoretically optimal frequency tuning scheme can be obtained, providing more options for practical engineering applications. It is worth noting that in Figure 7 The 90% frequency following curve close to the optimal curve can be used as an alternative solution for an application scenario in design and control. The optimal curve can be applied in scenarios with higher vibration reduction requirements. The key still depends on the cost and working conditions of the variable stiffness vibration absorber in actual engineering applications.

[0085] Step 3: Based on the analyzed influence law, the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system is segmented between 0 and 2.0 to obtain multiple truncation intervals.

[0086] The present invention adopts a segmented interception optimization algorithm to segment the ratio of the dominant frequency of external excitation to the natural frequency of the main vibration system r=ω / ω1 into 11 truncation intervals, namely (0.0-0.1), (0.1-0.2), (0.2-0.3), (0.3-0.4), (0.4-0.5), (0.5-0.6), (0.6-0.7), (0.7-0.8), (0.8-0.9), (0.9-1.0) and (1.0-2.0). Based on the above segmented interception method, when the dominant frequency of external excitation reaches the natural frequency of the main vibration system, a 100% frequency tracking scheme is adopted. Before the dominant frequency of external excitation reaches the natural frequency of the main vibration system, a nonlinear optimization method can be introduced to obtain the optimal frequency ratio of each truncation interval. By combining the nonlinear optimization method with the segmented interception method, the optimal frequency ratio of each segment is calculated, and the optimal tuning scheme of the variable stiffness vibration absorber can be obtained.

[0087] Step 4: Using the quadratic linear programming optimization method and taking the dynamic amplification factor as the optimization target, the optimal frequency ratio of each truncation interval is calculated to form the optimized frequency tuning scheme of the variable stiffness vibration absorber.

[0088] For each truncation interval, the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation f = ω2 / ω is taken as the independent variable, the dynamic amplification coefficient A1 / A0 is taken as the optimization target, and the sequential quadratic programming algorithm is used to search for the optimal solution of f = ω2 / ω as the optimal frequency ratio of the truncation interval; the specific process is as follows.

[0089] Assume a typical nonlinear optimization function is:

[0090] minf(x)(9)

[0091] The specific constraints are:

[0092]

[0093] Where x=[x1,x2,...,x n ] is the design parameter variable; f(x) is the objective function; G i (x)=[g1(x),g2(x),...,g m (x)] is the constraint function; me is the boundary value between equality constraint and inequality constraint; f(x) and G i (x) is a nonlinear function. Using the objective function f(x) and the constraint function G i (x) Construct the Lagrangian function and perform quadratic approximation to solve the QP (Quadratic Programming) subproblem:

[0094]

[0095] In the formula, λ i is the Lagrangian factor.

[0096] The Sequential Quadratic Programming (SQP) algorithm can be used to solve optimization problems with nonlinear constraints.

[0097] After linearizing the nonlinear constraints, we get the QP subproblem, and the objective function can be transformed into:

[0098]

[0099] The constraints are transformed into:

[0100]

[0101] In the formula, d is the optimization direction of global optimization; represents the gradient; H k The Hessian matrix is ​​positive definite quasi-Newton approximation, and the following iterative equation is obtained:

[0102] x k+1 =x k +α k d k (14)

[0103] Where, d k Represents x k Point to x k+1 A vector of k is a scalar step size parameter obtained by a suitable linearization.

[0104] The first step of the SQP algorithm is to update the Hessian matrix H k :

[0105]

[0106] In the formula

[0107]

[0108] s k =x k+1 -x k (17)

[0109] Each iteration process will obtain a positive quasi-Newton approximation of the Hessian matrix.

[0110] The second step of the SQP algorithm is to solve the quadratic programming problem:

[0111] Each main iteration solves the following QP subproblem, and its objective function is:

[0112]

[0113] The constraints of the QP subproblem can be expressed as:

[0114]

[0115] In the formula, A i A∈R m×n The solution process is analyzed twice: 1) Calculate the feasible point; 2) Generate an iterative sequence of feasible points, which converges to the solution of the problem.

[0116] The third step of the SQP algorithm involves a one-dimensional search and the calculation of the objective function:

[0117] Solving the QP subproblem can obtain a new vector, from which a new iteration can be obtained. The value must ensure that the indicator function has a sufficient reduction, and the corresponding objective function is obtained as follows:

[0118]

[0119] In the formula

[0120]

[0121] In summary, the optimal solution can be obtained by simplifying the original nonlinear programming problem into a quadratic programming problem with an approximate solution. To solve the nonlinear constrained optimization problem, it is necessary to combine the nonlinear objective function and the constraint conditions to construct the Lagrangian function, and calculate the optimal approximate solution to replace the original solution. In the optimization process, the quasi-Newton method can be used to calculate the Hessian matrix of the Lagrangian function. The BFGS variable scaling method is used to construct an approximate solution, and the one-dimensional linear search method is used to obtain the optimal step size. The optimal solution can be obtained through iterative calculation.

[0122] Finally, the optimal frequency ratio of the natural frequency of each truncation interval to the dominant frequency of the external excitation during the tuning process of the variable stiffness vibration absorber is obtained, as shown in Table 1.

[0123] Table 1 Optimal frequency ratio for each cutoff interval

[0124]

[0125]

[0126] Taking the truncation interval (0.3-0.4) as an example, we can get the curve of the optimization target changing with the number of iterations, such as Figure 8As shown in Figure 2. Other subdivision stages also have similar change trends. Each truncation interval and the optimal frequency ratio corresponding to each truncation interval constitute an optimized frequency tuning scheme, also known as an improved frequency tuning scheme.

[0127] Step 5: Use the optimized frequency tuning scheme to perform dynamic tuning and vibration elimination of the main vibration system.

[0128] According to the optimized frequency tuning scheme in Table 1, the dynamic tuning and vibration elimination of the main vibration system is performed, and the amplitude dynamic amplification coefficient of the main vibration system is calculated, as shown in Fig. 9 shown. Fig. 9 It shows that the improved frequency tuning scheme of the present invention has an amplitude magnification factor of less than 1 in the whole tuning process. When the dynamic magnification factor is used as the criterion, the improved frequency tuning scheme of the present invention is better than Figure 4 The 100% frequency tuning scheme in has a better vibration reduction effect.

[0129] The present invention proposes a method for optimizing the frequency tuning scheme of a variable stiffness dynamically tuned vibration absorber. Taking the natural frequency of the variable stiffness vibration absorber 100% following the external excitation frequency as a reference, a segmented interception optimization method is used to optimize the frequency tuning scheme, and the ratio of the natural frequency of the vibration absorber to the dominant frequency of the external excitation is continuously adjusted to achieve the purpose of minimizing the vibration response in the variable frequency vibration area. The vibration reduction performance of the variable stiffness dynamically tuned vibration absorber is comprehensively improved, so that it can be more widely used in mechanical transmission systems such as vehicles, ships, power generation fans, precision lathes, and operating tables.

[0130] A specific embodiment is used below to verify the vibration reduction effect of the method of the present invention. Fig.10 A simplified dynamic model of a torsional vibration system with a vibration absorber is established. Fig.10 Middle J a and J1 represents the inertia, θ a and θ1 are the angular displacements of the two inertias, k a and k1 is the stiffness, c a is the damping, T(t) is the torque. Table 2 shows the simulation parameters of the torsional vibration system.

[0131] Table 2 Torsional vibration system simulation parameters

[0132] <![CDATA[Inertia (kg·m 2 )]]> <![CDATA[Stiffness (N·m·rad -1 )]]> <![CDATA[Damping (N·m·s·rad -1 )]]> <![CDATA[J10.80]]> <![CDATA[k13158.3]]> ---- <![CDATA[J a 0.20]]> <![CDATA[k ap / k ao / k am ]]> <![CDATA[c ap / c ao / c am ]]>

[0133] The damping of the main vibration system is relatively small and can be ignored. The parameters of the passive vibration absorber can match the optimal frequency ratio and the optimal damping ratio. Set the amplitude T(t) of the external excitation to 20N·m and the average value to 0. The time history is 10s. When the frequency increases from 0Hz to 20Hz, the dominant frequency of the external excitation can cross the natural frequency of the main vibration system, 10Hz. The amplitude and frequency of the external excitation change with time as shown in Fig.11 shown.

[0134] The parameters of the passive vibration absorber are set as follows: the ratio of the dynamic rotation inertia to the inertia of the main vibration system is μ = J a / J1=0.25; the best passive vibration absorption stiffness is k ap , which can be calculated from the optimal frequency ratio formula bopt = ω2 / ω1 = 1 / (μ+1) and the torsional stiffness calculation formula k ap =(2π·ω2) 2 ·J A Obtained, 505.32N·m·rad -1 , optimal damping c ap The optimal damping ratio formula ζ opt =[3μ / [8(1+μ)]] 1 / 2 And the torsional damping calculation formula c ap =2·ω2·J A ·ζ is obtained as 5.51N·m·s·rad -1 .

[0135] The parameters of the vibration absorber using the 100% frequency tuning scheme are set as follows: the ratio of the dynamic rotation inertia to the main vibration system inertia is μ = J a / J1=0.25; variable stiffness k ao It can be obtained from the original frequency tuning scheme and the torsional stiffness calculation formula, k ao =(2π·ω2) 2 ·J A ,like Fig.12 The original tuning scheme curve is shown as follows; the optimal damping c ao 5.51N·m·s·rad -1 .

[0136] The parameters of the vibration absorber using the optimized frequency tuning scheme are set as follows: the ratio of the dynamic rotation inertia to the inertia of the main vibration system is μ = J a / J1=0.25; variable stiffness k ab It can be obtained by the improved frequency tuning scheme and torsional stiffness calculation formula, k ab =(2π·ω2) 2 ·J A ,like Fig.12 The improved tuning scheme is shown in the curve; the optimal damping c ao 5.51N·m·s·rad -1 .

[0137] The passive vibration absorber, the original variable stiffness vibration absorber (100% frequency tuning scheme) and the improved variable stiffness vibration absorber (improved frequency tuning scheme) are installed on the torsional vibration system and the simulation model is run to obtain the vibration response displacement of the main vibration system, such as Fig.13 As shown. Fig.13It can be seen from the results that the vibration response of the main vibration system with variable stiffness vibration absorber is significantly better than that of the passive vibration absorber. Fig.13 This reflects the superiority of the improved frequency tuning scheme of the present invention. Compared with the 100% frequency tuning scheme, the vibration reduction performance of the improved scheme of the present invention is improved by about 10%. In the entire tuning process, the improved scheme has a better vibration reduction effect than the passive vibration absorber.

[0138] The Hilbert-Huang transform (HHT) is used to process the non-stationary vibration response signal and conduct time-frequency comprehensive analysis. Fig.14 As shown. Fig.14 The results show that the energy of the vibration signal of the external excitation is evenly distributed in the entire time range, and the frequency increases linearly from 0Hz to 20Hz in the entire time range, which is consistent with Fig.11 The HHT analysis results fully reflect the time information, frequency information and signal energy information of the vibration response.

[0139] The time-frequency comprehensive analysis was applied to the vibration responses of the system without vibration absorber, passive vibration absorber, 100% frequency tuning scheme and the improved frequency tuning scheme of the present invention. The results are as follows: Figures 15 to 18 shown.

[0140] like Fig.15 As shown in the figure, in the absence of a vibration absorber, the main frequency of the system vibration response will gradually increase over time, which is consistent with the main frequency trend of the external excitation. However, when the main frequency of the external excitation reaches the natural frequency of the main vibration system, strong vibration degradation will occur, causing system resonance and the vibration tends to be non-convergent. In the following time range, the main frequency of the system vibration response only reflects the resonance peak frequency.

[0141] Will Fig.15 The results shown are similar to Fig.16 , Fig.17 and Fig.18 After the vibration absorber is installed, the main frequency of the system vibration response changes with the change of the main frequency of the external excitation in the entire frequency range, which shows the effectiveness and reliability of the HHT signal processing method. The comparison results also show that after the vibration absorber is installed, the vibration response of the entire system tends to converge, and there is no resonance trend in the entire time range, which proves the necessity of installing the vibration absorber in the system.

[0142] Fig.16The energy distribution of the passive vibration absorber vibration response signal is shown. The vibration signal energy is mainly concentrated at the two vibration peaks before and after the natural frequency of the original main vibration system. Therefore, after the passive vibration absorber is installed, the natural vibration of the original system is decomposed into two natural vibration frequencies of the new system. This result shows that the passive vibration absorber uses the frequency shift characteristic to reduce the vibration of the main vibration system.

[0143] The energy distribution of the vibration response signal of the variable stiffness vibration absorber is as follows: Fig.17 and Fig.18 The results show that the energy of the response signal after the variable stiffness vibration absorber is installed is mainly concentrated in the natural frequency area of ​​the main vibration system. The natural frequency following characteristic of the vibration absorber is used to track the main frequency of the external excitation and induce the resonance of the dynamic moment of inertia to absorb the vibration energy.

[0144] The energy distribution of the vibration response signal of the passive vibration absorber is compared with the energy distribution of the variable stiffness vibration absorber. Fig.16 , Fig.17 and Fig.18 The response signal energy of the passive vibration absorber is mainly concentrated on the two newly generated vibration peaks, and the response signal energy of the variable stiffness vibration absorber is mainly concentrated on the natural frequency of the original system, and the amplitude of the signal energy is similar. The comparison results show that the variable stiffness vibration absorber can reduce the vibration of the main vibration system more effectively than the passive vibration absorber.

[0145] contrast Fig.17 and Fig.18 , comparing the energy distribution of the response signal of the improved frequency tuning scheme of the present invention with that of the original frequency tuning scheme, it can be seen that the improved scheme of the present invention can further minimize the energy concentration area of ​​the response signal, reduce the vibration peak by about 16.7%, and reduce the vibration signal energy by about 10% in the initial tuning stage, achieving better vibration reduction effect.

[0146] Based on the method provided by the present invention, the present invention also provides a frequency tuning scheme optimization system for a variable stiffness vibration absorber, comprising:

[0147] Dynamic model building module, used to build the dynamic model of the main vibration system containing variable stiffness vibration absorber;

[0148] The influence law analysis module is used to analyze the influence of the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation on the dynamic amplification factor of the main vibration system response based on the dynamic model of the main vibration system;

[0149] The frequency ratio segmentation interception module is used to segmentally intercept the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system between 0 and 2.0 based on the analyzed influence law, and obtain multiple truncation intervals;

[0150] The optimal frequency ratio calculation module is used to adopt a quadratic linear programming optimization method, take the power amplification factor as the optimization target, calculate the optimal frequency ratio of each truncation interval to form an optimized frequency tuning scheme of the variable stiffness vibration absorber;

[0151] The dynamic tuning and vibration elimination module is used to perform dynamic tuning and vibration elimination of the main vibration system by adopting an optimized frequency tuning scheme.

[0152] Furthermore, the present invention also provides an electronic device, which may include: a processor, a communication interface, a memory, and a communication bus. The processor, the communication interface, and the memory communicate with each other via the communication bus. The processor may call a computer program in the memory to execute a frequency tuning scheme optimization method for a variable stiffness vibration absorber.

[0153] In addition, when the computer program in the above-mentioned memory is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a non-transitory computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories, random access memories, magnetic disks or optical disks.

[0154] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0155] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A frequency tuning scheme optimization method for a variable stiffness vibration absorber, characterized in that: include: Establish the dynamic model of the main vibration system including variable stiffness vibration absorber; Based on the dynamic model of the main vibration system, the influence of the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation on the dynamic amplification coefficient of the main vibration system response is analyzed; Based on the analyzed influence law, the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system is segmented between 0 and 2.0 to obtain multiple truncation intervals; The quadratic linear programming optimization method is used to take the dynamic amplification factor as the optimization target, and the optimal frequency ratio of each truncation interval is calculated to form the optimized frequency tuning scheme of the variable stiffness vibration absorber. The optimized frequency tuning scheme is used to perform dynamic tuning and vibration elimination of the main vibration system.

2. The frequency tuning scheme optimization method of the variable stiffness vibration absorber according to claim 1 is characterized in that: The establishment of the dynamic model of the main vibration system including the variable stiffness vibration absorber specifically includes: Using the momentum theorem of classical mechanics, the dynamic model of the single-degree-of-freedom master vibration system for dynamic tuning and vibration elimination is established as follows: ； Where m1 is the mass of the main vibration system, m2 is the mass of the variable stiffness vibration absorber; x1 is the displacement of the main vibration system, x2 is the displacement of the dynamic mass of the variable stiffness vibration absorber; c2 is the damping; k1 is the stiffness of the spring, k2 is the variable stiffness of the spring; the simple harmonic excitation applied to the main vibration system is F(t) = Fsinωt, F is the amplitude, and ω is the dominant frequency of the external excitation.

3. The frequency tuning scheme optimization method of the variable stiffness vibration absorber according to claim 2 is characterized in that: The influencing rules include: When the dominant frequency ω of external excitation is less than 0.8 times of the natural frequency ω1 of the main vibration system, the natural frequency ω2 of the variable stiffness vibration absorber does not have to follow the dominant frequency of external excitation 100%. The ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of external excitation f=ω2 / ω is less than 1, and the dynamic amplification coefficient A1 / A0 of the main vibration system is less than 1, the vibration is weakened, and the vibration reduction effect is enhanced; where A1 is the amplitude of the vibration displacement of the main vibration system; A0 is the equivalent static displacement of the main vibration system.

4. The frequency tuning scheme optimization method of the variable stiffness vibration absorber according to claim 3 is characterized in that: Based on the analyzed influence law, the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system is segmented between 0 and 2.0 to obtain multiple truncation intervals, specifically including: The ratio of the dominant frequency of external excitation to the natural frequency of the main vibration system, r = ω / ω1, is divided into 11 truncation intervals, including (0.0-0.1), (0.1-0.2), (0.2-0.3), (0.3-0.4), (0.4-0.5), (0.5-0.6), (0.6-0.7), (0.7-0.8), (0.8-0.9), (0.9-1.0) and (1.0-2.0).

5. The frequency tuning scheme optimization method of the variable stiffness vibration absorber according to claim 4 is characterized in that: The quadratic linear programming optimization method is used to take the dynamic amplification factor as the optimization target, and the optimal frequency ratio of each truncation interval is calculated to form an optimized frequency tuning scheme of the variable stiffness vibration absorber, which specifically includes: For each truncation interval, the ratio of the natural frequency of the variable stiffness absorber to the dominant frequency of the external excitation f = ω2 / ω is taken as the independent variable, the dynamic amplification coefficient A1 / A0 is taken as the optimization target, and the sequential quadratic programming algorithm is used to search for the optimal solution of f = ω2 / ω as the optimal frequency ratio of the truncation interval; Each truncation interval and the optimal frequency ratio corresponding to each truncation interval constitute an optimized frequency tuning scheme.

6. A frequency tuning scheme optimization system for a variable stiffness vibration absorber, characterized in that: include: Dynamic model building module, used to build the dynamic model of the main vibration system containing variable stiffness vibration absorber; The influence law analysis module is used to analyze the influence of the ratio of the natural frequency of the variable stiffness vibration absorber to the dominant frequency of the external excitation on the dynamic amplification factor of the main vibration system response based on the dynamic model of the main vibration system; The frequency ratio segmentation interception module is used to segmentally intercept the ratio of the dominant frequency of the external excitation to the natural frequency of the main vibration system between 0 and 2.0 based on the analyzed influence law, and obtain multiple truncation intervals; The optimal frequency ratio calculation module is used to adopt a quadratic linear programming optimization method, take the power amplification factor as the optimization target, calculate the optimal frequency ratio of each truncation interval to form an optimized frequency tuning scheme of the variable stiffness vibration absorber; The dynamic tuning and vibration elimination module is used to perform dynamic tuning and vibration elimination of the main vibration system by adopting an optimized frequency tuning scheme.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the frequency tuning scheme optimization method of the variable stiffness vibration absorber according to any one of claims 1 to 5 is implemented.

8. The electronic device according to claim 7, characterized in that: The memory is a non-transitory computer-readable storage medium.

Images