Gear meshing time-varying dynamic stiffness measuring device and method based on analysis of rotor vibration characteristics

Abstract

The invention discloses a gear meshing time-varying dynamic stiffness measuring device and method based on analysis of rotor vibration characteristics, and belongs to the technical field of test tools. In order to overcome the defects that an existing gear meshing rigidity testing device is complex in structure and large in size, calculation steps of a measuring method are tedious, calculation is complex and time cost is high, a random signal is given to a vibration exciter through a signal generator, and radial random excitation force is applied to the free end of a rotor; obtaining a rotor vibration test transfer function when the bevel gear is engaged; constructing a theoretical model of the rotor-bevel gear meshing system, and calculating vibration response and a theoretical transfer function of a rotor in the rotor-bevel gear meshing system; and deducing the gear meshing dynamic stiffness based on a numerical method by comparing the test transfer function with the theoretical transfer function. The device and the method are mainly used for measuring the gear meshing time-varying dynamic stiffness.

Description

Technical Field

[0001] The invention belongs to the technical field of test fixtures, and in particular relates to a gear meshing time-varying dynamic stiffness measurement device and method based on analyzing rotor vibration characteristics. Background Art

[0002] Carlo Rosso and Fabio Bruzzone designed and implemented a tailor-made test bench for measuring static transmission errors in two mating gears, proposing a non-dynamic method to ensure gear mesh stiffness.

[0003] Chuan Wen Chi, Ian Howard, and Jian De Wang designed and built a test bench for experimental investigations, where a nylon gear was placed in mesh with a fixed aluminum gear under various torques. The rotational measurements of the nylon gear at precise angular positions throughout the meshing cycle were used as the basis for determining the torsional mesh stiffness and static transmission error, and numerical analysis tools (FEA) were then used to calculate the theoretical static transmission error and single torsional mesh stiffness under the same conditions as the experiments. The validity of the single torsional mesh stiffness theory was investigated by comparing the experimental results with the FEA modeling results.

[0004] Taylor and Francis designed a vibration-based experimental method to evaluate parametric excitation, i.e., mesh stiffness variations in cylindrical gears. The entire test bench structure was also modeled using a lumped mass model with a mesh interface matrix, where the mesh stiffness variations were calculated using the finite element method and validated by comparison with experimental results.

[0005] Anhui University of Technology has designed a gear tooth meshing stiffness measurement test device and its test method, realizing a test device based on the meshing stiffness of parallel-axis spur gear teeth. The dynamic meshing stiffness of gear teeth can be obtained through simple calculations, and high measurement reliability can be guaranteed.

[0006] Usually the gear meshing stiffness test requires high-precision measurement and a stable test environment. In order to ensure the accuracy of the test, the equipment usually uses high-quality materials and complex mechanical structures, such as a solid base, precision sensors, and complex transmission systems. These components are usually large in size and weight, resulting in a relatively large volume of the entire test equipment.

[0007] Traditional measurement methods, especially those based on analytical methods, require a large number of calculations in multiple steps, including bending deformation, shear deformation, contact deformation, etc. of gear teeth, which increases the complexity and time cost of calculations. In terms of test equipment or simulation models, only the meshing relationship between two gears is considered, and the influence of the vibration of the shaft in the rotor system on the gear meshing stiffness is not comprehensively considered.

[0008] Therefore, there is a need for a gear meshing time-varying dynamic stiffness measurement device and method based on analyzing rotor vibration characteristics, which has a simple structure, a small size, a few measurement steps, and a fast calculation speed. Summary of the invention

[0009] The purpose of the present invention is to solve the defects of the existing gear meshing stiffness testing device, such as complex structure, large size, cumbersome calculation steps of the measurement method, complex calculation and high time cost, and to provide a gear meshing time-varying dynamic stiffness measurement device and method based on the analysis of rotor vibration characteristics, which has a simple structure, small size, few measurement steps and fast calculation speed.

[0010] The present invention discloses a gear meshing time-varying dynamic stiffness measuring device based on analyzing rotor vibration characteristics, comprising a first helical gear, a second helical gear, a rotor, a first fixture, a second fixture, a vibration sensor and an exciter; The first bevel gear is fixed on the rotor, and the rotor is mounted on a first fixture. The second bevel gear is rotatably arranged on the second fixture, and the second bevel gear is meshed with the first bevel gear on the rotor by adjusting the position of the second fixture, so that the two gears are meshed; The vibration sensor is arranged at the free end of the rotor, and the exciter is arranged at the free end of the rotor.

[0011] Furthermore: a hydraulic vise is provided between the first clamp and the second clamp, and the hydraulic vise is used to fix the rotor to realize a cantilever beam form.

[0012] Furthermore, a semicircular block is provided on the upper side of the hydraulic bench vise, and a groove is provided on the upper side of the semicircular block, and the groove matches the rotor and is used to support the rotor.

[0013] The present invention provides a method for measuring the time-varying dynamic stiffness of gear meshing based on analyzing the vibration characteristics of the rotor, comprising the following steps: S1. Give the exciter a random signal through the signal generator to apply radial random exciting force to the free end of the rotor; S2, obtain the rotor vibration test transfer function when the helical gears are meshing; S3, constructing a theoretical model of a rotor-helical gear meshing system, and calculating a vibration response and a theoretical transfer function of the rotor-helical gear meshing system; S4. By comparing the experimental transfer function and the theoretical transfer function, the gear mesh dynamic stiffness is derived based on the numerical method.

[0014] Further: in S2, the rotor vibration test transfer function when the helical gears are meshing is acquired by using a vibration sensor on the rotor and a dynamic data acquisition system.

[0015] Furthermore, there are two vibration sensors, namely a first sensor and a second sensor, and the rotor vibration test transfer function when the two helical gears are meshed is The calculation formula is: (1) in, is the amplitude of the first sensor, is the amplitude of the second sensor.

[0016] Further: in S3, when constructing the theoretical model of the rotor-helical gear meshing system, the rotor is simplified to an Euler beam and the dynamic stiffness of the meshing gear is simplified to a spring.

[0017] Furthermore: the motion equation of the rotor is: (2) In the formula, E represents the Young's modulus of the pipeline; I represents the moment of inertia; represents the mass per unit length; is the lateral displacement, which is a function of the rotor cross-sectional position ξ and time t; ∂ is the partial derivative.

[0018] Furthermore: the boundary conditions of the fixed end and the free end of the rotor are: (5) in, , are the lengths of the rotors on the left and right sides of the gear respectively, For the exciting force, is the displacement at the fixed end of the rotor, is the displacement at the free end of the rotor; The continuity condition at the meshing point between the rotor and the gear is: (6) In the formula, represents the displacement of the rotor at the left end with the gear as the node, represents the displacement of the rotor at the right end of the gear node, is the meshing stiffness of the gear, where θ is the gear meshing angle.

[0019] Furthermore: after the meshing dynamic stiffness corresponding to the current meshing angle is obtained, the meshing angles of the two helical gears are adjusted, and steps S1 to S4 are repeated to obtain the meshing dynamic stiffness at different meshing angles.

[0020] The beneficial effects of the present invention are: The present invention proposes a device and method for measuring the time-varying dynamic stiffness of gear meshing based on the analysis of rotor vibration characteristics, and a device and method for measuring the variable stiffness of bevel gear meshing based on the rotor vibration characteristics. The device is mainly composed of a fixture, a vibration sensor, a signal generator, an exciter, and a dynamic data acquisition system. By measuring the vibration response of the shaft in the rotor system with two bevel gears meshing and its transmission relationship, the bevel gear meshing stiffness is accurately derived, providing effective data support for the dynamic characteristics analysis of the rotor system. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a schematic diagram of the gear meshing stiffness measuring platform; Figure 2 yes Figure 1 The enlarged view of point A in the middle; Figure 3 yes Figure 1 The enlarged view of point B in the middle; Figure 4 It is a top view of the gear meshing stiffness measuring platform; Figure 5 It is the overall schematic diagram of the experimental equipment; In the figure, 1, the first clamp; 2, the hydraulic vise; 3, the semicircular block; 4, the rotor; 5, the first bevel gear; 6, the second bevel gear; 7, the second clamp; 8, the vibration sensor; 9, the exciter; 10, the optical platform. DETAILED DESCRIPTION

[0022] The following are only preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a technician familiar with the technical field within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. The embodiments described below are only used to explain the present invention and cannot be interpreted as limitations on the present invention. The protection scope of the present invention should be based on the protection scope of the claims. The embodiments of the present invention are described in detail below. In order to facilitate the description of the present invention and simplify the description, the technical terms used in the specification of the present invention should be interpreted in a broad sense, including but not limited to conventional replacement schemes not mentioned in this application, and also including direct implementation methods and indirect implementation methods.

[0023] Example 1 Combination Figure 1-Figure 5This embodiment describes a method for measuring the time-varying dynamic stiffness of gear meshing based on analyzing the vibration characteristics of the rotor, comprising the following steps: S1, a random signal is given to the exciter 9 through the signal generator 11, so as to apply a radial random exciting force to the free end of the rotor 4; S2, obtaining the rotor vibration test transfer function when the helical gears are meshing; the rotor vibration test transfer function when the helical gears are meshing is obtained by using two vibration sensors 8 on the rotor 4 and a dynamic data acquisition system to collect the rotor vibration test transfer function when the helical gears are meshing; like Figure 1 As shown, in order to measure the test transfer function, one end of the rotor 4 is fixed on the hydraulic bench vise 2. There are two vibration sensors 8, namely the first sensor and the second sensor. The radial random excitation is applied to the free end of the rotor 4 by the exciter 9. The rotor vibration test transfer function when the two helical gears are meshed is obtained by using the two vibration sensors 8 on the rotor 4. ; The rotor vibration test transfer function when the two helical gears are meshing The calculation formula is: (1) in, is the amplitude of the first sensor, is the amplitude of the second sensor.

[0024] S3. Construct a theoretical model of a rotor-helical gear meshing system, and calculate the vibration response and theoretical transfer function of the rotor-helical gear meshing system; when constructing the theoretical model of the rotor-helical gear meshing system, simplify the rotor into an Euler beam and simplify the dynamic stiffness of the meshing gear into a spring.

[0025] The motion equation of the rotor is: (2) In the formula, E represents the Young's modulus of the pipeline; I represents the moment of inertia; Mb represents the mass per unit length; is the lateral displacement, which is a function of the rotor cross-sectional position ξ and time t; ∂ is the partial derivative.

[0026] In order to calculate the theoretical transfer function and obtain the general solution, the rotor vibration must be assumed to be harmonic vibration. For the rotor 4 harmonic vibration, the complex symbol is used to represent the lateral displacement. The general solution is: (3) Where ξ is the rotor cross-sectional position, , are the lengths of the rotors on the left and right sides of the gear respectively, is the bending wave number of the toothed rotor, A1-A8 are waveform constants, and H(ξ) is the Heaviside step function; (4) S4. By comparing the experimental transfer function and the theoretical transfer function, the gear mesh dynamic stiffness is derived based on the numerical method.

[0027] The vibration performance of the rotor is optimized by presetting the boundary conditions of the rotor; the boundary conditions of the fixed end and the free end of the rotor are: (5) in, , are the lengths of the rotors on the left and right sides of the gear respectively, For the exciting force, is the displacement at the fixed end of the rotor, is the displacement at the free end of the rotor; The continuity condition at the meshing point between the rotor and the gear is: (6) In the formula, represents the displacement of the rotor at the left end with the gear as the node, represents the displacement of the rotor at the right end of the gear node, is the meshing stiffness of the gear, where θ is the gear meshing angle.

[0028] Applying the boundary conditions of formula (4) and the continuity conditions of formula (5) to the general solution formula (3) yields 8 constants in matrix form: (7) The theoretical transfer function between the rotor vibration response at ξ = (x1, x2) : (8) In the formula, represents the rotor displacement at ξ = x2, represents the rotor displacement at ξ=x1; By comparing the experimental transfer function with the theoretical transfer function , the specific process of deriving the gear meshing dynamic stiffness based on the numerical method is as follows: Compare the theoretical and experimental transfer functions between the rotor vibration responses: (9) In the formula, is the test transfer function, is the phase difference between theoretical and experimental transfer functions; Formula (9) is a function of the time-varying mesh stiffness.

[0029] For each frequency, the real part of the complex mesh stiffness can be derived using the Newton-Raphson iteration method: and the imaginary part .

[0030] (10) After the meshing dynamic stiffness corresponding to the current meshing angle is obtained, the meshing angles of the two helical gears are adjusted and steps S1 to S4 are repeated to obtain the meshing dynamic stiffness at different meshing angles.

[0031] Example 2 This embodiment is described in conjunction with Example 1. This embodiment discloses a gear meshing time-varying dynamic stiffness measurement device based on analyzing rotor vibration characteristics, which is arranged on an optical platform, and the optical platform can flexibly adjust the position of the components fixed thereon; it includes a first bevel gear 5, a second bevel gear 6, a rotor 4, a first fixture 1, a second fixture 7, a vibration sensor 8 and an exciter 9; The first bevel gear 5 is fixed on the rotor 4, and the rotor 4 is mounted on the first fixture 1. like Figure 3 As shown, the second bevel gear 6 is rotatably arranged on the second fixture 7. By adjusting the position of the second fixture 7, the second bevel gear 6 is meshed with the first bevel gear 5 on the rotor 4 to achieve meshing of the two gears; and the precise meshing between the two gears is achieved. The vibration sensor 8 is disposed at the free end of the rotor 4 , and the vibration exciter 9 is disposed at the free end of the rotor 4 .

[0032] A hydraulic vise 2 is provided between the first clamp 1 and the second clamp 7, and the hydraulic vise 2 is used to fix the rotor 4 to realize a cantilever beam. Two bearings are embedded at both ends of the first clamp 1 to limit the radial displacement and axial displacement of the rotor 4 and allow the rotor 4 to rotate along the axis.

[0033] like Figure 2 As shown, a semicircular block 3 is further provided on the upper side of the hydraulic bench vise 2 , and a groove is provided on the upper side of the semicircular block 3 , and the groove matches the rotor 4 for supporting the rotor 4 .

Claims

1. A gear meshing time-varying dynamic stiffness measurement device based on analyzing rotor vibration characteristics, characterized in that: It comprises a first bevel gear (5), a second bevel gear (6), a rotor (4), a first clamp (1), a second clamp (7), a vibration sensor (8) and an exciter (9); The first bevel gear (5) is fixed on the rotor (4), and the rotor (4) is mounted on the first fixture (1). The second bevel gear (6) is rotatably mounted on the second fixture (7), and the second bevel gear (6) is meshed with the first bevel gear (5) on the rotor (4) by adjusting the position of the second fixture (7), thereby achieving meshing of the two gears; The vibration sensor (8) is arranged at the free end of the rotor (4), and the vibration exciter (9) is arranged at the free end of the rotor (4).

2. The gear meshing time-varying dynamic stiffness measuring device based on analyzing rotor vibration characteristics according to claim 1, characterized in that: A hydraulic bench clamp (2) is provided between the first clamp (1) and the second clamp (7), and the hydraulic bench clamp (2) is used to fix the rotor (4) to achieve a cantilever beam form.

3. The gear meshing time-varying dynamic stiffness measuring device based on analyzing rotor vibration characteristics according to claim 2, characterized in that: A semicircular block (3) is also provided on the upper side of the hydraulic bench vise (2), and a groove is provided on the upper side of the semicircular block (3), and the groove matches the rotor (4) and is used to support the rotor (4).

4. A method for measuring the time-varying dynamic stiffness of gear meshing for analyzing rotor vibration characteristics according to claim 1, characterized in that: The steps include: S1, a random signal is given to the exciter (9) through a signal generator (11), so as to apply a radial random exciting force to the free end of the rotor (4); S2, obtain the rotor vibration test transfer function when the helical gears are meshing; S3, constructing a theoretical model of a rotor-helical gear meshing system, and calculating a vibration response and a theoretical transfer function of the rotor-helical gear meshing system; S4. By comparing the experimental transfer function and the theoretical transfer function, the gear mesh dynamic stiffness is derived based on the numerical method.

5. The method for measuring the time-varying dynamic stiffness of gear meshing based on analyzing the vibration characteristics of the rotor according to claim 4, characterized in that: In S2, the rotor vibration test transfer function when the helical gears are meshing is acquired by using a vibration sensor (8) on the rotor (4) and a dynamic data acquisition system (12).

6. The method for measuring the time-varying dynamic stiffness of gear meshing based on analyzing the vibration characteristics of the rotor according to claim 5, characterized in that: There are two vibration sensors (8), namely a first sensor and a second sensor. The rotor vibration test transfer function when the two helical gears are meshed is: The calculation formula is: （1）； in, is the amplitude of the first sensor, is the amplitude of the second sensor.

7. The method for measuring the time-varying dynamic stiffness of gear meshing based on analyzing the vibration characteristics of the rotor according to claim 4, characterized in that: In S3, when constructing the theoretical model of the rotor-helical gear meshing system, the rotor is simplified to an Euler beam and the dynamic stiffness of the meshing gear is simplified to a spring.

8. The method for measuring the time-varying dynamic stiffness of gear meshing based on analyzing the vibration characteristics of the rotor according to claim 7, characterized in that: The motion equation of the rotor in the theoretical model is: （2） In the formula, E represents the Young's modulus of the pipeline; I represents the moment of inertia; represents the mass per unit length; is the lateral displacement, which is a function of the rotor cross-sectional position ξ and time t; ∂ is the partial derivative.

9. The method for measuring the time-varying dynamic stiffness of gear meshing based on analyzing the vibration characteristics of the rotor according to claim 8, characterized in that: In the theoretical model, the vibration performance of the rotor is optimized by presetting the boundary conditions of the rotor, that is, the boundary conditions of the fixed end and the free end of the rotor are: （5） in, , are the lengths of the rotors on the left and right sides of the gear respectively, For the exciting force, is the displacement at the fixed end of the rotor, is the displacement at the free end of the rotor; The continuity condition at the meshing point between the rotor and the gear is: （6） In the formula, represents the displacement of the rotor at the left end with the gear as the node, represents the displacement of the rotor at the right end of the gear node, is the meshing stiffness of the gear, where θ is the gear meshing angle.

10. The method for measuring the time-varying dynamic stiffness of gear meshing based on analyzing the vibration characteristics of the rotor according to claim 4, characterized in that: After the meshing dynamic stiffness corresponding to the current meshing angle is obtained, the meshing angles of the two helical gears are adjusted and steps S1 to S4 are repeated to obtain the meshing dynamic stiffness at different meshing angles.

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