CN105234498A - Equal-arc-length slotting method of non-circular gears - Google Patents

Equal-arc-length slotting method of non-circular gears Download PDF

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Publication number
CN105234498A
CN105234498A CN201510794817.5A CN201510794817A CN105234498A CN 105234498 A CN105234498 A CN 105234498A CN 201510794817 A CN201510794817 A CN 201510794817A CN 105234498 A CN105234498 A CN 105234498A
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China
Prior art keywords
gear
slotting
tooth base
pinion cutter
arc length
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Pending
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CN201510794817.5A
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Chinese (zh)
Inventor
刘有余
李军
刁杰胜
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Anhui Polytechnic University
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Anhui Polytechnic University
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Priority to CN201510794817.5A priority Critical patent/CN105234498A/en
Publication of CN105234498A publication Critical patent/CN105234498A/en
Pending legal-status Critical Current

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Abstract

The invention belongs to the field of numerical control machining of gears and relates to an equal-arc-length slotting method of non-circular gears. Through the equal-arc-length slotting method of the non-circular gear, a workbench, gear blanks, a main shaft and a gear slotting cutter are used, wherein the workbench is used for driving the gear blanks to rotate; the main shaft drives the gear slotting cutter to rotate; a gear slotting cutter divided circle is tangent to a gear blank section curve and is capable of purely rolling; the gear slotting cutter moves along an X-axis direction in the plane to form the gear blank section curve; the gear slotting cutter moves along a Z-axis direction to form the whole-tooth depth of the gear blanks; the gear slotting cutter or the gear blanks are also capable of additionally rotating; the gear blanks also carry out equal-arc-length movement relative to a machine tool in the end surfaces of the gear blanks; other shafts are linked relative to the machine tool. The equal-arc-length slotting method is capable of slotting internally-meshed non-circular straight gears and bevel gears and is also capable of slotting externally-meshed non-circular straight gears and bevel gears; the gear blanks are also capable of additionally rotating during slotting the bevel gears; through the equal-arc-length slotting method, the purpose of processing the non-circular gears with high efficiency and high accuracy can be achieved; compared to other methods, the machining efficiency is highest under the requirement of same accuracy.

Description

A kind of arc length slotting methods such as tooth base of non-circular gear
Technical field
The invention belongs to gear manufacture field, especially tooth field processed on the wheel of radius of clean-up change, relates to a kind of arc length slotting methods such as tooth base of non-circular gear.
Background technology
Non-circular gear is again different in nature gear, its reference surface is not surface of revolution, application is had in fields such as engineering machinery, lathe, automobile, Aero-Space, non-circular gear drive refers in transmission to have at least the pitch surface of a gear not to be the gear drive of surface of revolution, application advantage is obvious, current industrial application is normal adopts line cutting technology processing non-circular gear, and Linear cut is inefficiency not only, and is difficult to without transformation directly application processing not rounded helical gear.
Gear shaping is a kind of highly-efficient processing non-circular gear method, Chinese patent CN200810000133.3 discloses a kind of method being processed with the incomplete circumference gear blocked, gear shapping machine and Special Slotting Cutters is adopted to process, but due to clamping trouble, and specific on-circular gear can only be processed, practicality is not strong; Chinese patent CN201220482831.3 discloses a kind of clamping apparatus for gear wheel processing, but it is only applicable to the batch shaping of thin type, large gear, is not described in detail for non-circular gear, is difficult to realize.
The effective ways solved the problem are the numerical control slotting technology adopting high-efficiency high-accuracy, the invention provides a kind of arc length slotting methods such as tooth base of non-circular gear.
Summary of the invention
The object of the invention is to: for above-mentioned prior art Problems existing, propose a kind of arc length slotting methods such as tooth base of non-circular gear.In the method, adopt pinion cutter rotating speed to be reference frequency, all the other axles are its interlock relatively.
The object of the invention is to be achieved through the following technical solutions.
The arc length slotting non-circular gear methods such as tooth base of the present invention, comprise workbench, tooth base, main shaft, pinion cutter, described workbench drives described tooth base to rotate, described main shaft drives described pinion cutter to rotate, described pinion cutter reference circle and described tooth base pitch curve tangent and make pure rolling, described pinion cutter planar moves along X axis and forms described tooth base pitch curve, and described pinion cutter moves along Z-axis direction and forms described tooth base fully teeth height in vertical plane, and described pinion cutter or described tooth base also have additional rotation; In described tooth base end face, described workbench drives described tooth base to rotate according to arc length methods such as tooth bases, and namely described tooth base is relative to the arc length such as lathe does motion, and all the other axles are its interlock relatively.
The arc length method slotting non-circular gears such as described tooth base, can insert internal messing non-circular gear processed, comprise internal messing not rounded spur gear and internal messing not rounded helical gear; It is inner that described pinion cutter is positioned at described tooth base pitch curve, and in plane, described main shaft drives described pinion cutter invariablenes turning speed, and described in unit interval internal shaping, tooth base pitch curve arc length is equal.
The arc length method slotting non-circular gears such as described tooth base, can insert external toothing non-circular gear processed, comprise external toothing not rounded spur gear and external toothing not rounded helical gear; It is outside that described pinion cutter is positioned at described tooth base pitch curve, and in plane, described main shaft drives described pinion cutter invariablenes turning speed, and described in unit interval internal shaping, tooth base pitch curve arc length is equal.
The arc length method slotting not rounded helical gears such as described tooth base, also have additional rotation in described pinion cutter slotting process.
The invention has the beneficial effects as follows: the arc length slotting non-circular gear methods such as tooth base of the present invention, the target of high-efficiency high-accuracy processing non-circular gear can be realized; Because unit interval internal shaping tooth base pitch curve arc length is equal, in gained non-circular gear different polar angle places flank profil, cut channel is evenly distributed, and each profile accuracy is balanced consistent, relative additive method, and under same precision requires, working (machining) efficiency is the highest.
Accompanying drawing explanation
Fig. 1 is gear ratio electronic gearbox transmission scheme figure of the present invention;
Fig. 2 is the arc length slotting internal messing non-circular gear method schematic diagrames such as tooth base of the present invention;
Fig. 3 is the arc length slotting internal messing non-circular gear method tooth base end view such as tooth base of the present invention;
Fig. 4 is the arc length slotting internal messing avette spur gear Path sectional views such as tooth base of the present invention;
Fig. 5 is the arc length slotting internal messing dextrorotation avette helical gear Path stereograms such as tooth base of the present invention;
Fig. 6 is the left-handed avette helical gear Path stereograms of arc length slotting internal messing such as tooth base of the present invention;
Fig. 7 is the arc length slotting external toothing non-circular gear method tooth base end view such as tooth base of the present invention;
Fig. 8 is arc length slotting external toothing three rank such as tooth base of the present invention oval spur gear Path sectional views;
Fig. 9 is the arc length slotting external toothing dextrorotation three rank elliptical skew gear Path stereograms such as tooth base of the present invention;
Figure 10 is the left-handed three rank elliptical skew gear Path stereograms of arc length slotting external toothing such as tooth base of the present invention.
Wherein: 1-tooth base, 2-pinion cutter
Detailed description of the invention
Non-circular gear slotting and the very large difference of roller gear slotting are, fixing generate relation is not had between slotting tool and workpiece, and the distance of slotting tool center and workpiece centre is not also stopping change, but slotting tool rotating speed, workpiece rotational frequency and the slotting tool translational speed on slotting tool center and workpiece centre line, has the mathematical relationship determined between this three.Emphasis of the present invention is when establishing slotting tool invariablenes turning speed, the interaction relation of all the other each axle speed of lathe and slotting tool rotating speed, adopting is equipped with the dedicated gear NC system of machining of gear ratio electronic gear box function to realize this interaction relation, and Fig. 1 is the gear ratio electronic gearbox transmission scheme figure adopted.
In order to slotting goes out a complete non-circular gear, pinion cutter and workpiece tooth base must possess following motion:
1) cutting movement: pinion cutter pumps fast along the axis direction of tooth base, this is the main motion of pinion cutter.
2) pitch curve feed motion: pinion cutter cutter shaft does gyration at a slow speed around itself axis.Its speed affects the speed of cutting.Pitch curve amount of feeding size, the arc length turned on its pitch curve with each reciprocating stroke of pinion cutter calculates.
3) radial feed motion: after pinion cutter starts Contact Tooth base, while pitch curve feeding, pinion cutter makes radial feed (or tooth base makes radial feed to pinion cutter) to tooth base, till entering tooth complete dark (referring to cutting at one time) always.The size of radial feeds, moves radially millimeter with each reciprocating stroke of pinion cutter and represents.
4) generating motion: circular pinion cutter is regarded as a gear, remains the meshing relation of a pair gear forcibly between itself and workpiece tooth base; In engagement process, pinion cutter forms the material removal of interfering by tooth base to its motion, thus processes non-circular gear tooth profile.
5) cutter relieving motion: pumping of pinion cutter is downwards impulse stroke, is upwards backstroke.In order to ensure that pinion cutter is got along well when returning face, in order to avoid oneself processing flank of tooth of scratch and reduce tool wear, tooth base should leave a distance relative to pinion cutter.
6) additional rotation: during slotting not rounded helical gear, while pinion cutter is done to pump, also must have the additional rotation that synchronous, the surface produced when moving to make cutting edge is equivalent to helical gear flank.
Below in conjunction with figure and embodiment the invention will be further described.
Embodiment one
See Fig. 2, illustrate each axle interaction relations of arc length slotting internal messing non-circular gear method such as tooth base of the present invention.In tooth base 1 end face, pinion cutter 2 is with ω brotate, tooth base 1 is with ω crotate, for ensureing pinion cutter 2 pitch circle and tooth base 1 pitch curve pure rolling in the same way in slotting process, ω in tooth base 1 end face bwith ω cstrict gearratio is kept by generating motion requirement.In tooth base 1 axial plane, for keeping pinion cutter 2 pitch circle to contact with tooth base 1 pitch curve inscribe, v made by pinion cutter 2 xmotion, axially has and moves back and forth slotting v z, thus slotting full-depth tooth, for ensureing that the flank of tooth is along axis uniform precision, v zwith ω blinear interlock; To not rounded helical gear, according to flank of tooth Z axis position, pinion cutter 2 adds gyration Δ ω b.
See Fig. 3, it is inner that pinion cutter 2 is positioned at tooth base 1 pitch curve, and both direction of rotation are identical; Pinion cutter 2 revolves round the sun and rotation clockwise counterclockwise, and slotting a period of time, pinion cutter 2 cutter location is from o bmove to o ' b, coordinate system S b(o b-x by bz b) revolution angle is λ, be β with pinion cutter 2 rotation angle, the total angle of rotation is become S ' b(o ' b-x ' by ' bz ' b).The arc length methods such as tooth base of the present invention require that described in slotting, tooth base nodel line arc length AT temporally linearly increases, hobboing cutter rotational speed omega bconstant, all the other axles are its interlock relatively.The pitch curve that TT ' is pinion cutter 2 and tooth base 1 is at the common tangent of T point, and the angle of TT ' positive direction and footpath, pole forward is μ.Based on said method, according to Differential Geometry principle, set up internal messing slotting not rounded spur gear or helical gear interlock equation be:
v x = rr b j d r d θ - r b j 2 sin μ d r d θ - rr b j 2 cos μ d μ d θ l r 2 + ( d r d θ ) 2 ω b = i x b ( θ ) ω b
ω c = l 2 1 - ( r b j c o s μ l ) 2 r b j - lr b j 2 s i n μ d μ d θ - r b j 2 c o s μ d l d θ l 2 1 - ( r b j cos μ l ) 2 r 2 + ( d r d θ ) 2 ω b = i c b ( θ ) ω b .
ω b * = ω b ± v z tanβ c r b j = ω b ± i b z ( θ ) v z
In formula, r is footpath, tooth base 1 pitch curve pole; θ is tooth base 1 polar angle; r bjfor pinion cutter 2 pitch radius; β cfor oblique gear spiral angle, to spur gear, β c=0; for the 2-in-1 one-tenth rotating speed of pinion cutter, get "-" when pinion cutter 2 helix rotation direction is consistent with pinion cutter 2 rotation direction, otherwise get "+"; μ=arctan [r/ (dr/d θ)] (0≤μ < π);
See Fig. 4, for adopting the inventive method slotting internal messing avette spur gear Path sectional view, described gear parameter is as follows: semi-major axis a=117.600mm, exponent number n=2, facewidth b=50mm, eccentric ratio e=0.1, normal module m n=3.75mm, gear number of teeth Z=63, pinion cutter number of teeth z=22.Avette spur gear is a kind of typical not rounded spur gear, and other not rounded spur gears with it difference are only that pitch curve equation is different, and visible, the method for the invention correctly can insert internal messing not rounded spur gear processed.
See Fig. 5, for adopting the inventive method slotting internal messing dextrorotation avette helical gear Path stereogram, described gear parameter is as follows: semi-major axis a=120mm, exponent number n=2, facewidth b=50mm, eccentric ratio e=0.1, normal module m n=3.75mm, helixangleβ c=11.617 °, gear number of teeth Z=63, pinion cutter number of teeth z=22; See Fig. 6, for adopting the left-handed avette helical gear Path stereogram of the inventive method slotting internal messing, described gear parameter is as follows: semi-major axis a=120mm, exponent number n=2, facewidth b=50mm, eccentric ratio e=0.1, normal module m n=3.75mm, helixangleβ c=-11.617 °, gear number of teeth Z=63, pinion cutter number of teeth z=22.In like manner visible, the method for the invention correctly can insert internal messing not rounded helical gear processed.
Embodiment two
See Fig. 7, illustrate each axle interaction relations of arc length slotting external toothing non-circular gear method tooth base end face such as tooth base of the present invention.All the other are identical with described embodiment one, and difference is, it is outside that pinion cutter 2 is positioned at tooth base 1 pitch curve, and both direction of rotation are contrary.Based on said method, according to Differential Geometry principle, set up external toothing slotting not rounded spur gear or helical gear interlock equation be:
v x = &lsqb; r d r d &theta; + r b j d r d &theta; s i n &mu; + rr b j d &mu; d &theta; c o s &mu; &rsqb; r b j &omega; b l r 2 + ( d r d &theta; ) 2 = i x b ( &theta; ) &omega; b
&omega; c = &lsqb; lr b j s i n &mu; d &mu; d &theta; + r b j c o s &mu; d l d &theta; + l 2 1 - ( r b j c o s &mu; l ) 2 &rsqb; r b j &omega; b l 2 1 - ( r b j c o s &mu; l ) 2 r 2 + ( d r d &theta; ) 2 = i c b ( &theta; ) &omega; b .
&omega; b * = &omega; b &PlusMinus; v z tan&beta; c r b j = &omega; b &PlusMinus; i b z ( &theta; ) v z
In formula, parameter definition as previously mentioned.
See Fig. 8, for adopting the inventive method slotting external toothing three rank oval spur gear Path sectional view, described gear parameter is as follows: semi-major axis a=98.560mm, exponent number n=3, facewidth b=50mm, eccentric ratio e=0.2, normal module m n=5mm, gear number of teeth Z=42, pinion cutter number of teeth z=22.The oval spur gear in three rank is a kind of typical not rounded spur gear, and other not rounded spur gears with it difference are only that pitch curve equation is different, and visible, the method for the invention correctly can insert external toothing not rounded spur gear processed.
See Fig. 9, for adopting the inventive method slotting external toothing dextrorotation three rank elliptical skew gear Path stereogram, described gear parameter is as follows: semi-major axis a=100mm, exponent number n=3, facewidth b=50mm, eccentric ratio e=0.2, normal module m n=5mm, helixangleβ c=9.54 °, gear number of teeth Z=42, pinion cutter number of teeth z=22; See Figure 10, for adopting the left-handed three rank elliptical skew gear Path stereograms of the inventive method slotting external toothing, described gear parameter is as follows: semi-major axis a=100mm, exponent number n=3, facewidth b=50mm, eccentric ratio e=0.2, normal module m n=5mm, helixangleβ c=-9.54 °, gear number of teeth Z=42, pinion cutter number of teeth z=22.In like manner visible, the method for the invention correctly can insert external toothing not rounded helical gear processed.
Above composition graphs is described the specific embodiment of the present invention; but these explanations can not be understood to limit range of application of the present invention; protection scope of the present invention is limited by the accompanying claims, and any change on application claims basis is all protection scope of the present invention.

Claims (4)

1. the arc length slotting method such as tooth base of a non-circular gear, comprise workbench, tooth base, main shaft, pinion cutter, described workbench drives described tooth base to rotate, described main shaft drives described pinion cutter to rotate, described pinion cutter reference circle and described tooth base pitch curve tangent and make pure rolling, described pinion cutter planar moves along X axis and forms described tooth base pitch curve, and described pinion cutter moves along Z-axis direction and forms described tooth base fully teeth height in vertical plane; It is characterized in that: in described tooth base end face, described workbench drives described tooth base to rotate according to arc length methods such as tooth bases, namely described tooth base is relative to the arc length such as lathe does motion, and all the other axles are its interlock relatively.
2. the arc length method slotting non-circular gear such as tooth base according to claim 1, can insert internal messing non-circular gear processed, comprise internal messing not rounded spur gear and internal messing not rounded helical gear; It is characterized in that: it is inner that described pinion cutter is positioned at described tooth base pitch curve, and in plane, described main shaft drives described pinion cutter invariablenes turning speed, and described in unit interval internal shaping, tooth base pitch curve arc length is equal.
3. the arc length method slotting non-circular gear such as tooth base according to claim 1, can insert external toothing non-circular gear processed, comprise external toothing not rounded spur gear and external toothing not rounded helical gear; It is characterized in that: it is outside that described pinion cutter is positioned at described tooth base pitch curve, and in plane, described main shaft drives described pinion cutter invariablenes turning speed, and described in unit interval internal shaping, tooth base pitch curve arc length is equal.
4. according to claim 1 and the arc length method slotting not rounded helical gear such as claim 2 or tooth base according to claim 3, it is characterized in that: in described pinion cutter slotting process, also have additional rotation.
CN201510794817.5A 2015-11-17 2015-11-17 Equal-arc-length slotting method of non-circular gears Pending CN105234498A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106624190A (en) * 2017-01-23 2017-05-10 合肥工业大学 Machining method for continuously generating non-circular gear into gear shaping
CN110479839A (en) * 2019-08-02 2019-11-22 武汉理工大学 For shaping the envelope roller parameter acquiring method of the high muscle Cylinder shape constructional element of thin-walled

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CN103769690A (en) * 2014-01-24 2014-05-07 安徽工程大学 Method for slotting non-circular gear at equal rotating angle relative to gear blank by slotting cutter
CN104259583A (en) * 2014-08-14 2015-01-07 合肥工业大学 Gear blank constant angular speed-rotating slotting method for angles for non-cylindrical gears
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
RO121502B1 (en) * 1997-08-26 2007-08-30 Numerical control machine for teething circular or non-circular spur wheels by mortising with wheel-cutter
CN103769690A (en) * 2014-01-24 2014-05-07 安徽工程大学 Method for slotting non-circular gear at equal rotating angle relative to gear blank by slotting cutter
CN104259583A (en) * 2014-08-14 2015-01-07 合肥工业大学 Gear blank constant angular speed-rotating slotting method for angles for non-cylindrical gears
CN104816045A (en) * 2014-11-28 2015-08-05 武汉理工大学 Gear shaping processing method of noncircular gear

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刘有余: "内啮合高阶椭圆齿轮多方案虚拟插削与分析", 《合肥工业大学学报》 *
刘有余: "外啮合椭圆齿轮多方案插齿三维仿真与分析", 《机械科学与技术》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106624190A (en) * 2017-01-23 2017-05-10 合肥工业大学 Machining method for continuously generating non-circular gear into gear shaping
CN106624190B (en) * 2017-01-23 2017-12-15 合肥工业大学 The processing method that a kind of non-circular gear continuously transforms into gear shaping
CN110479839A (en) * 2019-08-02 2019-11-22 武汉理工大学 For shaping the envelope roller parameter acquiring method of the high muscle Cylinder shape constructional element of thin-walled
CN110479839B (en) * 2019-08-02 2020-08-04 武汉理工大学 Envelope roller parameter obtaining method for forming thin-wall high-rib cylindrical component

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Application publication date: 20160113