CN108470102A - A kind of steamboat the optimum gear surface design method and processing method towards meshing performance pre-control - Google Patents
A kind of steamboat the optimum gear surface design method and processing method towards meshing performance pre-control Download PDFInfo
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- G06F30/17—Mechanical parametric or variational design
Abstract
The invention discloses a kind of steamboat the optimum gear surface design methods and processing method towards meshing performance pre-control, the face gear engagement of steamboat processing approximate with straight sword cutter one-parameter enveloping method, the design method of the steamboat the optimum gear surface includes preset, the steamboat flank of tooth the reverse of geometry driving error and reconfigures steamboat the optimum gear surface, the geometry driving error is the polynomial function of 2 to 8 ranks and is preset in during the reverse of the steamboat flank of tooth, and steamboat the optimum gear surface is reconfigured with elliptical length using the reverse flank of tooth and contact trace.The processing method for further illustrating steamboat the optimum gear surface, the processing method includes selecting the amendment for establishing sum number regulatory control rule of Qin Chuan numerically-controlled machine tool QMK50A and molding cutter, initial number regulatory control rule, pass through the iterated revision of numerical control rule, so that the digital control processing flank of tooth approaches steamboat the optimum gear surface and processes steamboat, this method being capable of geometry meshing performance that effectively pre-control steamboat is engaged with face gear.
Description
Technical field：
The present invention relates to gear drive fields, are set more particularly to a kind of steamboat the optimum gear surface towards meshing performance pre-control
Meter method and processing method.
Background technology：
Roller gear (steamboat) is known as face gear with the bevel gear in bevel gear engaged transmission, is based on conventional method machined surface
Gear leads to cutter poor universality and needs to develop special manufacturing equipment, and pole is unfavorable for the popularization and application of face gear, and most
Only it is adapted to orthogonal straight-tooth, pitch face gear.Using straight sword cutter on existing Bevel Gear Generator, and it can be added using special fixture
All kinds of face gears of work, as shown in Figure 1, its method exists《The process equipment and processing method of all kinds of face gears of straight sword cutter manufacture》In
It has been be elaborated that, including for reference herein.Double parameters envelop method can be used using straight sword cutter machined surface gear, in this way
The face gear of processing is as the face gear that conventional method is processed, but processing efficiency is not high, and one-parameter is based on using straight sword cutter
Envelope method machined surface gear, since line contacts, processing efficiency is very high, but opposite traditional diamond-making technique, can bring certain flank of tooth
Deviation, the deviation flank of tooth are known as the approximate flank of tooth Σ of face gear2p, the referred to as theoretical flank of tooth Σ of the flank of tooth of conventional method processing2, approximate
Flank of tooth Σ2pWith theoretical flank of tooth Σ2Interior public affairs are cut in curve Cp, as shown in Fig. 2, and Σ2pAlong Cp optimal approximations in Σ2, however the flank of tooth
Deviation, than more prominent, especially shortens the length of the Contact Ellipse long axis in geometry meshing performance to the adverse effect of meshing performance
Degree inevitably reduces it and is driven intensity.
However in gear drive, good meshing performance is important more than machining accuracy, usually to the flank of tooth of various gears into
Row Modification design makes the Modification design flank of tooth deviate its theoretical flank of tooth, existing patented technology disclose a series of flank of tooth it is modified or
Modification design method, such as：US6205879B1, US5580298, CN103577713A, CN103440356A,
CN104832623A.In addition, face gear or other gear-driven meshing performances that existing literature is processed also for conventional method
Many flank of tooth modifications or modification design have been carried out, such as：Journal of Mechanical Design, 2016,138 (4)：
043302-043302-13；XI AN JIAOTONG UNIVERSITY Subject Index, 2017,51 (07)：98-104；Aviation power journal, 2014,29
(07)：1752-1760；China Mechanical Engineering, 2012,23 (08)：992-996.Obviously straight sword cutter and one-parameter envelope are utilized
Method highly-efficient processing face gear, it is necessary to take the necessary measures and eliminate the adverse effect that tooth surface of face gear deviation is brought to meshing performance.
In order to solve the above technical problems, a kind of steamboat the optimum gear surface design method towards meshing performance pre-control is proposed,
And the processing method for further illustrating the optimum gear surface.
Invention content：
What the deviation to eliminate the face gear approximation flank of tooth of straight sword cutter one-parameter enveloping method processing was brought to meshing performance
Adverse effect, the present invention provide a kind of steamboat the optimum gear surface design method and processing method towards meshing performance pre-control.
To achieve the above object, the technical solution adopted by the present invention is：
A kind of steamboat the optimum gear surface design method towards meshing performance pre-control, it is characterised in that include the following steps：It is several
Preset, the steamboat flank of tooth the reverse of what driving error reconfigures steamboat the optimum gear surface；
The preset of geometry driving error includes the following steps：
S101 constructive geometry driving error multinomialsThe c0, c1, c2..., cσIt is to wait for
It determines that coefficient, σ are the polynomial exponent numbers of geometry driving error, generally takes the positive integer between 2~8, ε1It is steamboat corner；
S102 is according to the amplitude of the desired geometry driving error in mesh cycle, adjacent geometry driving error point of intersection
Slope determines the shape of geometry driving error curve；
S103 determines the polynomial exponent number σ of geometry driving error according to geometry driving error curve shape, is driven in geometry
Geometry driving error Δ ε is selected on error curve2And its 1 order derivative given value, the total numbers of these given values is σ+1, and
Determine Δ ε2And its 1 corresponding several ε of order derivative given value1Numerical value；
S104 is by Δ ε2And its 1 given value of order derivative, ε1Numerical value substitute into geometry driving error multinomial in, build square
Battle array equation, solves coefficient c to be determined0, c1, c2..., cσ, and back substitution enters in geometry driving error multinomial, obtains Δ ε2With steamboat
Corner ε1Functional relation.
The reverse process of the steamboat flank of tooth is：When steamboat with have approximate flank of tooth Σ2pThe engagement of face gear when, by corner
Relationship ε1=(ε2N2-Δε2N2)/N1Plane of rotation gear and steamboat, face gear approximation flank of tooth Σ2pThe packet of flank of tooth race on steamboat
Network is the reverse flank of tooth Σ of the steamboat12p；
The ε2It is the corner of face gear, the N1、N2It is the number of teeth of steamboat knead dough gear respectively；
The approximate flank of tooth Σ of the face gear2pIt is process by straight sword cutter one-parameter enveloping method.
The steamboat the optimum gear surface that reconfigures includes the following steps：
S301 determines face gear approximation flank of tooth Σ2pWith its theoretical flank of tooth Σ2Internal common tangent Cp, be used in combination a series of discrete
Point FiIndicate the internal common tangent Cp, i=1,2 ..., the odd number that n, n are >=3；
S302 points FiIt is flank of tooth Σ2p、Σ12pConjugate point, utilize Differential Geometry, solve flank of tooth Σ2p、Σ12pConjugate point Fi
Principal curvatures, the principal direction at place；
S303 utilizes conjugate point FiPrincipal curvatures, the principal direction at place determine the Contact Ellipse long axis direction at the point；
S304 is in conjugate point FiOn the Contact Ellipse long axis at place, FiBoth sides take two endpoint a respectivelyi1、ai2, and make length
|Fiai1|=| Fiai2|=a, a are the length of desired preset Contact Ellipse long axis；
S305 crosses the endpoint a of Contact Ellipse long axisi1、ai2It is parallel to conjugate point F respectivelyiLocate Σ2p、∑12pCommon normal
Straight line respectively with flank of tooth ∑12pIntersect at point bi1、bi2；
S306 is to ∑12pInside extends a respectivelyi1bi1、ai2bi2To Pi1、Pi2, and make length | bi1Pi1|=| bi2Pi2|=
0.00635mm；
S307 is to cross conjugate point FiWith point Pi1、Pi2Second order and its more than smooth full curve substitute conjugate point FiPlace
Σ2p、∑12pContact line L21, by this n second order and its more than smooth full curve constitute steamboat the optimum gear surface Σ1d。
The steamboat reconfigured using a kind of above-mentioned steamboat the optimum gear surface design method towards meshing performance pre-control
The processing method of the optimum gear surface, it is characterised in that the processing method includes the following steps：Process tool is selected, numerically-controlled machine tool selects
With the foundation of, initial number regulatory control rule, the amendment of numerical control rule.
It is by having for cutting or being ground the working curved surface of steamboat tooth socket that the process tool, which selects molding cutter, the cutter,
There is standard involute flank of tooth ∑1The normal plane transversal of steamboat tooth socket rotate a circle and formed around tool axis.
It includes 5 numerical control kinematic axis, three numerical control flats that the numerically-controlled machine tool, which selects Qin Chuan QMK50A numerically-controlled machine tools, the lathe,
Movement moving axis X, Y, Z, two numerical control rotary motions axis A, B, axis A is work spindle, and rotates freely cutter master at a high speed
Axis C.
The foundation of the initial number regulatory control rule includes the following steps：
S701, which establishes the tool sharpening, has standard involute flank of tooth ∑1Steamboat abstract processing model；
S702 is based in abstract processing with digital control processing, and cutter is equal with respect to the position vector of steamboat and normal vector
Principle, establishing has standard involute flank of tooth ∑1Steamboat digital control processing mathematical model；
S703 is determined with steamboat corner ψ1For the characteristics of motion of each numerical control axis of independent variable, the movement of each numerical control axis is advised
Rule expands into ψ1Taylor series at=0 obtain each numerical control axis initial number regulatory control rule multinomial：
K=X, Y, Z, A, B, gk0~gk6For numerical control axis k numerical control rule multinomial from 0 rank to the coefficient of 6 ranks；
S704 enters the above-mentioned numerical control rule multinomial back substitution of numerical control axis k in the digital control processing mathematical model of steamboat, obtains small
Take turns the numerical control flank of tooth
The amendment of the numerical control rule restrains polynomial each level number for correcting above-mentioned initial number regulatory control, makes steamboat numerical control
The flank of toothLevel off to steamboat the optimum gear surface ∑1d, and steamboat is processed, include the following steps：
S801 renumbers the subscript of each level number of each Shaft and NC Machining Test rule multinomial, and number rule is：κ=1=X0, κ
=2=X1, κ=3=X2 ..., κ=33=B4, κ=34=B5, κ=35=B6；
S802 is by steamboat standard involute flank of tooth ∑1, the numerical control flank of toothThe optimum gear surface ∑1dIt is divided into h-1 etc. along facewidth direction
Part, h longitudinal network ruling is obtained, is divided into w-1 equal portions along the high direction of tooth, obtains the vertical grid lines of w items, the friendship of longitudinal, vertical grid lines
Point is flank of tooth mesh point, from steamboat one end face to another end face, from tooth top to tooth root, the numbers of these mesh points be λ=
1,2,3 ..., w × d；
S803 calculates steamboat the optimum gear surface ∑1dOpposite steamboat standard involute gear face ∑1Norma l deviation vector：E1d=
n1dλ·(R1dλ-R1λ), n1dλ、R1dλIt is steamboat the optimum gear surface ∑ respectively1dUnit normal vector, the position arrow of the λ mesh point
Amount, R1λIt is steamboat standard involute flank of tooth ∑1The position vector of the λ mesh point；
The ξ times amendment each level number of numerical control rule multinomial of S804, includes the following steps：
Step 1：It solves the ξ times in correcting, the steamboat numerical control flank of toothOpposite steamboat standard involute gear face ∑1Normal direction
Bias vector：It is the steamboat numerical control flank of tooth respectivelyThe λ mesh point in the ξ times amendment
Unit normal vector, position vector；
Step 2：Solve the ξ times correction matrix
It is the steamboat numerical control flank of tooth respectivelyDuring the ξ times is corrected, numerical control rule multinomial level number gκThere is disturbance quantity Δ gκWhen, λ
Unit normal vector, the position vector of mesh point；
Step 3：Correction matrix equation is solved, obtaining the ξ times revised each level number of numerical control rule multinomial is：
As ξ=1, takes the polynomial each level number of initial number regulatory control rule to solve above-mentioned correction matrix equation, repeat step
One arrives step 3, iteratively solves above-mentioned correction matrix equation, untilLevel off to 0 vector when terminate, then steamboat numerical control tooth
FaceLevel off to steamboat the optimum gear surface ∑1d, obtain the polynomial each level number of final numerical control rule；
S805 is installed the cutter, steamboat, numerical control program is write using the polynomial each level number of final numerical control rule, is adjusted
Test-run a machine bed, processing steamboat.
Compared with the prior art, the present invention has the following advantages：
1. can pre-control straight sword cutter one-parameter enveloping method processing the face gear approximation flank of tooth meshing performance；
2. as long as the contact path of its meshing performance, geometry driving error, the length of Contact Ellipse energy quantificational expression, so that it may
To design and produce the corresponding steamboat flank of tooth, therefore the pre-control of meshing performance has very high flexibility；
3. having taken into account the processing efficiency of steamboat, face gear, the gear general number of teeth in face is more, and straight sword cutter one-parameter enveloping method adds
Work face gear efficiency is high, and small tooth number is few, although steamboat the optimum gear surface is more complex, flank profil direction is mainly by there is certain change
What the involute of position was constituted, it is processed using molding cutter, it is efficient.
Description of the drawings
Fig. 1 processes the schematic diagram of all kinds of face gears using straight sword cutter and special fixture on Bevel Gear Generator.
In figure：P --- straight sword cutter, 2 --- all kinds of face gears, 3 --- tool head, 4 --- workpiece spindle box,
5 --- cutter special fixture, 6 --- workpiece special fixture.
The face gear approximation flank of tooth Σ of Fig. 2 straight sword cutter one-parameter enveloping methods processing2pWith its theoretical flank of tooth Σ2Deviation show
It is intended to.
Fig. 3 high-order geometry driving error curve synoptic diagrams.
The reverse schematic diagram of Fig. 4 steamboat flank of tooth.
Fig. 5 steamboat standard involute flank of tooth ∑s1With reverse flank of tooth ∑12pSchematic diagram.
Fig. 6 reconfigures steamboat the optimum gear surface ∑1dSchematic diagram.
Fig. 7 steamboat the optimum gear surface ∑s1dWith on the flank of tooth second order and its more than smooth full curve schematic diagram.
Fig. 8 is for processing steamboat the optimum gear surface ∑1dNumerically-controlled machine tool schematic diagram.
Fig. 9 steamboat the optimum gear surface ∑s1dOn mesh point and its number schematic diagram.
Specific implementation mode
The present invention is described in further detail below in conjunction with the accompanying drawings：
Present invention solves the technical problem that being：For all kinds of face gear approximation teeth of straight sword cutter one-parameter enveloping method processing
The meshing performance in face is not very ideal problem, especially the too short problem of Contact Ellipse length, it is proposed that a kind of towards nibbling
Close the steamboat the optimum gear surface design method of performance pre-control, and the processing method for further illustrating the optimum gear surface.
Embodiment：Tiltedly steamboat the optimum gear surface design method and processing method in biasing pitch face gear drive.
Steamboat the optimum gear surface design method, includes the following steps：Preset, the steamboat flank of tooth the reverse of geometry driving error,
Reconfigure steamboat the optimum gear surface.
(1) geometry driving error is preset：
S101 constructive geometry driving error multinomialsThe c0, c1, c2..., cσIt is to wait for
It determines that coefficient, σ are the polynomial exponent numbers of geometry driving error, generally takes the positive integer between 2~8, ε1It is steamboat corner；
S102 is according to the amplitude of the desired geometry driving error in mesh cycle, adjacent geometry driving error point of intersection
Slope determines that the shape of geometry driving error curve, Fig. 3 are a kind of 4 rank driving error curves, which reflects engagement
Amplitude at cycle starting point, the amplitude and slope of terminal point, and the shape of error curve is determined；
S103 determines the polynomial exponent number σ of geometry driving error according to geometry driving error curve shape, is driven in geometry
Geometry driving error Δ ε is selected on error curve2And its 1 order derivative given value, the total numbers of these given values is σ+1, and
Determine Δ ε2And its 1 corresponding several ε of order derivative given value1Numerical value, there is known 3 Δ ε as shown in Figure 32And its 1 rank lead
2 several given values, the corresponding ε of these given values1Also it is to determine, such as ε11、ε12、ε13It is shown；
S104 is by Δ ε2And its 1 given value of order derivative, ε1Numerical value substitute into geometry driving error multinomial in, build square
Battle array equation, solves coefficient c to be solved0, c1, c2..., cσ, and back substitution enters in geometry driving error multinomial, obtains Δ ε2With steamboat
Corner ε1Functional relation, according to fig. 3, it may be determined that following equation：
It is further write as the form of matrix equation, solves each term coefficient in geometric error multinomial.
(2) reverse of the steamboat flank of tooth：
As shown in figure 4, working as steamboat and there is approximate flank of tooth Σ2pThe engagement of face gear when, by angle relation ε1=(ε2N2-Δ
ε2N2)/N1Plane of rotation gear and steamboat, face gear approximation flank of tooth Σ2pThe envelope of flank of tooth race on steamboat is the reverse tooth of steamboat
Face ∑12p, the reverse flank of tooth is with steamboat standard involute gear relation of plane as shown in figure 5, ε2It is the corner of face gear, N1、N2Point
It is not the number of teeth of steamboat knead dough gear；
The approximate flank of tooth Σ of face gear2pIt is process by straight sword cutter one-parameter enveloping method, is specifically described and can refer to《Directly
The process equipment and processing method of all kinds of face gears of sword cutter manufacture》.
(3) steamboat the optimum gear surface reconfigures：
S301 determines tiltedly biasing pitch face gear approximation flank of tooth Σ2pWith its theoretical flank of tooth Σ2Internal common tangent Cp, be used in combination one
The discrete point F of seriesiIndicate the internal common tangent Cp, i=1,2 ..., the odd number that n, n are >=3, Fig. 2 shows oblique biasing pitch faces
Gear approximation flank of tooth Σ2pWith its theoretical flank of tooth Σ2Internal common tangent Cp；
S302 points FiIt is flank of tooth Σ2p、∑12pConjugate point, utilize Differential Geometry, solve flank of tooth Σ2p、Σ12pConjugate point Fi
Principal curvatures, the principal direction at place；
S303 utilizes conjugate point FiPrincipal curvatures, the principal direction at place determine the Contact Ellipse long axis direction at the point, in Fig. 6
Vectorial η illustrates conjugate point FiLocate the direction of Contact Ellipse long axis；
S304 is as shown in fig. 6, in conjugate point FiOn the Contact Ellipse long axis at place, FiBoth sides take two endpoint a respectivelyi1、
ai2, and make length | Fiai1|=| Fiai2|=a, a are the length of desired preset Contact Ellipse long axis；
S305 is as shown in fig. 6, cross the endpoint a of Contact Ellipse long axisi1、ai2It is parallel to conjugate point F respectivelyiLocate Σ2p、
∑12pThe straight line of common normal respectively with flank of tooth ∑12pIntersect at point bi1、bi2；
S306 is as shown in fig. 6, to ∑12pInside extends a respectivelyi1bi1、ai2bi2To Pi1、Pi2, and make length | bi1Pi1|=|
bi2Pi2|=0.00635mm；
S307 is as shown in fig. 6, to cross conjugate point FiWith point Pi1、Pi2Second order and its more than smooth full curve Curve
Substitute conjugate point FiLocate Σ2p、∑12pContact line L21, the as shown in Figure 7 smooth full curve shares n items, by this n second order and
Smooth full curve more than it constitutes the optimum gear surface ∑ of steamboat1d。
The steamboat the optimum gear surface ∑ reconfigured with above-mentioned steamboat the optimum gear surface design method1dProcessing method, including
Following steps：The amendment of process tool is selected, numerically-controlled machine tool is selected, initial number regulatory control is restrained foundation, numerical control rule.
(1) process tool is selected：
Process tool selects molding cutter, as shown in figure 8, the cutter is used to cut or be ground the working curved surface of steamboat tooth socket
It is by with standard involute flank of tooth ∑1The normal plane transversal of steamboat tooth socket rotate a circle and formed around tool axis.
(2) numerically-controlled machine tool is selected：
Numerically-controlled machine tool selects Qin Chuan QMK50A numerically-controlled machine tools, and as depicted in figure 8, which includes 5 numerical control kinematic axis, three numbers
Translational motion axis X, Y, Z are controlled, two numerical control rotary motions axis A, B, axis A is work spindle, and steamboat passes through installation axle and work
Part principal axis A connects firmly, and high speed rotates freely cutter spindle C, and cutter is connected firmly by handle of a knife and cutter spindle C, transported by numerical control
The compound motion of moving axis X, Y, Z, A, B process steamboat the optimum gear surface ∑1d。
(3) foundation of initial number regulatory control rule：
S701, which establishes molding tool sharpening, has standard involute flank of tooth ∑1Steamboat abstract processing model；
S702 is based in abstract processing with digital control processing, and cutter is equal with respect to the position vector of steamboat and normal vector
Principle, establishing has standard involute flank of tooth ∑1Steamboat digital control processing mathematical model；
S703 is determined with steamboat corner ψ1For the characteristics of motion of each numerical control axis of independent variable, each axis characteristics of motion is unfolded
For ψ1Taylor series at=0 obtain each numerical control axis initial number regulatory control rule multinomial：
K=X, Y, Z, A, B, gk0~gk6For numerical control axis k numerical control rule multinomial from 0 rank to the coefficient of 6 ranks；
S704 enters the above-mentioned numerical control rule multinomial back substitution of numerical control axis k in the digital control processing mathematical model of steamboat, obtains small
Take turns the numerical control flank of tooth
(4) amendment of numerical control rule：
The amendment of numerical control rule makes steamboat digital control processing tooth for correcting above-mentioned initial number regulatory control rule each level number of multinomial
FaceLevel off to steamboat the optimum gear surface ∑1d, and steamboat is processed, include the following steps：
S801 renumbers the subscript of each level number of each Shaft and NC Machining Test rule multinomial, and number rule is：κ=1=X0, κ
=2=X1, κ=3=X2 ..., κ=33=B4, κ=34=B5, κ=35=B6；
S802 is as shown in figure 9, by steamboat standard involute flank of tooth ∑1, the numerical control flank of toothThe optimum gear surface ∑1dAlong facewidth side
To h-1 equal portions are divided into, h longitudinal network ruling is obtained, is divided into w-1 equal portions along the high direction of tooth, obtains the vertical grid lines of w items, it is longitudinal, vertical
The intersection point of grid lines is flank of tooth mesh point, from steamboat one end face to another end face, from tooth top to tooth root, these mesh points
Number is λ=1,2,3 ..., h × w；
S803 calculates steamboat the optimum gear surface ∑1dOpposite steamboat standard involute gear face ∑1Norma l deviation vector：E1d=
n1dλ·(R1dλ-R1λ), n1dλ、R1dλIt is steamboat the optimum gear surface ∑ respectively1dUnit normal vector, the position arrow of the λ mesh point
Amount, R1λIt is steamboat standard involute flank of tooth ∑1The position vector of the λ mesh point；
The ξ times amendment each level number of numerical control rule multinomial of S804, includes the following steps：
Step 1：It solves the ξ times in correcting, the steamboat numerical control flank of toothOpposite steamboat standard involute gear face ∑1Normal direction
Bias vector：It is the steamboat numerical control flank of tooth respectivelyThe λ mesh point in the ξ times amendment
Unit normal vector, position vector；
Step 2：Solve the ξ times correction matrix
It is the steamboat numerical control flank of tooth respectivelyDuring the ξ times is corrected, numerical control rule multinomial level number gκThere is disturbance quantity Δ gκWhen, λ
Unit normal vector, the position vector of mesh point；
Step 3：Correction matrix equation is solved, obtaining the ξ times revised each level number of numerical control rule multinomial is：
As ξ=1, takes the polynomial each level number of initial number regulatory control rule to solve above-mentioned correction matrix equation, repeat step
One arrives step 3, iteratively solves above-mentioned correction matrix equation, untilLevel off to 0 vector when terminate, then steamboat numerical control tooth
FaceLevel off to steamboat the optimum gear surface ∑1d, obtain the polynomial each level number of final numerical control rule；
S805 installations cutter, steamboat write numerical control program, debugging machine using the polynomial each level number of final numerical control rule
Bed, processing steamboat.
Above-mentioned all steps are applicable not only to tiltedly bias the design and manufacture of steamboat the optimum gear surface in pitch face gear drive,
It applies also in other kinds of face gear drive in the design and processing, such as Fig. 4 of steamboat the optimum gear surface as γ=90 °, q=
0 and face gear when being engaged with straight-tooth steamboat, it can design and process the straight-tooth steamboat optimal teeth in orthogonal straight-sided flank gear drive
Face can be designed and be processed in positive bias straight-sided flank gear drive when γ=90 °, q ≠ 0 and face gear are engaged with straight-tooth steamboat
Straight-tooth steamboat the optimum gear surface can design when γ ≠ 90 °, q=0 and face gear are engaged with straight-tooth steamboat and to process oblique straight
Straight-tooth steamboat the optimum gear surface in flank of tooth gear drive can be set when γ ≠ 90 °, q ≠ 0 and face gear are engaged with straight-tooth steamboat
Meter is engaged with the straight-tooth steamboat the optimum gear surface in processing tiltedly biasing straight-sided flank gear drive, same face-gear with helical teeth steamboat
When, helical teeth steamboat the optimum gear surface can be designed and be processed, when face-gear is engaged with double helical tooth steamboat, can design and process double helical tooth
Steamboat the optimum gear surface, the design and processing of the wherein the optimum gear surface of double helical tooth steamboat can regard as two helical teeth steamboat optimal teeths
The design and processing in face, the rotation direction of the two helical teeth steamboat gear teeth, one are left-handed, another is dextrorotation.
Based on above-mentioned steps, as long as desired preset geometry meshing performance can be given, it will be able to design and process and is small
Corresponding the optimum gear surface is taken turns, the optimum gear surface ∑1dFlank of tooth Σ approximate with face gear2pEngagement nibbled preset geometry is showed
Close performance.
According to the regulation of Patent Law, the above preferred embodiment is merely illustrative of the technical solution of the present invention, rather than is limited it
System, it should be understood by those skilled in the art that, with reference to above-described embodiment can to the present invention specific implementation mode into
It goes and changes or replace on an equal basis, these are without departing from any modification of the scope of the invention or same replacement in claims
Within.
Claims (8)
1. a kind of steamboat the optimum gear surface design method towards meshing performance pre-control, it is characterised in that include the following steps：Geometry
Preset, the steamboat flank of tooth the reverse of driving error reconfigures steamboat the optimum gear surface；
The preset of geometry driving error includes the following steps：
S101 constructive geometry driving error multinomialsThe c0, c1, c2..., cσIt is to be determined
Coefficient, σ are the polynomial exponent numbers of geometry driving error, generally take the positive integer between 2~8, ε1It is steamboat corner；
S102 is true according to the amplitude of desired geometry driving error, the slope of adjacent geometry driving error point of intersection in mesh cycle
Determine the shape of geometry driving error curve；
S103 determines the polynomial exponent number σ of geometry driving error according to geometry driving error curve shape, in geometry driving error
Geometry driving error Δ ε is selected on curve2And its 1 order derivative given value, the total numbers of these given values is σ+1, and is determined
Δε2And its 1 corresponding several ε of order derivative given value1Numerical value；
S104 is by Δ ε2And its 1 given value of order derivative, ε1Numerical value substitute into geometry driving error multinomial in, build matrix side
Journey solves coefficient c to be determined0, c1, c2..., cσ, and back substitution enters in geometry driving error multinomial, obtains Δ ε2With steamboat corner
ε1Functional relation.
2. a kind of steamboat the optimum gear surface design method towards meshing performance pre-control as described in claim 1, it is characterised in that
The reverse process of the steamboat flank of tooth is：When steamboat with have approximate flank of tooth Σ2pThe engagement of face gear when, by angle relation ε1=
(ε2N2-Δε2N2)/N1Plane of rotation gear and steamboat, face gear approximation flank of tooth Σ2pThe envelope of flank of tooth race on steamboat is steamboat
Reverse flank of tooth ∑12p；
The ε2It is the corner of face gear, the N1、N2It is the number of teeth of steamboat knead dough gear respectively；
The approximate flank of tooth Σ of the face gear2pIt is process by straight sword cutter one-parameter enveloping method.
3. a kind of steamboat the optimum gear surface design method towards meshing performance pre-control as described in claim 1, it is characterised in that
The steamboat the optimum gear surface that reconfigures includes the following steps：
S301 determines face gear approximation flank of tooth Σ2pWith its theoretical flank of tooth Σ2Internal common tangent Cp, a series of discrete point F is used in combinationi
Indicate the internal common tangent Cp, i=1,2 ..., the odd number that n, n are >=3；
S302 points FiIt is flank of tooth Σ2p、∑12pConjugate point, utilize Differential Geometry, solve flank of tooth ∑2p、∑12pConjugate point FiPlace
Principal curvatures, principal direction；
S303 utilizes conjugate point FiPrincipal curvatures, the principal direction at place determine the Contact Ellipse long axis direction at the point；
S304 is in conjugate point FiOn the Contact Ellipse long axis at place, FiBoth sides take two endpoint a respectivelyi1、ai2, and make length |
Fiai1|=| Fiai2|=a, a are the length of desired preset Contact Ellipse long axis；
S305 crosses the endpoint a of Contact Ellipse long axisi1、ai2It is parallel to conjugate point F respectivelyiLocate Σ2p、Σ12pThe straight line of common normal point
Not with flank of tooth ∑12pIntersect at point bi1、bi2；
S306 is to ∑12pInside extends a respectivelyi1bi1、ai2bi2To Pi1、Pi2, and make length | bi1Pi1|=| bi2Pi2|=
0.00635mm；
S307 is to cross conjugate point FiWith point Pi1、Pi2Second order and its more than smooth full curve substitute conjugate point FiLocate Σ2p、
∑12pContact line L21, by this n second order and its more than smooth full curve constitute steamboat the optimum gear surface ∑1d。
4. utilizing a kind of steamboat the optimum gear surface design method institute towards meshing performance pre-control as described in claim 1 again structure
The processing method for the steamboat the optimum gear surface made, it is characterised in that the processing method includes the following steps：Process tool selection, numerical control
The amendment of lathe is selected, initial number regulatory control is restrained foundation, numerical control rule.
5. a kind of processing method of the steamboat the optimum gear surface towards meshing performance pre-control as claimed in claim 4, feature exist
It is by gradually being opened with standard for cutting or being ground the working curved surface of steamboat tooth socket to select molding cutter, the cutter in process tool
Line flank of tooth ∑1The normal plane transversal of steamboat tooth socket rotate a circle and formed around tool axis.
6. a kind of processing method of the steamboat the optimum gear surface towards meshing performance pre-control as claimed in claim 4, feature exist
In numerically-controlled machine tool select Qin Chuan QMK50A numerically-controlled machine tools, the lathe include 5 numerical control kinematic axis, three numerical control translational motion axis X,
Y, Z, two numerical control rotary motions axis A, B, axis A is work spindle, and rotates freely cutter spindle C at a high speed.
7. a kind of processing method of the steamboat the optimum gear surface towards meshing performance pre-control as claimed in claim 4, feature exist
Include the following steps in the foundation of initial number regulatory control rule：
S701, which establishes the tool sharpening, has standard involute flank of tooth ∑1Steamboat abstract processing model；
S702 is based in abstract processing and digital control processing, the cutter original equal with respect to the position vector of steamboat and normal vector
Then, establishing has standard involute flank of tooth ∑1Steamboat digital control processing mathematical model；
S703 is determined with steamboat corner ψ1For the characteristics of motion of each numerical control axis of independent variable, by the characteristics of motion exhibition of each numerical control axis
It opens as ψ1Taylor series at=0 obtain each numerical control axis initial number regulatory control rule multinomial：
K=X, Y, Z, A, B, gk0~gk6For numerical control axis k numerical control rule multinomial from 0 rank to the coefficient of 6 ranks；
S704 enters the above-mentioned numerical control rule multinomial back substitution of numerical control axis k in the digital control processing mathematical model of steamboat, obtains steamboat number
Control the flank of tooth
8. a kind of processing method of the steamboat the optimum gear surface towards meshing performance pre-control as claimed in claim 4, feature exist
Polynomial each level number is restrained for correcting above-mentioned initial number regulatory control in the amendment of the numerical control rule, makes the steamboat numerical control flank of tooth
Level off to steamboat the optimum gear surface ∑1d, and steamboat is processed, include the following steps：
S801 renumbers the subscript of each level number of each Shaft and NC Machining Test rule multinomial, and number rule is：κ=1=X0, κ=2=
X1, κ=3=X2 ..., κ=33=B4, κ=34=B5, κ=35=B6；
S802 is by steamboat standard involute flank of tooth Σ1, the numerical control flank of toothThe optimum gear surface ∑1dIt is divided into h-1 equal portions along facewidth direction,
H longitudinal network ruling is obtained, is divided into w-1 equal portions along the high direction of tooth, obtains the vertical grid lines of w items, the intersection point of longitudinal, vertical grid lines is
Flank of tooth mesh point, from steamboat one end face to another end face, from tooth top to tooth root, the numbers of these mesh points is λ=1,2,
3 ..., h × w；
S803 calculates steamboat the optimum gear surface ∑1dOpposite steamboat standard involute gear face Σ1Norma l deviation vector：E1d=n1dλ·
(R1dλ-R1λ), n1dλ、R1dλIt is steamboat the optimum gear surface Σ respectively1dUnit normal vector, the position vector of the λ mesh point, R1λIt is
Steamboat standard involute flank of tooth ∑1The position vector of the λ mesh point；
The ξ times amendment each level number of numerical control rule multinomial of S804, includes the following steps：
Step 1：It solves the ξ times in correcting, the steamboat numerical control flank of toothOpposite steamboat standard involute gear face ∑1Norma l deviation to
Amount：It is the steamboat numerical control flank of tooth respectivelyThe unit of the λ mesh point in the ξ times amendment
Normal vector, position vector；
Step 2：Solve the ξ times correction matrix
It is the steamboat numerical control flank of tooth respectivelyDuring the ξ times is corrected, numerical control rule multinomial level number gκThere is disturbance quantity Δ gκWhen, λ
Unit normal vector, the position vector of mesh point；
Step 3：Correction matrix equation is solved, obtaining the ξ times revised each level number of numerical control rule multinomial is：
As ξ=1, takes the polynomial each level number of initial number regulatory control rule to solve above-mentioned correction matrix equation, repeat step 1 and arrive
Step 3 iteratively solves above-mentioned correction matrix equation, untilLevel off to 0 vector when terminate, then the steamboat numerical control flank of tooth
Level off to steamboat the optimum gear surface ∑1d, obtain the polynomial each level number of final numerical control rule；
S805 installs the cutter, steamboat, writes numerical control program, debugging machine using the polynomial each level number of final numerical control rule
Bed, processing steamboat.
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| CN116842664A (en) * | 2023-09-01 | 2023-10-03 | 溧阳渐开机械传动科技有限公司 | Tooth surface forward design method, device and medium for meshing performance requirements |
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