CN105299151A - Harmonic gear reducer - Google Patents
Harmonic gear reducer Download PDFInfo
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- CN105299151A CN105299151A CN201410259615.6A CN201410259615A CN105299151A CN 105299151 A CN105299151 A CN 105299151A CN 201410259615 A CN201410259615 A CN 201410259615A CN 105299151 A CN105299151 A CN 105299151A
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- flank profil
- gear
- tooth
- flexbile gear
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Abstract
The invention discloses a harmonic gear reducer which comprises a flexible gear, a rigid gear and an elliptical cam wave generator. The cup bottom of the flexible gear is connected with an output shaft. The elliptical cam wave generator is connected with an input shaft. The outer wall, along the cup rim, of the flexible gear is provided with an arc-involute-arc-tooth profile. The elliptical cam wave generator is arranged on the inner wall of the cup rim of the flexible gear. The rigid gear is fixedly connected with a shell and the inner wall is provided with an arc-involute-arc-tooth profile matched with the flexible gear tooth profile. The rigid gear is connected with the flexible gear through the tooth profiles in an engaged manner. In the engagement process, the flexible gear is in continuous conjugated engagement with the rigid gear, a convex tooth profile and a concave tooth profile of the flexible gear and a concave tooth profile and a convex tooth profile of the rigid gear are located in the double-conjugation engagement interval of the conjugation motion at the same time. The harmonic gear reducer has the beneficial effects that both arc tooth-shaped harmonic driving and involute-tooth-shaped harmonic driving are achieved; and deflection driving can be achieved, the gear tooth engagement region can be enlarged, and the engagement rigidity, driving efficiency and bearing capacity of the harmonic gear reducer are improved.
Description
Technical field
The present invention relates to Technology of Harmonic Wave Transmission field, particularly relate to a kind of harmonic gear reducer.
Background technique
Harmonic driving has that structure is simple, lightweight, gear range is large, transmission accuracy is high, backlash is little, simultaneously total number of teeth in engagement mainly with and the advantage that realizes to numerous uniquenesses such as confined space transmission campaign and power.In recent decades, Harmonic Gears technology and transmission device have been widely used in the fields such as space technology, lathe, instrument and apparatus, robot, automobile, shipbuilding, weaving, metallurgy, conventional weapon, precision optics equipment, printing packaging machinery and medical apparatus.Application practice both domestic and external proves, is no matter the accurate harmonic driving as high sensitivity followup system, or as transmitting the power harmonic driving of large torque, all shows good performance.
Along with the application in various automation equipment gets more and more, the specific operation servo power driving mechanisms such as joint of robot, aircraft servomechanism require more and more higher to Harmonic Gears, especially almost reach harsh stage to the requirement of the aspects such as volume, weight, dynamic property, reliability.And conventional involute profile harmonic driving exists shortcomings: tooth Root Stress is concentrated comparatively serious, fatiguability ruptures; Tooth contact stress is large, little between meshing zone, affects bearing capacity; During heavy load transmission, cusp engagement flexbile gear easily distorts, and is difficult to realize high rigidity, and contacting profile can be caused to interfere or slip teeth, serious restriction integrated carrying ability.Although common double circular arc profile improves bearing capacity to a certain extent, owing to conjugating, manufacturing ability is extremely restricted, and lacks actual use value.The research of harmonic driving profile of tooth, parameter and structural design is not deep enough, lags far behind the specific operation such as joint of robot, space flight servomechanism to the performance requirement of harmonic drive, constrains the development of Robotics and other precision drive technology.
Summary of the invention
The object of the present invention is to provide a kind of harmonic gear reducer, under overcoming common involute Harmonic Gears high-mechanic, easily occur the deficiencies such as tooth Root Stress is concentrated, fatigue fracture, cusp engagement, flexbile gear distortion, latch and slip teeth.
The technical solution realizing the object of the invention is: a kind of harmonic gear reducer, and comprise flexbile gear, just wheel, elliptical cam wave generator, be connected with output shaft at the bottom of the cup of flexbile gear, elliptical cam wave generator is connected with input shaft; Flexbile gear is provided with flank profil along the outer wall of rim of a cup, and flank profil initial position distance rim of a cup Edge Distance is b
1; Elliptical cam wave generator is arranged on flexbile gear rim of a cup inwall, and the axial width symmetrical line of elliptical cam wave generator overlaps with the flank profil width symmetrical line of flexbile gear; Firm wheel is fixedly connected with housing, firm wheel inwall is provided with the flank profil matched with above-mentioned flank profil, firm wheel is set in the outside that flexbile gear is provided with elliptical cam wave generator one end, and just wheel and flexbile gear are connected with a joggle by flank profil, and just the flank profil width symmetrical line of wheel overlaps with the flank profil width symmetrical line of flexbile gear; Above-mentioned flexbile gear adopts the flank profil of circular arc-involute-circular arc, and its basic rack tooth profile parameter is: addendum coefficient
dedendum of the tooth coefficient
tip clearance coefficient
pressure angle α=15 ° ~ 25 °, tooth top active section radius of arc coefficient
tooth root active section radius of arc coefficient
transverse tooth thickness compares K=E
r/ S
r=1.05 ~ 1.2, tooth root transition arc radius coefficient
the thick coefficient of tooth top
* the coefficient of relevant parameter divided by modulus is represented.
In order to prevent the flank profil of above-mentioned flexbile gear from engaging-in process, tooth top interference phenomenon occurring, tip portion does fillet process, fillet radius coefficient
Firm flank profil of taking turns employing circular arc-involute-circular arc, its pressure angle is consistent with the flank profil of above-mentioned flexbile gear, and its basic rack tooth profile parameter is: addendum coefficient
dedendum of the tooth coefficient
tip clearance coefficient
tooth top active section radius of arc is greater than flexbile gear tooth root active section radius of arc, its coefficient
tooth root active section radius of arc coefficient
transverse tooth thickness compares K=E
g/ S
g=1.05 ~ 1.2, tooth root transition arc radius coefficient
Complete engaging-in firm depth of engagement coefficient when taking turns of flexbile gear flank profil
The flank profil width of flexbile gear is b
r; The flank profil width of firm wheel is b
g, b
g=b
r+ (2 ~ 3), unit is mm.
Above-mentioned flank profil initial position distance rim of a cup Edge Distance is b
1, b
1=0.2b
r.
The present invention compared with prior art, its remarkable advantage is: in harmonic gear reducer of the present invention, the flank profil of flexbile gear and firm wheel adopts new flank profil to replace involute profile, reduce root stress to concentrate, eliminate EDGE CONTACT, under heavy load transmission, flexbile gear not easily distorts, and wedge shape sideshake is more conducive to oil film and is formed; On the other hand, replace common double circular arc profile with this, solve the problem that cutter cannot conjugate, effectively improve manufacturing capacity.In engagement process, flexbile gear and just wheel flank profil are in continuous conjugation engagement, and there is the wide and recessed flank profil of flexbile gear double wedge and take turns between recessed flank profil and wide " biconjugate " meshing zone being simultaneously in conjugate movement of double wedge respectively and just, expand gear teeth meshing region, increase the depth of engagement, also reduce contact stress simultaneously, improve the mesh stiffness of harmonic gear reducer, transmission efficiency and bearing capacity.
Accompanying drawing explanation
Fig. 1 is the sectional view of harmonic gear reducer of the present invention.
Fig. 2 is flexbile gear of the present invention and the overall mesh schematic representation of just taking turns.
Fig. 3 is the tooth curve of harmonic gear reducer flexbile gear of the present invention.
Fig. 4 is the tooth curve that harmonic gear reducer of the present invention has just been taken turns.
Fig. 5 is embodiment of the present invention flexbile gear and the local mesh schematic representation of just taking turns.
Fig. 6 is the benchmark model of flexbile gear hobboing cutter normal plane flank profil of the present invention.
Embodiment
Below in conjunction with drawings and Examples, the invention will be further described.
A kind of harmonic gear reducer, comprise flexbile gear 1, just take turns 2, elliptical cam wave generator 3 and housing, flexbile gear 1, just wheel 2 and elliptical cam wave generator 3 are all placed in housing, and be connected with output shaft at the bottom of the cup of flexbile gear 1, elliptical cam wave generator 3 is connected with input shaft; Flexbile gear 1 is provided with flank profil along the outer wall of rim of a cup, and flank profil initial position distance rim of a cup Edge Distance is b
1; Elliptical cam wave generator 3 is arranged on flexbile gear 1 rim of a cup inwall, and the axial width symmetrical line of elliptical cam wave generator 3 overlaps with the flank profil width symmetrical line of flexbile gear 1; Firm wheel 2 is fixedly connected with housing, firm wheel 2 inwall is provided with the flank profil matched with above-mentioned flank profil, firm wheel 2 is set in the outside that flexbile gear 1 is provided with elliptical cam wave generator 3 one end, firm wheel 2 is connected with a joggle by flank profil with flexbile gear 1, and just the wheel flank profil width symmetrical line of 2 overlaps with the flank profil width symmetrical line of flexbile gear 1; Above-mentioned flexbile gear 1 adopts the flank profil of circular arc-involute-circular arc, and its basic rack tooth profile parameter is: addendum coefficient
dedendum of the tooth coefficient
tip clearance coefficient
pressure angle α=15 ° ~ 25 °, tooth top active section radius of arc coefficient
tooth root active section radius of arc coefficient
transverse tooth thickness compares K=E
r/ S
r=1.05 ~ 1.2, tooth root transition arc radius coefficient
the thick coefficient of tooth top
* the coefficient of relevant parameter divided by modulus is represented.
In order to prevent the flank profil of above-mentioned flexbile gear 1 from engaging-in process, tooth top interference phenomenon occurring, tip portion does fillet process, fillet radius coefficient
Firm wheel 2 adopts the flank profil of circular arc-involute-circular arc, and its pressure angle is consistent with the flank profil of above-mentioned flexbile gear 1, and its basic rack tooth profile parameter is: addendum coefficient
dedendum of the tooth coefficient
tip clearance coefficient
tooth top active section radius of arc is greater than flexbile gear 1 tooth root active section radius of arc, its coefficient
tooth root active section radius of arc coefficient
transverse tooth thickness compares K=E
g/ S
g=1.05 ~ 1.2, tooth root transition arc radius coefficient
Depth of engagement coefficient during the complete engaging-in firm wheel 2 of flexbile gear 1 flank profil
The flank profil width of flexbile gear 1 is b
r; The flank profil width of firm wheel 2 is b
g, b
g=b
r+ (2 ~ 3), unit is mm.
Above-mentioned flank profil initial position distance rim of a cup Edge Distance is b
1, b
1=0.2b
r.
Composition graphs 1, a kind of harmonic gear reducer comprises flexbile gear 1, just takes turns 2, elliptical cam wave generator 3, wherein just taken turns 2 and elliptical cam wave generator 3 be rigid body, be connected with output shaft at the bottom of the cup of flexbile gear 1, elliptical cam wave generator 3 is connected with input shaft, and just wheel 2 is fixedly connected with housing; Flexbile gear 1 is provided with flank profil along the outer wall of rim of a cup; Elliptical cam wave generator 3 is arranged on flexbile gear 1 rim of a cup inwall, and the axial width symmetrical line of elliptical cam wave generator 3 overlaps with the flank profil width symmetrical line of flexbile gear 1; Firm wheel 2 inwall is provided with the flank profil matched with above-mentioned flank profil, firm wheel 2 is set in the outside that flexbile gear 1 is provided with elliptical cam wave generator 3 one end, firm wheel 2 is connected with a joggle by flank profil with flexbile gear 1, and just the wheel flank profil width symmetrical line of 2 overlaps with the flank profil width symmetrical line of flexbile gear 1.During installation, elliptical cam wave generator 3 adopts coordinating of H8/h7 with flexbile gear 1 inwall.Specific works process of the present invention is: after elliptical cam wave generator 3 loads flexbile gear 1, flexbile gear 1 is caused to produce flexible deformation, produce the rotation generation periodically deforming of flexbile gear 1 along with elliptical cam wave generator 3 of flexible deformation, the flank profil of the flexbile gear 1 at elliptical cam wave generator 3 major axis two ends place is in the flank profil of just taking turns 2 " biconjugate " state engaged completely, the flank profil of the flexbile gear 1 at elliptical cam wave generator 3 minor axis two ends place is in complete disengaged condition with the flank profil of just taking turns 2, is in half engagement or half disengaged condition at rest interval.
Composition graphs 6, Fig. 6 is the benchmark model of flexbile gear hobboing cutter normal plane flank profil of the present invention, and be made up of circular arc-straight line-circular arc, the flank profil of flexbile gear 1 designs as basic tooth profile.O
1for the center of circle of hobcutter tooth root active section circular arc, O
2for the center of circle of hobcutter tooth top active section circular arc, AB section is with O
2for the center of circle, R
fRfor the circular arc of radius, CD section is with O
1for the center of circle, R
aRfor the circular arc of radius, BC section is the common tangent of AB section circular arc and CD section circular arc.AB section, BC section and CD section are flexbile gear hobboing cutter normal plane reference profile, and its basic rack tooth profile parameter all should be consistent with the basic rack tooth profile parameter of flexbile gear 1 to be processed.For the needs of processing, all leave certain bottom clearance at the tooth top tooth root place of hobcutter, and do fillet process, radius is respectively R
1, R
2.In figure, each alphabetical implication is: m-modulus;
-flexbile gear addendum coefficient;
-flexbile gear dedendum of the tooth coefficient;
-flexbile gear tip clearance coefficient; α-flexbile gear pressure angle;
-flexbile gear tooth top active section radius of arc coefficient;
-flexbile gear tooth root active section radius of arc coefficient;
-hobcutter tooth root transition arc radius coefficient, value is 0.5 ~ 0.9;
-hobcutter tooth top transition arc radius coefficient, value is 0.3 ~ 0.8." * " represents the coefficient of relevant parameter divided by modulus.
Embodiment 1
Composition graphs 3, Fig. 3 is the tooth curve of harmonic gear reducer flexbile gear 1 of the present invention.Harmonic gear reducer flexbile gear 1 of the present invention is processed by hobcutter position changing cutting.The basic rack tooth profile curve of flexbile gear 1 is made up of circular arc-involute-circular arc, and in the present embodiment, the basic rack tooth profile parameter of flexbile gear 1 is:
Addendum coefficient
dedendum of the tooth coefficient
tip clearance coefficient
pressure angle α=20 °, modification coefficient x
r=3.52, tooth top active section radius of arc coefficient
tooth root active section radius of arc coefficient
transverse tooth thickness than K=1.05, tooth root transition arc radius coefficient
the thick coefficient of tooth top
in order to prevent the flank profil of flexbile gear from engaging-in process, tooth top interference phenomenon occurring, tip portion does fillet process, fillet radius coefficient
Composition graphs 4, Fig. 4 is the tooth curve that harmonic gear reducer of the present invention has just taken turns 2.The basic rack tooth profile curve that harmonic gear reducer of the present invention has just taken turns 2 is made up of circular arc-involute-circular arc, gear shaper cutter position changing cutting is used to process, its pressure angle should be consistent with flexbile gear, and other basic rack tooth profile parameter needs the flexbile gear parameter with reference to being engaged with to determine.In the present embodiment, just the basic rack tooth profile parameter of wheel 2 is:
Addendum coefficient
dedendum of the tooth coefficient
tip clearance coefficient
pressure angle α=20 °, modification coefficient x
g=3.15, tooth top active section radius of arc coefficient
tooth root active section radius of arc coefficient
transverse tooth thickness than K=1.05, tooth root transition arc radius coefficient
complete engaging-in firm depth of engagement coefficient when taking turns of flexbile gear flank profil
Composition graphs 2 and Fig. 5, Fig. 5 are above-described embodiment flexbile gear 1 and the local mesh schematic representation of just taking turns 2, and the single flank profil reflecting flexbile gear 1 has relatively just taken turns the engaging-in process of nibbling out of the flank profil of 2.Fig. 2 is above-described embodiment flexbile gear 1 and the overall mesh schematic representation of just taking turns 2.Embodiment shows, in engagement process, the flank profil of flexbile gear 1 does not exist with the flank profil of just taking turns 2 interferes and is in continuous conjugation engagement, there is the wide and recessed flank profil of flexbile gear 1 double wedge take turns between 2 recessed flank profils and wide " biconjugate " meshing zone being simultaneously in conjugate movement of double wedge respectively and just, and this transmission efficiency for raising harmonic gear reducer and bearing capacity have important function.Compared with same model involute profile, the while of adopting the harmonic gear reducer of novel tooth form in the course of the work, engaging tooth logarithm is about 2 times of involute profile; Under the same terms, ultimate bearing capacity is about 4 times of involute profile, and torsional stiffness improves about 50% than involute profile.
Claims (6)
1. a harmonic gear reducer, comprise flexbile gear (1), just wheel (2), elliptical cam wave generator (3), it is characterized in that: be connected with output shaft at the bottom of the cup of flexbile gear (1), elliptical cam wave generator (3) is connected with input shaft; Flexbile gear (1) is provided with flank profil along the outer wall of rim of a cup, and flank profil initial position distance rim of a cup Edge Distance is b
1; Elliptical cam wave generator (3) is arranged on flexbile gear (1) rim of a cup inwall, and the axial width symmetrical line of elliptical cam wave generator (3) overlaps with the flank profil width symmetrical line of flexbile gear (1); Firm wheel (2) inwall is provided with the flank profil matched with above-mentioned flank profil, firm wheel (2) is set in the outside that flexbile gear (1) is provided with elliptical cam wave generator (3) one end, firm wheel (2) and flexbile gear (1) are connected with a joggle by flank profil, and just the wheel flank profil width symmetrical line of (2) overlaps with the flank profil width symmetrical line of flexbile gear (1); Above-mentioned flexbile gear (1) adopts the flank profil of circular arc-involute-circular arc, and its basic rack tooth profile parameter is: addendum coefficient
dedendum of the tooth coefficient
tip clearance coefficient
pressure angle α=15 ° ~ 25 °, tooth top active section radius of arc coefficient
tooth root active section radius of arc coefficient
transverse tooth thickness compares K=E
r/ S
r=1.05 ~ 1.2, tooth root transition arc radius coefficient
the thick coefficient of tooth top
* the coefficient of relevant parameter divided by modulus is represented.
2. harmonic gear reducer according to claim 1, is characterized in that: in order to prevent the flank profil of above-mentioned flexbile gear (1) from engaging-in process, tooth top interference phenomenon occurring, tip portion does fillet process, fillet radius coefficient
3. harmonic gear reducer according to claim 2, it is characterized in that: just wheel (2) adopts the flank profil of circular arc-involute-circular arc, its pressure angle is consistent with the flank profil of above-mentioned flexbile gear (1), and its basic rack tooth profile parameter is: addendum coefficient
dedendum of the tooth coefficient
tip clearance coefficient
tooth top active section radius of arc is greater than flexbile gear (1) tooth root active section radius of arc, its coefficient
tooth root active section radius of arc coefficient
transverse tooth thickness compares K=E
g/ S
g=1.05 ~ 1.2, tooth root transition arc radius coefficient
4. harmonic gear reducer according to claim 3, is characterized in that: depth of engagement coefficient time flexbile gear (1) flank profil complete engaging-in firm wheel (2)
5. harmonic gear reducer according to claim 1, is characterized in that: the flank profil width of flexbile gear (1) is b
r; The flank profil width of firm wheel (2) is b
g, b
g=b
r+ (2 ~ 3), unit is mm.
6. harmonic gear reducer according to claim 1 or 5, is characterized in that: above-mentioned flank profil initial position distance rim of a cup Edge Distance is b
1, b
1=0.2b
r.
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|---|---|---|---|
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| CN105299151B CN105299151B (en) | 2018-06-12 |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN105587840A (en) * | 2016-02-29 | 2016-05-18 | 浙江来福谐波传动股份有限公司 | Flexible gear delta-shaped tooth of harmonic reducer |
| CN106090185A (en) * | 2016-06-16 | 2016-11-09 | 南通慧幸智能科技有限公司 | The flute profile method for designing of three-dimensional high rigidity harmonic speed reducer |
| CN107191570A (en) * | 2017-06-07 | 2017-09-22 | 天津工业大学 | The three-arc tooth Profile Design of continuous conjugation cup or carnival hat shape harmonic gear |
| CN107387721A (en) * | 2017-08-01 | 2017-11-24 | 北京新立机械有限责任公司 | Wide tooth bicircular arcs harmonic wave tooth form |
| WO2018000995A1 (en) * | 2016-06-30 | 2018-01-04 | 比亚迪股份有限公司 | Flexible wheel for harmonic speed reducer and manufacturing method thereof |
| CN110162924A (en) * | 2019-06-03 | 2019-08-23 | 珠海格力电器股份有限公司 | A kind of harmonic drive mechanism and harmonic speed reducer |
| CN110263492A (en) * | 2019-07-15 | 2019-09-20 | 北京工业大学 | A kind of harmonic speed reducer double circular arc tooth outline torsion stiffness calculation method |
| CN110566653A (en) * | 2019-09-27 | 2019-12-13 | 贵州群建精密机械有限公司 | Arc gear for harmonic gear transmission |
| CN111201389A (en) * | 2017-10-19 | 2020-05-26 | 谐波传动系统有限公司 | Wave gear device with 3-dimensional meshing tooth profile |
| CN112283317A (en) * | 2020-11-09 | 2021-01-29 | 武汉理工大学 | Arc cycloid harmonic tooth form, generation method and device thereof, and storage medium |
| CN113486476A (en) * | 2021-08-11 | 2021-10-08 | 重庆大学 | Grinding wheel tooth profile design method for grinding double-arc harmonic reducer rigid wheel slotting tool |
| CN114263708A (en) * | 2021-12-31 | 2022-04-01 | 浙江如川谐波传动科技有限公司 | Harmonic speed reducer |
| WO2023097802A1 (en) * | 2021-11-30 | 2023-06-08 | 重庆大学 | Design method for inner tooth profile of complex-wave oscillating-tooth speed reducer, and two-stage speed reducer |
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| CN105587840A (en) * | 2016-02-29 | 2016-05-18 | 浙江来福谐波传动股份有限公司 | Flexible gear delta-shaped tooth of harmonic reducer |
| CN106090185A (en) * | 2016-06-16 | 2016-11-09 | 南通慧幸智能科技有限公司 | The flute profile method for designing of three-dimensional high rigidity harmonic speed reducer |
| WO2017215621A1 (en) * | 2016-06-16 | 2017-12-21 | 南通慧幸智能科技有限公司 | Tooth profile design method for three-dimensional high-rigidity harmonic speed reducer |
| WO2018000995A1 (en) * | 2016-06-30 | 2018-01-04 | 比亚迪股份有限公司 | Flexible wheel for harmonic speed reducer and manufacturing method thereof |
| CN107191570A (en) * | 2017-06-07 | 2017-09-22 | 天津工业大学 | The three-arc tooth Profile Design of continuous conjugation cup or carnival hat shape harmonic gear |
| CN107191570B (en) * | 2017-06-07 | 2023-08-15 | 天津工业大学 | Three-arc tooth profile design of continuous conjugate cup-shaped or top-hat-shaped harmonic gear |
| CN107387721B (en) * | 2017-08-01 | 2020-03-10 | 北京新立机械有限责任公司 | Wide-tooth double-arc harmonic gear |
| CN107387721A (en) * | 2017-08-01 | 2017-11-24 | 北京新立机械有限责任公司 | Wide tooth bicircular arcs harmonic wave tooth form |
| CN111201389A (en) * | 2017-10-19 | 2020-05-26 | 谐波传动系统有限公司 | Wave gear device with 3-dimensional meshing tooth profile |
| CN111201389B (en) * | 2017-10-19 | 2023-04-28 | 谐波传动系统有限公司 | Wave gear device with 3-dimensional meshing profile |
| CN110162924A (en) * | 2019-06-03 | 2019-08-23 | 珠海格力电器股份有限公司 | A kind of harmonic drive mechanism and harmonic speed reducer |
| CN110263492A (en) * | 2019-07-15 | 2019-09-20 | 北京工业大学 | A kind of harmonic speed reducer double circular arc tooth outline torsion stiffness calculation method |
| CN110263492B (en) * | 2019-07-15 | 2023-05-02 | 北京工业大学 | Method for calculating torsional rigidity of double-arc tooth profile of harmonic reducer |
| CN110566653A (en) * | 2019-09-27 | 2019-12-13 | 贵州群建精密机械有限公司 | Arc gear for harmonic gear transmission |
| CN112283317A (en) * | 2020-11-09 | 2021-01-29 | 武汉理工大学 | Arc cycloid harmonic tooth form, generation method and device thereof, and storage medium |
| CN112283317B (en) * | 2020-11-09 | 2022-06-07 | 武汉理工大学 | Arc cycloid harmonic tooth form, generation method and device thereof, and storage medium |
| CN113486476A (en) * | 2021-08-11 | 2021-10-08 | 重庆大学 | Grinding wheel tooth profile design method for grinding double-arc harmonic reducer rigid wheel slotting tool |
| CN113486476B (en) * | 2021-08-11 | 2023-04-18 | 重庆大学 | Grinding wheel tooth profile design method for grinding double-arc harmonic reducer rigid wheel slotting tool |
| WO2023097802A1 (en) * | 2021-11-30 | 2023-06-08 | 重庆大学 | Design method for inner tooth profile of complex-wave oscillating-tooth speed reducer, and two-stage speed reducer |
| CN114263708A (en) * | 2021-12-31 | 2022-04-01 | 浙江如川谐波传动科技有限公司 | Harmonic speed reducer |
| CN114263708B (en) * | 2021-12-31 | 2024-02-06 | 浙江如川谐波传动科技有限公司 | Harmonic reducer |
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