DE19509448A1 - Formulated planet gearing with flat tooth mesh - Google Patents

Abstract

The planet gearing's tooth geometry is formulated and dimensioned in such a way that the relative change in flank angle can be cancelled or equalised by a change in entry angle ( DELTA beta = beta 45- beta 0) so that the self-ovalising exactly equals the optimal entry curve (X + Y) and (Rflex). (Rflex) variation is kept below 1% as per equation (10) and up to Z1 \< >120 the tooth count of the flexible gear equals (Z1 = Z2 + 2). When a second hollow or spur gear is used, the flank angle ( alpha 3) is found from equation (13). In a planet gearing including hollow gear (1) and centre spur gear, these have identical flank angles. When flank angles ( alpha 1 and alpha 2) differ only slightly, the diameter of the flexible gear is increased or decreased as per formula Dflexcorr. = Dflex x ((tg alpha 2)/(tg alpha 1)). The disc (3) is used as torque pickup, and pivot bearings spread out round the flexible planet gear (12) circumference contain pivotal bolts (31) carried radially adjustably in the disc (30) bore (32). A tensioning ring can be used to bear home in the disc bore in extreme ovalising.

Description

The invention relates to the interlocking of planets driven in accordance with the preamble of claim 1 specified characteristics.

The transmission according to the invention consists of an inside toothed ring gear or externally toothed spur gear. In the A thin-walled, flexible planet gear engages tooth gaps with a difference in the number of teeth of ΔZ ± 2 to the ring gear or Spur gear. The tooth flank shape is predominantly flat.

With these gears, large reductions can be achieved with a small construction volume. Gearboxes of this type are known from the publications considered, e.g. B .:
The Harmonic Drive Machine Design, April 14, 1960, pp. 160-173:
DE-AS 25 45 681
DE 33 36 661 C2
US 40 03 272
DE 37 38 521 C1

In the newer Harmonic-Drive catalog of the IH series, that is Transmission described in detail, such. B. in IH 3, Figures 1 + 2 stated that theoretically with flat toothing only one tooth is engaged per semicircle, but by the elliptical deformation of several teeth are engaged. In Picture 3 + 4 is a gear with curved tooth flanks shown, in which about 20% of the teeth are engaged. Similar tooth shapes were examined at the ATH-Achen and  are in the dissertation "Development of a method for Calculation of efficiency and performance limit for the Sliding Wedge Gear "by Dr. Ing. H.G. Paullik.

In Figure 3.7.5, page 48 the measured load factors for a gearbox i = 36 entered. The load shares are 21.6% of the total number of teeth.

In Figure 4.1, page 51, the intervention situation is one Single tooth in the tooth gap is shown enlarged. The quasi-elliptical rotation creates strongly curved tooth flanks. The curvature increases as the number of teeth decreases, so that the contact of the tooth flanks is linear. The Resilience is thus due to the permissible Hertzian Limited pressure.

From US-PS 40 99 472, part of DE-AS 25 45 681 corresponds to the type of GK gearbox Planetary gear known, which is structurally the same as the HD flat gear is designed. There are two inside or externally toothed gears with respect to a common axis arranged side by side, with a difference in the number of teeth ΔZ of 2 or 4 is present. In the axial direction considered is an overlap of the teeth of the two gears available so that so-called virtual tooth gaps arise, which for ΔZ = 2 after a rotation of 180 ° and at Δ Z = 4 after a 90 ° rotation from the toothing run out. This changes the tooth pitch and the  Flank angle depending on the translation and the Tooth depth (diagram 4). A flexible planet gear engages the virtual tooth gaps, being on both sides on the flanks there is a large area. The planet gear can be in simple form consist of a zigzag toothed band, thereby adapting to the flank angle and pitch change is made. The gears and the planet gear face each have a different tooth pitch.

Furthermore, the adaptation can be achieved through training as bar teeth, swiveling teeth or bar teeth with slight curvature respectively. The teeth of the flexible planet gear slide wedge-shaped with virtual contact on both sides Tooth gap of the two axially adjacent gears with a constant radial speed. The shape of the Rotary body or the drive cam is by semicircular Specified sectors, which by the amounts Δx and Δy from Pivot point are removed.

The load share of approx. 60% specified there requires Degrees of freedom to change pitch and flank angle, the with smaller numbers of teeth only with a high manufacturing effort let it be realized. As practice shows, the proportion of load decreases below i = 60 to approx. 20%.

The sliding-flex transmission is known from DE 37 38 521 C1. In this transmission, the ring gear and Spur gear arranged, which with an inside and outside  toothed flexible planet gear meshing, teeth difference in number ΔZ = (-) 2 to the ring gear and ΔZ = (+) 2 to Spur gear. There are four offset by 90 ° Engagement zones that overlap in areas.

The torque creates tensile and compressive stress in the flexible Planet gear. At high torques, the tensile stresses reduced by a clamping ring on the flexible planet gear. With this design, the teeth are on radial travel beams shifted so that the division change in some areas takes place continuously according to the tooth geometry.

According to the flank angle change shown in diagram 4, which is also unavoidable with all the types described above is, the load share is reduced with decreasing Number of teeth considerably.

The flank angle α₁ of the flexible planet gear is said to Entry angle β₀ can be increased.

This leads to jamming, especially with small numbers of teeth the teeth in the upper engagement area with the result that the load share is reduced and the uniformity factor worsened.

DE 33 36 661 C2 describes a transmission that DE 26 27 951 is similar, the engagement area near the smallest change in angle of the inlet angle is placed.  

The flank angle of the central wheel with the smallest Number of teeth and the flexible planet gear is around that double inlet angle β enlarged and for areas Curved to match the flank angle change.

Due to the large angle difference between the first The central gear and the flexible planet gear mesh the teeth not fully interlocked and jammed in the upper area. The Flank curvature causes discontinuity in penetration, so that the synchronism is disturbed.

The pressure range ϕ _E is in the range of the slightest change in the inlet angle. The large flank angle change Δα × n of the virtual tooth gaps and the flank angle α _{v of} the flexible planet gear is not compensated for, so that with small numbers of teeth, theoretically only one tooth per quarter circle is in flank contact. The degree of uniformity .DELTA.n is particularly great with small numbers of teeth.

The flexible planetary gear is ovalized at these gears by drive elements with predetermined oval shape.

The invention has for its object the interlocking to improve generic transmissions in such a way that regardless of the number of teeth, seen over the tips of the teeth Comb a maximum of Z₁ (-) 4 of the existing teeth and  with mostly flat tooth flanks over the entire area the teeth lie flat, the ovalization not like Usually done by the shape of the drive cam, but automatically thanks to the tooth geometry.

This reduces the restoring force (diagram 5) and significantly improves efficiency. The high, area-bearing tooth portion (e.g. Fig. 3 + 5) increases the resilience by a multiple compared to the generic arrangements.

The rolling bearings are loaded more evenly, whereby the Increase load capacities.

The torque is transmitted at a constant Winkelge speed; The measured deviation of Δn = 1 × 10 ^-4 has so far not been achieved by any type of gear.

This is guaranteed with at least one internal ( 20 ) or external toothing ( 21 ) ( Fig. 1 + 2) with triangular or wedge-shaped, mostly flat tooth gaps, which mesh with uniformly shaped teeth ( 14 + 16 ) from a flexible planet gear, the Outside diameter of the toothless flexible planet gear ( 12 ) according to equation 10 and the center position of M₂ by (-) X and (+) Y according to equation 8 + 9 are removed from the center M₁ ( Fig. 1 + 2).

Under this condition, the inlet angle β₀ ( Fig. 1 + 2) increases continuously with rotation from 0 to 45 ° to β _max and decreases continuously to β _{90 °} .

At a flank angle of α₁ ≈ 23 °, β _{90 is} almost identical to β₀ and the center M₂ is exactly X = Y = fm from M₁.

With a flank angle of α 1 <23 ° ( FIG. 2), X decreases according to equation 8.

The maximum entry angle β _{45 (<)} is then ϕ <55 ° D _flex (according to equation 10), becomes somewhat larger and no longer runs completely from tooth row 2 ( FIG. 2) at ϕ = 90 ° and becomes somewhat larger than β₀.

When designing the flank angle α₂ of the flexible planet gear ( 12 ) according to equation 11 or 12, the change from β₀ to β₄₅ = Δβ (equation 2a) corresponds to the relative angle change n × Δα (equation 5) Δβ-nΔα₁ = 0.

The ovalization takes place under these conditions automatically.

At α₁ ≈ 23 °, β₉₀ is virtually identical to β₀ and over that Tooth tips seen combing Z = Z₂ - 4 teeth exactly flat together.  

With smaller numbers of teeth, it is advisable to close the flank angle increase, since ovalization is reduced at the same time (Diagram 2). At the same time, β₉₀ <β₀. E.g .:

α₁ = 36 °, Z₁ = 80, β₀ = 0.9, β₉₀ = 1.5, β _diff = 0.6 °.

The relative change in angle is up to approx. 55 ° = 0 and then increases up to ϕ = 90 ° by β _diff = 0.6 °. The areal tooth contact is preserved through self-ovalization.

The teeth ( 14 + 16 ) of the flexible planet gear ( 12 ) penetrate a little deeper into the tooth gaps ( 20 + 21 ) from ϕ = 55 °, but this does not cause any kinematic disturbances.

The low ovalization force (diagram 5) and n _rel improve the efficiency.

Gearboxes with this gear arrangement are absolute free of play and can with a small surface pressure high Torques transmitted with little noise.

The measured running accuracy Δn = 0.03-0.1 × 10 ^-3 cannot be achieved by any other type.

In the arrangement Z₂ = Z₁ - 2 is α₂ <α₁ below Z₁ ≈ 130 (diagram 1) and the tooth ( 16 ) cannot penetrate fully into the tooth gap ( 20 ). The synchronism is disturbed kinematically.

Above Z₁ ≈ 130 these disturbances are prevented.

This problem is solved according to the in the Features specified claims. In the drawings are Illustrated embodiments of the invention. They show:

Fig. 1, the tooth geometry with planar flanks, and Z = 40 teeth, α₁ = 23 °,

FIG. 2 to FIG. 1, but with Z = 60 teeth and α₁ = 36 °,

Fig. 3, the engagement situation for an arrangement Z₁ = 60, α₁ = 23 ° expiring with pointed teeth,

Fig. 4 to the individual teeth 4 a kinematic disorder in involute

Fig. 4b the kinematic disorder in α₂ <α₁,

Fig. 4c the single tooth in penetrating the Hohlradlücken with the highly curved Paullik toothing,

Figure 5 is sectional quarter view disc drive. A gear arrangement with rolling,

Fig. 6 is a compact transmission having 2 externally toothed spur gears,

FIG. 6a is a longitudinal section to

Fig. 7 shows a gear kit with driven pulleys,

Fig. 7a the cross section of Fig. 7,

Fig. 8 a, b and c, the engagement situation in a harmonic drive type,

Fig. 9 shows the quarter section of a transmission with a second ring gear,

Fig. 10 shows the longitudinal section through a gear arrangement with an additional spur gear.

Diagram 1 shows the course of the flank angle, depending on α₁ and the number of teeth;
Diagram 2 shows the magnitude of the ovalization "e" depending on the flank angle α₁ and the number of teeth;
Diagram 3 shows the increase in rolling resistance at µ depending on the ovalization;
Diagram 4 shows the deviation of an involute toothing from the flat surface;
Diagram 5 the ovalization force for a ring, depending on "e";
Diagram 6 shows the change in the flank angle α depending on the number of teeth and ΔZ;
Diagram 7 the correction factor f over the flank angle α;
Table 1 Calculation formulas.

Fig. 1

Fig. 1 shows a quarter section of a row of teeth ( 20 ) for internal teeth and at the same time (2.1) for external teeth with triangular teeth, the outer radius R₁ and the inner radius R₂. The number of teeth is Z₁ = 40, the flank angle α₁ was chosen to be 23 °. The radial tooth height is halved by the radius R₀. The tooth pitch is marked by zero circles (2.4 + 2.5), where 2.4 = Z₁ + 2, ie 42 teeth and 2.5 = Z₁ (-) 2 = 38 correspond to the number of teeth Z₂ of the flexible planet gear. If you put intersection lines (2.6 + 2.7) through the center M₁ and the zero circles (2.4 + 2.5), the row of teeth is cut into 22 + 23 , which mark the tooth tips ( 16 ) of the flexible planet gear ( 12 ). The result is a quarter-circle arc whose center M₂ is very precisely f × m in the X and Y axes outside the quarter circle from the center M₁. The triangles a, b and c over the entire area are similar, so that a constant reduction of the pitch from 0 to 90 ° is ensured and the tooth shift takes place at a constant radial speed. Furthermore, the inlet angle β₀ increases steadily to β _{45 °} and then decreases steadily to β _{90 °} , whereby β₀ and β _{90 ° become} almost identical. The entry angles are calculated from equation 1 + 2. The change in the flank angle Δα for ΔZ = 42 is calculated according to equation 5.

In Fig. 1, for the sake of clarity, individual teeth ( 16 ) of the flexible planet gear ( 12 ) have been drawn in at different engagement positions. If one selects Z₂ = Z₁ + 2 for the flexible planetary gear ( 12 ), then the tooth pitch of the flexible planetary gear ( 12 ) is reduced over the tooth tips in the ratio Z₁ / Z₂.

The assigned flank angle is calculated according to equation 12 With Z₂ = Z₁ (-) 2 the division increases in reverse Relationship; the assigned flank angle then becomes:

α₂ = α₁-β₀-Δβ + nΔα (Eq. 12)

With Z₂ = Z₁ + 2 and α₂ according to equation 11, α₂ <α₁ and the right tooth flanks lie flat against the left tooth flanks of Z₁ and are automatically shifted. The resulting head curve R _flex coincides exactly with the optimal ovalization curve, created from the intersection lines with the pitch circle curve (2.6 + 2.7) with the pitch circle curve R₀.

With Z₂ = Z₁ (-) 2 the same curve is generated. Of the The flank angle is then on the opposite side.

With the chosen arrangement α₁ = 23 °, X = Y = fm, the relative change in angle n × Δα₁ (equation 5) becomes the same as the angle difference Δβ = β₄₅-β₀ (equation 2a), that is, nΔα₁-Δβ = 0, that is, that the flanks α₁ ( 20 ) and α₂ ( 16 ) mesh exactly with each other ( Fig. 3) and seen over the tooth tips Z₂ (-) 4 teeth are engaged. With Z₂ = Z₁ + 2, the direction of rotation of the flexible planet gear ( 12 ) and the drive shaft ( 82 ) in the same direction; the relative speed is n _rel = n _a (1-1 / j).

Fig. 2

In Fig. 2 a tooth geometry with Z₁ = 60, Z₂ = 62, α₁ = 36 ° is shown in a quarter circle, with R₁, R₃ and R _flex and the individual teeth of the flexible planet gear ( 12 ). The choice of α₁ = 36 ° is advantageous because α₂ = 36 ° becomes almost the same size as α₁, the maximum entry angle β _{45 <being} π ≈ 55 ° and X <Y.

The ovalization curve formed by M₁ and R _flex is ϕ = 90 ° still somewhat within the row of teeth ( 20 ) and requires a correction of the tooth tips ( Fig. 5). The remaining teeth then comb evenly.

For smaller numbers of teeth z. B. Z₁ = 40-120, it makes sense To increase flank angle α₁, which at the same time Ovalization e is reduced (diagram 3). But it will also nΔα₁ <Δβ.

If α₁ <23 ° is selected, nΔα₁ <Δβ.

This will make the area of engagement

reduced or enlarged.

This is avoided by increasing or decreasing the outer diameter of the flexible planet gear ( 12 ) according to equation 10: D _flex = D₀ [1 + 2 / π tg (nΔα₁-Δβ)]
The formulas (Table 1) apply to the center position M₂, the inlet angle β₀ and the flank angle α₂, whereby the center position M₂ inevitably results from self-ovalization as with α₁ = 23 °.

Fig. 3

In Fig. 3 the engagement situation for an arrangement with α₁ = 23 °, Z₁ = 60, Z₂ = 62, α₂ = 21.5 ° with pointed tooth flanks ( 20 + 16 ) is shown. The center M₂ is exactly X = Y = fm from the center M₁. The tooth flanks ( 20 + 16 ) comb exactly flat to Z₂ (-) 4, the slimmer tooth of the flexible planet gear ( 12 ) with α₂ = 21.5 ° being able to penetrate freely into the tooth gap ( 20 ) at eh = 0.

Fig. 4

Fig. 4a shows the breakdown (black) of a single tooth at Z₁ = 40 with involute curvature and after 45 ° rotation.

Fig. 4b, like Fig. 4a, but with flat edges and the number of teeth difference Z₂ = Z₁ (-) 2. α₁ = 30 °. The flank angle α₂ increases to 36 ° and jams with further penetration into the tooth gap ( 21 ). With this arrangement, the flanks of the flexible planet gear ( 12 ) must be curved (2.6).

Fig. 4c shows a detail of the tooth geometry in quasi elliptical rotation, said two hollow wheels with .DELTA.Z = 2 are arranged on one axis. The tooth forms differ greatly from one another. As a result of the strong curvature and linear contact, high Hertzian pressures occur which limit the torque. Gears of this type are expensive.

Fig. 5

Fig. 5 shows a quarter section in plan view of a gear with Z₁ = 60, Z₂ = 62, α₁ = α₂ = 36 °, e = 2.5% and roller drive (see also figure). The tooth geometry corresponds to Fig. 2. The tooth tips of 20 and 16 are somewhat corrected. The load share is then E = 80%. The toothing of the ring gear ( 1 ) meshes flat with the toothing ( 16 ) of the flexible planet gear ( 12 ), which is double toothed ( 14 ). The double toothing has the advantage that even with larger ovalization, here z. B. e = 2.5%, the restoring forces are virtually zero and manufacturing-related tolerances are compensated. Self-ovalization stabilizes the flexible planet gear so strongly that no kinematic shift is possible.

A support ring ( 221 ) with a slot "s" is arranged between the flexible planet gear ( 12 ) and the roller washers ( 9 ). The radial force F _r for radial tooth displacement is introduced via the roller drive. The roller disc drive consists of two circular discs ( 9 ) with the roller bearings ( 91 ), the double eccentric ( 89 ), which is attached to the drive cam ( 82 ).

The center M₃ is advantageously 2Y away from M₂. The rolling disks ( 9 ) only touch the support ring ( 221 ), which is also ovalized by the tooth geometry, in some areas. However, since the flexible planet gear ( 12 ) is stabilized, the position of the flexible planet gear ( 12 ) can only change insignificantly even at high torques.

The kinematic quality shows no difference compared to the ovalized roller bearing ( Fig. 7).

Rolling disc drives improve efficiency and are especially for large gearbox dimensions and high speeds suitable. For ovalization up to approx. E = 3% be used.

Theoretically, the gearbox efficiency improves as the flank angle α decreases, which reduces the radial force F _r = F _u × tg, but at the same time increases the ovalization e (diagram 2) and the rolling resistance (diagram 3). In addition, tooth friction losses increase due to increasing flank speed.

Comparative calculations for α₁ = 23 ° and α₁ = 36 ° show no significant differences.

The calculated value of α₂ according to equation 11 is 35.6 °. When interlocking with the same cutting tools, α₂ = 36 ° can be carried out if you correct D _flex according to equation 10.

Fig. 6

A particularly compact transmission results from the arrangement according to FIG. 6 with two externally toothed spur gears ( 6 + 7 ), in which the flexible planet gear ( 12 ) arranged on the outside engages. The low tension occurring between the individual teeth is reduced by a clamping ring ( 122 ).

The arrangement of the flexible planetary gear ( 12 ) outside the rows of teeth ( 6 + 7 ) reduces the percentage ovalization compared to the internal arrangement according to FIG. 5.

The outer diameter of the flexible planetary gear ( 12 ) is interrupted by cutouts ( 121 ) which reduce the bending stresses caused by ovalization to reliable dimensions.

The arrangement according to FIG. 6 is particularly suitable for smaller numbers of teeth.

Fig. 7

Fig. 7 shows a transmission in which the outer dimension of the ring gear ( 1 ) is identical to the ring gear dimension of HD U 100.

The flexible planet gear ( 12 ) is axially guided in the ring gear ( 1 ) through the thrust washers ( 111 ) and circlips ( 11 ).

In the free part of the flexible planet gear ( 12 ), holes ( 34 ) with pressed-in spherical bearings ( 33 ) and bolts ( 31 ) are evenly distributed over the circumference.

The drive flange ( 3 ) is drilled accordingly, with pressed-in, self-lubricating plain bearings ( 32 ).

A heavy-duty roller bearing with a slotted outer ring ( 221 ) serves as the drive bearing ( 22 ).

The torque is introduced into the gearbox flange via the spherical bearings ( 33 ) and bolts ( 31 ).

The sliding speed is V = 2mf × n _a for the transmission according to FIG. 7.

n _a = 1500, i = 80, V = 0.18 m / s.

The friction losses are therefore negligible low.

Fig. 7a

Fig. 7a shows a cross section through the drive flange ( 3 ) and the maximum pivoting movement at 45 °, shown enlarged.

In the case of larger ovalization, relief bores ( 113 ) can be arranged in the vicinity of the spherical plain bearings, so that very small changes in the bore caused by the ovalization can be compensated for.

The bearing play between the bolt ( 31 ) and slide bearing ( 32 ) is approximately d₃ / 1000, so that the torque transmission is virtually free of play.

The swivel movement follows the entry angle β exactly, which means that the load is evenly distributed to the bolts ( 31 ). Compared to generic types, in which the torque is transmitted by a second ring gear with the same number of teeth (Z₃ = Z₂), the efficiency improves by about half of the losses occurring there.

Gearboxes of this type are very compact (the overall length is approximately 1/3 of the HDUc series).

The spring constant Nm / radian is extremely large and comparable with the stub shaft connection.

Fig. 8

Fig. 8 shows the harmonic drive type with the ring gear ( 1 ) on the Flexspine ( 12 ).

Fig. 8a shows the transmission at the maximum ovalization, where e / is shown enlarged approximately three times 2 because of better graphical representation.

It can be seen that the tooth flanks are parallel to each other only after 90 ° rotation ( Fig. 8b).

With maximum ovalization due to the inclined position, Theoretically, torque transmission only takes place in one point instead.

An axial force acts on the rolling bearing, which is what the Practice shows that the bearing has a shifting effect.

In Fig. 8b is the tooth position of a harmonic drive toothing with Z₁ = 60 and Z₂ = Z₁ (-) 2 = 58 wear.

Due to the elliptical rotation of the wave generator (not theoretically only the tooth has ϕ = 0 surface contact. As the number of teeth grows, the Deviation less and the proportion of load increases.

Fig. 9

Fig. 9 shows in quarter section the top view of a transmission according to FIGS. 1, 2 and 5 with an additional ring gear ( 3 ).

The drive takes place via an ovalized roller bearing. The flank angles α₁, α₂, α₃ were determined according to equation 11-13. The so-called virtual tooth gaps formed by the tooth gaps ( 20-22 ) of FIGS. 1 and 3 evenly mesh with the tooth flanks ( 16 ) of the flexible planet gear ( 12 ).

The outer ring ( 221 ) of the roller bearing ( 22 ) is slanted obliquely or arrow-shaped at a point "s". The quarter circles of the drive cam ( 18 ) form a tip at the intersection of the Y axis, which is rounded off by a radius r lying on the Y axis.

This measure disengages the top tooth ( 121 ) and thus prevents synchronism when the direction of movement is reversed.

The outer bearing ring ( 221 ) slotted at "s" is acted upon by the radial forces F _K in area E, so that all rolling elements in area E are involved in the load distribution. This increases the basic dynamic load rating C₀ to about three times the unstressed rolling bearing.

The ovalization of the bearing ring ( 221 ) also takes place through the toothing geometry and generates hardly any restoring forces. The rolling resistance is shown in diagram 6 with a closed outer bearing ring. The ratio of the two is synonymous with the improvement in efficiency.

Fig. 10

Fig. 10 shows a longitudinal section through a gear arrangement with an additionally arranged spur gear ( 6 ).

The difference in the number of teeth ΔZ = 4 halves the reduction. The tooth geometry corresponds to equations 10, 11 and 14 with a roller drive ( 9 ).

Clamping rings ( 121 ) are arranged on both sides of the flexible planetary gear, which, as in FIG. 6a, lie in the ring gear with the greatest ovalization and thus reduce tensile and compressive stresses.

The spur gear ( 6 ) has an additional internal toothing ( 17 ) and meshes with a planetary preliminary stage ( 171 , 172 , 18 ), the eccentric being used as a planetary preliminary stage.

The reduction ratio of the preliminary stage can be up to i = 10, the total reduction ratio i _tot up to 800 without changing the construction volume.

Gearboxes of this type have a high efficiency, e.g. B. at i₁ = 40, i _p = 4, i _tot = 160, the efficiency is 94%.

In the Harmonic-Drive catalog a gear efficiency of 51% is given for a reduction of i = 160, n _a 1750 min ^-1 .

Diagram 1

Diagram 1 contains the change in the flank angle α₂, or α₁ if α₂ is given for different flank angles, plotted over the number of teeth.

From about Z₁ = 150, the deviations are so small that the Gearing can take place with a constant flank angle.

Chart 2

Diagram 2 contains the ovalization in% based on the Ring gear diameter for different flank angles α, traced gene on the number of teeth Z₁.

Experience has shown that ovalization should not exceed e = 2.5% step, thereby extending the natural limit of this design at i = 20, Z₁ = 40 and α₁ = 36 °.

Diagram 3

Diagram 3 shows the change in rolling resistance µ₁ depending on the ovalization for a standard bearing and a special camp is recorded, which is a determining factor for the Efficiency is.

For an ovalization e <1.5%, the roller drive is advantageously used. The ovalization is then carried out by means of eccentrically arranged disks on roller bearings ( Fig. 6 + 10).

Diagram 4

Diagram 4 shows the deviation of the arc height (in%) from the chord length (length of the tooth flank) over the number of teeth entered, which occurs in the involute teeth.  

In the event of a deviation of <1%, meshing and synchronism are recorded disturbed.

At least the row of teeth Z₁ should be toothed with flat flanks ( Fig. 4a).

With larger numbers of teeth, the deviation becomes smaller and has hardly any influence on the running quality.

Diagram 5

Diagram 5 shows the course of the ovalization force F _ov as a function of the ovalization size for a ring s / D = 0.025, B = 20 mm.

In curve 1, the ovalization is due to the tight fit Drive cam generated.

Curve 2 is obtained with ovalization by point load or Individual forces distributed over the circumference, with automatic ovalis sation.

As these forces act on the drive bearing the improves automatic ovalization the transmission efficiency.

Diagram 6

Diagram 6 shows the relative change in angle Δα for ΔZ = 2 and ΔZ = 4.

Diagram 7

In diagram 7 the course of the correction factor f is over entered the flank angle.  

The tooth geometry is mathematically determined by the Equations 1 through 15 are determined so that the relative edges change in angle nΔα₁ by the change in inlet angle Δβ = β₄₅-β₀ is canceled or balanced.

Under this condition, the rows of teeth 1 and 12 self-ovalize, whereby the teeth mesh with each other over the entire surface and the ovalization corresponds to the optimal run-in curve formed from R _flex and X + Y.

Formulas

Claims (8)

1. Planetary gear with an internal or external toothing ( 1 ) with predominantly flat tooth gaps ( 20 + 21 ), which meshes with a flexible planet gear ( 12 ) with similar teeth ( 14 + 16 ), the tooth flanks ( 20 + 21 , 14 + 16 ) comb exactly flat and seen over the tooth tips Z₂ (-) 4 teeth are engaged, characterized in that the tooth geometry ( Fig. 1 + 2) is mathematically determined by equations 1 to 15, Table 1, so that the relative flank angle change nΔα₁ is canceled or compensated for by a change in the running angle Δβ = β₄₅-β₀, the self-ovalization "e" corresponding to the optimal running-in curve, formed from X + Y and R _flex , exactly. 2. Planetary gear according to claim 1, characterized in that the deviation of R _flex according to equation 10 is not greater than 1%. 3. Planetary gear according to claim 1 + 2, characterized in that up to Z₁ ≈ 120 the number of teeth of the flexible planet gear ( 12 ) is Z₂ = Z₁ + 2. 4. Planetary gear according to claim 1 + 2 with a second, arranged side by side ring or spur gear ( 7 + 2 ) ( Fig. 6 + 9), characterized in that the flank angle α₃ is determined according to equation 13. 5. Planetary gear according to claim 1 + 2 with a ring gear ( 1 ) and a centrally arranged spur gear ( 6 ) ( Fig. 10), characterized in that the flank angle α₁ and α₄ of the ring gear ( 1 ) and the spur gear ( 6 ) of the same size is. 6. Planetary gear according to claim 1 with slight deviation of the flank angle α₁ and α₂, characterized in that the diameter of the flexible planet gear ( 12 ) according something is enlarged or reduced. 7. Planetary gear according to claim 1 + 2 with an inside the flexible planet gear ( 12 ) arranged disc ( 3 ) ( Fig. 7 + 7a), via which the torque is removed, characterized in that on the circumference of the flexible planet gear ( 12 ) Distributed joint bearings ( 33 + 34 ) are arranged, in which pivotable bolts ( 31 ) are fastened, which are mounted radially displaceably in the bore ( 32 ) of the disc ( 3 ). 8. Planetary gear according to claim 1 + 2 and according to Fig. 7 + 10 with a clamping ring ( 121 ), characterized in that with greater ovalization of the clamping ring ( 121 ) rests in the bore ( 122 ).