CN108062452B - 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 PDFInfo
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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 building and parameter identification are carried out to worm decelerating machine, and finite element analysis software is combined to 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, constructs Dynamic performance Optimization model, optimum optimization configuration is solved, to optimize worm decelerating machine complete machine dynamic property.
Description
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 technique
In speed reducer Dynamic Performance Analysis, model analysis is most basic content.Model analysis is to be with Theory of Vibration
Basis carries out direct dynamic property by calculating machine structure or vibration characteristics-eigenfrequncies and vibration models of machine components
Estimation.Model analysis can be used as other dynamic analysis problems such as transient dynamic analysis, harmonic responding analysis and spectrum analysis
Starting point.
Transient dynamic analysis is the technology for determining the load effect flowering structure response changed over time, and Transient Dynamics are
Carry out time-domain analysis.Input stimulus is the load changed over time, and what is found out is real-time response of the structure to dynamic loading.Its load
The load come usually is summarized from real load, be can be particularly used for impact loading response etc. and is analyzed.
In the retarder course of work, the tooth logarithm due to simultaneously participating in engagement is changed over time, and leads to 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
Situations such as at gear teeth meshing impact and 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, is considered in design the dynamic property of worm decelerating machine insufficient.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 measured through becoming.
Summary of the invention
The purpose of the present invention is for finite element model foundation side present in existing worm decelerating machine Dynamic Performance Analysis
The problem that the 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
Motor-driven state property can be carried out accurate assessment, then optimize to its dynamic property.
A kind of arc-shaped tooth worm decelerating machine evaluation of dynamic and optimization method, comprising the following steps:
1) worm decelerating machine physical model is established 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；
2) physical model part is simplified, the identical screw coupling member of material is subjected to physical model boolean merging
Operation converts .stp format for entity simplified model and imports in software ANSYS Workbench；
3) to physical model progress grid dividing is simplified, the grid for selecting tetrahedron element and hexahedral element to combine is drawn
Point method establishes complete machine finite element model, wherein worm gear, worm screw, worm gear seat, and output shaft uses hexahedron solid element, cabinet,
Bearing, end cap use tetrahedral solid elements.Unit size is selected as 15mm according to worm decelerating machine practical structures size reasonable,
Complex region need to carry out local refinement；
4) surface to contact with each other between speed reducer components, the i.e. feasible simulation of " faying face ": gear shaft and gear knot
The processing method in conjunction face is that gears and gears axis corresponding node is coupled in all directions；Bearing and gear shaft and axis
The processing for holding a faying face is that bearing is radially, axially all being coupled with gear shaft corresponding node, circumferential not to couple, bearing block
It is coupled with cabinet corresponding node in all directions；The processing of bearing (ball) cover is to carry out corresponding node whole on faying face
Coupling；
5) model analysis is carried out to worm decelerating machine using Block Lanczos method in ANSYS Workbench software,
The intrinsic frequency and natural mode of vibration of 20 ranks before worm decelerating machine have been obtained, the rotational frequency of worm gear pair and meshing frequency is allowed to avoid subtracting
The intrinsic frequency of fast machine avoids resonating to reach, the purpose of vibration and noise reducing；
6) complete machine Dynamic Performance Analysis: complete machine is carried out by ANSYS Workbench software transient dynamic analysis module
The Dynamic Response obtains worm decelerating machine vibration displacement, vibration velocity and vibration acceleration time domain response；Time domain response is believed
Number carry out Fast Fourier Transform (FFT), obtain using frequency as independent variable, using form signal each frequency content amplitude as dependent variable
Frequency function, for reaffirming the authenticity of potential resonance point.
7) Dynamic performance Optimization: the minimum worm decelerating machine Dynamic performance Optimization of vibration acceleration amplitude to input worm screw
Objective function, with the parameter being affected to dynamic performance, such as the head number of worm screw, modulus, worm spiral angle, worm gear become
It is motor-driven to establish worm speed-down with worm gear pair assembly relation etc. for constraint condition as design variable for potential coefficient, worm screw flank profil radius
State Performance Model writes mixed discrete optimization program based on Matlab platform and obtains optimal design variable and objective function
Value.
The concrete operations of simplified model include:
(1) knuckle, bolt hole, boss and groove everywhere is not considered.To the quality of speed reducer and just after simplification
Degree will not generate too much influence, and 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 at rigid
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 and needed after overtesting is reaffirmed 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, this
In J be rotary inertia, r is pitch radius；I1y、I2xThe respectively concentration rotary inertia of worm and worm wheel；x1、z1And y1For worm screw
Axial vibratory displacement along the x-axis direction with the transverse vibrational displacement in z-axis direction and along the y-axis direction respectively；y2、z2And x2For worm gear
Respectively 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 difference
Around the torsion angle of respective central axis；α is normal pitch pressure angle；γ is the helical angle of worm screw；r1For the pitch radius of worm screw；rmFor snail
The pitch radius of wheel；Fx1、Fy1、Fz1For the force of periphery, axial force and radial force of worm screw；Fx2、Fy2、Fz2For worm gear axial force,
The force of periphery and radial force.Wherein, Fx1=﹣ Fx2、Fy1=﹣ Fy2、Fz1=﹣ Fz2。
(2) Fourth order Runge-Kutta solving system oscillatory differential equation is used, each component vibration of worm decelerating machine is obtained and rings
It should be worth；
(3) the vibration acceleration amplitude minimal construction objective function based on input shaft worm screw, with worm gear pair modulus, number of teeth etc.
Parameter is design variable, and worm gear pair intensity, rigidity and assembly relation etc. are constraint condition, establishes worm decelerating machine gear train
Dynamic performance Optimization model obtains worm gear pair optimal design variable.
Detailed description of the invention
Fig. 1 is the model of vibration for the worm decelerating machine bending axis coupling established based on lumped parameter theory.
Specific embodiment
A kind of arc-shaped tooth worm decelerating machine evaluation of dynamic and optimization method, comprising the following steps:
Step 1 establishes worm decelerating machine physical model according to worm decelerating machine 2 D Part Drawings, in assembly modeling environment
Under, it is first determined then main parts size rigging position benchmark establishes physical model using parametric method.
Step 2 simplifies physical model part, and the identical screw coupling member of material is carried out physical model boolean
Union operation converts .stp format for entity simplified model and imports in software ANSYS Workbench.
Step 3 carries out grid dividing to simplified physical model, the net for selecting tetrahedron element and hexahedral element to combine
Lattice division methods establish complete machine finite element model, wherein worm gear, worm screw, worm gear seat, and output shaft uses hexahedron solid element, case
Body, bearing, end cap use tetrahedral solid elements.Unit size is selected as according to worm decelerating machine practical structures size reasonable
15mm, complex region need to carry out local refinement.
The surface to contact with each other between step 4, speed reducer components, the i.e. feasible simulation of " faying face ": gear shaft and tooth
The processing method for taking turns faying face is that gears and gears axis corresponding node is 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
It holds seat and is coupled with cabinet 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 to worm decelerating machine using Block Lanczos method in ANSYS Workbench software
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 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 carries out Fast Fourier Transform (FFT), obtains 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: the minimum worm decelerating machine dynamic property of vibration acceleration amplitude to input worm screw
The objective function of optimization, with the parameter being affected to dynamic performance, such as the head number, modulus, worm spiral angle, snail of worm screw
Wheel modification coefficient, worm screw flank profil radius establish worm speed-down with worm gear pair assembly relation etc. for constraint condition as design variable
Machine dynamic property Optimized model writes mixed discrete optimization program based on Matlab platform and obtains optimal design variable and target letter
Numerical value.
The concrete operations of simplified model include:
(1) knuckle, bolt hole, boss and groove everywhere is not considered.To the quality of speed reducer and just after simplification
Degree will not generate too much influence, and 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 at rigid
Property connection.
(3) bearing arrangement Property comparison is complicated, is simulated with stiffness spring.
The surface to contact with each other between speed reducer components is known as " faying face ".Speed reducer is usually in the ring of complicated dynamic loading
It works in border, this makes the micro breadth oscillation that can be generated multiple degrees of freedom between its faying face, have damping, 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 reasonably be simulated to it.
1) 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 gears and gears axis corresponding node is coupled in all directions.
2) processing of bearing and gear shaft and bearing block faying face: bearing and gear shaft corresponding node are radially, axially complete
Portion's coupling, it is circumferential not to couple.Bearing block is coupled with cabinet corresponding node in all directions.
3) processing of bearing (ball) cover: this faying face is smaller on the influence of the dynamic characteristic of speed reducer entirety, in practical 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 and needed after overtesting is reaffirmed 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, oscillatory differential equation group based on lumped parameter method
It 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, and r is pitch radius；
I1y、I2xThe respectively concentration rotary inertia of worm and worm wheel；
x1、z1And y1For the axial vibration of worm screw respectively along the x-axis direction with the transverse vibrational displacement in z-axis direction and along the y-axis direction
Dynamic displacement；
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 axis；
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 force of worm screw；
Fx2、Fy2、Fz2For the axial force, the force of periphery and radial force of worm gear.Wherein, Fx1=﹣ Fx2、Fy1=﹣ Fy2、Fz1=﹣ Fz2。
Fig. 1 be use lumped parameter theory establish multiple degrees of freedom coupling dynamical model: in the model axis of worm screw for
y1Axis, the axis of worm gear are 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 freedom degrees, generalized displacement array can be expressed asF}={x1, y1, z1,θ y1, x2,
y2, z2, θx2}T。x 1、z 1Withy 1It is worm screw respectively along x-axis, the oscillation crosswise in the direction z 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 axis.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 establish
Worm gear pair vibration analysis model be engagement type it is curved-turn round coupling dynamical model.
(2) Fourth order Runge-Kutta solving system oscillatory differential equation is used, each component vibration of worm decelerating machine is obtained and rings
It should be worth.
(3) the vibration acceleration amplitude minimal construction objective function based on input shaft worm screw, with worm gear pair modulus, number of teeth etc.
Parameter is design variable, and worm gear pair intensity, rigidity and assembly relation etc. are constraint condition, 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 comprises 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 identical screw coupling member of material is subjected to physical model boolean and merges fortune
It calculates, converts .stp format for entity simplified model and import in software ANSYS Workbench；
3) grid dividing is carried out to simplified physical model, the grid dividing side for selecting tetrahedron element and hexahedral element to combine
Method establishes complete machine finite element model, wherein worm gear, worm screw, worm gear seat, output shaft use hexahedron solid element, cabinet, bearing,
End cap uses tetrahedral solid elements；Unit size is selected as 15mm according to worm decelerating machine practical structures size reasonable, complicated
Position grid need to carry out local refinement；
4) surface to contact with each other between speed reducer components, the i.e. feasible simulation of " faying face ": gear shaft and gear faying face
Processing method be that gears and gears axis corresponding node is 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 method in ANSYS Workbench software, obtained
The intrinsic frequency and natural mode of vibration of 20 ranks, allow the rotational frequency of worm gear pair and meshing frequency to avoid speed reducer before worm decelerating machine
Intrinsic frequency；
6) Dynamic Performance Analysis: carrying out the Dynamic Response 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 the frequency function of dependent variable, use
In the authenticity for reaffirming potential resonance point；
7) Dynamic performance Optimization: the mesh of the minimum worm decelerating machine Dynamic performance Optimization of vibration acceleration amplitude to input 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 constraint condition, establishes worm decelerating machine Dynamic performance Optimization model, is write based on Matlab platform 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
Vibration, can carry out verification experimental verification first, after overtesting is reaffirmed, need to carry out the relevant parameter of worm decelerating machine excellent
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 that rotation is used
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 axis；
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 force of worm screw；
Fx2、Fy2、Fz2For the axial force, the force of periphery and radial force 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 radial stiffness coefficient and damped coefficient；
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 radial stiffness coefficient and damped coefficient；
2) Fourth order Runge-Kutta solving system oscillatory differential equation is used, each component vibratory response value of worm decelerating machine is obtained；
3) the vibration acceleration amplitude minimal construction objective function based on input shaft worm screw, with worm gear pair modulus, the parameter of the number of teeth
For design variable, worm gear pair intensity, rigidity and assembly relation are constraint condition, establish the dynamic of worm decelerating machine gear train
Energy Optimized model, obtains worm gear pair optimal design variable.
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| CN110795876B (en) * | 2019-10-23 | 2023-06-23 | 珠海格力智能装备有限公司 | Method for establishing finite element equivalent model of speed reducer |
| 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 |
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Address after: 226600 Haian, Jiangsu province Haian Zhenhai Road, No. 88, South Road, No. Co-patentee after: Jiangnan University Patentee after: Haian Shenling Electrical Appliance Manufacturing Co., Ltd. Address before: 226600 Haian, Jiangsu province Haian Zhenhai Road, No. 88, South Road, No. Co-patentee before: Jiangnan University Patentee before: Haian Shenling Electrical Appliance Manufacturing Co., Ltd. |