Phase tuning parameter selection method for planet-like transmission rotary machinery

Abstract

The invention discloses a phase tuning parameter selection method for a planetary-like transmission rotary machine, and the method comprises the steps: building a two-dimensional rectangular coordinate system with the geometric centroid of the rotary machine as an original point, enabling a horizontal axis to pass through a certain middle force transmission component and to be called as a first component, and sequentially numbering the other components according to an anticlockwise sequence; calculating the space-time phase of each force transmission component according to the symmetry of the structure and the movement of the rotating machine; calculating the overall center-of-mass coordinates of all the middle force transmission components, and calculating the overall rotational inertia; according to the operation property of the trigonometric function, giving a mapping relation among the basic parameters, the centroid coordinates and the rotational inertia; reasonable basic parameters are screened through the mapping relation, so that the mass center position and the rotational inertia of the transmission system are kept in a fixed state, and the technical target of stable operation of rotating machinery is directly achieved in the design stage. The method aims to predict the change rule of the mass center position and the rotational inertia of the rotating machine, and provides a parameter selection criterion according to the change rule, and finally inhibits the translation / torsional vibration.

Description

Technical Field

[0001] This invention relates to the field of dynamic characteristic analysis of rotating machinery, and in particular to a method for selecting phase tuning parameters. This method can rely on the symmetry of geometric configuration and motion process to accurately predict the overall center of mass position and the change law of rotational inertia of planetary-type rotating machinery. Background Technology

[0002] To achieve efficient energy transfer and conversion, various types of rotating machinery are widely used in the engineering field. As rotating machinery develops towards higher speeds, heavier loads, lighter weights, higher precision, and longer service lives, vibration and noise problems are becoming increasingly prominent, and have now become a key factor restricting technological research and development as well as user experience.

[0003] Among various types of rotating machinery, there is a category of planetary-type rotating machinery containing moving / oscillating components, such as radial piston motors (pumps), vane motors (pumps), planetary gear drives, and radial cam roller engines. These components typically consist of several central components and transmission components located between them. The central components are equipped with several functional units for driving or transmission, such as the profile of a cam disk, while the transmission components include pistons, vanes, teeth, and rollers. During the operation of rotating machinery, the pistons in radial piston motors (pumps) and the vanes in vane motors (pumps) exhibit radial reciprocating motion. The teeth in planetary gear drives exhibit radial movement or a certain degree of oscillation, while the piston-roller assembly in radial cam roller engines exhibits radial movement. Therefore, during the operation of the mechanism, the overall center of mass position and moment of inertia of the rotating machinery exhibit time-varying characteristics. Changes in the center of mass cause lateral vibration, which more easily radiates a large amount of noise from the housing through components such as bearings. Changes in the moment of inertia cause torsional vibration, resulting in torque fluctuations and affecting accuracy.

[0004] The aforementioned time-varying mass and moment of inertia are internal excitations of the rotating machinery system, which are inherent properties and cannot be suppressed simply by improving machining and assembly precision. Existing literature typically reduces the amplitude of time-varying excitations by adjusting the structure or optimizing parameters. For example, the profile shape of the internal cam can be designed, using a modified cardioid curve. [1] Or the law of motion of a fifth-order polynomial [2]However, the basic premise for the effective implementation of these two methods is that the mapping relationship between the basic parameters and the time-varying internal excitation must be obtained. Reference [3] reveals the relationship between the basic parameters and the vibration characteristics, but does not consider the time-varying nature of the overall center of mass and rotational inertia formed by the radial motion of the piston. In the field of live gear transmission and internal combustion engine based on cam mechanism, there is also a time-varying phenomenon of the overall center of mass and rotational inertia formed by the movement / oscillation of live gear and cam roller, which in turn generates time-varying internal excitation and causes lateral or torsional vibration of the transmission system. On the other hand, profile design is the core key content of this type of mechanism, but the predecessors have not considered the influence of profile shape on the center of mass and inertia, and have not revealed the influence law of basic configuration parameters on time-varying internal excitation and lateral and torsional vibration.

[0005] References

[0006] [1] Yu Hongying, Zhong Hantian, Li Shuo. Pulsation analysis of modified cardioid inner curve radial piston motor [J]. Journal of Harbin Institute of Technology, 2012, 44(3): 44−48.

[0007] [2] Yu Wei, Wang Tao, Xie Chongyang. Stator curve design and dynamic modeling of internal curve hydraulic motor [J]. Hydraulics and Pneumatics, 2024, 48(6): 91-101.

[0008] [3] Wang Shiyu, Huo Mina, Chen Dongliang, et al. A method for improving the performance of multi-acting internal curve radial piston pumps or motors [P]. Chinese Invention Patent, Authorization No.: ZL201110093939.3.

[0009] [4] Qu Jifang, Theory of Live Gear Transmission [M]. Beijing: Machinery Industry Press, 1993. Summary of the Invention

[0010] This invention provides a method for selecting phase tuning parameters for planetary-type rotating machinery. First, a two-dimensional rectangular coordinate system is established with its origin at the geometric centroid of the rotating machinery, assuming the horizontal axis passes through an intermediate force-transmitting component. Then, based on the structural and kinematic symmetry of the rotating machinery, the spatiotemporal phase of each force-transmitting component is calculated. Next, the overall centroid coordinates of all intermediate force-transmitting components are calculated, and the overall moment of inertia is calculated accordingly. Finally, based on the operational properties of trigonometric functions, the mapping relationship between the basic parameters and the centroid coordinates and moment of inertia is given. This invention aims to predict the variation law of the centroid position and moment of inertia of rotating machinery, and based on this, propose parameter selection criteria to ultimately suppress translational / torsional vibrations, as detailed below:

[0011] A method for selecting phase tuning parameters in a planetary-type rotating machine, characterized in that the method includes:

[0012] A two-dimensional rectangular coordinate system is established with the geometric centroid of the rotating machinery as the origin. The horizontal axis passes through a certain intermediate force transmission component and is called component one. The remaining components are numbered in counterclockwise order.

[0013] Based on the structural and kinematic symmetry of the rotating machinery, the spatiotemporal phase of each force-transmitting component is calculated;

[0014] Calculate the coordinates of the center of mass of all intermediate force transmission components and the overall moment of inertia;

[0015] Based on the operational properties of trigonometric functions, the mapping relationship between basic parameters and the coordinates of the center of mass and the moment of inertia is given;

[0016] By selecting reasonable basic parameters through mapping relationships, the center of mass position and moment of inertia of the transmission system are kept fixed, thus achieving the technical goal of smooth operation of rotating machinery directly in the design stage.

[0017] The method includes:

[0018] If there are Z intermediate force transmission components in the transmission system, the initial displacement phase of the first intermediate force transmission component is zero, and the number of symmetrical elements of the central component is X, then the initial phase of the displacement of the i-th force transmission component is:

[0019] .

[0020] The method includes:

[0021] The instantaneous radial displacement of the i-th intermediate force transmission component is Then the x and y coordinates of the centroids of all intermediate force-transmitting components are as follows:

[0022] ,

[0023] in, For the mass of the intermediate force transmission component, Let be the spatial position angle of the i-th intermediate force transmission component. When the intermediate force transmission components are uniformly distributed circumferentially, we have: .

[0024] Wherein, the overall moment of inertia is:

[0025] Let the center of mass inertia tuning factor be:

[0026]

[0027] In the formula, mod() represents the modulo operation. If k=1 or If the position of the center of mass of the intermediate force transmission component is time-varying, then the position of the center of mass of the intermediate force transmission component is time-varying; otherwise, the position of the center of mass remains unchanged.

[0028] Similarly, the moment of inertia of the intermediate force-transmitting component is expressed as:

[0029]

[0030]

[0031] in, and , respectively, are the cosine and sine coefficients of the l-th harmonic; if k=0, the moment of inertia is time-varying, otherwise the moment of inertia remains constant.

[0032] The beneficial effects of the technical solution provided by this invention are:

[0033] 1. This invention fully utilizes the symmetry of the topological configuration of planetary-like rotating machinery and the periodicity of rigid body motion. It uses the phase tuning method and Fourier series to give the mathematical characterization of the coordinates of the global time-varying center of mass and the moment of inertia, thus providing a calculation and analysis tool for time-varying excitation analysis and prediction.

[0034] 2. This invention calculates the spatiotemporal phase of the force transmission component by combining structural and kinematic symmetry, which can accurately construct the mapping relationship between basic parameters and the overall center of mass coordinates and moment of inertia. Based on this, the installation phase and dimensional parameters of the force transmission component in planetary-type rotating machinery can be selected in a targeted manner, so as to stably control the overall center of mass near the geometric center, while realizing the on-demand matching of the moment of inertia, minimizing the center of mass offset or sudden change in moment of inertia, and ensuring uniform force during the operation of the transmission mechanism.

[0035] 3. This invention provides a clear prediction path for the variation law of the center of mass position and moment of inertia, which can guide the precise design of structural parameters and achieve optimal coordination of motion phase and load distribution of each force transmission component. This not only reduces repeated trial and error in the structural design stage and reduces the difficulty of matching between components, but also fully utilizes the performance potential of each force transmission component and ensures the power transmission efficiency of the overall transmission system.

[0036] 4. The time-varying excitation prediction technology proposed in this invention has the significant advantage of being easily expandable. Based on this invention, further research can be conducted on time-varying excitation prediction and suppression technology for space rotating machinery. Attached Figure Description

[0037] Figure 1 A schematic diagram of a planetary-type rotating machinery provided by the present invention;

[0038] Figure 2 A schematic diagram of a radial piston motor provided by the present invention;

[0039] Figure 3 A schematic diagram of a blade motor provided by the present invention;

[0040] Figure 4 This is a schematic diagram of the live gear transmission provided by the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0042] To overcome the difficulties in the prior art, this invention proposes a phase tuning method for predicting the time-varying center of mass and moment of inertia of planetary-type rotating machinery based on geometric configuration symmetry and the periodicity of rigid body motion. This invention uses hydraulic components, gear drives, and internal combustion engine drive mechanisms as typical examples in engineering. Based on the symmetry of configuration and motion, and the principle of harmonic decomposition, it provides tuning rules for the number of symmetrical units in the central component and intermediate transmission components in relation to the time-varying center of mass and moment of inertia. Furthermore, it proposes methods for suppressing time-varying internal excitation and selecting basic parameters. This method includes the following steps:

[0043] 101: Establish a two-dimensional rectangular coordinate system with the geometric centroid of the rotating machinery as the origin, let the horizontal axis pass through a certain intermediate force transmission component and call it component one, and number the remaining components in counterclockwise order;

[0044] 102: Calculate the spatiotemporal phase of each force-transmitting component based on the structural and kinematic symmetry of the rotating machinery;

[0045] 103: Calculate the overall center of mass coordinates of all intermediate force transmission components, and calculate the overall moment of inertia based on these coordinates;

[0046] 104: Based on the operational properties of trigonometric functions, give the mapping relationship between basic parameters, centroid coordinates, and moment of inertia;

[0047] 105: By selecting reasonable basic parameters through the above mapping relationship, the center of mass position and moment of inertia of the transmission system can be kept fixed, and the technical goal of smooth operation of rotating machinery can be achieved directly in the design stage.

[0048] If we assume that there are Z intermediate force transmission components in the transmission system, the initial displacement phase of the first intermediate force transmission component is zero, and the number of symmetrical elements of the central component is X, then the initial phase of the displacement of the i-th force transmission component can be written as:

[0049]

[0050] Due to the influence of phase, the position of the center of mass of the intermediate force transmission component may change during the motion, resulting in a time-varying centrifugal excitation force.

[0051] Assume the instantaneous radial displacement of the i-th intermediate force transmission component is Then the x and y coordinates of the centroids of all intermediate force-transmitting components are as follows:

[0052] ,

[0053] in, For the mass of the intermediate force transmission component, Let be the spatial position angle of the i-th intermediate force transmission component. When the intermediate force transmission components are uniformly distributed circumferentially, we have: .Will by Taking the Fourier series expansion of the fundamental frequency, we get:

[0054]

[0055] Where l represents the harmonic order, and These are the cosine and sine coefficients of the l-th harmonic, respectively.

[0056] Let the center of mass inertia tuning factor be:

[0057]

[0058] In the formula, mod() represents the remainder operation. From the formula... ~style It can be seen that if k=1 or If the position of the center of mass of the intermediate force transmission component is time-varying, then the position of the center of mass remains unchanged.

[0059] Similarly, the moment of inertia of the intermediate force-transmitting component can be expressed as:

[0060]

[0061] In fact, Frequency components and They are identical, differing only in the harmonic coefficients of each term. Therefore, they can also be considered as... Taking the Fourier series expansion of the fundamental frequency, we can obtain:

[0062]

[0063] in, and These are the cosine and sine coefficients of the l-th harmonic, respectively.

[0064] From the formula Japanese style Therefore, if k=0, the moment of inertia is time-varying; otherwise, the moment of inertia remains constant.

[0065] In engineering practice, the parity of the number of functional units in the intermediate force transmission components and the central component of rotating machinery affects the contact phase between the components, thereby changing the motion characteristics of the intermediate components.

[0066] Assuming the greatest common factor of the number of symmetrical elements X of the central member and the number of intermediate force-transmitting members Z is C, then:

[0067] ,

[0068] in, and These are the coprime factors obtained by dividing X and Z by C, respectively. Since they are coprime, the equation... In the middle, there are:

[0069]

[0070] Right now:

[0071]

[0072] In the formula, q is a positive integer. Simplifying, we get:

[0073]

[0074] It can be seen that k is an integer multiple of the greatest common factor C.

[0075] Therefore, when the greatest common factor C of the number of functional units and the number of intermediate force transmission components is greater than 1, we have .on the other hand, .visible It cannot be an integer multiple of C, in which case we have .

[0076] Based on the structural configuration and motion symmetry of rotating machinery, this invention uses Fourier series as a tool and the operational properties of trigonometric functions to reveal the mapping relationship between the two basic parameters of the number of symmetrical units of the central component and the number of intermediate force transmission components and the position of the center of mass and the moment of inertia of the rotating machinery, as shown in Table 1.

[0077]

[0078] The following is combined with Figures 2-4The described technique, without altering its fundamental principles, can be further improved in many ways to enhance analytical performance. This is illustrated below with reference to the embodiments shown in the accompanying drawings.

[0079] This invention provides two embodiments to illustrate the analysis process of time-varying mass and inertia excitation of a radial piston motor based on the principles of symmetry and phase tuning, such as... Figure 2 As shown.

[0080] Example 1

[0081] Assuming an action number of 7 and a plunger number of 10, the centroid inertia tuning theory proposed in this embodiment yields the patterns shown in Table 2. Since the action number and plunger number are coprime, the centroid position is not constant for the 3rd and 7th harmonics, thus exciting lateral vibrations, while other harmonics are suppressed. Simultaneously, torsional vibrations are only excited when the harmonic order is 10. If other factors are disregarded and the profile is designed as a pure harmonic form, only the 1st harmonic needs to be considered. Under this parameter configuration, the centroid position and moment of inertia are constant, thus simultaneously suppressing lateral and torsional vibrations. If the influence of various factors is considered and a non-pure harmonic profile is designed, the influence of other harmonic orders also needs to be considered. However, since the profile shape is close to pure harmonic, the influence of other harmonics is small and can even be ignored. This parameter scheme can be adopted for applications that are sensitive to both lateral and torsional vibrations.

[0082]

[0083] Example 2

[0084] If the number of actions is 8 and the number of plungers is 10, then according to the centroid inertia tuning theory proposed in this embodiment of the invention, the laws shown in Table 3 can be obtained. Since the greatest common factor of the number of actions and the number of plungers is greater than 1, the centroid position is constant, and lateral vibration is not excited. However, according to the phase tuning relationship, the moment of inertia exhibits a floating characteristic for all harmonic orders, thus exciting torsional vibration. For a pure harmonic profile, only the influence of the first harmonic needs to be considered. In this case, the centroid position is constant, but the moment of inertia is not constant, i.e., lateral vibration is suppressed, but torsional vibration is excited simultaneously. To improve performance, other techniques should be used for appropriate suppression. Similar to the coprime scheme in Table 1, since the overall cam profile shape is close to pure harmonic, the influence of other harmonics is small and can be ignored when performance requirements are not high. Therefore, this parameter scheme can be used for applications that are sensitive to lateral vibration but not torsional vibration.

[0085]

[0086] Furthermore, following the same analytical approach, we can also analyze... Figure 3 and Figure 4This invention illustrates the time-varying center of mass and moment of inertia laws and vibration modes of planetary transmission mechanisms, and proposes corresponding basic parameter selection techniques. Furthermore, based on this invention, a phase-tuning method can be used to analyze mechanical vibrations and flow pulsations caused by hydraulic pressure, inertial force, and friction. This analysis can be combined with the conclusions regarding the time-varying center of mass and moment of inertia to reveal more profound dynamic laws. In addition, based on this invention, parametric vibration suppression techniques and parameter selection techniques based on center of mass and moment of inertia phase tuning can be provided.

[0087] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0088] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for selecting phase tuning parameters of a quasi-planetary transmission rotary machine, characterized in that, The method comprises: A two-dimensional rectangular coordinate system is established with the geometric center of the rotating machine as the origin, and the horizontal axis is passed through a certain intermediate force transmission component and is called component one, and the remaining components are numbered in reverse clockwise order; According to the symmetry of the structure and motion of the rotating machine, the space-time phase of each force transmission component is calculated; The overall centroid coordinates of all intermediate force transmission components are calculated, and the overall moment of inertia is calculated; According to the operation properties of trigonometric functions, a mapping relationship between the basic parameters and the centroid coordinates and the moment of inertia is given; Through the mapping relationship, reasonable basic parameters are screened, so that the centroid position and the moment of inertia of the transmission system remain in a fixed state, and the technical goal of stable operation of the rotating machine is directly achieved in the design stage.

2. A method of selecting phase tuning parameters for a pseudo-planetary rotary machine according to claim 1, characterized in that, The method comprises: If there are Z intermediate force transmission components in the transmission system, the initial displacement phase of the first intermediate force transmission component is zero, the number of symmetric units of the central component is X, and the initial phase of the displacement of the ith force transmission component is: 。 3. A method of selecting phase tuning parameters for a pseudo-planetary rotary machine according to claim 1, characterized in that, The method comprises: The instantaneous radial displacement of the i-th intermediate force transmission member is The horizontal and vertical coordinates of the center of mass of all intermediate force transmission members are respectively ， ； wherein, is the mass of the intermediate force transmitting member, is the spatial position angle of the i-th intermediate force transmitting member, when the intermediate force transmitting members are uniformly distributed in the circumferential direction, .

4. A method of selecting phase tuning parameters for a pseudo-planetary rotary machine according to claim 1, characterized in that, The overall moment of inertia is: Let the centroid inertia tuning factor be: ； where mod() denotes the modulo operation, and if k = 1 or then the centroid position of the intermediate force transmission member is time-varying, otherwise the centroid position is constant; Similarly, the moment of inertia of the intermediate force transmission component is represented as: ； ； wherein and are the cosine and sine coefficients of the 1st harmonic, respectively; if k = 0, the moment of inertia is time-varying, otherwise it is constant.

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