CN108062452A - A kind of arc-shaped tooth worm decelerating machine evaluation of dynamic and optimization method - Google Patents

A kind of arc-shaped tooth worm decelerating machine evaluation of dynamic and optimization method Download PDF

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CN108062452A
CN108062452A CN201810015268.0A CN201810015268A CN108062452A CN 108062452 A CN108062452 A CN 108062452A CN 201810015268 A CN201810015268 A CN 201810015268A CN 108062452 A CN108062452 A CN 108062452A
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worm
dynamic
decelerating machine
gear
frequency
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吉卫喜
范小斌
马玉娟
李春涛
程峰
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Haian Shenling Electrical Appliance Manufacturing Co., Ltd.
Jiangnan University
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Haian Shenling Electrical Appliance Manufacturing Co Ltd
Jiangnan University
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Abstract

A kind of arc-shaped tooth worm decelerating machine evaluation of dynamic and optimization method, belong to lifting conveyance engineering device technique field, kinetic model structure and parameter identification are carried out to worm decelerating machine, and combine finite element analysis software and carry out Dynamic Performance Analysis, obtain worm decelerating machine vibration displacement, vibration velocity and vibration acceleration time domain response;Fast Fourier Transform (FFT) is carried out to time domain response signal, is obtained using frequency as independent variable, using form signal each frequency content amplitude as the frequency function of dependent variable, frequency-domain analysis is used to determine the authenticity of potential resonance point;Gear train Coupling Dynamic Model is established based on lumped parameter method on this basis, establishes optimization object function, builds Dynamic performance Optimization model, optimum optimization configuration is solved, so as to optimize worm decelerating machine complete machine dynamic property.

Description

A kind of arc-shaped tooth worm decelerating machine evaluation of dynamic and optimization method
Technical field
The invention belongs to lifting conveyance engineering device technique fields, and in particular to arc-shaped tooth worm decelerating machine dynamic property Optimization method.
Background technology
In speed reducer Dynamic Performance Analysis, model analysis is most basic content.Model analysis be using Theory of Vibration as Basis by calculating machine structure or vibration characteristics-eigenfrequncies and vibration models of machine components, carries out direct dynamic property Estimation.Model analysis can be as other dynamic analysis problems such as transient dynamic analysis, harmonic responding analysis and spectrum analysis Starting point.
Transient dynamic analysis is to determine the technology of the load effect lower structure response changed over time, and Transient Dynamics are Carry out time-domain analysis.Input stimulus are the load changed over time, and what is be obtained is real-time response of the structure to dynamic loading.Its load The load come usually is summarized from real load, impact loading response etc. is can be particularly used for and is analyzed.
In the retarder course of work, since the tooth logarithm for simultaneously participating in engagement changes over time, cause gear teeth meshing rigidity Change with gear teeth elastic deformation amount also generating period, the influence of the factors such as foozle and installation error in addition, it would be possible to make Into gear teeth meshing impact and situations such as unbalance loading, vibration and noise so as to cause gear train.Current worm decelerating machine design In, designer is mainly from the static strength and Static stiffness of the function of product, dimensional parameters, kinematic parameter, kinetic parameter and structure Angle is set out, and is designed by rule of thumb with Analogy, considers deficiency to the dynamic property of worm decelerating machine in design.However snail The dynamic property of bar speed reducer structure has a great impact to its working performance, efficiency, stability and reliability etc., it has been at present The important indicator of worm decelerating machine structural behaviour quality is weighed through becoming.
The content of the invention
The purpose of the present invention is be directed to finite element model foundation side present in existing worm decelerating machine Dynamic Performance Analysis The problem of accuracy of method is poor, precision is low, provides a kind of worm decelerating machine evaluation of dynamic and optimum design method, can be to whole Machine dynamic property is accurately assessed, and then its dynamic property is optimized.
A kind of arc-shaped tooth worm decelerating machine evaluation of dynamic and optimization method, comprise the following steps:
1)Worm decelerating machine physical model is established according to worm decelerating machine 2 D Part Drawings, under assembly modeling environment, first It determines main parts size rigging position benchmark, physical model is then established using parametric method;
2)Physical model part is simplified, the screw coupling member of material identical is carried out physical model boolean merges fortune It calculates, entity simplified model is converted into .stp forms imports in software ANSYS Workbench;
3)Mesh generation is carried out to simplifying physical model, the mesh generation side that tetrahedron element and hexahedral element is selected to be combined Method establishes complete machine finite element model, wherein worm gear, worm screw, worm gear seat, and output shaft uses hexahedron solid element, babinet, bearing, End cap uses tetrahedral solid elements.Unit size is complicated according to worm decelerating machine practical structures size reasonable selected as 15mm Position need to carry out local refinement;
4)The feasible simulation on the surface to contact with each other between speed reducer parts, i.e. " faying face ":Gear shaft and gear faying face Processing method be that gear and gear shaft corresponding node are coupled in all directions;Bearing and gear shaft and bearing block The processing of faying face is that bearing is radially, axially all being coupled with gear shaft corresponding node, circumferential not to couple, bearing block and case Body corresponding node is coupled in all directions;The processing of bearing (ball) cover is that corresponding node whole on faying face is carried out coupling It closes;
5)Model analysis is carried out to worm decelerating machine using Block Lanczos methods in ANSYS Workbench softwares, is obtained The intrinsic frequency and natural mode of vibration of 20 ranks, allow the rotational frequency of worm gear pair and the meshing frequency to avoid speed reducer before worm decelerating machine Intrinsic frequency, avoid resonating so as to reach, the purpose of vibration and noise reducing;
6)Complete machine Dynamic Performance Analysis:Complete machine dynamic is carried out by ANSYS Workbench software transient dynamic analysis module Response analysis obtains worm decelerating machine vibration displacement, vibration velocity and vibration acceleration time domain response;To time domain response signal into Row Fast Fourier Transform (FFT) is obtained using frequency as independent variable, using form signal each frequency content amplitude as dependent variable frequency Rate function, for reaffirming the authenticity of potential resonance point.
7)Dynamic performance Optimization:To input the minimum worm decelerating machine Dynamic performance Optimization of the vibration acceleration amplitude of worm screw Object function, with the parameter being affected to dynamic performance, such as the head number of worm screw, modulus, worm spiral angle, worm gear become Potential coefficient, worm screw flank profil radius, with worm gear pair assembly relation etc. for constraints, it is motor-driven to establish worm speed-down as design variable State Performance Model writes mixed discrete optimization program based on Matlab platforms and obtains optimal design variable and object function Value.
The concrete operations of simplified model include:
(1)Without considering knuckle, bolt hole, boss and groove everywhere.After simplification to the quality and rigidity of speed reducer not Too much influence can be generated, computational accuracy can be completely secured.
(2)By the worm gear of speed reducer and the connection of worm gear seat, the connection of worm gear seat and axis and consideration is bolted into firm Property connection.
(3)Bearing arrangement Property comparison is complicated, is simulated with stiffness spring.
Frequency-domain analysis is carried out to the potential resonance point that time-domain analysis is found out, if frequency-domain analysis can exclude all resonance Point, that illustrates that the worm decelerating machine dynamic property is good, if frequency-domain analysis show that a certain or certain several resonance point really may Cause the resonance of speed reducer complete machine, verification experimental verification can be carried out first, after overtesting is reaffirmed, it is necessary to worm decelerating machine Relevant parameter optimize.
The worm decelerating machine Dynamic performance Optimization method includes:
(1)Gear train Coupling Dynamic Model is established based on lumped parameter method, oscillatory differential equation group is as follows:
In above formula:m1、m2Respectively effective mass of the worm and worm wheel in its pitch radius, general formula are m=J/r, here J It is rotary inertia, r is pitch radius;I1y、I2xThe respectively concentration rotary inertia of worm and worm wheel;x1、z1And y1For worm screw point Axial vibratory displacement not along the x-axis direction with the transverse vibrational displacement in z-axis direction and along the y-axis direction;y2、z2And x2For worm gear point Not along y-axis, the oscillation crosswise in z-axis direction and axial vibratory displacement along the x-axis direction;θy1And θx2For worm and worm wheel rotating around The torsion angle of respective central shaft;α is normal pitch pressure angle;γ is the helical angle of worm screw;r1For the pitch radius of worm screw;rmFor worm gear Pitch radius;Fx1、Fy1、Fz1For the force of periphery, axial force and radial load of worm screw;Fx2、Fy2、Fz2Axial force, circle for worm gear Zhou Li and radial load.Wherein, Fx1=﹣ Fx2、Fy1=﹣ Fy2、Fz1=﹣ Fz2
(2)Using Fourth order Runge-Kutta solving system oscillatory differential equation, obtain each component vibration of worm decelerating machine and ring It should be worth;
(3)Vibration acceleration amplitude minimal construction object function based on input shaft worm screw, with parameters such as worm gear pair modulus, the numbers of teeth For design variable, worm gear pair intensity, rigidity and assembly relation etc. are constraints, establish the dynamic of worm decelerating machine gear train Performance Model obtains worm gear pair optimal design variable.
Description of the drawings
Fig. 1 is the model of vibration based on the theoretical worm decelerating machine bending axis coupling established of lumped parameter.
Specific embodiment
A kind of arc-shaped tooth worm decelerating machine evaluation of dynamic and optimization method, comprise the following steps:
Step 1 establishes worm decelerating machine physical model according to worm decelerating machine 2 D Part Drawings, under assembly modeling environment, Main parts size rigging position benchmark is determined first, and physical model is then established using parametric method.
Step 2 simplifies physical model part, and the screw coupling member of material identical is carried out physical model boolean Entity simplified model is converted into .stp forms and imported in software ANSYS Workbench by union operation.
Step 3 carries out mesh generation to simplifying physical model, the net that tetrahedron element and hexahedral element is selected to be combined Lattice division methods establish complete machine finite element model, wherein worm gear, and worm screw, worm gear seat, output shaft is using hexahedron solid element, case Body, bearing, end cap use tetrahedral solid elements.Unit size is according to worm decelerating machine practical structures size reasonable selected as 15mm, complex region need to carry out local refinement.
The feasible simulation on the surface to contact with each other between step 4, speed reducer parts, i.e. " faying face ":Gear shaft and tooth The processing method for taking turns faying face is that gear and gear shaft corresponding node are coupled in all directions;Bearing and gear shaft And the processing of bearing block faying face is that bearing is radially, axially all being coupled with gear shaft corresponding node, circumferential not to couple, axis Bearing is coupled with babinet corresponding node in all directions;The processing of bearing (ball) cover is by corresponding node whole on faying face It is coupled.
Step 5 carries out mode using Block Lanczos methods in ANSYS Workbench softwares to worm decelerating machine Analysis, has obtained the intrinsic frequency and natural mode of vibration of 20 ranks before worm decelerating machine, allows the rotational frequency and meshing frequency of worm gear pair The intrinsic frequency of speed reducer is avoided, avoids resonating so as to reach, the purpose of vibration and noise reducing.
Step 6, complete machine Dynamic Performance Analysis:It is carried out by ANSYS Workbench software transient dynamic analysis module Complete machine the Dynamic Response obtains worm decelerating machine vibration displacement, vibration velocity and vibration acceleration time domain response;Time domain is rung Induction signal carry out Fast Fourier Transform (FFT), obtain using frequency as independent variable, using form signal each frequency content amplitude as because The frequency function of variable, for reaffirming the authenticity of potential resonance point.
Step 7, Dynamic performance Optimization:To input the minimum worm decelerating machine dynamic property of the vibration acceleration amplitude of worm screw The object function of optimization, with the parameter being affected to dynamic performance, such as the head number of worm screw, modulus, worm spiral angle, snail Modification coefficient, worm screw flank profil radius are taken turns as design variable, with worm gear pair assembly relation etc. for constraints, establishes worm speed-down Machine dynamic property Optimized model writes mixed discrete optimization program based on Matlab platforms and obtains optimal design variable and target letter Numerical value.
The concrete operations of simplified model include:
(1)Without considering knuckle, bolt hole, boss and groove everywhere.After simplification to the quality and rigidity of speed reducer not Too much influence can be generated, computational accuracy can be completely secured.
(2)By the worm gear of speed reducer and the connection of worm gear seat, the connection of worm gear seat and axis and consideration is bolted into firm Property connection.
(3)Bearing arrangement Property comparison is complicated, is simulated with stiffness spring.
The surface to contact with each other between speed reducer parts is known as " faying face ".Speed reducer is usually in the ring of complicated dynamic loading It works in border, this so that between its faying face multiple degrees of freedom, the micro breadth oscillation for having damping can be generated, and faying face is made to show complexity Dynamic characteristic.This characteristic will generate significant impact to the dynamic characteristic of speed reducer entirety.Therefore, speed reducer entirety is established After finite element model, when studying its dynamic characteristic, the influence of faying face be can not ignore, it is necessary to which it is reasonably simulated.
1)The processing of gear shaft and gear faying face:Gear shaft and gear are in elastic conjunction state.The place of the faying face Reason method is that gear and gear shaft corresponding node are coupled in all directions.
2)The processing of bearing and gear shaft and bearing block faying face:Bearing is with gear shaft corresponding node radially, axially complete Portion couples, circumferential not to couple.Bearing block is coupled with babinet corresponding node in all directions.
3)The processing of bearing (ball) cover:This faying face is smaller on the dynamic characteristic influence of speed reducer entirety, in actual calculating When corresponding node whole on faying face is coupled.
Frequency-domain analysis is carried out to the potential resonance point that time-domain analysis is found out, if frequency-domain analysis can exclude all resonance Point, that illustrates that the worm decelerating machine dynamic property is good, if frequency-domain analysis show that a certain or certain several resonance point really may Cause the resonance of speed reducer complete machine, verification experimental verification can be carried out first, after overtesting is reaffirmed, it is necessary to worm decelerating machine Relevant parameter optimize.
The worm decelerating machine Dynamic performance Optimization method includes:
(1)As shown in Figure 1, establishing gear train Coupling Dynamic Model based on lumped parameter method, oscillatory differential equation group is as follows:
In formula:m1、m2Respectively effective mass of the worm and worm wheel in its pitch radius, general formula are m=J/r, wherein, J is Rotary inertia, r are pitch radius;
I1y、I2xThe respectively concentration rotary inertia of worm and worm wheel;
x1、z1And y1For the axial vibration position of worm screw respectively along the x-axis direction with the transverse vibrational displacement in z-axis direction and along the y-axis direction It moves;
y2、z2And x2It is worm gear respectively along y-axis, the oscillation crosswise in z-axis direction and axial vibratory displacement along the x-axis direction;
θy1And θx2It is worm and worm wheel rotating around the torsion angle of respective central shaft;
α is normal pitch pressure angle;
γ is the helical angle of worm screw;
r1For the pitch radius of worm screw;
rmFor the pitch radius of worm gear;
Fx1、Fy1、Fz1For the force of periphery, axial force and radial load of worm screw;
Fx2、Fy2、Fz2For the axial force, the force of periphery and radial load of worm gear.Wherein, Fx1=﹣ Fx2、Fy1=﹣ Fy2、Fz1=﹣ Fz2
Fig. 1 is using the theoretical multiple degrees of freedom coupling dynamical model established of lumped parameter:The axis of worm screw is in the model y1Axis, the axis of worm gear is x2Axis, two axial lines serrated vertical.T 1WithT 2Respectively input torque and loading moment;c ij Withk ij (i= 1,2;j=x, y, z) it is respectively damping and rigidity of the spring bearing along x, y and z axes direction;ω1、ω2Respectively worm and worm wheel Rotational angular velocity;C m It is damped for the engagement of worm gear pair;K m For the average mesh stiffness of worm gear pair;e(t)For worm gear pair driving error. The model of vibration of worm gear pair is processed into 8 degree of freedom, generalized displacement array can be expressed asF}={x1, y1, z1,θ y1, x2, y2, z2, θx2}Tx 1z 1Withy 1It is worm screw respectively along x-axis, the oscillation crosswise in z directions and axial vibration in the y-direction;y2、z2And x2 It is worm gear respectively along y-axis, the oscillation crosswise in z-axis direction and axial vibration along the x-axis direction;θ y1Withθ x2For worm and worm wheel point Not around the twisting vibration of respective central shaft.Translation freedoms and rotational freedom are respectively coupled in equation, and this coupling is existing As if as caused by the intermeshing of the gear teeth so that the translational vibration of worm gear pair interacts with twisting vibration, therefore establishes Worm gear pair vibration analysis model for engagement type it is curved-turn round coupling dynamical model.
(2)Using Fourth order Runge-Kutta solving system oscillatory differential equation, obtain each component vibration of worm decelerating machine and ring It should be worth.
(3)Vibration acceleration amplitude minimal construction object function based on input shaft worm screw, with worm gear pair modulus, number of teeth etc. Parameter is that design variable, worm gear pair intensity, rigidity and assembly relation etc. is constraints, establishes worm decelerating machine gear train Dynamic performance Optimization model obtains worm gear pair optimal design variable.

Claims (3)

1. a kind of arc-shaped tooth worm decelerating machine evaluation of dynamic and optimization method, which is characterized in that comprise the following steps:
1)Worm decelerating machine physical model is established according to worm decelerating machine 2 D Part Drawings, under assembly modeling environment, first It determines main parts size rigging position benchmark, physical model is then established using parametric method;
2)Physical model part is simplified, the screw coupling member of material identical is carried out physical model boolean merges fortune It calculates, entity simplified model is converted into .stp forms imports in software ANSYS Workbench;
3)Mesh generation is carried out to simplifying physical model, the mesh generation side that tetrahedron element and hexahedral element is selected to be combined Method establishes complete machine finite element model, wherein worm gear, worm screw, worm gear seat, and output shaft uses hexahedron solid element, babinet, bearing, End cap uses tetrahedral solid elements;Unit size is complicated according to worm decelerating machine practical structures size reasonable selected as 15mm Position grid need to carry out local refinement;
4)The feasible simulation on the surface to contact with each other between speed reducer parts, i.e. " faying face ":Gear shaft and gear faying face Processing method be that gear and gear shaft corresponding node are coupled in all directions;Bearing and gear shaft and bearing block The processing of faying face is that bearing is radially, axially all being coupled with gear shaft corresponding node, circumferential not to couple, bearing block and case Body corresponding node is coupled in all directions;The processing of bearing (ball) cover is that corresponding node whole on faying face is carried out coupling It closes;
5)Model analysis is carried out to worm decelerating machine using Block Lanczos methods in ANSYS Workbench softwares, is obtained The intrinsic frequency and natural mode of vibration of 20 ranks, allow the rotational frequency of worm gear pair and the meshing frequency to avoid speed reducer before worm decelerating machine Intrinsic frequency;
6)Dynamic Performance Analysis:The Dynamic Response is carried out by ANSYS Workbench software transient dynamic analysis module, Obtain worm decelerating machine vibration displacement, vibration velocity and vibration acceleration time domain response;Quick Fu is carried out to time domain response signal In leaf transformation, obtain using frequency as independent variable, using form signal each frequency content amplitude as dependent variable frequency function, use In the authenticity for reaffirming potential resonance point;
7)Dynamic performance Optimization:To input the mesh of the minimum worm decelerating machine Dynamic performance Optimization of the vibration acceleration amplitude of worm screw Scalar functions, using the head number of worm screw, modulus, worm spiral angle, addendum modification coefficient of wormwheel, worm screw flank profil radius as design variable, with Worm gear pair assembly relation is constraints, establishes worm decelerating machine Dynamic performance Optimization model, is write based on Matlab platforms mixed It closes discrete optimization program and obtains optimal design variable and target function value.
2. worm decelerating machine evaluation of dynamic according to claim 1 and optimization method, which is characterized in that the time domain The potential resonance point found out in response signal carries out frequency-domain analysis, if frequency-domain analysis can exclude all resonance points, worm screw Speed reducer dynamic property is good, if frequency-domain analysis show that a certain or certain several resonance point may cause being total to for speed reducer really It shakes, verification experimental verification can be carried out first, it is necessary to be carried out to the relevant parameter of worm decelerating machine excellent after overtesting is reaffirmed Change.
3. worm decelerating machine evaluation of dynamic according to claim 1 and optimization method, which is characterized in that the worm screw Speed reducer dynamic property optimization method includes:
1)Gear train Coupling Dynamic Model is established based on lumped parameter method, oscillatory differential equation group is as follows:
In formula:
m1、m2Respectively effective mass of the worm and worm wheel in its pitch radius, general formula are m=J/r, and wherein J is to rotate to be used to Amount, r is pitch radius;
I1y、I2xThe respectively concentration rotary inertia of worm and worm wheel;
x1、z1And y1For the axial vibration position of worm screw respectively along the x-axis direction with the transverse vibrational displacement in z-axis direction and along the y-axis direction It moves;
y2、z2And x2It is worm gear respectively along y-axis, the oscillation crosswise in z-axis direction and axial vibratory displacement along the x-axis direction;
θy1And θx2It is worm and worm wheel rotating around the torsion angle of respective central shaft;
α is normal pitch pressure angle;
γ is the helical angle of worm screw;
r1For the pitch radius of worm screw;
rmFor the pitch radius of worm gear;
Fx1、Fy1、Fz1For the force of periphery, axial force and radial load of worm screw;
Fx2、Fy2、Fz2For the axial force, the force of periphery and radial load of worm gear, wherein, Fx1=﹣ Fx2、Fy1=﹣ Fy2、Fz1=﹣ Fz2
kx1And cx1Respectively worm screw is supported on circumferential stiffness coefficient and damped coefficient;
ky1And cy1Respectively worm screw is supported on axial stiffness coefficient and damped coefficient;
kz1And cz1Respectively worm screw is supported on the stiffness coefficient and damped coefficient of radial direction;
kx2And cx2Respectively worm gear is supported on axial stiffness coefficient and damped coefficient;
ky2And cy2Respectively worm gear is supported on circumferential stiffness coefficient and damped coefficient;
kz2And cz2Respectively worm gear is supported on the stiffness coefficient and damped coefficient of radial direction;
2)Using Fourth order Runge-Kutta solving system oscillatory differential equation, each component vibratory response value of worm decelerating machine is obtained;
3)Vibration acceleration amplitude minimal construction object function based on input shaft worm screw, with parameters such as worm gear pair modulus, the numbers of teeth For design variable, worm gear pair intensity, rigidity and assembly relation etc. are constraints, establish the dynamic of worm decelerating machine gear train Performance Model obtains worm gear pair optimal design variable.
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CN109002608A (en) * 2018-07-16 2018-12-14 太原科技大学 A kind of ladle carne dynamic optimization method considering driver's comfort
CN109543340A (en) * 2018-12-07 2019-03-29 海安县申菱电器制造有限公司 A kind of modeling method of nonlinear contact arc-shaped tooth
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CN111337246A (en) * 2020-03-26 2020-06-26 海安市申菱电器制造有限公司 Dynamic performance evaluation and optimization method for arc-shaped tooth surface worm speed reducer
CN112632699A (en) * 2020-12-21 2021-04-09 华南理工大学 Method for optimizing performance of dual-mass flywheel based on uncertain parameters
CN113987713A (en) * 2021-11-04 2022-01-28 华北电力大学 Wind turbine generator gearbox helical angle optimization method and system
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