CN101135357A - Harmonic gear drive with double arc tooth profile - Google Patents

Abstract

The present invention has a double-arc tooth profile harmonic gear transmission, which is composed of a wave generator, a flexible spline, and a rigid spline. The wave generator is in the form of an elliptical cam. arc profile. The harmonic gear transmission with double arc tooth profile can effectively improve the stress condition of the flexspline tooth root and the meshing quality of the transmission, improve the load capacity and torsional stiffness of the harmonic transmission, and further reduce the minimum transmission ratio of the harmonic transmission. Different from the cosine cam wave generator used abroad, the present invention uses an elliptical cam wave generator with excellent process performance.

Description

Harmonic Gears with double circular arc tooth outline

Technical field

The present invention relates to a kind of Harmonic Gears, particularly a kind of Harmonic Gears with double circular arc tooth outline.

Background technique

Technology of Harmonic Wave Transmission is the development along with space science, aerospace flight technology in twentieth century mid-term, a kind of novel drive technology that occurs on the basis of elastic thin shell theory.It has the kinematic accuracy height, velocity ratio is big, in light weight, volume is little, bearing capacity is big, and can be under the operating mode of confined space and working medium radiation advantage such as proper functioning, be successfully applied in the fields such as space technology, instrument and apparatus, robot, printing machinery and medical apparatus.

Harmonic drive is made up of members such as wave-generator, flexbile gear and firm wheels usually, is commonly called as " three-major-items ".Its kinology can be summarized as follows.

The harmonic driving with built-in wave-generator as shown in Figure 1, under the effect of wave-generator 1, cross section is that resiliently deformable takes place circular elastic thin-wall member flexbile gear 2.In the major axis of wave generator direction, the outer wall of flexbile gear 2 is pressed on the inwall of cross section for circular firm wheel 3.When wave-generator 1 rotation, flexbile gear 2 along then just the inwall of wheel 1 roll.If be nonslipping rolling, then flexbile gear 2 turns over the angles that determined by its girth difference mutually with firm wheel 3.Suppose that the radius before flexbile gear 2 outer walls are not out of shape is r, the radius of just having taken turns 3 inwalls is R, and its girth difference is 2 π (R-r)=2 π w ₀Wave-generator 1 is whenever goed around, and the corner that two-wheeled turns over relatively is: when firm wheel 3 fixedly the time, flexbile gear 2 turns over φ=2 π w along the sense of rotation of wave-generator 1 ₀The angle of/r; When flexbile gear 2 fixedly the time, just taken turns 3 opposite directions and turned over φ=-2 π w along wave-generator 1 rotation ₀The angle of/R.In these cases, 2 velocity ratio is from wave-generator 1 to flexbile gear $i_{}^{}$ ${}_{12}^3=r/w_0=r/(R-r),$ Velocity ratio from wave-generator 1 to firm wheel 3 is $i_{13}^2=-R/w_0=-R/(R-r).$ In common friction driving, velocity ratio equals two friction wheel diameter ratios, if flexbile gear 2 is shaped on the gear teeth respectively with the just surface of contact of wheel 3, then above-mentioned ratio should be for the ratio of the number of teeth with number of teeth difference, and the harmonic wave friction driving promptly develops into Harmonic Gears.The main at present involute profile that adopts of the Harmonic Gears of domestic production.

The main criteria of Harmonic Gears ability to work, can classify the following aspects as: the fatigue strength of flexbile gear, the wearing and tearing of the gear teeth, the gear teeth or wave-generator produce slippage, the intensity of flexible bearing and heating problem etc., and the fatigue fracture of flexbile gear is the main cause that causes Harmonic Gears to lose efficacy.

Flexspline's toothed ring influence coefficient and flexbile gear tooth root theoretical stress concentration factor are the principal elements that influences the flexbile gear fatigue fracture.

The rigidity of flexspline's toothed ring is discontinuous, and to make the circumferential stress of flexspline's toothed ring be the k of bare hull _tDoubly, therefore claim k _tBe gear teeth influence coefficient.Because actual involute profile equation is very complicated, have the trapezoidal of thickness on pitch circle and pitch circle pressure angle so the gear teeth are reduced to.In fact, gear teeth influence coefficient changes than (h/t), flexbile gear modification coefficient and the number of teeth with tooth depth thickness.Calculating shows, along with h/t increase and the number of teeth increase k _tIn rising trend, wherein the most remarkable with the influence of tooth depth wall ratio.Because along with the increase of modification coefficient, pitch circle place pressure angle increases, and the transverse tooth thickness coefficient reduces to some extent, causes the ratio of teeth groove and tooth root moment of inertia to rise, so k _tReduce along with the increase of modification coefficient.

Because in fact the existence of Fillet exists stress in the tooth root part and concentrate, on the basis of photoelastic experiment and tooth bar test, the approximative value of the stress concentration factor of acquisition is 1.8～2.0 ^[1]In order to describe the influence of Fillet radius quantitatively, can utilize the Shuwalov formula:

$k_{\mathrm{\σ}}=1+0.5(1-\frac{0.1}{r_0+0.2})\sqrt{\frac{h}{r_0}}---\left(1\right)$

$r_0=\frac{{\[m(h_a^{*}+c^{*}-x_f)-r_t\]}^2}{m(h_a^{*}+c^{*}-x_f)-r_t+0.5{\mathrm{mz}}_f}+r_t---\left(2\right)$

K in the formula _σBe the tooth root effective stress concentration factor, h is a tooth depth, mm, r ₀Be Fillet radius, mm, r _tBe the cutter Outside radius, mm, m are modulus, and mm is for modulus m≤1mm situation, r _tCan be taken as 0.4m.

Present domestic Harmonic Gears mainly adopts involute profile, and the flexbile gear Fillet radius with involute profile can be calculated by formula (2), but fillet radius is less.

Identical for main design parameters, and have the harmonic driving of identical tooth depth thickness than (h/t) and the flexbile gear number of teeth, its gear teeth influence coefficient is more or less the same.But because the flank profil difference, the difference of tooth root knuckle radius has big Fillet radius person, and its theoretical stress concentration factor reduces many, has therefore improved the bearing capacity of harmonic driving, perhaps can reduce the minimum speed ratio of harmonic driving.For example speed ratio is 100, the flexbile gear modification coefficient is that the Fillet radius of 3 involute profile is about 0.4m, flexbile gear tooth root theoretical stress concentration factor is 1.7795, for same flexbile gear, adopt double circular arc tooth outline, Fillet radius is 0.7498m, and this moment, flexbile gear tooth root theoretical stress concentration factor was 1.6113, had reduced by 9.45% than involute profile.For Harmonic Gears, the advantage with double circular arc tooth outline is not only in this.

Theory engagement calculating for the flexbile gear with single circle-arc tooth shows ^[2], since 0 ° in the interval of a broad, all have conjugate profiles to exist.This explanation is different from " the finite conjugate motion " of involute profile harmonic driving, promptly only has conjugate movement in very little meshing zone, does not contact in other position flank profil, and under the therefore low load, transmission stiffness is lower.In the whole process of the circular arc profile Harmonic Gears gear teeth, can be in the conjugate movement state all the time between the gear teeth, this result causes the gear teeth to go up contact at the whole arc of contacts in major axis M-M both sides (4 ), the mesh stiffness of transmission is improved, simultaneously because load acts on all engaging tooths simultaneously to last, this makes the load distribution that affacts on flexbile gear and the flexible bearing even, the life-span of flexbile gear and flexible bearing is improved, consider that again the intensity of flexbile gear is further enhanced because arc toothed tooth root knuckle radius is bigger.This just provides powerful guarantee for bearing capacity and its fastest ratio that can realize of reduction that improves harmonic driving.The data of Japan harmonic wave company are claimed (www.harmonic-drive.com), above transmission performance, and as the life-span of flexible bearing, transmission stiffness, mesh stiffness etc. all is doubled.

Because can not adapt to multi-form wave-generator and flexbile gear radial deformation flow coefficient by the displacement of circular tooth gear, to improve the gear meshing performance, so from reducing the cutter number of circular tooth gear, before exploitation circular arc harmonic wave gear transmission basic tooth profile, must limit wave-generator form and flexbile gear radial deformation flow coefficient.For example the Soviet Union defines roller angle β=25 and β=35 to four roller wave-generators, and Japan then mainly adopts cosine-cam wave generator.On this basis, they have developed the double circular arc tooth outline of oneself, but reason as described above, these flank profils can not be used to have the Harmonic Gears of elliptical wave generator.

For the double wave harmonic gear transmission that flexbile gear has the imposed deformation shape, domestic present employing elliptical wave generator Japan then adopts the cosine wave generator.

What the present invention designed is the double circular arc tooth outline Harmonic Gears that adopts the elliptical wave generator.

Adopt different wave-generators, the basic rack tooth profile difference that causes flexbile gear or just taken turns.Basic rack tooth profile based on different wave-generator exploitations can not be suitable for mutually.But for suitable adjustment roller angle β so that under the four roller wave-generator effects deformed shape of flexbile gear approach the way of the deformation of flexible wheel shape under cosine cam or the elliptic cam effect as far as possible, the harmonic driving that may be had suitable roller angle four roller wave-generators based on the double circular arc tooth outline of cosine cam or elliptic cam block-regulations adopts.

Summary of the invention

The Harmonic Gears that the purpose of this invention is to provide a kind of double circular arc tooth outline, flexbile gear and firm wheel have novel pair of circular arc conjugate profiles, can improve the stress state of flexbile gear tooth root and the meshing quality of transmission effectively, improve harmonic driving bearing capacity and torsional stiffness, and can further reduce the fastest ratio of harmonic driving.

The present invention is by the following technical solutions:

Description of drawings

Fig. 1 is a harmonic driving principle explanation sketch;

Fig. 2 is elliptical cam wave generator profile figure;

Fig. 3 is the production process of the wide theoretical conjugate profiles of flexbile gear double wedge;

Fig. 4 is the recessed flank profil S of explanation flexbile gear ₁₂Design must guarantee its theoretical conjugate profiles S ₂₂' with the theoretical conjugate profiles S of the second of flexbile gear double wedge exterior feature ₂₂Consistent.Otherwise, in the engagement process of Harmonic Gears, the recessed flank profil S of flexbile gear ₁₂Will with the interference of firm wheel double wedge exterior feature.

Fig. 5 be the explanation double-circular arc harmonic wave gear transmission conjugate profiles that adopts elliptical cam wave generator development process.

Fig. 6 is based on two circular arc flexbile gear flank profils of elliptical cam wave generator.

Fig. 7 is based on two circular arcs of elliptical cam wave generator and has just taken turns flank profil.

Fig. 8 is two circular arc harmonic driving sketches, and 1-is the flexbile gear with double circular arc tooth outline among the figure, and 2-is the firm wheel with double circular arc tooth outline, and 3-is an elliptical cam wave generator, and 4-is a flexible bearing.M-M is a major axis of wave generator, and S-S is a minor axis of wave generator. is the harmonic driving cornerite.

Embodiment

The present invention adopts elliptical cam wave generator.

The inside and outside circle and the flexbile gear that are elliptical wave generator outer profile, flexible bearing as shown in Figure 2 mesh the gear ring middle section under the effect of elliptical wave generator, all become the equidistant curve of this curve in theory.

The standard ellipse equation can be written as polar form

$\mathrm{\ρ}=\frac{\mathrm{ab}}{\sqrt{{\left(a\sin \mathrm{\θ}\right)}^2+{\left(b\sin \mathrm{\θ}\right)}^2}}---\left(1\right)$

In the formula, a is oval major semi axis, and b is oval semi-minor axis, and ρ is P point pole footpath.

Oval eccentricity e=c/a＜1, focal length is $2c=2\sqrt{a^2-{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="A20061011275500081.png"\; state="\{\{state\}\}">b</figure-callout>}}^2},$ Compressibility coefficient u=b/a,

$u^2=\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20061011275500081.png"\; state="\{\{state\}\}">e</figure-callout>}}^2}.$

R is the neutral circle radius of flexbile gear if make, and then Tuo Yuan major semi axis is

a＝r+w ₀ (2)

Be taken as π (a+b) if oval girth is approximate, then

b＝2r-a＝r-w ₀ (3)

If equal neutral circumference condition by the cam girth, can be by the CMHpHOB formula

$r=0.75(a+b)-0.5\sqrt{\mathrm{ab}}---\left(4\right)$

Determine b.

As shown in Figure 3, under the elliptical cam wave generator effect, studies show that by mesh theory calculating same double wedge circular arc profile forms two theoretical conjugate profiles respectively in two zones, these two zones are denoted as I _S11Zone and II _S11The zone, two theoretical conjugate profiles are designated as S respectively ₂₁And S ₂₂,

The genesis sequence of the wide theoretical conjugate profiles of the flexbile gear double wedge that underdraws now.Along with the rotation of wave-generator, the wide tooth top A of flexbile gear double wedge ₁₁At first enter conjugate movement, its theoretical conjugate point A ₂₁Become theoretical conjugate profiles S ₂₁Starting point, this moment wave-generator corner be designated as  ₁₁= _{A11, A21}, follow on the flexbile gear double wedge exterior feature from A ₁₁To B ₁₁Each point enters conjugate movement successively, and the end of article one conjugate profiles is the wide terminal B of flexbile gear double wedge ₁₁Conjugate point B ₂₁, the wave-generator corner of this moment is designated as  ₁₂= _{B11, B21}

Along with the rotation of wave-generator, flexbile gear double wedge exterior feature begins to enter the second conjugate movement district II _S11, and produce the theoretical conjugate profiles of second, the terminal B of flexbile gear flank profil flank profil ₁₁Second conjugate point B ₂₂Become the theoretical conjugate profiles S of second ₂₂Starting point, begin thus, on the flexbile gear flank profil from B ₁₁Point is to A ₁₁Point enters conjugate movement successively, and along with A ₁₁Point and its conjugate point A ₂₂Disengaging and finish.

Can finely fit theoretical conjugate profiles S with circular arc ₂₁, fit the tooth profile error that causes less than 10 by circular arc ^-5Mm, less than the requirement of actual manufacturing tolerances, therefore, S ₂₁The match circular arc can be used as the recessed flank profil of firm wheel.

Just wheel double wedge exterior feature can adopt the theoretical conjugate curve S of second of flexbile gear double wedge exterior feature ₂₂The match circular arc, still, the recessed flank profil S of flexbile gear ₁₂Design must guarantee its theoretical conjugate profiles S ₂₂' with the theoretical conjugate profiles S of the second of flexbile gear double wedge exterior feature ₂₂Consistent.Otherwise, in the engagement process of Harmonic Gears, the recessed flank profil S of flexbile gear ₁₂Will with the interference of firm wheel double wedge exterior feature.As shown in Figure 4.

Adopt elliptical cam wave generator double-circular arc harmonic wave gear transmission conjugate profiles develop software and undertaken by following program:

As shown in Figure 5, at first to guarantee that improving flexspline strength is target, the wide S of the double wedge of design flexbile gear ₁₁With recessed flank profil S ₁₂, the wide S of double wedge is found the solution in design according to the harmonic driving theory of engagement ₁₁Theoretical conjugate profiles S ₂₁And S ₂₂, to S ₂₁Carry out match with optimum circular arc, determine parameters such as the center of circle of match circular arc and radius, as the just base of design of the recessed flank profil of wheel circular arc, secondly the recessed flank profil S of flexbile gear is found the solution in design according to the harmonic driving theory of engagement with this ₁₂Theoretical conjugate profiles S ₂₃, check S ₂₃Whether with S ₂₂Interfere, guarantee S ₂₃With S ₂₂Consistent, so that flexbile gear can both satisfy conjugate movement just taking turns in the engaging-in process of nibbling out of teeth groove.

Adopt the theory of engagement analysis of the Harmonic Gears of elliptical cam wave generator to relate to the elliptic integral computing, therefore can not expect to obtain the accurate and analytical expression of circular arc profile, adopt the design of conjugate profiles of the double circular arc tooth outline Harmonic Gears of elliptical wave generator all to adopt numerical computation method to obtain.Designed two circular arc flexbile gear basic rack tooth profiles and firm wheel basic rack tooth profile are respectively as shown in Figure 6 and Figure 7.

Having the two circular arc flexible wheel of harmonic gear drive basic rack tooth profile parameters of elliptical cam wave generator is:

The fillet radius coefficient $r_g^{*}=0.6-0.9,$ Addendum coefficient $h_a^{*}=0.7-1.2,$ The dedendum of the tooth coefficient $h_f^{*}=0.7-1.2,$ H on the whole depth coefficient ^*=1.4-2.4, the wide radius of arc coefficient of double wedge ${\mathrm{\&rho;}}_a^{*}=1.4-2.0,$ The wide center of circle of double wedge is moved apart from flow coefficient $X_a^{*}=0-0.5,$ The wide center of circle of double wedge side-play amount coefficient $l_a^{*}=0.4-1.2,$ Recessed flank profil radius of arc coefficient ${\mathrm{\&rho;}}_f^{*}=1.4-2.0,$ The recessed flank profil center of circle is moved apart from flow coefficient $X_f^{*}=0-0.5,$ Recessed flank profil center of circle side-play amount coefficient $l_f^{*}=0.4-1.2,$ Process corner γ=6 °-12 °.

Band asterisk person is the coefficient of relevant parameter divided by modulus m, for example the wide radius of arc coefficient of double wedge ${\mathrm{\&rho;}}_a^{*}=\frac{{\mathrm{\&rho;}}_a}{m},$ All the other roughly the same.

Having the two circular arc harmonic driving of elliptical cam wave generator has just taken turns the basic rack tooth profile parameter and is:

The fillet radius coefficient $r_g^{*}=0.2-0.6,$ Addendum coefficient $h_a^{*}=0.7-1.2,$ The dedendum of the tooth coefficient $h_f^{*}=0.7-1.2,$ The whole depth coefficient h ^*=1.4-2.4, the wide radius of arc coefficient of double wedge ${\mathrm{\&rho;}}_a^{*}=1.4-2.0,$ The wide center of circle of double wedge is moved apart from flow coefficient $X_a^{*}=0-0.5,$ The wide center of circle of double wedge side-play amount coefficient $l_a^{*}=0.4-1.2,$ Recessed flank profil radius of arc coefficient ${\mathrm{\&rho;}}_f^{*}=1.4-2.0,$ The recessed flank profil center of circle is moved apart from flow coefficient $X_f^{*}=0-0.5,$ Recessed flank profil center of circle side-play amount coefficient $l_f^{*}=0.4-1.2,$ Process corner γ=6 °-12 °.

Beneficial effect of the present invention

The present invention has the Harmonic Gears of double circular arc tooth outline, can effectively improve the stress of flexbile gear tooth root The meshing quality of situation and transmission improves harmonic drive bearing capacity and torsional rigidity, and can further fall The fastest ratio of low harmonic drive. Different from external employing cosine-cam wave generator, the present invention adopts ellipse Boss wheel wave producer, processing performance is good.

Different and can not adapt to by the displacement of wildhaber-novikov gear multi-form ripple except parts of tooth Generator and flexbile gear radial deformation coefficient of discharge beyond the meshing performance that improves gear, adopt elliptical wave to take place The structural design of the double circular arc tooth outline harmonic gear transmission device of device with have the involute profile harmonic gear and pass Moving basic identical.

Reference

1.[Soviet Union] the M.N. Vyacheslav Ivanov. Harmonic Gears. Shen Yunwen, Li Kemei translate. Beijing: National Defense Industry Press, 19872. Xin Hongbings. circular arc profile Tooth Profile of Harmonic several problems with design. mechanical transmission 1999,23 (2): 11～12

Claims (4)

1. a Harmonic Gears comprises wave-generator, flexbile gear, just takes turns, and it is characterized in that: described harmonic driving wave-generator form is an elliptic cam.

2. Harmonic Gears according to claim 1 is characterized in that: described flexbile gear and firm wheel have double circular arc tooth outline respectively.

3. Harmonic Gears according to claim 1 and 2 is characterized in that: described flexbile gear basic rack tooth profile parameter is:

The fillet radius coefficient $r_g^{*}=0.6-0.9,$ Addendum coefficient $h_a^{*}=0.7-1.2,$ The dedendum of the tooth coefficient $h_f^{*}=0.7-1.2,$ The whole depth coefficient h ^*=1.4-2.4, the wide radius of arc coefficient of double wedge ${\mathrm{\&rho;}}_a^{*}=1.4-2.0,$ The wide center of circle of double wedge is moved apart from flow coefficient $X_a^{*}=0-0.5,$ The wide center of circle of double wedge side-play amount coefficient $l_a^{*}=0.4-1.2,$ Recessed flank profil radius of arc coefficient ${\mathrm{\&rho;}}_f^{*}=1.4-2.0,$ The recessed flank profil center of circle is moved apart from flow coefficient $X_f^{*}=0-0.5,$ Recessed flank profil center of circle side-play amount coefficient $l_f^{*}=0.4-1.2,$ Process corner γ=6 °-12 °.

Band asterisk person is the coefficient of relevant parameter divided by modulus m, for example the wide radius of arc coefficient of double wedge ${\mathrm{\&rho;}}_a^{*}=\frac{{\mathrm{\&rho;}}_a}{m},$ All the other roughly the same.

4. according to claim 1 or 2 or 3 described harmonic driving, it has just been taken turns the basic rack tooth profile parameter and is:

The fillet radius coefficient $r_g^{*}=0.2-0.6,$ Addendum coefficient $h_a^{*}=0.7-1.2,$ The dedendum of the tooth coefficient $h_f^{*}=0.7-1.2,$ The whole depth coefficient h ^*=1.4-2.4, the wide radius of arc coefficient of double wedge ${\mathrm{\&rho;}}_a^{*}=1.4-2.0,$ The wide center of circle of double wedge is moved apart from flow coefficient $X_a^{*}=0-0.5,$ The wide center of circle of double wedge side-play amount coefficient $l_a^{*}=0.4-1.2,$ Recessed flank profil radius of arc coefficient ${\mathrm{\&rho;}}_f^{*}=1.4-2.0,$ The recessed flank profil center of circle is moved apart from flow coefficient $X_f^{*}=0-0.5,$ Recessed flank profil center of circle side-play amount coefficient $l_f^{*}=0.4-1.2,$ Process corner γ=6 °-12 °.

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