Calculation method for horizontal vibration frequency of radial support type rack

Abstract

The invention discloses a method for calculating the horizontal vibration frequency of a radial support type rack, and relates to the technical field of hydro-generators, comprising the following steps: step 1, analyzing the structural composition of the rack, and calculating the radial rigidity of a single support arm of the rack; 2, establishing a calculation model; 3, the overall rigidity is calculated through the calculation model; 5, calculating the total mass of the rack participating in vibration according to the vibration mode characteristics of horizontal vibration of the rack; according to the method, the actual structure of the rack is fully considered, the rigidity of one supporting arm and the influence on the overall rigidity are accurately calculated, and the overall rigidity of the rack is obtained by superposing the influence on the overall rigidity of all the supporting arms. Finally, the horizontal vibration frequency of the rack is calculated through the overall rigidity of the rack and the mass participating in vibration, the calculation method does not depend on a three-dimensional model, a result can be rapidly calculated only through basic structural data, and the calculation precision is high.

Description

Technical Field

[0001] The invention relates to the technical field of hydro-generators, in particular to a method for calculating the horizontal vibration frequency of a radially supported frame. Background Art

[0002] Hydropower has been extensively developed as a clean energy source. During operation, hydro-generator sets are subject to various unbalanced excitation forces such as hydraulic, mechanical and electromagnetic forces. Most of these external excitation forces act in the horizontal direction. In order to ensure that the hydro-generator has good stability, in addition to the shaft system itself having a high critical speed, the various frames that provide radial support for the shaft system should also avoid the frequencies of various external excitations to prevent the frames from resonating. Therefore, how to quickly and accurately calculate the frequency of the horizontal vibration of the frame, so as to ensure that the frequencies of various horizontal excitation forces are staggered and have a certain margin, is the key to a successful design, but also the difficulty.

[0003] The radially supported frame mainly consists of a frame center body and several supporting arms. Due to its simple structure, easy maintenance and excellent support effect, it is a frame structure widely used in hydro-turbine generators. The calculation of its horizontal natural frequency is mainly divided into empirical methods and numerical simulation methods. The former cannot obtain a specific frequency value. It only uses a method with similar structures and dimensions by comparison with similar projects. It is a borrowing based on the successful experience of existing projects. However, if there are no similar projects to learn from or the power station has special circumstances that require some changes, it is difficult to determine whether the frame's own horizontal frequency can effectively avoid the excitation frequency. The latter requires three-dimensional modeling of the frame, then setting material parameters and correct boundary conditions according to actual conditions, and then using numerical simulation methods to calculate the numerical solution of the frame's horizontal frequency. This method is time-consuming and cumbersome, and has high requirements for the calculator. It is generally used for reviewing the final design scheme, but is not suitable for application scenarios such as comparing and optimizing multiple schemes in the early design stage. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for calculating the horizontal vibration frequency of a radially supported frame, mainly to solve the problems in the existing calculation process of the horizontal vibration frequency of a hydro-generator frame, that is, the accuracy of the empirical method cannot be guaranteed, and the numerical simulation method is time-consuming and labor-intensive, and the calculation efficiency is low. A method is provided that does not rely on a three-dimensional model and can quickly calculate the horizontal vibration frequency of a radially supported frame for a hydro-generator using only basic structural data. The method can be used to guide the design and optimization of the hydro-generator frame, ensure the safe operation of the hydro-generator set, and solve the problems raised in the above-mentioned background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for calculating the horizontal vibration frequency of a radially supported frame, comprising the following steps:

[0006] Step 1: Analyze the structural composition of the frame, and calculate the radial stiffness of a single arm of the frame according to the structure, size and material properties of the frame arms.

[0007] Step 2: Establish a calculation model. According to the actual structure of the frame, the central body of the frame is equivalent to a mass point, and the frame arms are equivalent to springs, and a calculation model of several springs uniformly distributed around the mass point is established.

[0008] Step 3: Calculate the overall stiffness of the calculation model. Introduce the mode shape influence factor for each arm, and at the same time superimpose the stiffness of each arm in the vibration direction to obtain the overall stiffness.

[0009] Step 4: Calculate the total vibration mass. According to the mode shape characteristics of the horizontal vibration of the frame, calculate the total mass of the frame participating in the vibration.

[0010] Step 5: Calculate the horizontal vibration frequency of the frame. Calculate the horizontal vibration frequency of the frame according to the obtained total vibration mass.

[0011] Preferably, the method for calculating the radial stiffness of a single arm in Step 1 includes the following steps. First, segment the arm according to its actual structure. Second, calculate the radial stiffness of each segment of the arm separately using different calculation methods. Finally, connect the radial stiffnesses of all segments of the arm in series to obtain the total radial stiffness of a single arm.

[0012] Preferably, the mode shape influence factor in Step 3 includes the influence of the angle between each arm and the vibration direction on the overall stiffness.

[0013] Preferably, the contribution of each arm to the overall stiffness is the arm stiffness * COS(θ), and the overall stiffness is the sum of the contributions of all arms to the overall stiffness.

[0014] Preferably, the total mass of the frame participating in the vibration in Step 4 includes the weight ratio of each arm participating in the horizontal vibration, which is set as the vibration participation coefficient α of the arm mass, and 0.5 ≤ α ≤ 0.7.

[0015] Preferably, the total mass of the frame participating in the vibration in Step 4 also includes the mass of the central body of the frame.

[0016] Preferably, the total vibration mass m in Step 4 = m1 + α * m 2， where m1 is the mass of the central body of the frame and m2 is the mass of the arm.

[0017] Preferably, the horizontal vibration frequency of the frame in Step 5 is where k total is the overall stiffness.

[0018] Preferably, the stiffness k of each arm is k = AE / l, where E is the Young's modulus of the material, A is the cross-sectional area, and l is the length of the arm segment.

[0019] In summary, the beneficial effects of the present invention are as follows:

[0020] By fully considering the actual structure of the frame, accurately calculating the stiffness of one arm and its influence on the overall stiffness, and obtaining the overall stiffness of the frame by superimposing the influence of each arm on the overall stiffness, considering the masses of the frame central body and the arms participating in vibration respectively according to the characteristics of the horizontal vibration of the frame, and finally calculating the horizontal vibration frequency of the frame through the overall stiffness of the frame and the masses participating in vibration. This calculation method does not depend on a 3D model, can quickly calculate the result with only basic structural data and has a high calculation accuracy, and can be used to guide the design and optimization of the hydrogenerator frame to ensure the safe operation of the hydrogenerator set. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions in the embodiments of the invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0022] Figure 1 It is a schematic diagram of the overall process framework structure of a calculation method for the horizontal vibration frequency of a radially supported frame according to the present invention;

[0023] Figure 2 It is a cross-sectional view of an embodiment in a calculation method for the horizontal vibration frequency of a radially supported frame according to the present invention;

[0024] Figure 3 It is a top view of an embodiment in a calculation method for the horizontal vibration frequency of a radially supported frame according to the present invention.

[0025] The reference numerals in the drawings are described separately as follows: 1, frame central body; 2, frame arm; Ⅰ, arm Ⅰ; Ⅱ, arm Ⅱ; Ⅲ, arm Ⅲ; Ⅳ, arm Ⅳ; Ⅴ, arm Ⅴ; Ⅵ, arm Ⅵ. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] All the features disclosed in this specification, or all the steps in any method or process disclosed, except for mutually exclusive features and / or steps, can be combined in any manner.

[0027] Any feature disclosed in this specification (including any appended claims, abstract and drawings), unless specifically recited, may be replaced by other equivalent or similar-purpose alternative features. That is, unless specifically recited, each feature is only an example of a series of equivalent or similar features.

[0028] In the present invention, unless otherwise expressly specified and limited, the terms "mounted", "connected", "coupled", "fixed", etc. shall be construed broadly. For example, it may be a fixed connection, a detachable connection, or integral; it may be a mechanical connection, a direct connection, or an indirect connection through an intermediate medium, and may be the communication inside at least two elements or the interaction relationship between at least two elements, unless otherwise expressly limited. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0029] The following will Figures 1-3 describe the present invention in detail. An embodiment provided by the present invention: A method for calculating the horizontal vibration frequency of a radially supported frame, comprising the following steps:

[0030] The first step: Analyze the structural composition of the frame, and calculate the radial stiffness of a single arm of the frame according to the structure, size and material properties of the frame arms.

[0031] Taking the radially supported frame as an example, the main structure of the frame is divided into a frame central body and 6 arms, numbered I to VI. The outer diameter side of the arm is the support point. The frame central body and the arms are made of the same material, which is carbon structural steel. The mass of the frame central body is m1 kg, and the total mass of the 6 arms is m2 kg. Since the structure, size and material properties of each arm are exactly the same, the radial stiffness of each arm is the same.

[0032] According to the structural characteristics of the arm, it is obvious that the arm can be divided into 5 segments. In the order from the inside to the outside in the radial direction, the stiffness k of each arm segment = AE / l, where E is the Young's modulus of the material, A is the cross-sectional area, and l is the length of the arm segment:

[0033] The stiffness of the first segment A1 = 2b×t1 + t2×h1, and E is the Young's modulus of the material;

[0034] The stiffness of the second segment A2 = b×h2;

[0035] The stiffness of the third segment

[0036] The stiffness of the fourth segment

[0037] The stiffness of the fifth segment

[0038] So the total stiffness of a single arm

[0039] Step 2: Establish a calculation model

[0040] The structure of the frame is mainly divided into the frame central body and the arms. The frame central body is composed of a cylinder, upper and lower ring plates, and stiffening plates, and has good stiffness and anti-deformation ability. Therefore, when calculating, the frame central body can be considered as an equivalent mass point, each arm is equivalent to a spring, and the stiffness calculation model of the frame is equivalent to a mass point at the center, and then 6 springs with the mass point and the outer diameter side support points as the two ends are used to represent 6 arms. The 6 springs are evenly distributed along the circumference, and the stiffness of each spring is k;

[0041] Step 3: Use the calculation model to calculate the overall stiffness

[0042] Calculate the influence of each arm on the overall stiffness according to the angle between each arm and the vibration direction, and at the same time superimpose the stiffness of each arm in the vibration direction to obtain the overall stiffness:

[0043] The influence of the angle between each arm and the vibration direction on the overall stiffness can be reflected by calculating the effective stiffness contribution of each arm in the vibration direction. In a multi-degree-of-freedom system, the stiffness matrix contains stiffness elements in various directions, and these elements are jointly determined by the geometric dimensions, material properties of the arms, and their angles relative to the vibration direction;

[0044] Taking vertical vibration as an example, according to the angle θ between each arm and the vibration direction, when the angle θ is 0, the arm is parallel to the vibration direction, and its stiffness fully functions; as the angle θ increases, the effective stiffness will decrease because the projected area of the arm in the vibration direction decreases, resulting in a weakened effect on vibration suppression;

[0045] The contribution of arm I to the overall stiffness is k;

[0046] The contribution of arm II to the overall stiffness is

[0047] The contributions of arm III, arm V, and arm VI to the overall stiffness are the same as that of arm II;

[0048] The contribution of arm IV to the overall stiffness is the same as that of arm I;

[0049] Therefore, the overall stiffness of the model

[0050] Step 4: Calculate the total vibration mass

[0051] Considering the masses of the central body and each arm involved in the vibration according to the vibration mode characteristics of the horizontal vibration of the frame, the vibration mode characteristics of the horizontal vibration of the frame refer to the different vibration modes or forms presented in the horizontal direction when the frame is excited. In the phase relationship, it can be found that there may be a phase difference among different parts during the vibration process, that is, although they vibrate at the same frequency, the time when each part reaches the maximum displacement may not be the same. Therefore, for the central body of the frame with good stiffness and located at the center of the frame, all its mass participates in the horizontal vibration, while the vibration amplitude of the arm gradually decreases from the inner diameter to the outer diameter. Therefore, not all masses participate in the vibration;

[0052] Therefore, the final total vibration mass can be expressed as m = m1 + α×m2, where α = 0.5 - 0.7 is the vibration participation coefficient of the arm mass;

[0053] Step 5: Calculate the horizontal vibration frequency of the frame

[0054] Finally, the horizontal vibration frequency of the frame is obtained

[0055] In summary, through the calculation method of the present invention, the actual structure of the frame is fully considered, the stiffness of one arm and its influence on the overall stiffness are accurately calculated, and the overall stiffness of the frame is obtained by superimposing the influence of each arm on the overall stiffness. According to the characteristics of the horizontal vibration of the frame, the masses of the central body and the arms involved in the vibration are considered separately. Finally, the horizontal vibration frequency of the frame is calculated based on the overall stiffness of the frame and the mass involved in the vibration. This calculation method does not depend on a 3D model and can quickly calculate the result with high calculation accuracy using only basic structure data. It can be used to guide the design and optimization of the water turbine generator frame to ensure the safe operation of the water turbine generator set

[0056] As described above, it is only the specific implementation manner of the invention, but the protection scope of the invention is not limited thereto. Any change or replacement that can be thought of without creative work should be covered within the protection scope of the invention. Therefore, the protection scope of the invention should be subject to the protection scope defined by the claims.

Claims

1. A calculation method for the horizontal vibration frequency of a radially supported frame, characterized in that: It includes the following steps: Step 1: Analyze the structural composition of the frame, and calculate the radial stiffness of a single arm of the frame according to the structure, size and material properties of the frame arm; Step 2: Establish a calculation model. According to the actual structure of the frame, the central body of the frame is equivalent to a mass point, and the frame arms are equivalent to springs, and a calculation model with several springs evenly distributed around the mass point is established; Step 3: Calculate the overall stiffness of the calculation model. Introduce the mode shape influence factor for each arm, and at the same time superimpose the stiffness of each arm in the vibration direction to obtain the overall stiffness; Step 4: Calculate the total vibration mass. According to the mode shape characteristics of the horizontal vibration of the frame, calculate the total mass of the frame participating in the vibration; Step 5: Calculate the horizontal vibration frequency of the frame. Calculate the horizontal vibration frequency of the frame according to the obtained total vibration mass.

2. The calculation method of the horizontal vibration frequency of a radially supported frame according to claim 1, characterized in that: The method for calculating the radial stiffness of a single arm in the above Step 1 includes the following steps. First, segment the arm according to its actual structure; second, calculate the radial stiffness of each segment of the arm separately using different calculation methods; finally, connect the radial stiffnesses of all segments of the arm in series to obtain the total radial stiffness of a single arm.

3. The calculation method for the horizontal vibration frequency of a radially supported frame according to claim 1, characterized in that: The mode shape influence factor in the above Step 3 includes the influence of the angle between each arm and the vibration direction on the overall stiffness.

4. The calculation method of the horizontal vibration frequency of a radially supported frame according to claim 2, characterized in that: The contribution of each arm to the overall stiffness is the arm stiffness * COS(θ), and the overall stiffness is the sum of the contributions of all arms to the overall stiffness.

5. The calculation method of the horizontal vibration frequency of a radially supported frame according to claim 1, characterized in that: The total mass of the frame participating in the vibration in the above Step 4 includes the weight ratio of each arm participating in the horizontal vibration, which is set as the vibration participation coefficient α of the arm mass, and 0.5 ≤ α ≤ 0.

7.

6. The calculation method of the horizontal vibration frequency of a radially supported frame according to claim 5, characterized in that: The total mass of the frame participating in the vibration in the above Step 4 also includes the mass of the central body of the frame.

7. The calculation method of the horizontal vibration frequency of a radially supported frame according to claim 6, characterized in that: The total vibration mass m in the above Step 4 = m1 + α * m2, where m1 is the mass of the central body of the frame and m2 is the mass of the arms.

8. A calculation method for the horizontal vibration frequency of a radially supported frame according to claim 7, characterized in that: The horizontal vibration frequency of the frame in the fifth step is where k total is the overall stiffness.

9. The calculation method of the horizontal vibration frequency of a radially supported frame according to claim 2, characterized in that: The stiffness k of each segment of the arm = AE / l, where E is the Young's modulus of the material, A is the cross-sectional area, and l is the length of the arm segment.

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