CN108534966A - A kind of gear time-variant mesh stiffness survey calculation method - Google Patents
A kind of gear time-variant mesh stiffness survey calculation method Download PDFInfo
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- CN108534966A CN108534966A CN201710121029.9A CN201710121029A CN108534966A CN 108534966 A CN108534966 A CN 108534966A CN 201710121029 A CN201710121029 A CN 201710121029A CN 108534966 A CN108534966 A CN 108534966A
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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
- G01M5/0041—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings by determining deflection or stress
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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
- G01M13/00—Testing of machine parts
- G01M13/02—Gearings; Transmission mechanisms
- G01M13/021—Gearings
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Abstract
The invention discloses a kind of gear time-variant mesh stiffness survey calculation methods, the rotation multiple tooth root dynamic strain of gear are directly measured using fibre-optical grating sensor, convert acquisition root stress strain signal to by data processing method the deformation of tooth root, the stressing conditions at each tooth root are calculated by torque measurement and load distribution, and then obtain single gear tooth time-variant mesh stiffness, pair then but tooth engagement rigidity is added into row interpolation sum number value, further obtains the synthesis mesh stiffness of gear engagement.The method of the present invention can strain multiple tooth roots in Meshing Process of Spur Gear and measure, while not influence the normal operation of gear, be suitable for practical dynamic operation condition.
Description
Technical field
The invention belongs to gear testing technical field more particularly to a kind of gear time-variant mesh stiffness survey calculation methods.
Background technology
Gear is one of the most important parts in mechanical system, as gear train assembly is sent out to high speed, overload direction
Exhibition, gear-driven dynamic performance is increasingly by manufacturing and designing and user is paid attention to.Compared to other driving forms,
Gear drive can not only generate dynamic response because of external drive, at the same can due to the change of engaging tooth logarithm in transmission process,
The flexible deformation and error of the gear teeth cause mesh stiffness to change, such due to nibbling to generate gear teeth dynamic engagement power
Dynamic exciting is one of most important dynamic exciting form in gear drive caused by closing the time variation of rigidity, therefore is passed to gear
The research of time-variant mesh stiffness is of great significance in dynamic.
Currently, the acquisition methods of gear time-variant mesh stiffness mainly have FInite Element, analytic method, experimental method.FInite Element
It is to carry out its discretization to model by the way that reasonable boundary conditions are arranged on the basis of establishing the finite element model of gear engagement
Solution obtains mesh stiffness；Analytic method is that the mathematical model solution gear of gear teeth meshing is established based on mechanics of materials Elasticity etc.
Time-variant mesh stiffness, but the simplification during theoretical model foundation brings certain error to result of calculation, the stone in analytic method
River method is widely used, and does not consider that the deformation of gear wheel body causes result of calculation larger；The positive pressure engaged according to gear in experimental method
The method of power and gear tooth deformation calculating Gear Meshing Stiffness is subject to conditions to be difficult to realize, in addition patent of invention《Straight tooth column
The measurement method of Gear Meshing Stiffness》It proposes and is established using driving error fourier series and dynamic friction torque Fourier series
Mesh stiffness expression formula is solved.Mesh stiffness theoretical calculation method or experimental method can not react in approach described above
The rigidity of the operating mode lower gear gear teeth and its variation, therefore propose the online real-time rigidity acquisition side based on root stress strain detecting
Method.Gear is one of most important parts in machine driving, and health operation is the important leverage of mechanical equipment safety.Fatigue
Fracture is the most common failure of gear, is usually happened on the maximum dangerouse cross-section of gear root bending stress.
Invention content
The present invention is directed to the problems of the prior art, provides a kind of gear time-variant mesh stiffness survey calculation method, solves
Evaluation problem of the gear in operating mode lower gear time-variant mesh stiffness.
The technical solution adopted by the present invention to solve the technical problems is：A kind of gear time-variant mesh stiffness meter is provided
Calculation method, this approach includes the following steps:Step 1 arranges that fiber-optic grating sensor measures gear and engaged at Gear Root
The output end of dynamic strain process in journey, fiber-optic grating sensor is drawn from gear mounting shaft centre bore, passes through fiber spinning
The measurement data of fiber-optic grating sensor is transported to demodulating system by connector, and demodulating system exports fiber-optic grating sensor
Optical signal is converted into digital signal and is delivered to host computer, and the temperature signal that host computer measures fiber grating is believed with tooth root dynamic strain
Number separation；Step 2, installation torque sensor carries out torque measurement in the corresponding input of tested gear or output shaft, by torque
Torque data measured by sensor and fiber grating data synchronous transport to host computer；Step 3 passes through surveyed torque data
The size of the total loading force of gear is calculated, and is calculated in double-teeth toothing region or multi-tooth meshing area according to weight distribution factor relationship
The stress of each monodentate obtains the deformation at tooth root in conjunction with fiber-optic grating sensor measurement, to according to power and deformation
Correspondence obtains monodentate time-variant mesh stiffness；Step 4, to the multiple monodentate time-variant mesh stiffness being calculated in step 3
Into row interpolation so that the time-variant mesh stiffness sequence length of each monodentate is equal, then according to the principle of time synchronization to adjacent
Monodentate time-variant mesh stiffness carries out calculating fusion, and time-variant mesh stiffness is integrated to obtain gear.
According to the above technical scheme, fiber-optic grating sensor is fixed on the tooth root of gear by way of burying and applying or paste
Place.
According to the above technical scheme, host computer is moved the tooth root of temperature signal and rotation gear by the method for returning or filtering
Strain signal detaches.Since temperature change is mostly ramped composition, and tooth root dynamic strain is radio-frequency component, therefore can pass through filtering
Method filters out low-frequency component, to eliminate temperature caused by measure variation.
According to the above technical scheme, in the step 3, by measuring torque, and according to gear geometry parameter, Yi Jichi
Between weight distribution factor the stress of monodentate in engagement process is calculated.
According to the above technical scheme, in the step 4, to rotating the monodentate time-variant mesh stiffness of gear into row interpolation and root
It is merged to obtain comprehensive time-variant mesh stiffness according to the principle of time synchronization, specifically, according to first double-teeth toothing region, monodentate
Region of engagement, second double-teeth toothing region are divided the time-variant mesh stiffness for obtaining single gear is measured within a mesh cycle
Section interpolation, after the completion of interpolation, respectively using the starting point and ending point of different region of engagements as reference point, according to the second of previous tooth
Section double-teeth toothing region is overlapped with the first segment double-teeth toothing region of next tooth, and the mesh stiffness signal of multiple teeth is overlapped,
To obtain comprehensive time-variant mesh stiffness.
It carries out Multipoint synchronous dynamic during gear rotary work to measure, and will by subsequent data processing method
Distributed Multi dynamic measuring data is merged.Torque is measured simultaneously, finally by monodentate or multiple tooth strain conjunction gear wheel load
Lotus is converted to the dynamic time-variant mesh stiffness of gear by physical relation.
The beneficial effect comprise that：Gear time-variant mesh stiffness survey calculation method of the present invention utilizes distributed light
Fiber grating sensor to rotation the multiple tooth root dynamic strain of gear directly measure, will acquisition root stress strain signal by data at
Reason method is converted into the deformation of tooth root, and the stressing conditions at each tooth root are calculated by torque measurement and load distribution, into
And single gear tooth time-variant mesh stiffness is obtained, then pair but tooth engagement rigidity is added into row interpolation sum number value, further obtains tooth
Take turns the synthesis mesh stiffness of engagement.The method of the present invention can strain multiple tooth roots in Meshing Process of Spur Gear and measure, simultaneously
The normal operation of gear is not influenced, is suitable for practical dynamic operation condition.
Description of the drawings
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing：
Fig. 1 is that fiber-optic grating sensor arranges side view in the embodiment of the present invention；
Fig. 2 is that fiber-optic grating sensor arranges front view in the embodiment of the present invention；
Fig. 3 is monodentate strain variation schematic diagram under middle gear operating mode of the embodiment of the present invention；
Fig. 4 is monodentate time-variant mesh stiffness schematic diagram under middle gear operating mode of the embodiment of the present invention；
Fig. 5 is comprehensive time-variant mesh stiffness schematic diagram under middle gear operating mode of the embodiment of the present invention；
Fig. 6 is gear time-variant mesh stiffness survey calculation method flow diagram of the embodiment of the present invention.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific of rigidity is arrived in specific embodiment described herein and strain
Calculation formula only to explain the present invention, is not intended to limit the present invention.
In the embodiment of the present invention, a kind of gear time-variant mesh stiffness survey calculation method is provided, this method includes following step
Suddenly:Step 1, the dynamic strain process in arrangement fiber-optic grating sensor measurement Meshing Process of Spur Gear at Gear Root, optical fiber
The output end of grating sensor is drawn from gear mounting shaft centre bore, by fiber rotation connector by fiber-optic grating sensor
Measurement data is transported to demodulating system, and demodulating system converts the optical signal that fiber-optic grating sensor exports to digital signal and conveys
To host computer, temperature signal and tooth root dynamic strain Signal separator that host computer measures fiber grating；Step 2, in tested gear
It is corresponding input or output shaft on installation torque sensor carry out torque measurement, by measured by torque sensor torque data with
Fiber grating data synchronous transport is to host computer；Step 3 calculates the big of the total loading force of gear by surveyed torque data
It is small, and the stress of each monodentate in double-teeth toothing region or multi-tooth meshing area is calculated according to weight distribution factor relationship, in conjunction with
Fiber-optic grating sensor measurement obtains the deformation at tooth root, is engaged to obtain monodentate time-varying with the correspondence of deformation according to power
Rigidity；Step 4, to multiple monodentate time-variant mesh stiffness for being calculated in step 3 into row interpolation so that the time-varying of each monodentate
Mesh stiffness sequence length is equal, then to adjacent monodentate time-variant mesh stiffness calculate according to the principle of time synchronization and melt
It closes, time-variant mesh stiffness is integrated to obtain gear.
Further, fiber-optic grating sensor is fixed on by way of burying and applying or paste at the tooth root of gear.
Further, host computer is believed the tooth root dynamic strain of temperature signal and rotation gear by the method for returning or filtering
Number separation.Since temperature change is mostly ramped composition, and tooth root dynamic strain is radio-frequency component, therefore can be filtered by filtering method
Except low-frequency component, to eliminate temperature caused by measure variation.
Further, in the step 3, by measuring torque, and according to gear geometry parameter and Transverse Load
The stress of monodentate in engagement process is calculated in distribution coefficient.
Further, in the step 4, to rotating the monodentate time-variant mesh stiffness of gear into row interpolation and according to the time
Synchronous principle is merged to obtain comprehensive time-variant mesh stiffness, specifically, being engaged according to first double-teeth toothing region, monodentate
Area, second double-teeth toothing region will measure obtain single gear time-variant mesh stiffness carried out within a mesh cycle segmentation insert
It is worth, it is double according to the second segment of previous tooth respectively using the starting point and ending point of different region of engagements as reference point after the completion of interpolation
Tooth engagement area is overlapped with the first segment double-teeth toothing region of next tooth, and the mesh stiffness signal of multiple teeth is overlapped, to
Obtain comprehensive time-variant mesh stiffness.
In presently preferred embodiments of the present invention, a kind of gear time-variant mesh stiffness survey calculation method is also provided, such as Fig. 6 institutes
Show.Method and step is as follows：
(1) fiber-optic grating sensor is pasted at 1 end face tooth root of gear, as shown in Figure 1, Figure 2.By the defeated of fiber-optic grating sensor
Outlet is drawn from 2 centre bore of gear mounting shaft, is conveyed the measurement data of fiber-optic grating sensor 4 by fiber rotation connector
It to demodulating system, is conveyed by optical fiber 3, while installation torque sensor carries out in the corresponding input of tested gear or output shaft
Torque measurement.
(2) by the method that returns or filter by the tooth root dynamic strain Signal separator of gradual temperature signal and rotation gear,
To eliminate interference of the temperature to strain signal, tooth root dynamic strain is obtained, as shown in figure 3,0-c is a mesh cycle, wherein
0-a is the first double-teeth toothing region, and a-b is monodentate region of engagement, and b-c is the second double-teeth toothing region.
(3) loaded according to actual measurement torque arithmetic gear institute:
F=2T/d
--- wherein F is the force of periphery suffered by gear, and T is actual measurement torque, and d is reference diameter
And the stress of each monodentate in double-teeth toothing region or multi-tooth meshing area is calculated according to weight distribution factor relationship:
--- wherein FsFor monodentate load, a, b, c, d, x is tooth matching angle, and a-b is the first double-teeth toothing region, and b-c is single
Tooth engagement area, c-d are second pair and hold region of engagement.
(4) strain is surveyed by fiber-optic grating sensor and obtains the deformation at tooth root, to corresponding with deformation according to power
Relationship obtains the time-variant mesh stiffness of monodentate：
--- wherein K is monodentate mesh stiffness, and ε is that actual measurement strains, and L is fiber grating length.
It is illustrated in figure 4 monodentate time-variant mesh stiffness schematic diagram, 0-c is a mesh cycle, and wherein 0-a is the first bidentate
Region of engagement, a-b are monodentate region of engagement, and b-c is the second double-teeth toothing region.
(5) to calculating multiple monodentate time-variant mesh stiffness of gained into row interpolation so that the time-variant mesh stiffness of each monodentate
Sequence length is equal, then according to the principle of time synchronization, i.e., second segment double-teeth toothing region and the next tooth of previous tooth
First segment double-teeth toothing region overlaps, and calculating fusion is carried out to adjacent monodentate time-variant mesh stiffness, obtains gear synthesis time-varying and nibbles
Rigidity is closed, as shown in figure 5,0-g is to indicate three mesh cycles, wherein 0-a, b-c, d-e, f-g are double-teeth toothing region, a-b, c-
D, e-f are monodentate region of engagement.
Obtained time-variant mesh stiffness is strained to tooth root and carries out processing analysis, the load to detect gear is uniformly distributed, balance, with
And the various forms of tooth failures of analysis provide foundation.
It should be understood that for those of ordinary skills, it can be modified or changed according to the above description,
And all these modifications and variations should all belong to the protection domain of appended claims of the present invention.
Claims (5)
1. a kind of gear time-variant mesh stiffness survey calculation method, which is characterized in that this approach includes the following steps:Step 1,
Dynamic strain process in arrangement fiber-optic grating sensor measurement Meshing Process of Spur Gear at Gear Root, fiber-optic grating sensor
Output end from gear mounting shaft centre bore draw, it is by fiber rotation connector that the measurement data of fiber-optic grating sensor is defeated
It is sent to demodulating system, demodulating system converts the optical signal that fiber-optic grating sensor exports to digital signal and is delivered to host computer,
The temperature signal that host computer measures fiber grating and tooth root dynamic strain Signal separator；Step 2, it is corresponding defeated in tested gear
Enter or output shaft on installation torque sensor carry out torque measurement, by the torque data and fiber grating measured by torque sensor
Data synchronous transport is to host computer；Step 3, calculates the size of the total loading force of gear by surveyed torque data, and according to
Weight distribution factor relationship calculates the stress of each monodentate in double-teeth toothing region or multi-tooth meshing area, is passed in conjunction with fiber grating
Sensor measurement obtains the deformation at tooth root, to obtain monodentate time-variant mesh stiffness according to the correspondence of power and deformation；Step
Four, to multiple monodentate time-variant mesh stiffness for being calculated in step 3 into row interpolation so that the time-variant mesh stiffness of each monodentate
Sequence length is equal, then carries out calculating fusion to adjacent monodentate time-variant mesh stiffness according to the principle of time synchronization, to
Obtain gear synthesis time-variant mesh stiffness.
2. gear time-variant mesh stiffness survey calculation method according to claim 1, which is characterized in that optical fiber grating sensing
Device is fixed on by way of burying and applying or paste at the tooth root of gear.
3. gear time-variant mesh stiffness survey calculation method according to claim 1 or 2, which is characterized in that host computer is logical
Recurrence or the method filtered are crossed by the tooth root dynamic strain Signal separator of temperature signal and rotation gear.
4. gear time-variant mesh stiffness survey calculation method according to claim 1 or 2, which is characterized in that the step
In three, by measuring torque, and it is calculated in engagement process according to gear geometry parameter and load share between teeth
The stress of monodentate.
5. gear time-variant mesh stiffness survey calculation method according to claim 1 or 2, which is characterized in that the step
In four, integrated to rotating the monodentate time-variant mesh stiffness of gear into row interpolation and being merged according to the principle of time synchronization
Time-variant mesh stiffness, specifically, will be measured according to first double-teeth toothing region, monodentate region of engagement, second double-teeth toothing region
Time-variant mesh stiffness to single gear carries out piecewise interpolation within a mesh cycle, after the completion of interpolation, is nibbled respectively with difference
The starting point and ending point for closing area is reference point, according to the first segment of the second segment double-teeth toothing region and next tooth of previous tooth
Double-teeth toothing region overlaps, and the mesh stiffness signal of multiple teeth is overlapped, to obtain comprehensive time-variant mesh stiffness.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110657983A (en) * | 2019-09-18 | 2020-01-07 | 佛山科学技术学院 | Measurement test platform and measurement method for dynamic/static meshing stiffness of gear |
| CN114526906A (en) * | 2022-01-05 | 2022-05-24 | 南京航空航天大学 | Measuring device for measuring transmission error of gear pair |
| 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 |
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| CN110657983A (en) * | 2019-09-18 | 2020-01-07 | 佛山科学技术学院 | Measurement test platform and measurement method for dynamic/static meshing stiffness of gear |
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| 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 |
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| 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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