CN106840652B - A kind of motion transmission error prediction method based on gear global error - Google Patents
A kind of motion transmission error prediction method based on gear global error Download PDFInfo
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- 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
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Abstract
The motion transmission error prediction method based on gear global error that the invention discloses a kind of, belongs to gear-driven accuracy measuring technique, Precision Inspection, instrument and technical field of mechanical transmission.Based on the global error data for obtaining gear using integral error measuring technology, error and the operating condition effect of intercoupling are considered, construct the nonlinear kinetics prediction model of gear dynamic transmission prediction.Firstly, obtaining gear static state driving error using Gear integrated error measuring data according to the coordinate system of gear engaged transmission principle building.Then, the dynamic displacement of prediction model is obtained using the method for numerical solution.The interaction principle for finally utilizing gear error, has synthesized dynamic transmission error of gear.This method can be applicable in the requirement of complex environment and consider that error and operating condition intercouple the requirement of effect.
Description
Technical field
The motion transmission error prediction method based on gear global error that the present invention relates to a kind of, belongs to gear-driven accuracy
Measuring technique, Precision Inspection, instrument and technical field of mechanical transmission.
Background technique
Gear is one of most commonly used basic transmission element of the industrial applications such as machinery, space flight, ship, it can not only be passed
The functions such as graduating power, the deceleration that can also realize transmission system, speedup and deflecting, play key effect in a device.Into new
Since century, along with the high speed development in the fields such as automobile, wind-powered electricity generation, high-speed rail, China's gear industry achieves huge progress.Tooth
Wheel with its stable drive, reliable operation and the excellent performance such as high-efficient by the favor of people, with the raising of industrial level,
Requirement of the people to gear performance is also higher and higher, and gear is just sent out towards the direction of high-precision, high revolving speed, biggish bearing capacity
Exhibition.Based on gear and important driving member, quality directly affect the finger such as kinematic accuracy, vibration, noise, service life of host
Mark, the quality of working performance directly affect the transmission quality of transmission system, it has also become there is an urgent need to what is studied and solve to ask
Topic.
Gear measurement technology is design of gears, processing and the important tie used, obtains the error of gear by measurement
The important means for the problems such as matter, guidance processing and use are the bearing capacity for solving gear, transmission efficiency, vibrating noise.In tooth
It takes turns in the measurement of individual event error in geometrical form, each error requires individually to measure, and the measurement one of these individual errors
As require dedicated instrument.These detecting instruments and equipment are not that precision is lower, complicated for operation, human factor is big, are exactly set
Standby expensive, environment height, operator's technical level require height, or even many technologies by external company and institute, R&D institution ridge
It is disconnected.Static driving error measurement is during gear drive, and at certain intervals, static measurement steamboat and bull wheel turn
Angle, and compare.This method be it is intermittent, do not account for the influence of the dynamic load, inertia and variation rigidity in actual condition, and real
Border situation has bigger gap.Due to shape, error, flexible deformation and the load of each part in gear and transmission system
There is close connection, in entire transmission system the geometry of each part with elasticity with error distortions mutually transmit, phase
Mutually influence.Only the gear static accuracy based on gear geometry, kinematics research achievement evaluates the performance of gear, not
It is able to satisfy the requirement for considering the gear dynamic precision based on nonlinear dynamic behavior research achievement.
It is measured in the wideband sound range systems of satisfaction energy low speed measuring condition being not only able to satisfy high speed, is simulating different works
Under condition, the dynamic transmission error of gear of acquisition can predict the dynamic property of gear very well.Dynamic transmission error of gear test system
System needs to have wider Hz-KHz, can test the gear drive error under high speed and low-speed conditions.Therefore, this type gear
Motion transmission error testing system needs to have the driving equipment that can be adjusted the speed in a wider range, and the load that can be controlled
Equipment, for simulating the drive error testing under different operating conditions, thus be tooth on the basis of realizing drive error testing function,
Multifunction should be realized as far as possible.Vibration and noise due to gear drive error and gear have direct relationship, institute
The higher vibration of precision and noise-measuring system are needed with dynamic transmission error of gear test macro, while to have carry out mode
The relevant device of test.Dynamic transmission error of gear test macro needs to have good repeatability, answers under multiple experiment
This can obtain consistent or similar data conclusion.
1970 Tong Nian Yihuang Mr.s Nian are that the China Gear expert of representative has been put forward for the first time gear global error in the world
Concept, and on the basis of gear single-sided is engaged and measured, " one flank gearing raker tooth mensuration " is proposed, and then it is whole to have invented gear
Body error measurement technology.The practical registration of master gear and tested gear will not go out less than 1 in non-monodentate region of engagement when measurement
Now it is more than the case where a pair of of flank of tooth simultaneously participates in engagement, the point on energy resolution error curve is by the previous flank of tooth or the latter
Caused by the error of the flank of tooth.High-precision circle is respectively provided on " jump tooth " worm screw and tested gear shaft in global error measurement process
Grating can obtain the driving error curve under the conditions of raker tooth list is nibbled by this two-way Circular gratings signal.Complete tooth is measured
Wide kinematic error curve has obtained the control information for being included than TE curve more comprehensively Method of Gear Integrated Error Curve, has obtained
It obtained and traditional singly nibble measurement and cannot obtain the measurement result of the analysis modes such as total profile deviation, circular pitch deviation.
The present invention is directed to that static driving error amount does not account for error and operating condition intercouples the influence of effect, and dynamic passes
Dynamic error measuring device structure is complicated and easily by measurement environmental disturbances the problem of, propose a kind of based on gear global error
Motion transmission error prediction method.
Summary of the invention
In order to overcome static driving error amount not account for error and operating condition intercouple effect influence and motion transmission
Error measuring device structure is complicated and easily by measurement environmental disturbances the problem of, the present invention provides one kind integrally to be missed based on gear
The motion transmission error prediction method of difference, can more accurately obtain the motion transmission error of gear.
Motion transmission error prediction method based on gear global error is to obtain tooth using integral error measuring technology
Based on the global error data of wheel, error and the operating condition effect of intercoupling are considered, construct the non-of gear dynamic transmission prediction
Linear dynamics prediction model.Firstly, being surveyed in the coordinate system according to gear engaged transmission principle building using gear global error
Data are measured, gear static state driving error is obtained.Then, the dynamic displacement of prediction model is obtained using the method for numerical solution.Most
The interaction principle for utilizing gear error afterwards, has synthesized dynamic transmission error of gear.This method can be applicable in complex environment
It is required that and being able to satisfy and considering that error and operating condition intercouple the requirement of effect.This combines Fig. 1 to Fig. 5, method used by inventing
Content includes:
(1) expression of dynamic transmission error of gear；The motion transmission error of i-th pair gear as shown in Figure 2, gear are passing
When dynamic power, there is only mismachining tolerances in contact point for the gear teeth of gear, and there are flexible deformations, the i-th of master and slave gear
To the gear teeth along path of contact direction at contact point (x, y), i indicates the serial number of contact gear mesh, and i=1,2 ..., n are positive whole
Number, the global error of master and slave gear are denoted as respectivelyWithAlong path of contact direction it is loaded after, master and slave gear it is comprehensive
Flexible deformation is closed to be denoted as respectivelyWith(x, y) indicates horizontal, vertical seat of the contact point in Gear Contact coordinate system
Mark.For Gear Contact coordinate system as shown in Figure 1, B indicates the facewidth in figure, B/2 is half facewidth；L indicates the practical contact of a pair of of gear teeth
The length of line, L/2 are the half of wire length, also illustrate that the width of contact area；Δ indicates gear along the normal direction in engagement direction
Tooth pitch；β indicates helical angle；α indicates pressure angle；o1,o2Respectively indicate the center of gear 1 and gear 2；rbIndicate base radius；r
Indicate pitch radius；The value of coordinate x indicates that the position of contact area center line is right relative to i (i=1,2 ..., n are positive integer)
It is r that the position of the mid-plane of the contact line of tooth, which is one of base radius,bGear Angle Position θ function, x=rbθ。
The position of the contact area of the position and x=0 of θ=0 is overlapped；Y value indicates axial position one general contact point p in contact line
Position.Motion transmission error on any i-th pair gear teeth at contact point (x, y)For (1) formula or (2) formula, wherein quiet
State driving error
(2) calculating of dynamic displacement；
If the registration of gear pair is between 1~2, according to mechanical kinetics and mechanical vibration theory, a pair of of gear pair tooth
Dynamics lumped parameter model is taken turns as shown in figure 3, the model can be indicated with equation (3)-(6).
It is represented as being used to indicate flexibility when engaging, side along one column of path of contact direction attachment in this model middle gear
The rigid body disk of the element of gap and geometrical deviation.For the rotation displacement of the i-th pair tooth of driving wheel；Respectively the i-th of follower
To the rotation displacement of tooth；WithThe respectively first derivative and second dervative of the rotation displacement of the i-th pair tooth of driving wheel；With
The respectively first derivative and second dervative of the rotation displacement of the i-th pair tooth of follower；IjBased on, the rotary inertia of follower, j
=1,2 respectively represent active and passive wheel；mjBased on, by the quality of gear；ωjBased on, by the acceleration of gear；rjBased on, by tooth
The base radius of wheel；Based on, by the i-th pair tooth of gear engagement direction on dynamic displacement；For the edge of gear j
The bearing support rigidity of path of contact direction x；For the bearing damp coefficient along path of contact direction x of gear j；K (t) gear pair
Engage integral stiffness；C is that the engagement of gear pair damps；B is the sideshake of gear pair；It is missed for the entirety of the i-th tooth of driving wheel
Difference；For the global error of the i-th tooth of follower；TjIt (j=1,2) is the external applied load torque acted on active and passive gear.
Using the method for numerical solution, simultaneous equations (2)-(5) are solved, and are just obtainedWithDynamic displacementWithIt is calculated respectively with formula (7) and (8).
Then it by formula (1) or (2) formula, is passed in all meshing gears of gear-driven whole cycle to dynamic is sought respectively
Dynamic error, so that it may obtain the motion transmission error of gear pair.
The implementation method of motion transmission error prediction method based on gear global error is as follows:
1) coordinate system is constructed；Gear Contact coordinate system as shown in Figure 1 is constructed, B indicates the facewidth, and B/2 is half facewidth；L is indicated
The length of the practical contact line of a pair of of tooth, L/2 are the general of wire length, also illustrate that the width of contact area；Δ indicates gear
Normal pitch along engagement direction；β indicates helical angle；α indicates pressure angle；o1,o2Respectively indicate the center of gear 1 and gear 2；
rbIndicate base radius；R indicates pitch radius；I indicates the serial number of contact gear mesh, i (i=1,2 ..., n are positive integer)；
The position of the value expression contact area center line of coordinate x is relative to i (i=1,2 ..., n are positive integer) to the contact line of tooth
It is r that the position of mid-plane, which is one of base radius,bGear Angle Position θ function, x=rbθ.The position of θ=0 with
The position of the contact area of x=0 is overlapped；Y value indicates position of the one contact point p of axial position in contact line.
2) static driving error is calculatedBuilding coordinate system by the measurement of gear global error, tooth pair is installed
The sequence of contact be successively unfolded in engagement.According to the tooth for the tooth root promotion driven wheel for during gear drive being all driving wheel
The characteristics of top is successively engaged, in the case where engaging coordinate system, the tooth root of each unit of driving wheel withstands on the right side in left and right tooth, and curve indicates
Be global error from tooth root to tooth top, and passively the tooth root of each unit in right tooth top on a left side, what curve indicated be from
Global error of the tooth top to tooth root.Then according to static driving errorCalculate free gear
Static driving error, calculating process is as shown in figure 5, the global error of three gear teeth of 1,2,3 difference driving wheels in figure is bent
Line, a, b, c distinguish the global error curve of three gear teeth of follower.
3) dynamic displacement is calculatedWithUsing the method for numerical solution, simultaneous equations (2-5) are solved, just
It obtainsWithDynamic displacementWithIt can be calculated respectively with formula (9) and (10).
4) motion transmission error calculation
Motion transmission error on any i-th pair gear teeth at contact point (x, y)For (11) formula or (12) formula,
Middle static state driving error
Consider that error and operating condition intercouple the influence of effect, without structure is complicated and easily by measurement environmental disturbances
The motion transmission error prediction method based on gear global error of motion transmission error measuring device has the advantage that
1, it in the case where only obtaining gear static state geometric accuracy index, can be obtained only by the method for equation solution
Obtain the relatively accurate motion transmission error criterion of gear；
2, pass through the method with Gear integrated error measuring and numerical solution, so that it may obtain dynamic transmission error of gear, be
The acquisition of dynamic transmission error of gear provides a kind of new method；
3, this method can be also used for the monitoring and diagnosis of gear health situation, be the monitoring and diagnosis of gear train assembly
Provide a kind of new method；
4, this method is not only mentioned it is not necessary that structure is complicated and easily by the dynamic transmission error of gear measuring device of environmental disturbances
The precision of high driving error measurement also as save cost, brings biggish economic benefit；
5, this method is executed automatically by computer program, is avoided the interference for thinking factor, is improved driving error and refer to
Target precision and confidence level；
6, this method can predict the motion transmission error of gear when knowing gear static state geometric error, be gear
Dynamic design provides a kind of new method, gear dynamic can be instructed to design.
Detailed description of the invention
Fig. 1 Gear Contact coordinate system
Fig. 2 gear error indicates
Fig. 3 nonlinear dynamic behavior lumped parameter model
Fig. 4 dynamic transmission error of gear predicts calculation process
Fig. 5 gear pair static state driving error synthesis flow
Specific embodiment
1) coordinate system is constructed；Gear Contact coordinate system as shown in Figure 1 is constructed, B indicates the facewidth, and B/2 is half facewidth；L is indicated
The length of the practical contact line of a pair of of tooth, L/2 are the general of wire length, also illustrate that the width of contact area；Δ indicates gear
Normal pitch along engagement direction；β indicates helical angle；α indicates pressure angle；o1,o2Respectively indicate the center of gear 1 and gear 2；
rbIndicate base radius；R indicates pitch radius；I indicates the serial number of contact gear mesh, i (i=1,2 ..., n are positive integer)；
The position of the value expression contact area center line of coordinate x is relative to i (i=1,2 ..., n are positive integer) to the contact line of tooth
It is r that the position of mid-plane, which is one of base radius,bGear Angle Position θ function, x=rbθ.The position of θ=0 with
The position of the contact area of x=0 is overlapped；Y value indicates position of the one contact point p of axial position in contact line.
2) static driving error is calculatedBuilding coordinate system by the measurement of gear global error, tooth pair is installed
The sequence of contact be successively unfolded in engagement.Driven wheel is pushed according to the tooth root for during gear drive being typically all driving wheel
Tooth top the characteristics of successively engaging, in the case where engaging coordinate system, the tooth root of each unit of driving wheel withstands on the right side, curve in left and right tooth
What is indicated is global error from tooth root to tooth top, and passively the tooth root of each unit is indicated in right tooth top on a left side, curve
It is the global error from tooth top to tooth root.Then according to static driving errorWork can be calculated
The static driving error of moving gear, calculating process is as shown in figure 5,1,2,3 in figure distinguish the whole of three gear teeth of driving wheels
Body error curve, a, b, c distinguish the global error curve of three gear teeth of follower.
3) dynamic displacement is calculatedWithUsing the method for numerical solution, simultaneous equations (2-5) are solved, just
It obtainsWithDynamic displacementWithIt can be calculated respectively with formula (9) and (10).
4) motion transmission error calculation
Motion transmission error on any i-th pair gear teeth at contact point (x, y)For (11) formula or (12) formula,
Middle static state driving error
Claims (1)
1. the motion transmission error prediction method based on gear global error, it is characterised in that: dynamic based on gear global error
State driving error prediction technique is to consider to miss based on the global error data for obtaining gear using integral error measuring technology
Difference and the operating condition effect of intercoupling construct the nonlinear kinetics prediction model of gear dynamic transmission prediction；Firstly, in basis
The coordinate system of gear engaged transmission principle building obtains gear static state driving error using Gear integrated error measuring data；So
Afterwards, the dynamic displacement of prediction model is obtained using the method for numerical solution；The interaction principle for finally utilizing gear error, is closed
At dynamic transmission error of gear；This method can be applicable in the requirement of complex environment and consider that error and operating condition are mutual
The requirement of coupling；Used method content includes:
(1) expression of dynamic transmission error of gear；The motion transmission error of i-th pair gear, gear in transfer motion power, gear
There is only mismachining tolerances in contact point for the gear teeth, and there are flexible deformation, the i-th pair gear teeth of master and slave gear in contact point
Along path of contact direction at (x, y), i indicates the serial number of contact gear mesh, and i=1,2 ..., n are positive integer, master and slave gear
Global error is denoted as respectivelyWithAlong path of contact direction it is loaded after, the comprehensive elastic deformation of master and slave gear point
It is not denoted asWith(x, y) indicates cross, ordinate of the contact point in Gear Contact coordinate system；Gear Contact is sat
Mark system, B indicate the facewidth, and B/2 is half facewidth；L indicates the length of the practical contact line of a pair of of gear teeth, and L/2 is the one of wire length
Half, also illustrate that the width of contact area；Δ indicates gear along the normal pitch in engagement direction；β indicates helical angle；α indicates pressure
Angle；o1,o2Respectively indicate the center of gear 1 and gear 2；rbIndicate base radius；R indicates pitch radius；The value of coordinate x indicates
The position of contact area center line, to the position of the mid-plane of the contact line of tooth, is that one of base radius is relative to i
rbGear Angle Position θ function, x=rbθ；The position of the contact area of the position and x=0 of θ=0 is overlapped；Y value indicates axis
To position of the contact point p of position one in contact line；Motion transmission error on any i-th pair gear teeth at contact point (x, y)For (1) formula or (2) formula, wherein static driving error
(2) calculating of dynamic displacement；
If the registration of gear pair is between 1~2, according to mechanical kinetics and mechanical vibration theory, a pair of of gear pinion is dynamic
Mechanics lumped parameter model is indicated with equation (3)-(6)；
This model middle gear be represented as along path of contact direction attachment one column for indicates engage when flexibility, sideshake and
The rigid body disk of the element of geometrical deviation；For the rotation displacement of the i-th pair tooth of driving wheel；The respectively i-th pair of follower
The rotation displacement of tooth；WithThe respectively first derivative and second dervative of the rotation displacement of the i-th pair tooth of driving wheel；With
The respectively first derivative and second dervative of the rotation displacement of the i-th pair tooth of follower；IjBased on, the rotary inertia of follower, j
=1,2 respectively represent active and passive wheel；mjBased on, by the quality of gear；ωjBased on, by the acceleration of gear；rjBased on, by tooth
The base radius of wheel；Based on, by the i-th pair tooth of gear engagement direction on dynamic displacement；It is gear j along path of contact
The bearing support rigidity of direction x, j=1,2；For the bearing damp coefficient along path of contact direction x of gear j；K (t) gear pair
Engagement integral stiffness；C is that the engagement of gear pair damps；B is the sideshake of gear pair；It is missed for the entirety of the i-th tooth of driving wheel
Difference；For the global error of the i-th tooth of follower；TjFor the external applied load torque acted on active and passive gear；Utilize numerical value
The method of solution, simultaneous equations (2)-(5) solve, and just obtainWithComprehensive elastic deformationWithIt is calculated respectively with formula (7) and (8)；
Then it by formula (1) or (2) formula, is missed in all meshing gears of gear-driven whole cycle to motion transmission is sought respectively
Difference just obtains the motion transmission error of gear pair.
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| CN108050946B (en) * | 2017-11-30 | 2019-07-16 | 北京工业大学 | A kind of gear tooth thickness measurement method based on line-structured light |
| CN108052760B (en) * | 2017-12-25 | 2021-03-16 | 长安大学 | Nonlinear dynamics calculation method for gear pair |
| CN109489599B (en) * | 2018-11-12 | 2020-01-24 | 北京工业大学 | Self-calibration involute gear pair vibration displacement and dynamic transmission error measurement method |
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| CN109282986A (en) * | 2018-11-14 | 2019-01-29 | 北京工业大学 | Plastic Gear Transmission error testing testing stand |
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| CN111060309B (en) * | 2020-01-17 | 2021-09-10 | 瑞斯恩智能科技(苏州)有限公司 | Gear detection machine and detection method |
| CN112182803B (en) * | 2020-09-29 | 2024-05-14 | 南京高速齿轮制造有限公司 | Excitation calibration method of dynamic model |
| CN113063589B (en) * | 2021-03-18 | 2023-07-04 | 重庆青山工业有限责任公司 | Gear microscopic error vibration prediction method based on neural network |
| CN113607409B (en) * | 2021-10-08 | 2021-12-17 | 山东世纪智慧农业科技有限公司 | Testing system and method for gear |
| CN115143922B (en) * | 2022-06-19 | 2023-09-26 | 北京工业大学 | Gear tooth surface roughness measurement and evaluation method for transmission performance analysis |
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