A kind of three-arc harmonic wave wheel gear shaped cutter and its tooth Profile Design methodTechnical field
The invention belongs to the technical fields of harmonic speed reducer gear cutting tool, humorous in particular to a kind of three-arcWave gear slotting cutter and its tooth Profile Design method.
Background technique
Harmonic gear transmission is a kind of acted on by wave producer to control the flexible deformation of flexbile gear come transmission force and movementTransmission device.It has a systems such as big transmission ratio, light weight, small in size while more, stable drive precision height of rodent population numberColumn advantage has become the core key of the fields such as industrial robot, aerospace, lathe and medical instrument equipment transmission systemComponents.
American scholar MUSSER is when obtaining the patent of the harmonic gear transmission nineteen fifty-nine, using a kind of large pressure angleStraight line tooth form, although which is able to satisfy stable drive ratio requirement, but do not account for the tangential displacement on the flexbile gear neutral conductor andFlexbile gear gear teeth line of symmetry caused by Curvature varying is mobile etc. when the neutral conductor deforms, this tooth form in application there are it is some notFoot.
Due to the tooth form of harmonic gear transmission flexbile gear and firm gear, the performance of harmonic speed reducer can be significantly affected, is furtherThe performance of harmonic drive is improved, harmonic wave gear teeth Study of Tooth obtains very big concern, and present Research is as follows:
Involute profile is most widely used due to easy to process, manufacture mature many advantages, such as, but this flank profilConjugation region is distributed in the lesser section in major axis of wave generator two sides when engagement, since loaded deformation rodent population mostly occurs greatly(theory of bibliography Shen Yunwen, Ye Qingtai harmonic gear transmission and design Beijing [M]: mechanical industry is published for cusp engagementSociety, 1985:1-33,127-136.)；
Bicircular arcs tooth form with S-shaped is proposed by ISHIKAWA and patented (bibliography ISHIKAWA S.ToothProfile of spline of strain wave:US Patent, No.4823638 [P] .1989.), nineteen ninety-fiveISHIKAWA is improved (bibliography ISHIKAWA S.Flexing contact again in existing flexbile gear tooth formtype gear drive of non-profile-shifted two-circular-arc composite toothProfile:US Patent, No.5458023 [P] .1995.).This kind of tooth form not only realizes continuously contacting with for region of engagement, andAnd because simultaneously more (the bibliography: the movement of Zeng Shiqiang, Yang Jiajun, Wang Xuanfu bicircular arcs tooth form harmonic gear transmission of rodent populationSpecificity analysis [J] Huazhong University of Science and Technology journal, 2000,28 (01): 12-14.), engagement tooth socket is wider in addition, improves tooth rootStress state and transmission meshing quality, improve bearing capacity and torsion stiffness；
The common tangent flank profil of the convex circular arc profile of flexbile gear and concave arc flank profil will be connected in common tangent formula double circular arc tooth outline with oneSection circularity substitution, then can be obtained three-arc flank profil, which had both had many advantages, such as bicircular arcs tooth form, also avoided straightwayFlank profil part is not easily formed the shortcomings that conjugate profiles when profile angle is smaller.And theoretically three-arc flank profil can obtain more(bibliography: Chen Xiaoxia, Xing Jingzhong are continuously conjugated the three-arc of cupuliform or carnival hat shape harmonic gear in big theoretical conjugation sectionTooth Profile Design: China, CN201710436032.X), the meshing performance of harmonic gear transmission can be improved, therefore, exploitation can addThe process tool of the corresponding three-arc harmonic gear of work is very necessary.
Summary of the invention
In view of this, in order to solve the above problems existing in the present technology, the purpose of the present invention is to provide three circles of one kindArc harmonic wave wheel gear shaped cutter is to achieve the purpose that process three-arc harmonic gear work flank profil according to process requirements, togetherWhen, a kind of tooth Profile Design method applied to three-arc harmonic wave wheel gear shaped cutter is additionally provided, to realize to each of pinion cutterThe purpose that parameter is accurately calculated.
The technical scheme adopted by the invention is as follows: a kind of three-arc harmonic wave wheel gear shaped cutter, including knife handle and be set to the knifeThe contoured surface of cutter hub on handle, the cutter hub is equipped with cutter tooth, and the tooth top anterior angle of cutter tooth and tooth top relief angle are respectively γ and αt, instituteState the basic rack tooth profile of cutter tooth by three sections successively tangent arc section constitute, and three sections of arc sections are respectively upper arc section, middle circular arcSection and lower arc section；The radius of the upper arc section is ρ1, middle arc section radius be ρ2And the radius ρ of lower arc section3；InstituteIt states formation incision superius between arc section and middle arc section and incision superius angle is δ1, formed between middle arc section and lower arc sectionIncision inferius and incision inferius angle is δ2；The center of circle offset of the upper arc section is xaMoving with the center of circle away from amount is ya, lower arc sectionCenter of circle offset is xfMoving with the center of circle away from amount is yf；The ρ1、ρ2、ρ3、δ1、δ2、xa、ya、xfAnd yfParameter value by be processedThe work flank profil of three-arc harmonic gear is computed engagement and determines.
Further, the basic rack tooth profile of the cutter tooth further includes tooth top fillet, root fillet, tooth top, tooth root, bottom clearance and rootGap, the radius of the tooth top fillet are ra, the radius of root fillet is rf, tooth top height be ha, tooth root height be hf, topGap is ca, root gap be cf.The ra、rf、ha、hf、caAnd cfParameter value by processed three-arc harmonic gear process requirementsIt determines.
Further, the normal profile of the cutter tooth is by tooth top fillet, root fillet, the upper arc section, middle arc sectionIt is constituted with lower arc section.
The present invention also provides a kind of tooth Profile Design method of three-arc harmonic wave wheel gear shaped cutter, the tooth Profile Design method packetsInclude following steps:
(1) it is wanted according to the design that the flexbile gear of harmonic gear meets " biconjugate " and " secondary conjugation " with firm gear engagement processIt asks, designs the flexbile gear three-arc flank profil and firm gear three-arc flank profil of the condition of satisfaction；
(2) rigid by solving pinion cutter cutting using gear gear motion method according to obtained firm gear three-arc flank profilThe mesh equation of wheel, obtain in pinion cutter respectively with three sections of circular arc, middle circular arc and lower circular arc circular arcs upper in firm gear three-arc flank profilThe theoretical conjugate profiles of the A section of flank profil conjugation, B sections of theoretical conjugate profiles and C sections of theoretical conjugate profiles；
(3) circular fitting is all made of to A sections of theoretical conjugate profiles and C sections of theoretical conjugate profiles, respectively obtains arc sectionAc1 and lower arc section Ac3, to determine the radius ρ of upper arc section1, lower arc section radius ρ3, upper arc section center of circle offsetxa, upper arc section the center of circle move away from amount ya, lower arc section center of circle offset xf, lower arc section the center of circle move away from amount yf；
(4) by plane analytic geometry method, middle arc section Ac2 corresponding with B sections of theory conjugate profiles is acquired, with determinationThe radius ρ of middle arc section2, incision superius angle δ1With incision inferius angle δ2；
(5) auxiliary parameter is determined by the process requirements of processed harmonic gear, which includes: radius at tooth tipra, tooth fillet radius rf, height of teeth top ha, height of teeth root hf, bottom clearance ca, root gap cf。
Further, the step (2) is to A sections of theoretical conjugate profiles, B sections of theoretical conjugate profiles and C sections of theoretical conjugation teethThe method that exterior feature is calculated is as follows:
(2.1) coordinate transform of firm gear in pinion cutter processing harmonic gear, the coordinate system S being connected with firm gear are established1(O1,x1,y1) to the coordinate system S being fixedly connected with pinion cutter2(O2,x2,y2) transformation matrix M21Are as follows:
Wherein, r1For the reference radius for being processed firm gear, r2For the reference radius of pinion cutter original section；
(2.2) coordinate system S is established1To S2Bottom swear transformation matrix W21It is as follows:
(2.3) according at the contact point of mutual generated profile, the normal of the velocity vector of relative motion perpendicular to flank profilVector, two curved surfaces must satisfy following mesh equation at contact point:
ni·vi(12)=0 (i=1,2)
In formula, niAnd vi(12)It is illustrated respectively in coordinate system SiIn public law resultant of two conjugate surfaces at contact point it is relatively fastDegree arrow；
(2.4) in coordinate system S2The mesh equation in step (2.3) is substituted into, is translated into:
(2.5) matrix Ф is defined, is enabledThen haveThat is n1TΦr1=0
Wherein:
It substitutes intoIn, it can obtain:
(2.6) to each section of circular arc profile of the firm gear indicated by different functions, respective tooth profile equation and normal side need to only be inputtedJourney calls the same Ф matrix, can calculate the conjugate profiles of pinion cutter.
Further, the calculation method of the step (2.6) is specific as follows:
(2.6.1) uses numerical discretization schemes, will be using arc length u as s discrete point table of the firm gear three-arc flank profil of parameterSign enables: u any point jjFor the parameter value of the point；
(2.6.2) is by ujThe radius vector and normal vector put in flexbile gear flank profil corresponding to (j=1,2 ..., s) substitute into equationn1TΦr1In=0, the rotational angle of firm gear relative initial position when conjugate movement occurs for the point is obtainedIts value is denoted as
(2.6.3) is according to eachDetermine corresponding M12In each element value, obtain corresponding transformation matrix M12, then substitute intoIn following equation:
(2.6.4) by coordinate transform, obtain respectively with circular arc upper in firm gear three-arc flank profil, middle circular arc and lower circular arc threeThe theoretical conjugate profiles of A section, B sections of theoretical conjugate profiles and the C sections of theoretical conjugate profiles of section circular arc profile conjugation.
Further, A sections in pinion cutter theoretical conjugate profiles and C sections of theoretical conjugate profiles are adopted in the step (3)Circular fitting is carried out with " least square method ".
The invention has the benefit that
1. using three-arc harmonic wave wheel gear shaped cutter disclosed in this invention, the cutter tooth basic rack tooth profile of the pinion cutter is by three sectionsSuccessively tangent arc section is constituted, since the parameter of each section of arc section in the cutter tooth is by processed three-arc harmonic gearWork flank profil to be computed engagement determining, therefore, the three-arc tooth being process using the three-arc harmonic wave wheel gear shaped cutterWide harmonic gear can effectively increase total number of teeth in engagement, meshing backlass between flexbile gear flank profil and firm gear flank profil is made to exist in transmission processIt is distributed more uniform on entire engagement section, is conducive to the bearing capacity and transmission accuracy that improve harmonic gear；Can gramTake the smaller model that its conjugation region in the harmonic gear transmission of involute profile is distributed in major axis of wave generator areas adjacent mostlyIt the defects of encloses, can also overcome the harmonic gear transmission of common tangent formula double circular arc tooth outline, the convex circular arc profile of connection flexbile gear and recessedThe straightway flank profil part of circular arc profile is not easily formed the defect of conjugate profiles when profile angle is smaller.
2. being engaged using the tooth Profile Design method of disclosed three-arc harmonic wave wheel gear shaped cutter of the present invention using gearA sections of theoretical conjugate profiles, B sections of theoretical conjugate profiles and C sections of theoretical conjugate profiles are calculated in kinematic method, then theoretical by A sectionsConjugate profiles and C sections of theoretical conjugate profiles are all made of circular fitting, to obtain upper arc section Ac1 and lower arc section Ac3 and phaseThe parameter value answered, then by plane analytic geometry method, middle arc section Ac2 is calculated, it is basic to be accurately obtained in pinion cutterThe corresponding parametric values of flank profil can process essence using tooth Profile Design method three-arc harmonic wave wheel gear shaped cutter obtainedTrue three-arc flank profil harmonic gear, and in transmission can effectively increase total number of teeth in engagement, make between flexbile gear flank profil and firm gear flank profilMeshing backlass entirely engagement section on be distributed it is more uniform, be conducive to improve harmonic gear bearing capacity and transmission accuracy.
Detailed description of the invention
Fig. 1 is the overall structure diagram of three-arc harmonic wave wheel gear shaped cutter provided by the invention；
Fig. 2 is the schematic front view of three-arc harmonic wave wheel gear shaped cutter provided by the invention；
Fig. 3 is the A-A of Fig. 2 to schematic cross-sectional view；
Fig. 4 is the schematic diagram of cutter tooth basic rack tooth profile in three-arc harmonic wave wheel gear shaped cutter provided by the invention；
Fig. 5 is that have same direction revolution in the tooth Profile Design method of three-arc harmonic wave wheel gear shaped cutter provided by the inventionThe schematic diagram of coordinates of motion transformation.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present inventionIn attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment isA part of the embodiment of the present invention, instead of all the embodiments.The present invention being usually described and illustrated herein in the accompanying drawings is implementedThe component of example can be arranged and be designed with a variety of different configurations.
Therefore, the detailed description of the embodiment of the present invention provided in the accompanying drawings is not intended to limit below claimedThe scope of the present invention, but be merely representative of selected embodiment of the invention.Based on the embodiments of the present invention, this field is commonTechnical staff's every other embodiment obtained without creative efforts belongs to the model that the present invention protectsIt encloses.
It should be noted that in the absence of conflict, the feature in embodiment and embodiment in the present invention can phaseMutually combination.
As Figure 1-Figure 4, a kind of three-arc harmonic wave wheel gear shaped cutter, including 1 He of knife handle are disclosed in the present embodimentCutter hub 2 on the knife handle 1, the contoured surface of the cutter hub 2 are equipped with cutter tooth 3, and the tooth top anterior angle of cutter tooth 3 and tooth top relief angle pointIt Wei not γ and αt, the structure design of three-arc harmonic wave wheel gear shaped cutter and general involute spur gear pinion cutter in the present embodimentIt is similar, main difference is that the basic rack tooth profile part of cutter hub 2.
The basic rack tooth profile of the cutter tooth 3 by three sections successively tangent arc section constitute, and three sections of arc sections are respectively upper circleSegmental arc, middle arc section and lower arc section, middle arc section are intermediate connection circular arc；The radius of the upper arc section is ρ1, middle circleThe radius of segmental arc is ρ2And the radius ρ of lower arc section3；Incision superius, incision superius are formed between the upper arc section and middle arc sectionTangent line and Y-axis between angle be incision superius angle and incision superius angle is δ1, formed between middle arc section and lower arc sectionIncision inferius, the angle between the tangent line and Y-axis of incision inferius is incision inferius angle and incision inferius angle is δ2；The upper arc sectionCenter of circle offset is xaMoving with the center of circle away from amount is ya, lower arc section center of circle offset be xfMoving with the center of circle away from amount is yf；The ρ1、ρ2、ρ3、δ1、δ2、xa、ya、xfAnd yfParameter value by the work flank profil of processed three-arc harmonic gear to be computed engagement trueIt is fixed.As shown in figure 4,3 basic rack tooth profile schematic diagram of cutter tooth provided by the present embodiment, the basic rack tooth profile is by upper section dome curved toothExterior feature, lower section concave arc flank profil, intermediate connection concave arc flank profil, tooth top fillet and root fillet this five Duan Zucheng.
The basic rack tooth profile of the cutter tooth 3 further includes tooth top fillet, root fillet, tooth top, tooth root, bottom clearance and root gap, describedThe radius of tooth top fillet is ra, the radius of root fillet is rf, tooth top height be ha, tooth root height be hf, bottom clearance ca, rootGap is cf.The ra、rf、ha、hf、caAnd cfParameter value be auxiliary parameter, the auxiliary parameter is humorous by processed three-arcThe process requirements of wave gear determine.
Above-mentioned incision superius angle δ1With incision inferius angle δ2Parameter value wanted in actual tooth Profile Design according to differentIt asks, incision superius angle δ1With incision inferius angle δ2The parameter value of the two can adjust accordingly.
The normal profile of the cutter tooth 3 is by tooth top fillet, root fillet, the upper arc section, middle arc section and lower circular arcSection is constituted, it is preferred that and upper arc section is dome shape, middle arc section is recessed circle shape and lower arc section is recessed circle shape, ifThe structure is counted into, the precision of the three-arc harmonic gear of processing is higher.
For three-arc harmonic wave wheel gear shaped cutter disclosed in above-described embodiment, additionally provide it is a kind of be suitable for processing this threeThe tooth Profile Design method of circular arc harmonic wave wheel gear shaped cutter, the tooth Profile Design method the following steps are included:
(1) it is wanted according to the design that the flexbile gear of harmonic gear meets " biconjugate " and " secondary conjugation " with firm gear engagement processIt asks, designs the flexbile gear three-arc flank profil and firm gear three-arc flank profil of the condition of satisfaction；Wherein, flexbile gear and firm gear are harmonic gearsIn essential characteristic, details are not described herein again.
(2) rigid by solving pinion cutter cutting using gear gear motion method according to obtained firm gear three-arc flank profilThe mesh equation of wheel, obtains in pinion cutter A sections of theoretical conjugate profiles, B section theoretical conjugate profiles and C sections of theory conjugate profiles, and A sectionsTheoretical conjugate profiles, B sections of theoretical conjugate profiles and C section theoretical conjugate profiles respectively with gone up in firm gear three-arc flank profil circular arc, inThree sections of circular arc profile conjugation of circular arc and lower circular arc.
(3) circular fitting is all made of to A sections of theoretical conjugate profiles and C sections of theoretical conjugate profiles, respectively obtains arc sectionAc1 and lower arc section Ac3, to determine the radius ρ of upper arc section1, lower arc section radius ρ3, upper arc section center of circle offsetxa, upper arc section the center of circle move away from amount ya, lower arc section center of circle offset xf, lower arc section the center of circle move away from amount yf；
Preferably, A sections in pinion cutter theoretical conjugate profiles and C sections of theoretical conjugate profiles are all made of " most in this stepSmall square law " carries out circular fitting；Wherein, least square method (also known as least squares method) is a kind of mathematical optimization techniques, it is logicalThe optimal function matching for minimizing the quadratic sum searching data of error is crossed, can easily be acquired using least square method unknownData, and the quadratic sum of error is minimum between the data and real data that these are acquired, least square method is mainly used forCurve matching.
(4) by plane analytic geometry method, middle arc section Ac2 corresponding with B sections of theory conjugate profiles is acquired, with determinationThe radius ρ of middle arc section2, incision superius angle δ1With incision inferius angle δ2；Wherein, plane analytic geometry is a kind of by means of parsingFormula carries out the geometry branch of figure research, and analytic geometry studies straight line, circle, circle usually using two-dimensional plane right-angle coordinateThe various general plane curves such as curve, cycloid, astroid are bored, come studying plane, ball etc. using three-dimensional rectangular coordinate system in spaceVarious General Spatial curved surfaces, while their equation is studied, and define the concept and parameter of some figures.
(5) auxiliary parameter is determined by the process requirements of processed harmonic gear, which includes: radius at tooth tipra, tooth fillet radius rf, height of teeth top ha, height of teeth root hf, bottom clearance ca, root gap cf。
A sections of theoretical conjugate profiles, B sections of theoretical conjugate profiles and C sections of theoretical conjugate profiles are counted in the step (2)The method of calculation is as follows:
(2.1) coordinate transform for establishing firm gear in pinion cutter processing harmonic gear, as shown in figure 5, the seat being connected with firm gearMark system S1(O1,x1,y1) to the coordinate system S being fixedly connected with pinion cutter2(O2,x2,y2) transformation matrix M21Are as follows:
Wherein, r1For the reference radius for being processed firm gear, r2For the reference radius of pinion cutter original section；
(2.2) coordinate system S is established1To S2Bottom swear transformation matrix W21It is as follows:
(2.3) according at the contact point of mutual generated profile, the normal of the velocity vector of relative motion perpendicular to flank profil(bibliography: Li Tewen Ф Л Principles of Gear Connection (second edition) [M] Lu Xianzhan translates the Shanghai: Shanghai scientific publication to vectorSociety, 1984:33-80.), two curved surfaces must satisfy following mesh equation at contact point:
ni·vi(12)=0 (i=1,2)
In above formula, niAnd vi(12)It is illustrated respectively in coordinate system SiIn public law resultant of two conjugate surfaces at contact point it is oppositeSpeed arrow；
(2.4) in coordinate system S2The mesh equation in step (2.3) is substituted into, is translated into:
(2.5) matrix Ф is defined, is enabledThen haveThat is n1TΦr1=0
Wherein:
It substitutes intoIn, it can obtain:
(2.6) when the firm gear flank profil of three-arc harmonic gear is indicated as parameter with piecewise function using arc length, it is ensured that toothThe uniqueness and continuity of wide mathematical description.Improved kinematic method is the kinematic parameter envelope that will describe firm gear compound movement ruleIn Ф matrix, because Ф matrix does not include the geometric parameter of conjugate surface, as long as the characteristics of motion and coordinate system are chosen centainly,No matter which kind of form two conjugate surfaces are, Ф matrix has uniqueness.Therefore, each section of circular arc of firm gear indicated by different functionsFlank profil only need to input respective circular arc profile equation and normal equation, call the same Ф matrix, can conjugation tooth to pinion cutterExterior feature is calculated.
The calculation method of the step (2.6) is specific as follows:
(2.6.1) uses numerical discretization schemes, will be using arc length u as s discrete point table of the firm gear three-arc flank profil of parameterSign enables: u any point jjFor the parameter value of the point；
(2.6.2) is by ujThe radius vector and normal vector put in flexbile gear flank profil corresponding to (j=1,2 ..., s) substitute into equationn1TΦr1In=0, the rotational angle of firm gear relative initial position when conjugate movement occurs for the point is obtainedIts value is denoted as
(2.6.3) is according to eachDetermine corresponding M12In each element value, obtain corresponding transformation matrix M12, then substitute intoIn following equation:
(2.6.4) by coordinate transform, obtain respectively with circular arc upper in firm gear three-arc flank profil, middle circular arc and lower circular arc threeThe theoretical conjugate profiles of A section, B sections of theoretical conjugate profiles and the C sections of theoretical conjugate profiles of section circular arc profile conjugation.
The application of the tooth Profile Design method of above-mentioned disclosed three-arc harmonic wave wheel gear shaped cutter includes but is not limited to processThree-arc flank profil in taper shank shape pinion cutter, disk slotting cutter or bowl-shape gear shaping tool, and taper shank shape pinion cutter, disk slotting cutter orBowl-shape gear shaping tool is processable to be gone out to meet the three-arc harmonic gear of user demand.
The three-arc harmonic gear processed by the tooth Profile Design method of above-mentioned three-arc harmonic wave wheel gear shaped cutter, is passingTotal number of teeth in engagement can be effectively increased in dynamic, be distributed meshing backlass between flexbile gear flank profil and firm gear flank profil more on section in entire engageAdd the bearing capacity and transmission accuracy for being uniformly conducive to improve harmonic gear.
The present invention is not limited to above-mentioned optional embodiment, anyone can show that other are various under the inspiration of the present inventionThe product of form, however, make any variation in its shape or structure, it is all to fall into the claims in the present invention confining spectrumTechnical solution, be within the scope of the present invention.