CN112664638B - Three-dimensional tooth profile shaping method for flexible gear of harmonic reducer - Google Patents
Three-dimensional tooth profile shaping method for flexible gear of harmonic reducer Download PDFInfo
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Abstract
The application relates to a three-dimensional tooth profile shaping method for a flexible gear of a harmonic reducer, which comprises the following steps: flexible measuring gearAn outward expansion inclination angle alpha on the outer wall of the long shaft and an inward contraction inclination angle beta on the outer wall of the short shaft; and obtaining the long axis a of each section of the flexible gear ti And a minor axis b ti The distance i from the bottom end of the flexible gear; establishing a rigid wheel fixed connection coordinate system S in the section of the harmonic reducer i (O i ,X i ,Y i ) Obtaining a rigid wheel fixed connection coordinate system S i Tooth profile equation f of medium rigid wheel g (i) And according to the major axis a of the flexible gear in the section of the harmonic reducer ti And a minor axis b ti Establishing a flexspline tooth profile equation f r (i) (ii) a According to the equation f of the tooth profile of a rigid wheel g Sum flexspline tooth profile equation f r Obtaining the modification quantity delta of the convex teeth of the flexible gear in each section i Said modification amount Δ i The displacement of the tooth profile of the outer teeth of the flexible gear moving towards the center of the flexible gear along the radial direction when the outer teeth of the flexible gear and the inner teeth of the rigid gear do not interfere with each other. The flexible gear has the effect of reducing the probability of interference between the outer teeth of the flexible gear and the inner teeth of the rigid gear.
Description
Technical Field
The application relates to the field of tooth profile design of a speed reducer, in particular to a three-dimensional tooth profile modification method for a flexible gear of a harmonic speed reducer.
Background
The harmonic reducer comprises a wave generator, a flexible gear with external teeth and a rigid gear with internal teeth. The wave generator comprises an elliptical cam and a flexible bearing sleeved on the outer side of the elliptical cam, and the whole wave generator is elliptical. The flexspline is a thin-wall cylindrical part, and when the wave generator is arranged in the flexspline and is in contact with the inner wall of the flexspline, the cross section of the flexspline is elliptical, and the flexspline is enabled to have a long axis direction and a short axis direction. The flexible wheel is in an outwards-expanding state in the long axis direction and in an inwards-contracting state in the short axis direction. The number of teeth of the flexible gear is 2 more than that of the rigid gear, and when the flexible gear is arranged in the rigid gear, the flexible gear and the rigid gear are in a symmetrical meshing state in the long axis direction and are not meshed in the short axis direction.
With respect to the related art in the above, the inventors considered that after the wave generator was attached to the flexspline, the amount of deformation of the flexspline was different in each cross section in the axial direction, resulting in different meshing states of the external teeth of the flexspline and the internal teeth of the rigid spline in each cross section, so that the external teeth of the flexspline and the internal teeth of the rigid spline were liable to interfere.
Disclosure of Invention
In order to reduce the probability of interference between the outer teeth of the flexible gear and the inner teeth of the rigid gear, the application provides a three-dimensional tooth profile modification method for the flexible gear of the harmonic reducer.
The application provides a three-dimensional tooth profile shaping method for a flexible gear of a harmonic reducer, which adopts the following technical scheme:
a three-dimensional tooth profile shaping method for a flexible gear of a harmonic reducer comprises the following steps: measuring an extension inclination angle alpha of the flexible gear on the outer wall of the long shaft and a retraction inclination angle beta of the flexible gear on the outer wall of the short shaft; and obtaining the long axis a of each section of the flexible gear ti And a minor axis b ti The distance i from the bottom end of the flexible gear;
establishing a rigid wheel fixed connection coordinate system S in the section of the harmonic reducer i (O i ，X i ，Y i ) Obtaining a rigid wheel fixed connection coordinate system S i Tooth profile equation f of medium rigid wheel g (i) And according to the major axis a of the flexible gear in the section of the harmonic reducer ti And a minor axis b ti Establishing a flexspline tooth profile equation f r (i)；
According to the equation f of the tooth profile of a rigid wheel g Sum flexspline tooth profile equation f r Obtaining the modification quantity delta of the convex teeth of the flexible gear in each section i Said modification amount Δ i The displacement of the tooth profile of the outer gear of the flexible gear moving towards the center of the flexible gear along the radial direction when the outer gear of the flexible gear and the inner gear of the rigid gear do not interfere.
By adopting the technical scheme, after the wave generator is installed on the flexible gear, the flexible gear is in an outwards-expanding state on the outer wall of the long shaft, and an outwards-expanding inclination angle alpha is generated by outwards expanding the outer wall of the long shaft; the flexible gear is in a retraction state on the outer wall of the short shaft and retracts on the outer wall of the short shaft to generate a retraction inclination angle beta; and both the flare inclination angle alpha and the retraction inclination angle beta can be obtained by measurement. According to the flare inclination angle alpha and the retraction inclination angle beta, the long axis a of the flexible gear in each section can be obtained ti And a minor axis b ti And the distance i from the bottom end of the flexible gear.
Fixedly connecting a coordinate system S on a rigid wheel i (O i ，X i ，Y i ) Rear rigid wheel fixed connection coordinate system S i (O i ，X i ，Y i ) Fixedly connected with a rigid wheel, and the parameters of the rigid wheel are conventionalEvaluating, then obtaining the rigid wheel fixed connection coordinate system S i (O i ，X i ，Y i ) Tooth profile equation f of medium rigid wheel g (ii) a Due to the long axis a of the flexspline in each section ti And a minor axis b ti Can be determined by the distance i from the bottom end of the flexible gear, and can also be acquired in a coordinate system S i (O i ，X i ，Y i ) Tooth profile equation f of medium flexible gear r . Because the rigid wheel is fixedly connected with the coordinate system S i (O i ，X i ，Y i ) Tooth profile equation f of medium rigid wheel g Sum flexspline tooth profile equation f r All are constant values, namely the modification quantity delta can be obtained i 。
Wherein the modification amount delta i The tooth profile of the outer teeth of the flexible gear moves towards the center of the flexible gear along the radial direction when the outer teeth of the flexible gear and the inner teeth of the rigid gear do not interfere with each other, the tooth profile of the outer teeth of the flexible gear is different from a direct cutting type modification method for the outer teeth of the flexible gear, the tooth profile of the outer teeth of the flexible gear moves towards the center of the flexible gear along the radial direction, meshing transmission of the flexible gear and the rigid gear is facilitated to be smoother, and the transmission performance is more ideal.
Optionally, according to the rigid wheel tooth profile equation f g Sum flexspline tooth profile equation f r Obtaining the modification amount delta of the convex teeth of the flexible gear in each section i The method comprises the following steps: the radial direction in the rigid wheel is matched with Y i The inner teeth which are parallel to the axis and are positioned at the upper part of the rigid gear are defined as measuring inner teeth, and the circle center coordinate (x) of the tooth root tooth profile of the measuring inner teeth is obtained gf ，y gf ) And the center coordinates (x) of tooth top tooth profile ga ，y ga ) (ii) a One outer tooth in the unmodified flexible gear is defined as a measurement outer tooth, and the center coordinates (x) of a convex tooth profile of the measurement outer tooth when the measurement outer tooth is meshed with the measurement inner tooth are acquired ra ，y ra ) And the center coordinates (x) of the concave tooth profile rf ，y rf )；
When the measuring and calculating outer teeth are meshed with the measuring and calculating inner teeth, the circle center coordinate of the convex tooth profile of the measuring and calculating outer teeth of the modified flexible gear is (x) ra ，y ra -Δ i ) And the circle center coordinate of the concave tooth profile of the external teeth is measured and calculated by the modified flexible gear is (x) rf ，y rf -Δ i )；
The condition that the working tooth profile of the measuring and calculating outer teeth of the modified rear flexible gear and the tooth root profile of the measuring and calculating inner teeth of the rigid gear do not interfere with each other is as follows:
where ρ is gf Measuring the tooth root tooth profile radius of the inner teeth; rho ra Measuring and calculating the convex tooth profile radius of the external teeth;
the condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear and the tooth top tooth profile of the measuring and calculating internal teeth of the rigid gear do not interfere is as follows:
where ρ is ga Measuring and calculating the tooth crest tooth profile radius of the internal teeth; rho rf The method is used for measuring and calculating the radius of the concave tooth profile of the external teeth.
Calculating and obtaining a modification quantity delta according to the condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear and the tooth root profile of the measuring and calculating internal teeth of the rigid gear do not interfere with each other and the condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear and the tooth root profile of the measuring and calculating internal teeth of the rigid gear do not interfere with each other i The value range of (a).
By adopting the technical scheme, the tooth profiles of all the internal teeth in the rigid gear are kept consistent, and the tooth profiles of all the external teeth in the flexible gear are kept consistent, so that the trimming amount of the measuring and calculating external teeth when the measuring and calculating internal teeth do not interfere is only calculated. The modification amount of other external teeth of the flexible gear is consistent with the modification amount of the measured external teeth, namely all the external teeth of the flexible gear are ensured not to interfere with the internal teeth of the rigid gear. The calculation can obtain the modification quantity delta in each section of the flexible gear i And a distance i from the bottom end of the flexible gear, so that the external teeth of the flexible gear can be modified, and the external teeth of the flexible gear and the internal teeth of the rigid gear do not generateAnd (5) interference.
Optionally, calculating the acquisition a ti Equal to the flexible gear design long axis a t The value of the distance i from the bottom end of the time-distance flexible gear is i m ；
When i < i m Then, the modification amount delta is calculated and obtained according to the condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear and the tooth top tooth profile of the measuring and calculating internal teeth of the rigid gear do not interfere i And obtaining the minimum modification quantity delta imin A functional relation with i.
When i > i m Then, the modification quantity delta is calculated and obtained according to the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear and the condition that the tooth roots of the measuring and calculating internal teeth of the rigid gear do not interfere i And obtaining the minimum modification quantity delta imin A functional relation with i.
By adopting the technical scheme, the three-dimensional tooth profile modification method of the flexible gear of the harmonic reducer is simplified, and i is calculated firstly m Substituting different i value regions into corresponding non-interference conditions to obtain corresponding modification quantity delta i Value range and minimum modification amount delta of imin A functional relation with i.
In summary, the present application includes at least one of the following beneficial technical effects:
1. by providing the three-dimensional tooth profile modifying method for the flexible gear of the harmonic reducer, the outer teeth of the flexible gear are modified, the probability of interference between the outer teeth of the flexible gear and the inner teeth of the rigid gear is reduced, and the service life of the harmonic reducer is prolonged;
2. obtaining a by calculation ti Equal to the flexible gear design long axis a t The value of the distance i from the bottom end of the time-distance flexible gear is i m Then substituting different i value regions into corresponding non-interference conditions to obtain corresponding modification quantity delta i The value range of the harmonic reducer simplifies the three-dimensional tooth profile modification method of the flexible gear of the harmonic reducer.
Drawings
Fig. 1 is a schematic structural diagram of a harmonic reducer in the present application.
Fig. 2 is a schematic sectional view of the wave generator at the outer wall of the major axis and at the outer wall of the minor axis after being mounted to the flexspline in the present application.
Fig. 3 is a diagram of the present application when i ═ i m The locus diagram of the outer teeth at the inner teeth.
FIG. 4 shows the equation when i < i in the present application m The locus diagram of the outer teeth at the inner teeth.
FIG. 5 shows the case where i > i in the present application m The locus diagram of the outer teeth at the inner teeth.
Description of reference numerals: 1. a rigid wheel; 11. installing a cavity; 12. internal teeth; 2. a flexible gear; 21. a cup mouth; 22. an outer tooth; 3. a wave generator; 31. a compliant bearing; 32. a cam.
Detailed Description
The present application is described in further detail below with reference to figures 1-5.
The embodiment of the application discloses a three-dimensional tooth profile shaping method for a flexible gear of a harmonic reducer.
Referring to fig. 1, a schematic diagram of a harmonic reducer includes a rigid gear 1, a flexible gear 2, and a wave generator 3.
The wave generator 3 comprises a flexible bearing 31 and a cam 32. The cam 32 is an elliptical cam. When the cam 32 is mounted to the flexible bearing 31, the cam 32 supports the flexible bearing 31 and deforms the flexible bearing 31 so that the outer side wall profile of the entire wave generator 3 is elliptical.
Referring to fig. 1 and 2, the flexspline 2 is a thin-walled cylindrical part in its entirety and has a cup 21 for mounting the wave generator 3 to the internal cavity. The outer side wall of the flexspline 2 is circumferentially provided with outer teeth 22. The wave generator 3 is installed to the flexbile gear 2 and is installed in the cup mouth 21 department of flexbile gear 2 in interference fit, and the flexbile gear 2 is supported by the wave generator 3 so that the flexbile gear 2 takes place to warp, and the cross-section of one section of the flexbile gear 2 of installing wave generator 3 all tends to ellipse.
Referring to fig. 1 and 2, the rotation center of the rigid wheel 1 coincides with the rotation center of the wave generator 3. The rigid wheel 1 is provided with a mounting cavity 11 for mounting the flexible wheel 2, the section of the mounting cavity 11 is circular, and the rigid wheel 1 is provided with internal teeth 12 matched with external teeth 22 of the flexible wheel 2 on the inner wall of the mounting cavity 11. When the flexible gear 2 is mounted on the rigid gear 1, the flexible gear 2 and the rigid gear 1 are symmetrically engaged in the long axis direction and are not engaged in the short axis direction.
When the flexible gear 2 is assembled with the wave generator 3, the barrel wall of the flexible gear 2 is in an outwards-expanding state in the long axis direction and in an inwards-contracting state in the short axis direction, the barrel wall of the flexible gear 2 is outwards expanded in the long axis direction to generate an outwards-expanding inclination angle alpha, and the barrel wall of the flexible gear 2 is inwards contracted in the short axis direction to generate an inwards-contracting inclination angle beta, so that the long axis and the short axis of each section perpendicular to the axis of the flexible gear are different, the long axis of the section closer to the cup opening 21 is larger, and the short axis of the section closer to the cup opening 21 is smaller. Since the deformation amount of each section of the flexible gear 2 in the axial direction is different, the degree of meshing between the tooth profile of the external teeth 22 of the flexible gear 2 and the tooth profile of the internal teeth 12 of the rigid gear 1 is different in each section, which easily causes the interference between the flexible gear 2 and the rigid gear 1.
The values of the camber angle alpha and the camber angle beta are approximate, and the camber angle alpha and the camber angle beta can be calculated equivalently in the calculation process.
Referring to fig. 2 and 3, when the wave generator 3 is installed into the flexspline 2, there exists a section in which the length of the major axis of the flexspline 2 is equal to the designed length of the major axis and the length of the minor axis of the flexspline 2 is equal to the designed length of the minor axis in each section of the flexspline 2, and interference does not occur between the external teeth of the flexspline 2 and the internal teeth of the rigid spline 1. At this time, the distance i between the cross section and the bottom end of the flexible gear is i m ；
Referring to FIGS. 2 and 4, when i < i m When the working tooth profile of the external teeth 22 and the tooth top tooth profile of the internal teeth 21 interfere;
referring to FIGS. 2 and 5, when i > i m At this time, the working tooth profile of the external teeth 22 and the dedendum tooth profile of the internal teeth 21 interfere.
With reference to fig. 1 to 5, an embodiment of the present application discloses a three-dimensional tooth profile modification method for a flexible gear of a harmonic reducer, including:
s1, measuring the flare inclination angle alpha of the flexible gear 2 on the outer wall of the long shaft and the retraction inclination angle beta of the flexible gear 2 on the outer wall of the short shaft, and acquiring the long shaft a of each section of the flexible gear 2 ti And a minor axis b ti In relation to the distance i from the bottom end of the flexspline 2.
S2, establishing a rigid wheel fixed connection coordinate system S in the section of the harmonic reducer i (O i ，X i ，Y i ) Rigid-wheel fixed coordinate system S i (O i ，X i ，Y i ) Is fixedly connected with a rigid wheel 1, and Y i The axis coincides with the symmetrical line of the tooth space of the rigid wheel 1, and the origin O i Is positioned at the revolution center of the rigid wheel.
S3, acquiring a rigid wheel fixed connection coordinate system S i (O i ，X i ，Y i ) Tooth profile equation f of medium rigid wheel g (ii) a And according to the major axis a of the flexible gear 2 in the section of the harmonic reducer ti And a minor axis b ti Establishing a flexspline tooth profile equation f r 。
S4, connecting the radial direction of the rigid wheel 1 with the Y i The inner teeth which are coincident with each other in axis and positioned at the upper part of the rigid gear 1 are defined as measuring inner teeth, and the circle center coordinate (x) of the tooth root tooth profile of the measuring inner teeth is obtained gf ，y gf ) And the center coordinates (x) of tooth top tooth profile ga ，y ga )。
One external tooth of the unmodified flexible gear 2 is defined as a measurement external tooth, and a center coordinate (x) of a tooth profile of a convex tooth of the measurement external tooth is acquired when the measurement external tooth is meshed with the measurement internal tooth ra ，y ra ) And the center coordinates (x) of the concave tooth profile rf ，y rf )。
When the measuring and calculating outer teeth are meshed with the measuring and calculating inner teeth, the circle center coordinates of the convex tooth profile of the measuring and calculating outer teeth of the modified flexible gear 2 are (x) ra ，y ra -Δ i ) And the circle center coordinate of the concave tooth profile of the external teeth of the flexible gear 2 after modification is (x) rf ，y rf -Δ i )。
The condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear 2 and the tooth root tooth profile of the measuring and calculating internal teeth of the rigid gear 1 do not interfere with each other is as follows:
in the formula: rho gf Measuring and calculating the tooth root tooth profile radius of the inner teeth; rho ra The convex tooth profile radius of the external teeth is measured.
The condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear 2 and the tooth top tooth profile of the measuring and calculating internal teeth of the rigid gear 1 do not interfere is as follows:
in the formula, ρ ga Measuring and calculating the tooth crest tooth profile radius of the internal teeth; rho rf The method is used for measuring and calculating the radius of the concave tooth profile of the external teeth.
S5, calculating and acquiring a ti Equal to the design major axis a of the flexspline t The value of the distance i from the bottom end of the time-distance flexible gear is i m 。
When i < i m Then, the modification amount delta is calculated and obtained according to the condition that the working tooth profile of the measuring external teeth of the modified rear flexible gear 2 and the tooth top tooth profile of the measuring internal teeth of the rigid gear 1 do not interfere i And obtaining the minimum modification quantity delta imin A functional relation with i;
when i > i m Then, the modification amount delta is calculated and obtained according to the condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear 2 and the tooth root of the measuring and calculating internal teeth of the rigid gear 1 do not interfere i And obtaining the minimum modification quantity delta imin A functional relation with i.
The above embodiments are preferred embodiments of the present application, and the protection scope of the present application is not limited by the above embodiments, so: all equivalent changes made according to the structure, shape and principle of the present application shall be covered by the protection scope of the present application.
Claims (1)
1. A three-dimensional tooth profile shaping method for a flexible gear of a harmonic reducer is characterized by comprising the following steps: measuring the flare inclination angle alpha of the flexible gear (2) on the outer wall of the long shaft and the retraction inclination angle beta of the flexible gear on the outer wall of the short shaft; and obtaining the long axis a of each section of the flexible gear (2) ti And a minor axis b ti The distance i from the bottom end of the flexible gear (2); establishing a rigid wheel fixed connection coordinate system S in the section of the harmonic reducer i (O i ,X i ,Y i ) Obtaining a rigid wheel fixed connection coordinate system S i Tooth profile equation f of medium rigid wheel g According to whichMajor axis a of flexible gear (2) in section of harmonic reducer ti And a minor axis b ti Establishing a flexible gear tooth profile equation f r (ii) a According to the equation f of the tooth profile of a rigid wheel g Sum flexspline tooth profile equation f r Obtaining the modification quantity delta of the external teeth (22) of the flexible gear (2) in each section i Said modification amount Δ i The displacement is the displacement of the external tooth profile of the flexible gear (2) moving towards the center of the flexible gear (2) along the radial direction when the external tooth (22) of the flexible gear (2) and the internal tooth (12) of the rigid gear (1) do not interfere;
according to the equation f of the tooth profile of a rigid wheel g Sum flexspline tooth profile equation f r Obtaining the modification quantity delta of the external teeth (22) of the flexible gear (2) in each section i The method comprises the following steps: the radial direction of the rigid wheel (1) is aligned with Y i The inner teeth which are parallel to the axis and are positioned at the upper part of the rigid wheel (1) are defined as measuring inner teeth, and the circle center coordinate (x) of the tooth root tooth profile of the measuring inner teeth is obtained gf ,y gf ) And the center coordinates (x) of tooth top tooth profile ga ,y ga ) (ii) a One outer tooth (22) of the unmodified flexible gear (2) is defined as a measurement outer tooth, and a circle center coordinate (x) of a convex tooth profile of the measurement outer tooth is acquired when the measurement outer tooth is meshed with the measurement inner tooth ra ,y ra ) And the center coordinates (x) of the concave tooth profile rf ,y rf )；
When the measuring and calculating outer teeth are meshed with the measuring and calculating inner teeth, the circle center coordinate of the convex tooth profile of the measuring and calculating outer teeth of the modified flexible gear (2) is (x) ra ,y ra -Δ i ) The circle center coordinate of the concave tooth profile of the external teeth of the flexible gear (2) after modification is (x) rf ,y rf -Δ i )；
The condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear (2) and the tooth root profile of the measuring and calculating internal teeth of the rigid gear (1) do not interfere is as follows:
in the formula, ρ gf Measuring the tooth root tooth profile radius of the inner teeth; rho ra Measuring and calculating the convex tooth profile radius of the external teeth;
the condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear (2) and the tooth top tooth profile of the measuring and calculating internal teeth of the rigid gear (1) do not interfere is as follows:
where ρ is ga Measuring and calculating the tooth crest tooth profile radius of the internal teeth; rho rf Measuring and calculating the concave tooth profile radius of the external teeth;
calculating and obtaining a modification quantity delta according to the condition that the working tooth profile of the measuring external teeth of the modified rear flexible gear (2) and the tooth root profile of the measuring internal teeth of the rigid gear (1) do not interfere with each other and the condition that the working tooth profile of the measuring external teeth of the modified rear flexible gear (2) and the tooth top profile of the measuring internal teeth of the rigid gear (1) do not interfere with each other i The value range of (a); computing and obtaining a ti Equal to the design major axis a of the flexible gear (2) t The value of the distance i from the bottom end of the time-distance flexible gear (2) is i m ；
When i < i m Then, the modification quantity delta is calculated and obtained according to the condition that the working tooth profile of the measurement external teeth of the modified rear flexible gear (2) and the tooth top tooth profile of the measurement internal teeth of the rigid gear (1) do not interfere i And obtaining the minimum modification amount delta imin A functional relation with i;
when i > i m Then, the modification quantity delta is calculated and obtained according to the condition that the working tooth profile of the measuring and calculating external teeth of the modified rear flexible gear (2) and the tooth root tooth profile of the measuring and calculating internal teeth of the rigid gear (1) do not interfere i The value range of (a); and obtaining the minimum modification amount delta imin A functional relation with i.
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