CN108534966B - Gear time-varying meshing rigidity measurement and calculation method - Google Patents
Gear time-varying meshing rigidity measurement and calculation method Download PDFInfo
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- CN108534966B CN108534966B CN201710121029.9A CN201710121029A CN108534966B CN 108534966 B CN108534966 B CN 108534966B CN 201710121029 A CN201710121029 A CN 201710121029A CN 108534966 B CN108534966 B CN 108534966B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
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- G—PHYSICS
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- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract
The invention discloses a gear time-varying meshing rigidity measuring and calculating method, which is characterized in that dynamic strain of a plurality of tooth roots of a rotating gear is directly measured by using a distributed fiber bragg grating sensor, collected tooth root stress strain signals are converted into deformation of the tooth roots through a data processing method, the stress condition of each tooth root is obtained through torque measurement and load distribution calculation, further, the gear single-tooth time-varying meshing rigidity is obtained, then interpolation and numerical addition are carried out on the tooth meshing rigidity, and further, the comprehensive meshing rigidity of gear meshing is obtained. The method can measure the strain of a plurality of tooth roots in the gear meshing process, does not influence the normal operation of the gear, and is suitable for the actual dynamic operation condition.
Description
Technical Field
The invention belongs to the technical field of gear detection, and particularly relates to a gear time-varying meshing stiffness measurement and calculation method.
Background
The gear is one of the most important parts in the mechanical system, and as the gear transmission system develops toward high speed and heavy load, the dynamic performance of the gear transmission is more and more emphasized by the design and manufacture and the user. Compared with other transmission forms, the gear transmission not only generates dynamic response due to external excitation, but also generates gear tooth dynamic meshing force due to the change of the number of meshing teeth in the transmission process, the elastic deformation of gear teeth and the change of meshing rigidity caused by errors.
At present, the method for acquiring the time-varying meshing stiffness of the gear mainly comprises a finite element method, an analytical method and an experimental method. The finite element method is to discretize a gear meshing finite element model on the basis of establishing the gear meshing finite element model, and solve the model by setting reasonable boundary conditions to obtain meshing stiffness; the analytic method is to solve the gear time-varying meshing stiffness by establishing a gear tooth meshing mathematical model based on material mechanics, elasticity and the like, but certain errors are brought to a calculation result by simplification in the theoretical model establishing process, and the Ishikawa method is widely applied in the analytic method and does not consider the larger calculation result caused by gear body deformation; in addition, the invention patent of 'measuring method of meshing rigidity of straight tooth cylindrical gear' provides that a meshing rigidity expression is established by utilizing a transmission error Fourier series and a dynamic friction torque Fourier series for solving. In the method, neither a meshing stiffness theoretical calculation method nor an experimental method can reflect the stiffness and the change of the gear teeth under the working condition, so that an online real-time stiffness acquisition method based on tooth root stress-strain detection is provided. The gear is one of the most important parts in mechanical transmission, and the healthy operation of the gear is an important guarantee for the safety of mechanical equipment. Fatigue fracture is the most common failure of a gear, and usually occurs on the dangerous section where the bending stress at the root of the gear is the greatest.
Disclosure of Invention
The invention provides a gear time-varying meshing rigidity measurement and calculation method aiming at the problems in the prior art, and solves the problem of evaluating the gear time-varying meshing rigidity under the working condition.
The technical scheme adopted by the invention for solving the technical problems is as follows: step one, arrange the dynamic strain process in the optical fiber grating sensor measurement gear engagement process at the gear root, the output end of the optical fiber grating sensor is drawn out from the gear mounting shaft centre hole, transmit the measured data of the optical fiber grating sensor to the demodulation system through the optical fiber rotary connector, the demodulation system turns the optical signal that the optical fiber grating sensor outputs into the digital signal and transmits to the upper computer, the upper computer separates the temperature signal that the optical fiber grating sensor measures from the dynamic strain signal of the tooth root; step two, a torque sensor is arranged on an input shaft or an output shaft corresponding to the gear to be measured to measure torque, and torque data measured by the torque sensor and measurement data of the fiber bragg grating sensor are synchronously transmitted to an upper computer; calculating the total load force of the gear according to the measured torque data, calculating the stress state of each single tooth in the double-tooth meshing area or the multi-tooth meshing area according to the load distribution coefficient relation, and measuring by combining a fiber grating sensor to obtain the deformation at the tooth root, so that the single-tooth time-varying meshing rigidity is obtained according to the corresponding relation of the force and the deformation; and step four, interpolating the plurality of single-tooth time-varying meshing rigidities obtained by calculation in the step three to enable the lengths of the time-varying meshing rigidity sequences of the single teeth to be equal, and calculating and fusing adjacent single-tooth time-varying meshing rigidities according to a time synchronization principle to obtain the comprehensive time-varying meshing rigidity of the gear.
According to the technical scheme, the fiber grating sensor is fixed at the tooth root of the gear in a burying or sticking mode.
According to the technical scheme, the upper computer separates the temperature signal from the tooth root dynamic strain signal of the rotary gear by a regression or filtering method. Because temperature change is mostly a slowly-varying component, and tooth root dynamic strain is a high-frequency component, a low-frequency component can be filtered out through a filtering method, and therefore measurement change caused by temperature is eliminated.
According to the technical scheme, in the third step, the stress state of the single tooth in the meshing process is calculated by measuring the torque and according to the geometric parameters of the gear and the load distribution coefficient between the teeth.
According to the technical scheme, in the fourth step, interpolation is carried out on the single-tooth time-varying meshing stiffness of the rotary gear, and the time-varying meshing stiffness is fused according to a time synchronization principle to obtain the comprehensive time-varying meshing stiffness.
And carrying out multipoint synchronous dynamic measurement in the rotating working process of the gear, and fusing distributed multipoint dynamic measurement data by a subsequent data processing method. And simultaneously measuring the torque, and finally converting the strain of single teeth or multiple teeth combined with the gear load into the dynamic time-varying meshing rigidity of the gear through a physical relation.
The invention has the following beneficial effects: the gear time-varying meshing rigidity measuring and calculating method utilizes a distributed fiber grating sensor to directly measure the dynamic strain of a plurality of tooth roots of a rotating gear, converts collected tooth root stress strain signals into the deformation of the tooth roots through a data processing method, obtains the stress condition of each tooth root through torque measurement and load distribution calculation, further obtains the gear single-tooth time-varying meshing rigidity, then interpolates the tooth meshing rigidity and adds numerical values, and further obtains the comprehensive meshing rigidity of gear meshing. The method can measure the strain of a plurality of tooth roots in the gear meshing process, does not influence the normal operation of the gear, and is suitable for the actual dynamic operation condition.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a side view of a fiber grating sensor arrangement in an embodiment of the present invention;
FIG. 2 is a front view of a fiber grating sensor arrangement in an embodiment of the present invention;
FIG. 3 is a schematic diagram of the variation of single tooth strain under the working condition of the gear in the embodiment of the invention;
FIG. 4 is a schematic diagram of single tooth time varying meshing stiffness under the gear operating conditions in the embodiment of the invention;
FIG. 5 is a schematic diagram of integrated time varying mesh stiffness under gear operating conditions in an embodiment of the present invention;
FIG. 6 is a flow chart of a measurement and calculation method for time-varying meshing stiffness of a gear according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments and equations for strain to stiffness described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the invention provides a gear time-varying meshing stiffness measurement and calculation method which comprises the following steps that firstly, a fiber bragg grating sensor is arranged at the tooth root of a gear to measure the dynamic strain process in the gear meshing process, the output end of the fiber bragg grating sensor is led out from the central hole of a gear installation shaft, the measurement data of the fiber bragg grating sensor is transmitted to a demodulation system through an optical fiber rotary connector, the demodulation system converts the optical signal output by the fiber bragg grating sensor into a digital signal and transmits the digital signal to an upper computer, and the upper computer separates the temperature signal measured by the fiber bragg grating from a tooth root dynamic strain signal; step two, a torque sensor is arranged on an input shaft or an output shaft corresponding to the gear to be measured to measure torque, and torque data measured by the torque sensor and fiber bragg grating data are synchronously transmitted to an upper computer; calculating the total load force of the gear according to the measured torque data, calculating the stress state of each single tooth in the double-tooth meshing area or the multi-tooth meshing area according to the load distribution coefficient relation, and measuring by combining a fiber grating sensor to obtain the deformation at the tooth root, so that the single-tooth time-varying meshing rigidity is obtained according to the corresponding relation of the force and the deformation; and step four, interpolating the plurality of single-tooth time-varying meshing rigidities obtained by calculation in the step three to enable the lengths of the time-varying meshing rigidity sequences of the single teeth to be equal, and calculating and fusing adjacent single-tooth time-varying meshing rigidities according to a time synchronization principle to obtain the comprehensive time-varying meshing rigidity of the gear.
Further, the fiber grating sensor is fixed at the tooth root of the gear in a manner of embedding or pasting.
Further, the upper computer separates the temperature signal from the tooth root dynamic strain signal of the rotating gear through a regression or filtering method. Because temperature change is mostly a slowly-varying component, and tooth root dynamic strain is a high-frequency component, a low-frequency component can be filtered out through a filtering method, and therefore measurement change caused by temperature is eliminated.
Further, in the third step, the stress state of the single tooth in the meshing process is calculated by measuring the torque and according to the geometric parameters of the gear and the load distribution coefficient between the teeth.
And further, in the fourth step, interpolating the single-tooth time-varying meshing stiffness of the rotary gear and fusing the single-tooth time-varying meshing stiffness according to a time synchronization principle to obtain the comprehensive time-varying meshing stiffness, specifically, performing segmented interpolation on the measured time-varying meshing stiffness of the single gear in a meshing cycle according to a first double-tooth meshing zone, a single-tooth meshing zone and a second double-tooth meshing zone, and after the interpolation is completed, overlapping the meshing stiffness time-varying signals of the plurality of teeth according to the fact that the second-segment double-tooth meshing zone of the previous tooth is overlapped with the first-segment double-tooth meshing zone of the next tooth by taking the starting point and the ending point of the different meshing zones as reference points, so that the comprehensive meshing stiffness is obtained.
In a preferred embodiment of the present invention, a method for measuring and calculating the time-varying meshing stiffness of a gear is further provided, as shown in fig. 6. The method comprises the following steps:
(1) and (3) adhering a fiber grating sensor to the tooth root of the end face of the gear 1 as shown in figures 1 and 2. The output end of the fiber grating sensor is led out from the central hole of the gear mounting shaft 2, the measured data of the fiber grating sensor 4 is transmitted to a demodulation system through an optical fiber rotary connector and is transmitted through an optical fiber 3, and meanwhile, a torque sensor is mounted on the input or output shaft corresponding to the measured gear to measure the torque.
(2) And separating the slowly-changed temperature signal from the tooth root dynamic strain signal of the rotating gear by a regression or filtering method so as to eliminate the interference of the temperature to the strain signal and obtain the tooth root dynamic strain, wherein 0-c is a meshing period as shown in fig. 3, wherein 0-a is a first double-tooth meshing area, a-b is a single-tooth meshing area, and b-c is a second double-tooth meshing area.
(3) Calculating the load borne by the gear according to the measured torque:
F＝2T/d
wherein F is the circumferential force applied to the gear, T is the measured torque, and d is the reference circle diameter
And calculating the stress state of each single tooth in the double-tooth meshing zone or the multi-tooth meshing zone according to the load distribution coefficient relation:
- - (O- -X- -O) - -in which FsThe load is single-tooth load, a, b, c, d and x are meshing angles, a-b is a first double-tooth meshing area, b-c is a single-tooth meshing area, and c-d is a second double-holding meshing area.
(4) The deformation of the tooth root is obtained through the strain measured by the fiber bragg grating sensor, so that the time-varying meshing rigidity of the single tooth is obtained according to the corresponding relation between the force and the deformation:
-wherein K is the single tooth mesh stiffness, epsilon is the measured strain, and L is the fiber grating length.
As shown in FIG. 4, a diagram of the single-tooth time-varying meshing stiffness is shown, and 0-c is a meshing period, wherein 0-a is a first double-tooth meshing area, a-b is a single-tooth meshing area, and b-c is a second double-tooth meshing area.
(5) Interpolating the calculated multiple single-tooth time-varying meshing stiffnesses to enable the time-varying meshing stiffness sequences of the single teeth to be equal in length, then calculating and fusing the adjacent single-tooth time-varying meshing stiffnesses according to a time synchronization principle, namely a second-stage double-tooth meshing zone of a previous tooth is overlapped with a first-stage double-tooth meshing zone of a next tooth, and obtaining the comprehensive time-varying meshing stiffness of the gear, as shown in fig. 5, wherein 0-g represents three meshing cycles, wherein 0-a, b-c, d-e and f-g are double-tooth meshing zones, and a-b, c-d and e-f are single-tooth meshing zones.
The time-varying meshing stiffness obtained by tooth root strain is processed and analyzed, and a basis is provided for detecting the uniform load distribution and balance of the gear and analyzing different forms of tooth faults.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.
Claims (5)
1. Step one, arrange the dynamic strain process in the fiber grating sensor measurement gear engagement process at the gear dedendum, the output end of the fiber grating sensor is drawn out from the gear mounting shaft centre hole, transmit the measured data of the fiber grating sensor to the demodulation system through the fiber optic rotary connector, the demodulation system turns the optical signal that the fiber grating sensor outputs into the digital signal and transmits to the host computer, the host computer separates the temperature signal measured by the fiber grating sensor from the dynamic strain signal of the dedendum; step two, a torque sensor is arranged on an input shaft or an output shaft corresponding to the gear to be measured to measure torque, and torque data measured by the torque sensor and measurement data of the fiber bragg grating sensor are synchronously transmitted to an upper computer; calculating the total load force of the gear according to the measured torque data, calculating the stress state of each single tooth in the double-tooth meshing area or the multi-tooth meshing area according to the load distribution coefficient relation, and measuring by combining a fiber grating sensor to obtain the deformation at the tooth root, so that the single-tooth time-varying meshing rigidity is obtained according to the corresponding relation of the force and the deformation; and step four, interpolating the plurality of single-tooth time-varying meshing rigidities obtained by calculation in the step three to enable the lengths of the time-varying meshing rigidity sequences of the single teeth to be equal, and calculating and fusing adjacent single-tooth time-varying meshing rigidities according to a time synchronization principle to obtain the comprehensive time-varying meshing rigidity of the gear.
2. The method for measuring and calculating the gear time-varying meshing stiffness according to claim 1, wherein the fiber grating sensor is fixed at the tooth root of the gear in a manner of embedding or pasting.
3. The gear time-varying meshing stiffness measurement and calculation method according to claim 1 or 2, wherein the upper computer separates the temperature signal from a tooth root dynamic strain signal of the rotating gear through a regression or filtering method.
4. The gear time-varying meshing stiffness measurement and calculation method according to claim 1 or 2, wherein in the third step, the stress state of a single tooth in the meshing process is calculated by measuring the torque and according to the geometric parameters of the gear and the load distribution coefficient between teeth.
5. The method for measuring and calculating the time-varying gear meshing stiffness of the gear according to claim 1 or 2, wherein in the fourth step, the time-varying single gear meshing stiffness of the rotary gear is interpolated and fused according to a time synchronization principle to obtain the comprehensive time-varying meshing stiffness, and specifically, the time-varying single gear meshing stiffness obtained by measurement is segmented and interpolated within one meshing cycle according to a first double-tooth meshing zone, a single-tooth meshing zone and a second double-tooth meshing zone, after interpolation is completed, the meshing stiffness signals of a plurality of teeth are superposed according to the coincidence of a second double-tooth meshing zone of a previous tooth and a first double-tooth meshing zone of a next tooth by respectively taking the starting point and the ending point of different meshing zones as reference points, so that the comprehensive time-varying meshing stiffness is obtained.
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| CN110657983B (en) * | 2019-09-18 | 2021-06-01 | 佛山科学技术学院 | Measurement test platform and measurement method for dynamic/static meshing stiffness of gear |
| CN114689313A (en) * | 2021-11-26 | 2022-07-01 | 哈尔滨理工大学 | On-line detection device for gear meshing stiffness of nine-gear automatic transmission and multi-signal fusion detection method |
| CN114526906B (en) * | 2022-01-05 | 2023-01-06 | 南京航空航天大学 | Measuring device for measuring transmission error of gear pair |
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| CN101770538B (en) * | 2010-01-15 | 2011-11-09 | 北京工业大学 | Method for simulation analysis on meshing stiffness of cylindrical spur gear undergoing damaged single-tooth failure |
| CN102542105B (en) * | 2011-12-24 | 2013-07-24 | 中国煤炭科工集团太原研究院 | Gear load wireless monitoring system and interactive multi-stage gear physical simulation method finished based on same |
| CN104535318B (en) * | 2014-12-29 | 2017-02-22 | 盐城工学院 | Method for measuring variable stiffness in process of gear mesh |
| CN105698695B (en) * | 2016-03-25 | 2019-06-25 | 武汉理工大学 | Novel Dedenda's bending stress on-Line Monitor Device and method based on fiber grating |
| CN105784360A (en) * | 2016-05-12 | 2016-07-20 | 重庆长安汽车股份有限公司 | Method for determining gear engagement dynamic stiffness based on engagement contact line length variation |
| CN106441867B (en) * | 2016-09-22 | 2019-01-29 | 北京航空航天大学 | Based on the considerations of the spiral bevel gear Dedenda's bending stress test method of similarity theory dynamic loading |
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