CN113324008B - Method for improving stress concentration of flexible gear outer contour - Google Patents

Method for improving stress concentration of flexible gear outer contour Download PDF

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CN113324008B
CN113324008B CN202110571803.2A CN202110571803A CN113324008B CN 113324008 B CN113324008 B CN 113324008B CN 202110571803 A CN202110571803 A CN 202110571803A CN 113324008 B CN113324008 B CN 113324008B
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curve
straight line
coordinate system
flexible gear
point
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CN113324008A (en
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胡秋实
王超
王广
李磊
周宏根
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Guohua Qingdao Intelligent Equipment Co ltd
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Jiangsu University of Science and Technology
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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
    • 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
    • F16H55/0833—Flexible toothed member, e.g. harmonic drive
    • 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
    • F16H55/17—Toothed wheels

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Gears, Cams (AREA)
  • Retarders (AREA)

Abstract

The invention discloses a method for improving the stress concentration of the outer contour of a flexible gear, which comprises the step of establishing a coordinate system for the structural shape of the outer contour of the flexible gear, wherein the outer contour of the flexible gear comprises a cup bottom flange straight line section, a cup bottom flange and cup body connecting curve section, a cup bottom curve transition section, a cup body connecting curve section, a tooth rear end connecting straight line section, a tooth top straight line section, a tooth front end straight line section and a tooth root curve section which are sequentially connected. The invention carries out mathematical description of the flexible gear outline through a continuous curve equation, and the connecting section of the cup bottom flange and the cup body and the connecting section of the cup body adopt curves to replace the traditional straight lines, thereby effectively reducing the stress concentration at the connecting parts of the flexible gear cup bottom, the flexible gear cup body and the flange; the tooth root adopts a curve instead of a straight line, so that the interference between the front end of the flexible gear tooth and the rigid gear caused by the support of the wave generator is effectively reduced, and the stress concentration phenomenon is reduced; in addition, the outer contour of the flexible gear is characterized by adopting a continuous curve equation, a mathematical model is provided for processing and detecting the flexible gear, and the flexible gear has a good application prospect.

Description

Method for improving stress concentration of flexible gear outer contour
Technical Field
The invention relates to a method for improving stress concentration, in particular to a method for improving stress concentration of an outer contour of a flexible gear.
Background
The harmonic reducer for the robot joint belongs to a gear transmission device with high precision and high reduction ratio, and is an essential core part for realizing the motion function of the robot. The structure of the current mainstream harmonic reducer is shown in fig. 1, the core components of the harmonic reducer are a hat-shaped flexible gear and a rigid gear which are shown in fig. 2, the harmonic reducer mainly depends on an elliptical wave generator to support the hat-shaped flexible gear to generate elastic deformation in the motion process, and the hat-shaped flexible gear and the rigid gear form differential gear transmission in the rotation process of the wave generator, so that the mechanical property of the deformed flexible gear is particularly critical.
As the hat-shaped flexible gear is supported by the wave generator to generate larger strain, stress concentration is easily formed at the front end and the rear end of the flexible gear tooth part, the flexible gear cup bottom and the connection part of the flexible gear cup body and the flange, as shown in figures 3 and 4, the harmonic reducer is broken in the using process, and the fatigue life of the harmonic reducer is greatly reduced.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a method for improving the stress concentration of the outer contour of a flexible gear so as to prolong the service life of a harmonic reducer.
The technical scheme is as follows: the invention comprises the following steps:
(1) establishing a coordinate system for the structural shape of the outer contour of the flexible gear, wherein the outer contour of the flexible gear comprises a cup bottom flange straight line segment AB, a cup bottom flange and cup body connecting curve segment BC, a cup bottom curve transition segment CD, a cup body connecting curve segment DE, a tooth rear end connecting straight line segment EF, a tooth top straight line segment FG, a tooth front end straight line segment GH and a tooth root curve segment EH which are sequentially connected;
(2) the cup bottom flange and the cup body are connected with a curve segment BC, and the curve equation is as follows:
Figure GDA0003586391030000011
in the formula, yBCIs the ordinate value, x, of any point on the curve BC in the Cartesian coordinate system XOYBCAn abscissa value of any point on the curve BC in a Cartesian coordinate system XOY is shown, h is the thickness of the cup bottom, m is the thickness of a cup bottom flange, n is the distance from the cup bottom flange to the abscissa, and K is the width of the cup bottom;
(3) the cup body is connected with a curve section DE, and the curve equation is as follows:
Figure GDA0003586391030000021
in the formula, yDEIs the ordinate value, x, of any point on the curve DE in the Cartesian coordinate system XOYDEIs an abscissa value of any point on the curve DE in a Cartesian coordinate system XOY, and L is the length of the hat-shaped flexible wheel cup body;
(4) the tooth root curve segment EH has the curve equation:
Figure GDA0003586391030000022
in the formula, yEHIs the ordinate value, x, of any point on the curve EH in the Cartesian coordinate system XOYEHThe abscissa of any point on the curve EH in the cartesian coordinate system XOY is shown.
The linear equation of the straight-line segment AB of the cup bottom flange in the step (1) is as follows:
Figure GDA0003586391030000023
in the formula, xABThe abscissa value, y, of any point on the straight line segment AB in the Cartesian coordinate system XOYABIs the longitudinal coordinate value of any point on the straight line segment AB in a Cartesian coordinate system, m is the thickness of the cup bottom flange, n is the distance from the cup bottom flange to the abscissa, and K is the width of the cup bottom.
The curve equation of the cup bottom curve transition section CD in the step (1) is as follows:
Figure GDA0003586391030000024
in the formula, xCDIs the abscissa value, y, of any point on the curve segment CD in the Cartesian coordinate system XOYCDIs the ordinate value of any point on the curve segment CD in the Cartesian coordinate system XOY, and L is the length of the hat-shaped flexible wheel cup body.
The linear equation of the connecting straight-line segment EF at the rear end of the tooth in the step (1) is as follows:
Figure GDA0003586391030000025
in the formula, yEFIs the ordinate, x, of any point on the straight line EF in the Cartesian coordinate system XOYEFIs the abscissa value, R, of any point on the straight line EF in the Cartesian coordinate system XOY1The addendum circle radius.
The linear equation of the tooth top straight line segment FG in the step (1) is as follows:
Figure GDA0003586391030000026
in the formula, yFGIs the ordinate value, x, of any point on the straight line FG in the Cartesian coordinate system XOYFGThe abscissa value of any point on the straight line FG in the cartesian coordinate system XOY.
The linear equation of a straight line segment GH at the front end of the tooth in the step (1) is as follows:
Figure GDA0003586391030000031
in the formula, yGHIs the ordinate value, x, of any point on the straight line GH in the Cartesian coordinate system XOYGHIs the abscissa value of any point on the straight line GH in the Cartesian coordinate system XOY.
And (2) the coordinate system in the step (1) is a Cartesian coordinate system which takes the central axis of the flexible gear as an abscissa axis and the cup bottom flange as an ordinate axis.
Has the advantages that: the invention carries out mathematical description of the flexible gear outer contour through a continuous curve equation, and the connecting section of the cup bottom flange and the cup body and the connecting section of the cup body adopt accurately described curves to replace the traditional straight lines, thereby effectively reducing the stress concentration at the connecting positions of the flexible gear cup bottom and the flexible gear cup body and the flange; the tooth root adopts a curve accurately described to replace a straight line, so that the interference between the front end of the flexible gear tooth and the rigid gear caused by the support of the wave generator is effectively reduced, and the stress concentration phenomenon is reduced; in addition, the outer contour of the flexible gear is characterized by adopting a continuous curve equation, a mathematical model is provided for the processing and detection of the flexible gear, and the flexible gear has a good application prospect; the implementation of the invention can effectively improve the stress concentration phenomena of the front end and the rear end of the flexible gear tooth part, the flexible gear cup bottom, the connection part of the flexible gear cup body and the flange and the front end of the flexible gear tooth, improve the fatigue life of the flexible gear in the working process and provide theoretical and technical basis for the research and development of the long-life harmonic reducer.
Drawings
FIG. 1 is a schematic diagram of a conventional harmonic reducer;
FIG. 2 is a view showing the construction of a conventional silk hat-shaped flexible gear and a conventional rigid gear;
FIG. 3 is a cross-sectional view of a conventional silk hat-shaped flexspline;
FIG. 4 is a schematic diagram showing a deformation of a conventional silk hat-shaped flexible wheel after being supported;
fig. 5 is a diagram illustrating an outer profile of a silk hat type flexible gear of the present invention.
Detailed Description
The invention will be further explained with reference to the drawings.
As shown in FIG. 5, the flexible gear outer contour of the invention adopts a continuous mathematical representation method to structurally define and describe the curve equation of the hat-shaped flexible gear outer contour of the harmonic reducer, thereby reducing the stress concentration phenomenon of dangerous points and prolonging the service life of the harmonic reducer. The method specifically comprises the following steps:
(1) and establishing a Cartesian coordinate system which takes the central axis of the silk hat-shaped flexible gear as an abscissa axis and the cup bottom flange as an ordinate axis and is used for curve equation representation of the external contour structure shape of the silk hat-shaped flexible gear.
(2) The outer contour of the hat-shaped flexible gear comprises a cup bottom flange straight line section AB, a cup bottom flange and cup body connecting curve section BC, a cup bottom curve transition section CD, a cup body connecting curve section DE, a tooth rear end connecting straight line section EF, a tooth top straight line section FG, a tooth front end straight line section GH and a tooth root curve section EH.
(3) A straight line segment AB of the cup bottom flange has the following linear equation:
Figure GDA0003586391030000041
in the formula, xABIs the abscissa value, y, of any point on the straight line segment AB in the Cartesian coordinate system XOYABIs the longitudinal coordinate value of any point on the straight line segment AB in a Cartesian coordinate system, m is the thickness of the cup bottom flange, n is the distance from the cup bottom flange to the abscissa, and K is the width of the cup bottom.
(4) The cup bottom flange and the cup body are connected with a curve segment BC, and the curve equation is as follows:
Figure GDA0003586391030000042
in the formula, yBCIs the ordinate value, x, of any point on the curve BC in the Cartesian coordinate system XOYBCThe abscissa of any point on the curve BC in the Cartesian coordinate system XOY is shown, and h is the thickness of the cup bottom.
(5) The curve equation of the transition section CD of the cup bottom curve is as follows:
Figure GDA0003586391030000043
in the formula, xCDIs the abscissa value, y, of any point on the curve segment CD in the Cartesian coordinate system XOYCDIs the ordinate value of any point on the curve segment CD in the Cartesian coordinate system XOY, and L is the length of the hat-shaped flexible wheel cup body.
(6) The cup body is connected with a curve section DE, and the curve equation is as follows:
Figure GDA0003586391030000044
in the formula, yDEIs the ordinate value, x, of any point on the curve DE in the Cartesian coordinate system XOYDEThe abscissa value of any point on the curve DE in the cartesian coordinate system XOY.
(7) The rear end of the tooth is connected with a straight line section EF, and the straight line equation is as follows:
Figure GDA0003586391030000051
in the formula, yEFIs the ordinate, x, of any point on the straight line EF in the Cartesian coordinate system XOYEFIs the abscissa value, R, of any point on the straight line EF in the Cartesian coordinate system XOY1The addendum circle radius.
(8) A straight line segment FG of the tooth crest has a straight line equation:
Figure GDA0003586391030000052
in the formula, yFGIs the ordinate value, x, of any point on the straight line FG in the Cartesian coordinate system XOYFGThe abscissa of any point on the straight line FG in the cartesian coordinate system XOY is shown.
(9) A straight line segment GH at the front end of the tooth has the following linear equation:
Figure GDA0003586391030000053
in the formula, yGHIs the ordinate value, x, of any point on the straight line GH in the Cartesian coordinate system XOYGHIs the abscissa value of any point on the straight line GH in the Cartesian coordinate system XOY.
(10) The tooth root curve segment EH has the curve equation:
Figure GDA0003586391030000054
in the formula, yEHIs the ordinate value, x, of any point on the curve EH in the Cartesian coordinate system XOYEHThe abscissa of any point on the curve EH in the cartesian coordinate system XOY is shown.
The outer contour of the hat-shaped flexible gear formed according to the curve equation can relieve stress concentration caused by the support of the hat-shaped flexible gear shown in fig. 4 by the wave generator, and the service life of the hat-shaped flexible gear is prolonged.

Claims (5)

1. A method for improving stress concentration of an outer contour of a flexible gear is characterized by comprising the following steps:
(1) establishing a coordinate system for the structural shape of the outer contour of the flexible gear, wherein the outer contour of the flexible gear comprises a cup bottom flange straight line segment AB, a cup bottom flange and cup body connecting curve segment BC, a cup bottom curve transition segment CD, a cup body connecting curve segment DE, a tooth rear end connecting straight line segment EF, a tooth top straight line segment FG, a tooth front end straight line segment GH and a tooth root curve segment EH which are sequentially connected;
(2) the cup bottom flange and the cup body are connected with a curve segment BC, and the curve equation is as follows:
Figure FDA0003606934340000011
in the formula, yBCIs the ordinate value, x, of any point on the curve BC in the Cartesian coordinate system XOYBCAn abscissa value of any point on the curve BC in a Cartesian coordinate system XOY is shown, h is the thickness of the cup bottom, m is the thickness of a cup bottom flange, n is the distance from the cup bottom flange to the abscissa, and K is the width of the cup bottom;
(3) the cup body is connected with a curve section DE, and the curve equation is as follows:
Figure FDA0003606934340000012
in the formula, yDEIs the ordinate value, x, of any point on the curve DE in the Cartesian coordinate system XOYDEIs an abscissa value of any point on the curve DE in a Cartesian coordinate system XOY, and L is the length of the hat-shaped flexible gear cup body;
(4) the tooth root curve segment EH has the curve equation:
Figure FDA0003606934340000013
in the formula, yEHIs the ordinate value, x, of any point on the curve EH in the Cartesian coordinate system XOYEHThe abscissa value of any point on the curve EH in the Cartesian coordinate system XOY;
(5) the linear equation of the straight line segment AB of the cup bottom flange is as follows:
Figure FDA0003606934340000014
in the formula, xABIs the abscissa value, y, of any point on the straight line segment AB in the Cartesian coordinate system XOYABThe vertical coordinate value of any point on the straight line segment AB in a Cartesian coordinate system is shown, m is the thickness of the cup bottom flange, n is the distance from the cup bottom flange to the horizontal coordinate, and K is the width of the cup bottom;
(6) the curve equation of the cup bottom curve transition section CD is as follows:
Figure FDA0003606934340000015
in the formula, xCDIs the abscissa value, y, of any point on the curve segment CD in the Cartesian coordinate system XOYCDIs the ordinate value of any point on the curve segment CD in the Cartesian coordinate system XOY, and L is the length of the hat-shaped flexible wheel cup body.
2. The method for improving the stress concentration of the outer contour of the flexible gear according to claim 1, wherein the linear equation of the tooth rear end connecting straight line segment EF in the step (1) is as follows:
Figure FDA0003606934340000021
in the formula, yEFIs the ordinate, x, of any point on the straight line EF in the Cartesian coordinate system XOYEFIs the abscissa value, R, of any point on the straight line EF in the Cartesian coordinate system XOY1The addendum circle radius.
3. The method for improving the stress concentration of the outer contour of the flexible gear according to claim 1, wherein the linear equation of the tooth top linear segment FG in step (1) is as follows:
Figure FDA0003606934340000022
in the formula, yFGFor any point on the straight line FG in a Cartesian coordinate system XOOrdinate value in Y, xFGIs the abscissa value, R, of any point on the straight line FG in the Cartesian coordinate system XOY1The addendum circle radius.
4. The method for improving the stress concentration of the outer contour of the flexible gear according to claim 1, wherein the linear equation of the tooth front end straight line segment GH in the step (1) is as follows:
Figure FDA0003606934340000023
in the formula, yGHIs the ordinate value, x, of any point on the straight line GH in the Cartesian coordinate system XOYGHIs the abscissa value, R, of any point on the straight line GH in the Cartesian coordinate system XOY1The addendum circle radius.
5. The method for improving stress concentration of an outer contour of a flexible gear according to claim 1, wherein the coordinate system in step (1) is a cartesian coordinate system with a central axis of the flexible gear as an abscissa axis and a cup bottom flange as an ordinate axis.
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Publication number Priority date Publication date Assignee Title
CN117628141A (en) * 2024-01-26 2024-03-01 广东极亚精机科技有限公司 Flexible externally toothed gear, harmonic gear device, and joint device for robot

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5269202A (en) * 1991-05-20 1993-12-14 Harmonic Drive Systems, Inc. Cup-type harmonic drive having a short, flexible cup member
US20100319484A1 (en) * 2009-06-23 2010-12-23 Harmonic Drive Systems Inc. Wave Gear Device
CN104747660A (en) * 2015-04-14 2015-07-01 上海鑫君传动科技有限公司 Harmonic reducer structure for extending service life
CN109578551A (en) * 2018-12-06 2019-04-05 北京工业大学 A kind of harmonic reducer flexible wheel cup body based on continuous transition curve
CN111255876A (en) * 2020-01-20 2020-06-09 珠海格力电器股份有限公司 Flexible gear and harmonic reducer
CN211231485U (en) * 2019-09-05 2020-08-11 广东省智能制造研究所 Double-arc flexible gear structure

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5269202A (en) * 1991-05-20 1993-12-14 Harmonic Drive Systems, Inc. Cup-type harmonic drive having a short, flexible cup member
US20100319484A1 (en) * 2009-06-23 2010-12-23 Harmonic Drive Systems Inc. Wave Gear Device
CN104747660A (en) * 2015-04-14 2015-07-01 上海鑫君传动科技有限公司 Harmonic reducer structure for extending service life
CN109578551A (en) * 2018-12-06 2019-04-05 北京工业大学 A kind of harmonic reducer flexible wheel cup body based on continuous transition curve
CN211231485U (en) * 2019-09-05 2020-08-11 广东省智能制造研究所 Double-arc flexible gear structure
CN111255876A (en) * 2020-01-20 2020-06-09 珠海格力电器股份有限公司 Flexible gear and harmonic reducer

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