CN113513573A - Method for modifying harmonic gear by applying sinusoidal tooth profile - Google Patents
Method for modifying harmonic gear by applying sinusoidal tooth profile Download PDFInfo
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- CN113513573A CN113513573A CN202110533824.5A CN202110533824A CN113513573A CN 113513573 A CN113513573 A CN 113513573A CN 202110533824 A CN202110533824 A CN 202110533824A CN 113513573 A CN113513573 A CN 113513573A
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- flexible gear
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- gear
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
- F16H55/088—Profiling with corrections on tip or foot of the teeth, e.g. addendum relief for better approach contact
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H49/00—Other gearings
- F16H49/001—Wave gearings, e.g. harmonic drive transmissions
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Abstract
The invention discloses a method for modifying a harmonic gear by applying a sinusoidal tooth profile, which comprises the following steps of 1: a flexible gear shaping process; step 101: determining the wall thickness of the flexible gear; the wall thickness s is n x d, and according to the maximum design moment, the wall thickness coefficient n of the flexible gear is 0.01-0.0125 times of the diameter d of the flexible gear bearing; step 102: determining the tooth form of the flexible gear according to the wall thickness and the tooth height coefficient of the flexible gear determined in the step 101; step 103: according to the addendum circle diameter d1, the flexible gear dedendum circle diameter d2, addendum transition fillet trimming parameters and dedendum transition fillet trimming parameters, trimming the tooth form of the flexible gear to obtain a trimmed flexible gear tooth form; step 2: determining the modification process of the rigid wheel; step 201: determining the addendum circle diameter D1 of the rigid gear; step 202: and (4) modifying the tooth profile of the rigid wheel according to the tooth top circle diameter D1, the tooth top transition fillet modification parameter and the tooth root transition fillet modification parameter of the rigid wheel to obtain the modified rigid wheel tooth profile.
Description
Technical Field
The invention belongs to the technical field of design and manufacture of harmonic reducers, and particularly relates to a method for modifying a harmonic gear by applying a sinusoidal tooth profile.
Background
The harmonic reducer is mainly composed of three basic parts, namely a wave generator, a flexible gear and a rigid gear. The wave generator drives the flexible gear to carry out elliptical deformation, and the flexible gear and the rigid gear are forced to generate staggered tooth motion, so that the motion transmission of the driving wave generator and the flexible gear is realized, and the aim of reducing speed is fulfilled. The harmonic reducer has the characteristics of high precision, large transmission ratio, compact structure and light weight.
In order to improve the precision and the bearing capacity of the reducer, harmonic reducer production companies at home and abroad perform shape modification treatment on gear tooth shapes, and the existing main tooth shapes are two types: one is the traditional short tooth involute tooth profile, and a standard cutter is used for gear modification processing during processing; the other is double circular arc teeth, and a special cutter is used for processing during processing; the first tooth form meshing angle is a constant pressure angle, when the input rotating speed is high, a resonance point is easy to reach, the second tooth form machining is a mathematical simulation calculation variable pressure angle, the curve is complex, and the machining precision requirement is high.
Disclosure of Invention
In view of the above, the main objective of the present invention is to provide a method for modifying a sinusoidal tooth profile applied to a harmonic gear.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
the embodiment of the invention provides a modification method for applying a sinusoidal tooth profile to a harmonic gear, wherein the harmonic gear comprises a flexible gear and a rigid gear, and the method is realized by the following steps:
step 1: a flexible gear shaping process;
step 101: determining the wall thickness of the flexible gear;
the wall thickness s is n x d, and according to the maximum design moment, the wall thickness coefficient n of the flexible gear is 0.01-0.0125 times of the diameter d of the flexible gear bearing;
step 102: determining the tooth form of the flexible gear according to the wall thickness and the tooth height coefficient of the flexible gear determined in the step 101;
step 103: according to the addendum circle diameter d1, the flexible gear dedendum circle diameter d2, addendum transition fillet trimming parameters and dedendum transition fillet trimming parameters, trimming the tooth form of the flexible gear to obtain a trimmed flexible gear tooth form;
step 2: determining the modification process of the rigid wheel;
step 201: determining the addendum circle diameter D1 of the rigid gear;
step 202: and (4) modifying the tooth profile of the rigid wheel according to the tooth top circle diameter D1, the tooth top transition fillet modification parameter and the tooth root transition fillet modification parameter of the rigid wheel to obtain the modified rigid wheel tooth profile.
In the foregoing scheme, the determining the tooth form of the flexible gear according to the wall thickness and the tooth height coefficient of the flexible gear determined in the step 101 specifically includes: let formula s be mS*sin(2*x/mS) Obtaining a curve s, wherein x is a curve position angle, and the angle value range of x is [0, pi ]]，mSIs the tooth height factor;
i.e. when the length of the curve in the Y direction is 2mSWhen the x-direction length is pi x mS；
The tooth height coefficient mSIt can be calculated by the following equation that the circumferential perimeter (π d) along the reference circle equals the x-directional length (π m)S) Multiplied by the number of teeth z, i.e.: pi d pi mS*z；
And drawing the curve S through CAD software, and projecting the curve S onto the reference circle circumference by using a drawing command to obtain a final tooth-shaped curve S' of the flexible gear.
In the above-mentioned scheme, according to flexbile gear addendum circle diameter d1, flexbile gear dedendum circle diameter d2, addendum transition fillet profile modification parameter, dedendum transition fillet profile modification parameter, the flexbile gear profile of tooth after the profile modification is obtained to the profile modification, specifically do:
step 1031: determining the addendum circle diameter d1 of the flexible gear;
the modification formula of the addendum circle diameter d1 of the flexible gear is as follows: d1 ═ d +2 × s +2.2 × mS(ii) a Wherein d is the diameter of the compliant bearing;
step 1032: determining the diameter d2 of the root circle of the flexible gear;
the modification formula of the diameter d2 of the flexible gear tooth root circle is as follows: d2 ═ d1-1.75 × mS；
Step 1033: and modifying the tooth form of the flexible gear according to the addendum circle diameter d1, the flexible gear dedendum circle diameter d2, the addendum transition fillet modification parameter and the dedendum transition fillet modification parameter to obtain the modified tooth form of the flexible gear.
In the foregoing scheme, the determining the addendum circle diameter D1 of the rigid gear specifically includes: d1-m according to the formula D1S0.8-N determines the diameter D1 of the addendum circle of the rigid wheel, wherein N is the meshing backlash and 0.8 is the addendum coefficient.
In the above scheme, the method further comprises: and obtaining the deformed flexible gear profile of the modified flexible gear tooth profile along the cam curve array, performing pattern overlapping with the modified rigid gear tooth profile, and determining that the modified flexible gear tooth profile meets the processing requirement if the gap is smaller than the gap threshold.
Compared with the prior art, the invention has the characteristics of short design and processing period, low processing equipment cost, low product precision requirement and low natural frequency.
Drawings
FIG. 1 is a flow chart of a method for modifying a harmonic gear to have a sinusoidal tooth profile according to an embodiment of the present invention;
FIG. 2 is a diagram of a flexible wheel for a 14 model designed by the invention;
FIG. 3 is a cam diagram for the 14 model designed by the invention;
FIG. 4 is a drawing of a 14 model steel wheel designed by the invention;
FIG. 5 is an assembly drawing of a 14 model part designed using the present invention;
fig. 6 is a modified assembly detail view of a 14 model part designed by the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the invention provides a modification method for applying a sinusoidal tooth profile to a harmonic gear, wherein the harmonic gear comprises a flexible gear and a rigid gear, and the method is realized by the following steps:
step 1: a flexible gear shaping process;
specifically, step 101: determining the wall thickness of the flexible gear;
the wall thickness s is n x d, and according to the maximum design moment, the wall thickness coefficient n of the flexible gear is 0.01-0.0125 times of the diameter d of the flexible gear bearing;
according to the maximum design torque of 12N.M, the flexspline material is 30CrMnSiA, and the yield strength sigma is0.2The diameter d of the flexible bearing is 32mm, for example, 830MPa, and in order to make the idle current of the reducer smaller, the wall thickness coefficient of the flexible gear is 0.01, namely the wall thickness s is 0.01 x 32mm which is 0.32 mm;
force analysis is carried out on the strength of the flexible gear through simulation in SolidWorks, the boundary conditions are set to be that one end is fixed, the other end is loaded with 12N.M torque, and the maximum torque obtained by analyzing data is 660MPa<σ0.2And the strength is rich.
When the torque is increased, the wall thickness coefficient of the flexible gear is selected to be 0.01-0.03.
Step 102: determining the tooth form of the flexible gear according to the wall thickness and the tooth height coefficient of the flexible gear determined in the step 101;
wherein, let the formula s be mS*sin(2*x/mS) Obtaining a curve s, wherein x is a curve position angle, and the angle value range of x is [0, pi ]]，mSIs the tooth height factor;
i.e. when the length of the curve in the Y direction is 2mSWhen the x-direction length is pi x mS
Coefficient of tooth height mSCan be calculated by the following equation
The circumferential perimeter (pi x d) along the reference circle is equal to the length (pi x m) in the x directionS) Multiplied by the number of teeth z
Namely: pi d pi mS*z
And drawing the curve S through CAD software, and projecting the curve S onto the reference circle circumference by using a drawing command to obtain a final tooth-shaped curve S' of the flexible gear.
Examples of the invention
Using the British 14 model with 100 teeth as the tooth count, the above calculation was performed
The flexible gear adjusting parameters are selected as follows: m isS0.355 tooth profile curve S'
Step 103: according to the addendum circle diameter d1, the flexible gear dedendum circle diameter d2, addendum transition fillet trimming parameters and dedendum transition fillet trimming parameters, trimming the tooth form of the flexible gear to obtain a trimmed flexible gear tooth form;
wherein, step 1031: determining the addendum circle diameter d1 of the flexible gear;
the modification formula of the addendum circle diameter d1 of the flexible gear is as follows: d1 ═ d +2 × s +2.2 × mS(ii) a Wherein d is the diameter of the compliant bearing;
step 1032: determining the diameter d2 of the root circle of the flexible gear;
the modification formula of the diameter d2 of the flexible gear tooth root circle is as follows: d2 ═ d1-1.75 × mS；
For example, the addendum circle diameter d1 of the flexspline needs to be designed with the addendum clearance, so the addendum circle calculation formula is adjusted as follows:
d1＝d+2*s+2.2*mS36.18 mm; the adjustment calculation formula of the root circle diameter d2 of the flexible gear is as follows: d2 ═ d1-1.75 × mS＝34.933mm。
Because the minimum diameter of the existing wire-moving silk thread is 0.2mm, the used sine curve section needs to be modified during design, the gear top circles of the rigid wheel and the flexible wheel are adjusted during modification (as shown in figures 2 and 3), and all sharp points are chamfered to have a diameter phi of 0.24, so that the wire-moving silk thread cutting processing is adapted.
Step 1033: according to the addendum circle diameter d1, the flexible gear dedendum circle diameter d2, addendum transition fillet trimming parameters and dedendum transition fillet trimming parameters, trimming the tooth form of the flexible gear to obtain a trimmed flexible gear tooth form;
and the tooth top transition fillet trimming parameters and the tooth root transition fillet trimming parameters are determined according to the diameter of the molybdenum wire used for processing and parameters for verifying that the gear engagement does not generate interference.
And modifying the tooth profile of the flexible gear by adopting the tooth top transition fillet modification parameter of R0.1 and the tooth root transition fillet modification parameter of R0.15.
Step 2: the shaping process of the rigid wheel;
specifically, step 201: determining the addendum circle diameter D1 of the rigid gear;
d1-m according to the formula D1SAnd 0.8-N determines the addendum circle diameter D1 of the rigid wheel, wherein N is an engagement backlash, the engagement backlash is 0.03, and 0.8 is an addendum coefficient.
Step 202: and (3) modifying the tooth profile of the rigid wheel according to the tooth top circle diameter D1, the tooth top transition fillet modification parameter and the tooth root transition fillet modification parameter of the rigid wheel to obtain the modified rigid wheel tooth profile, as shown in FIG. 4.
Further, the method further comprises: and (3) obtaining the deformed flexible gear profile of the flexible gear tooth profile after modification along the cam curve array, performing pattern overlapping with the modified rigid gear tooth profile, and determining that the modified flexible gear tooth profile meets the processing requirement if the gap is smaller than a gap threshold, wherein as shown in fig. 5 and 6, the minimum tooth gap is measured to be 0.003mm and the maximum tooth gap is measured to be 0.226mm through drawing, which indicates that the modified flexible gear tooth profile meets the precision requirement without performing secondary modification on the tooth profile.
The model modification method is a repeated checking calculation process, a group of parameters is selected firstly during the first model modification, secondary modification is carried out after the first model modification, and if the first model modification does not meet the requirement, tertiary modification is carried out until the requirement is met.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.
Claims (5)
1. A modification method for applying a sinusoidal tooth profile to a harmonic gear, wherein the harmonic gear comprises a flexible gear and a rigid gear, and is characterized by comprising the following steps:
step 1: a flexible gear shaping process;
step 101: determining the wall thickness of the flexible gear;
the wall thickness s is n x d, and according to the maximum design moment, the wall thickness coefficient n of the flexible gear is 0.01-0.0125 times of the diameter d of the flexible gear bearing;
step 102: determining the tooth form of the flexible gear according to the wall thickness and the tooth height coefficient of the flexible gear determined in the step 101;
step 103: according to the addendum circle diameter d1, the flexible gear dedendum circle diameter d2, addendum transition fillet trimming parameters and dedendum transition fillet trimming parameters, trimming the tooth form of the flexible gear to obtain a trimmed flexible gear tooth form;
step 2: determining the modification process of the rigid wheel;
step 201: determining the addendum circle diameter D1 of the rigid gear;
step 202: and (4) modifying the tooth profile of the rigid wheel according to the tooth top circle diameter D1, the tooth top transition fillet modification parameter and the tooth root transition fillet modification parameter of the rigid wheel to obtain the modified rigid wheel tooth profile.
2. The method for modifying a harmonic gear according to claim 1, wherein the tooth profile of the flexspline is determined according to the wall thickness and the tooth height coefficient of the flexspline determined in the step 101, and specifically comprises: let formula s be mS*sin(2*x/mS) Obtaining a curve s, wherein x is a curve position angle, and the angle value range of x is [0, pi ]]，mSIs the tooth height factor;
i.e. when the length of the curve in the Y direction is 2mSWhen the x-direction length is pi x mS；
The tooth height coefficient mSIt can be calculated by the following equation that the circumferential perimeter (π d) along the reference circle equals the x-directional length (π m)S) Multiplied by the number of teeth z, i.e.: pi d pi mS*z；
And drawing the curve S through CAD software, and projecting the curve S onto the reference circle circumference by using a drawing command to obtain a final tooth-shaped curve S' of the flexible gear.
3. The method of claim 1 or 2, wherein the step of modifying the tooth profile of the flexspline according to the flexspline addendum circle diameter d1, the flexspline dedendum circle diameter d2, the addendum transition fillet modification parameter and the dedendum transition fillet modification parameter to obtain the modified tooth profile of the flexspline comprises:
step 1031: determining the addendum circle diameter d1 of the flexible gear;
the modification formula of the addendum circle diameter d1 of the flexible gear is as follows: d1 ═ d +2 × s +2.2 × mS(ii) a Wherein d is the diameter of the compliant bearing;
step 1032: determining the diameter d2 of the root circle of the flexible gear;
the modification formula of the diameter d2 of the flexible gear tooth root circle is as follows: d2 ═ d1-1.75 × mS；
Step 1033: and modifying the tooth form of the flexible gear according to the addendum circle diameter d1, the flexible gear dedendum circle diameter d2, the addendum transition fillet modification parameter and the dedendum transition fillet modification parameter to obtain the modified tooth form of the flexible gear.
4. The method of claim 3, wherein the determining of the addendum diameter D1 is performed by: d1-m according to the formula D1S0.8-N determines the diameter D1 of the addendum circle of the rigid wheel, wherein N is the meshing backlash and 0.8 is the addendum coefficient.
5. A method of contouring a harmonic gear with a sinusoidal tooth profile as defined in claim 4, further comprising: and obtaining the deformed flexible gear profile of the modified flexible gear tooth profile along the cam curve array, performing pattern overlapping with the modified rigid gear tooth profile, and determining that the modified flexible gear tooth profile meets the processing requirement if the gap is smaller than the gap threshold.
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| WO2013067039A1 (en) * | 2011-10-31 | 2013-05-10 | Genesis Partners, L.P. | Gear tooth profile with transition zone blending relief |
| US20150107387A1 (en) * | 2013-10-21 | 2015-04-23 | Hiwin Technologies Corp. | Harmonic Drive Gear Reduction Mechanism |
| DE202015009214U1 (en) * | 2015-12-01 | 2016-11-29 | Schaeffler Technologies AG & Co. KG | The wave gear |
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| 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 |
| CN109707822A (en) * | 2019-01-18 | 2019-05-03 | 陕西渭河工模具有限公司 | The design method of robot and detector low module harmonic drive engaging tooth shape |
| CN110486444A (en) * | 2019-08-20 | 2019-11-22 | 西安长剑飞控机电有限责任公司 | The repairing type method of nonstandard modulus harmonic gear |
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2021
- 2021-05-17 CN CN202110533824.5A patent/CN113513573B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2013067039A1 (en) * | 2011-10-31 | 2013-05-10 | Genesis Partners, L.P. | Gear tooth profile with transition zone blending relief |
| US20150107387A1 (en) * | 2013-10-21 | 2015-04-23 | Hiwin Technologies Corp. | Harmonic Drive Gear Reduction Mechanism |
| DE202015009214U1 (en) * | 2015-12-01 | 2016-11-29 | Schaeffler Technologies AG & Co. KG | The wave gear |
| CN206017626U (en) * | 2016-01-26 | 2017-03-15 | 东莞市鑫拓智能机械科技有限公司 | A kind of flexbile gear with sinusoidal tooth of 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 |
| CN109707822A (en) * | 2019-01-18 | 2019-05-03 | 陕西渭河工模具有限公司 | The design method of robot and detector low module harmonic drive engaging tooth shape |
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