CN117620323A - Displacement tooth form method for generating non-orthogonal offset helical gear pair by using disc-shaped grinding wheel - Google Patents
Displacement tooth form method for generating non-orthogonal offset helical gear pair by using disc-shaped grinding wheel Download PDFInfo
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Abstract
The invention provides a method for generating a shift tooth profile of a non-orthogonal offset bevel gear pair by a disc-shaped grinding wheel, which belongs to the technical field of gear processing, and comprises the steps of firstly deducing a tooth surface equation of the shift disc-shaped grinding wheel according to the motion relation of two virtual shift tooth-shaping cutters and tooth surface parameters of the virtual shift tooth-shaping cutters, deducing tooth surface equations of the virtual shift tooth-shaping cutters and a shift small wheel, deducing the tooth surface equation of the shift disc-shaped grinding wheel according to the tooth surface equation of the virtual shift tooth-shaping cutters, and finally deducing the shift tooth profile of the non-orthogonal offset bevel gear according to the motion relation of the virtual shift tooth-shaping cutters and the non-orthogonal offset bevel gear and the tooth surface equation of the shift disc-shaped grinding wheel. The shift pinion and the non-orthogonal offset shift helical gear thus generated may constitute a non-orthogonal offset shift helical gear pair. The gear pair with the non-orthogonal offset deflection bevel gear surface is processed by adopting the deflection disc-shaped grinding wheel, so that the structure is simple, and the gear surface with higher precision can be obtained.
Description
Technical Field
The invention relates to the technical field of gear machining, in particular to a method for generating a shift tooth profile of a non-orthogonal offset helical gear pair by using a disc-shaped grinding wheel.
Background
The bevel gear pair has important application in the aviation field, especially in helicopter transmission systems. Most of researches on the helical gear pair are now the researches on the orthogonal or orthogonal offset helical gear pair, and the researches on the helical gear pair which is the most complex and has the most general meaning and is integrated with the non-orthogonal offset deflection are ignored.
Common machining methods for face gears include gear shaping, gear hobbing, and gear grinding. The gear shaper cutter processes the face gear principle, the same-face gear transmission meshing principle is highly consistent, and the principle is the theoretical basis for the subsequent research of face gear tooth surfaces, shape modification, hobbing, grinding teeth and the like. Litvin et al establishes the meshing theory of point contact face gear transmission based on the face gear shaping principle, and elaborates the conditions of face gear tooth root undercut and tooth top sharpening. The Canadian NorthStar Aerospace company also successfully develops a face gear numerical control gear shaper to realize the gear shaping processing of the face gear. The students in China research the machining interference, tooth surface design, meshing simulation and the like, and master the gear shaping technology of the orthogonal face gear.
The grinding method is a key technology of the tooth surface precision of the face gear. Litvin et al propose a method of grinding face gears with worm wheels, but the wheel dressing apparatus and tools are complex. The method for grinding the face gear by using the grinding wheel and the straight blade cutter is respectively proposed by Stadtfeld doctor of Gleason company in the United states, and domestic scholars have conducted intensive researches on the grinding wheel because the grinding wheel has the advantages of simple structure, convenience in design, manufacture and trimming, easiness in realization of machine tool movement and the like.
The gear pair with non-orthogonal offset deflection bevel gear faces generated by the gear shaping cutter has low precision, and the worm grinding wheel has complex manufacture, difficult trimming and the gear faces are affected by singularities, thus being not applicable to the gear pair with certain parameters.
Disclosure of Invention
The invention aims to provide a method for generating a shift tooth profile of a non-orthogonal offset helical tooth surface gear pair by a disc-shaped grinding wheel, which solves the technical problems that the precision of the non-orthogonal offset shift helical tooth surface gear pair generated by a gear shaper cutter is not high, the manufacturing of a worm grinding wheel is complex, the trimming is difficult, the tooth surface is affected by singularity, and the method is not suitable for a face gear pair with certain parameters. The non-orthogonal offset bevel gear pair is processed by adopting the offset disc-shaped grinding wheel, so that the gear pair has a simple structure, is convenient to design, manufacture and repair, is not limited by design parameters of a face gear, and can obtain a tooth face with higher precision.
The invention provides a non-orthogonal offset bevel gear pair with a disc-shaped grinding wheel, wherein if a positive-displacement bevel gear and a negative-displacement bevel gear are processed by the disc-shaped grinding wheel respectively, the obtained negative-displacement bevel gear and positive-displacement bevel gear can form the non-orthogonal offset bevel gear pair. The non-orthogonal offset bevel gear pair is processed by adopting the offset disc-shaped grinding wheel, so that the gear pair has a simple structure, is convenient to design, manufacture and repair, is not limited by design parameters of a face gear, and can obtain a tooth face with higher precision. The invention is mainly used for generating the shift tooth profile of the non-orthogonal offset helical gear pair, and provides a technical method for processing the non-orthogonal offset shift helical gear pair.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a method for generating a shift tooth form of a non-orthogonal offset bevel gear pair by using a grinding wheel includes the steps of machining a shift small wheel by using a first shift grinding wheel, machining a non-orthogonal offset bevel gear by using a second shift grinding wheel, simulating the generating motion of the first virtual shift gear shaper and the shift small wheel by the rotation and the swing of the first shift grinding wheel around the first virtual shift gear shaper, simulating the generating motion of the second virtual shift gear shaper and the non-orthogonal offset bevel gear by the rotation and the swing of the second shift grinding wheel around the second virtual shift gear shaper, enabling the centers of the first shift grinding wheel and the second shift grinding wheel to reciprocate along an axis parallel to the first virtual shift gear shaper to form feeding motion, and enabling the centers of the second shift grinding wheel to reciprocate along an axis parallel to the second virtual shift gear shaper to form feeding motion.
Further, the first virtual shift pinion cutter and the second virtual shift pinion cutter have the same modulus, the same end face pressure angle, the second virtual shift pinion cutter and the same position vector of the shift pinion, if the first virtual shift pinion cutter is positively shifted, the second virtual shift pinion cutter and the shift pinion are negatively shifted, the non-orthogonal offset bevel gear is positively shifted, and the generated negative shift pinion and the positively shifted non-orthogonal offset bevel gear form a pair of non-orthogonal offset bevel gear pairs.
Further, the specific process of the generating motion of the first virtual shift gear shaper cutter, the second virtual shift gear shaper cutter and the shift small wheel is as follows: coordinate system S 1 、S g1 、S i Fixedly connected with the first virtual shift gear shaper, the first shift disc-shaped grinding wheel, the second virtual shift gear shaper and the shift small wheel respectively, wherein i=2, 3 respectively represent coordinate systems or tooth surface parameters of the second virtual shift gear shaper and the shift small wheel, S p 、S t To assist the coordinate system, three motion relationships exist during grinding: the first indexing disc wheel has an angular velocity omega 1 Z around the first virtual indexing gear shaper cutter 1 The rotary pendulum of the shaft, the rotation of the first simulated virtual shift gear shaper cutter and the second virtual shift gear shaper cutter and the shift small wheel are driven at the angular velocity omega i Around axis Z i Is rotated to form an generating motion, and omega i ＝ω 1 m i1 ，m i1 For the gear ratio of the first virtual shift gear shaper, the second virtual shift gear shaper and the shift pinion, the projections of the center distances of the first virtual shift gear shaper and the first shift disc grinding wheel in the X-axis and Z-axis directions are E respectively g1 And L g1 Z of first virtual shift gear shaper cutter 1 The shaft and the end face of the first deflection abrasive disk form a helix angle beta, and the first deflection abrasive disk is parallel to the Z of the first virtual deflection gear shaper cutter 1 Axial feed movement, indexing the disc wheel at angular velocity omega g1 High-speed rotation constitutes cutting motion.
Further, the tooth surface equation of the first virtual shift pinion is:
in the section parameters of the first virtual shift gear shaper cutter, R p1 、R b1 Respectively representing the reference circle radius and the base circle radius theta of the first virtual shift gear shaper cutter 1 Indicating rotation of the gearAngle parameter, theta b1 Represents the central angle lambda corresponding to 1/2 of the tooth groove width on the base circle 1 Representing the rotation angle, p, of the involute of the end surface of the first virtual shift gear shaper cutter around the axis 1 Representing the spiral motion parameters, at S 1 In the coordinate system, the tooth surface of the first virtual shift pinion is represented by the following formula:
D＝θ b1 +θ 1 ±λ 1 ，/>
θ b1 ＝π/(2N 1 )-(tanα t -α t )-(xm n ·tanα t )/R p1 ，N 1 representing the number of teeth, alpha, of the first virtual indexing gear shaper cutter t Represents the end face pressure angle of the virtual shift gear shaper cutter, xm n Indicating the amount of displacement.
Further, the tooth surface equation of the first indexing dish wheel is:
the generating line of the first deflection grinding wheel is the end surface section line of the first virtual deflection gear shaper cutter, so that the tooth surface of the first deflection grinding wheel is an involute rotating curved surface, and L g1 ＝0，θ g1 Is the angle parameter of the curved surface of the grinding wheel 1, M t1 、M pt 、M g1p Coordinate system S 1 To a coordinate system S t Coordinate system S t To a coordinate system S p Coordinate system S p To a coordinate system S g1 Coordinate transformation matrix of (2), at S g1 The position vector and unit normal vector of the first indexed disc wheel 1 are represented by the following formulas: r is R g1 (θ 1 ,λ 1 ,θ g1 )＝M g1p (θ g1 )M pt M t1 R 1 (θ 1 ,λ 1 )，n g1 (θ 1 ,λ 1 ,θ g1 )＝L g1p (θ g1 )L pt L t1 n 1 (θ 1 ,λ 1 )
Further, the tooth surface equation of the second virtual shift pinion and the shift pinion is:
in the generating coordinate system of the second virtual shift gear shaper cutter and the shift small wheel, S m 、S n L is an auxiliary coordinate system 0 Representing the center distance phi of the first virtual shift gear shaper cutter 2 and the second virtual shift gear shaper cutter 3 i ＝φ g1 m i1 In S i In the coordinate system, the tooth surface equations of the second virtual shift pinion and the shift pinion are represented by the following formulas:
R i (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝M in M nm M m1 (φ g1 )M 1t M tg1 (L g1 )R g1 (θ 1 ,λ 1 ,θ g1 )
f 1 (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝n g1 ν 1 ＝0
f 2 (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝n g1 ν 2 ＝0
n i (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝L in L nm L m1 (φ g1 )L 1t L tg1 (L g1 )n g1 (θ 1 ,λ 1 ,θ g1 )
above simultaneous cancellation parameter θ g1 Can use R i (θ 1 ,λ 1 ,φ g1 ,L g1 ) Representing tooth surfaces of the virtual second virtual shift pinion and the shift pinion;
ν 1 ＝[0 0 1]，
ν 1 、ν 2 the center speed of the first deflection grinding wheel, the second virtual deflection gear shaper cutter, the deflection small wheel and the relative speed of the first deflection grinding wheel are respectively.
Further, the tooth surface equation of the second virtual shift grinding wheel is:
the generating line of the second virtual deflection grinding wheel is the end surface section line of the virtual deflection gear shaper cutter, so that the tooth surface of the second virtual deflection grinding wheel is an involute rotating curved surface, and L g2 =0, coordinate system S 2 And a coordinate system S g2 Fixedly connected with a second virtual shift gear shaping cutter and a second shift disc-shaped grinding wheel respectively, S p 、S t The projections of the center distance between the second virtual shift gear shaper cutter and the second shift disc grinding wheel in the X-axis and Z-axis directions are E respectively g2 And L g2 Z of the second virtual shift gear shaper cutter 2 The shaft and the end face of the second deflection disc-shaped grinding wheel form a helix angle beta, theta g2 Is the angle parameter of the curved surface of the second deflection disc-shaped grinding wheel, M t2 、M pt 、M g2p Coordinate system S 2 To a coordinate system S t Coordinate system S t To a coordinate system S p Coordinate system S p To a coordinate system S g2 Coordinate transformation matrix of (2), at S g2 The position vector and unit normal vector of the second indexed dish wheel 4 are represented by:
R g2 (θ 2 ,θ g2 ,λ 2 ,φ g2 )＝M g2p (θ g2 )M pt M t2 R 2 (θ 2 ,λ 2 ,φ g2 )
n g1 (θ 2 ,θ g2 ,λ 2 ,φ g2 )＝L g1p (θ g2 )L pt L t1 n 1 (θ 2 ,λ 2 ,φ g2 )
θ 2 ＝-θ 1 m 21 ，m 21 is the gear ratio of the first virtual shift gear shaper cutter to the second virtual shift gear shaper cutter
λ 2 ＝-λ 1 ，φ g2 ＝m 21 φ g1 ；
θ b2 ＝π/(2N 2 )-(tanα t -α t )-(xm n ·tanα t )/R p2 ，N 2 Representing the number of teeth of the second virtual shift gear shaper cutter, R p2 Representing the pitch circle radius of the second virtual shift gear shaper cutter;
further, the motion process of generating the non-orthogonal offset shifted skew tooth face gear is as follows:
the second virtual shift gear shaping cutter shaft line is not parallel to and is not intersected with the gear shaft line of the non-orthogonal offset shift bevel gear surface and has an offset angle gamma m And an offset E, L 1 Representing the center distance between the second virtual shift gear shaper cutter and the non-orthogonal offset helical gear, wherein three motion relations exist during grinding: the second deflection disc wheel is at angular velocity omega 2 Z around the second virtual indexing gear shaper cutter 2 The axial rotation and swing simulate the rotation of a second virtual displacement gear shaper cutter and the angular speed omega of a non-orthogonal offset displacement helical gear 4 Around axis Z 4 Is rotated to form an generating motion, and omega 4 ＝ω 2 m 42 ，m 42 For the gear ratio of the second virtual shift gear shaper and the non-orthogonal offset shift bevel gear, the second shift disk is parallel to the Z of the second virtual shift gear shaper 2 Axial feed movement, indexing the disc wheel at angular velocity omega g2 High-speed rotation constitutes cutting motion.
Further, the shift tooth surface equation of the non-orthogonal offset helical tooth surface gear is:
coordinate system S 2 And a coordinate system S 4 Respectively fixedly connected with a second virtual shift gear shaper cutter and a non-orthogonal offset helical gear, S m 、S t 、S k 、S r 、S n In order to assist in the coordinate system, for the gear ratio of the second virtual shift slotting cutter and the non-orthogonal offset helical face gear, at S 4 In the coordinate system, the tooth surface equation of the non-orthogonal offset helical tooth surface gear is expressed by the following formula:
R 4 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝M 4n M nr M rk M km M m2 M 2t M tg2 (L g2 )R g2 (θ 2 ,θ g2 ,λ 2 ,φ g2 )
n 4 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝L 4n L nr L rk L km L m2 L 2t L tg2 (L g2 )n g2 (θ 2 ,θ g2 ,λ 2 ,φ g2 )
f 3 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝n g2 ν 3 ＝0
f 4 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝n g2 ν 4 ＝0
above simultaneous cancellation parameter θ g2 By R 4 (θ 2 ,λ 2 ,φ 4 ,L 2g ) Representing tooth surfaces of a non-orthogonally offset helical tooth face gear;
ν 3 、ν 4 the center speed of the second deflection disc-shaped grinding wheel and the relative speed of the non-orthogonal offset bevel gear and the second deflection disc-shaped grinding wheel are respectively;
ν 3 ＝[0 0 1]，
due to the adoption of the technical scheme, the invention has the following beneficial effects:
according to the motion relation of the two virtual shift gear shaping cutters and the tooth surface parameters of the virtual shift gear shaping cutters, the tooth surface equation of the shift disc-shaped grinding wheel is deduced, the tooth surface equations of the virtual shift gear shaping cutters and the shift small wheel are deduced, the tooth surface equation of the shift disc-shaped grinding wheel is deduced according to the tooth surface equation of the virtual shift gear shaping cutters, and finally the shift tooth shape of the non-orthogonal shift bevel-shaped gear is deduced according to the motion relation of the virtual shift gear shaping cutters and the non-orthogonal shift bevel-shaped tooth surface gear and the tooth surface equation of the shift disc-shaped grinding wheel. The shift pinion and the non-orthogonal offset shift helical gear thus generated may constitute a non-orthogonal offset shift helical gear pair. The gear pair with the non-orthogonal offset deflection bevel gear surface is processed by adopting the deflection disc-shaped grinding wheel, so that the structure is simple, and the gear surface with higher precision can be obtained.
Drawings
FIG. 1 is a diagram illustrating the motion process of the virtual indexing pinion cutter and the indexing wheel according to the present invention;
FIG. 2 is a cross-sectional parametric view of a virtual shifting tooth shaper cutter according to the present invention;
FIG. 3 is a diagram of two grinding wheel generation coordinate systems according to the present invention;
FIG. 4 is a diagram of a virtual indexing pinion cutter and indexing small wheel generating coordinate system according to the present invention;
FIG. 5 is a coordinate transformation diagram of a virtual indexing gear shaper cutter to indexing abrasive disc of the present invention;
FIG. 6 is a diagram illustrating the motion of a virtual shifted shaper cutter according to the present invention and a non-orthogonally offset shifted bevel flank gear.
In the drawing, the gear wheel is 1-first deflection abrasive disc, 2-first virtual deflection gear shaper cutter, 3-second virtual deflection gear shaper cutter, 4-second deflection abrasive disc and 5-non-orthogonal offset deflection bevel gear.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail below by referring to the accompanying drawings and by illustrating preferred embodiments. It should be noted, however, that many of the details set forth in the description are merely provided to provide a thorough understanding of one or more aspects of the invention, and that these aspects of the invention may be practiced without these specific details.
As shown in fig. 1-2, the method for generating the shift tooth shape of the non-orthogonal offset helical gear pair by using the disc-shaped grinding wheel is characterized in that a first shift disc-shaped grinding wheel 1 is used for processing a shift small wheel, and a second shift disc-shaped grinding wheel 4 is used for processing a non-orthogonal offset helical gear 5. Simulating the generating motion of the first virtual deflection gear shaper cutter 2 and the deflection small wheel through the rotation and the swing of the first deflection abrasive disc wheel 1 around the first virtual deflection gear shaper cutter 2; the second modified abrasive disk 4 is rotated around the second virtual modified pinion 3 to simulate the generating motion of the second virtual modified pinion 3 and the non-orthogonal offset modified bevel gear 5. The shifting disc-shaped grinding wheel rotates at a high speed to form cutting movement, and the center of the shifting disc-shaped grinding wheel moves back and forth along a direction parallel to the virtual shifting gear shaping cutter shaft to form feeding movement. Wherein, the modulus of the first virtual shift gear shaper cutter 2 is the same as that of the second virtual shift gear shaper cutter 3, and the end face pressure angle is the same. The second virtual shift pinion 3 is identical to the shift pinion in position vector, so if the first virtual shift pinion 2 is positively shifted, the second virtual shift pinion 3 is negatively shifted from the shift pinion, and the non-orthogonal offset helical gear is positively shifted, and the generated negative shift pinion and the positive shift non-orthogonal offset helical gear form a pair of non-orthogonal offset helical gear face gear pairs 5.
The movement process of the second virtual shift gear shaper cutter 3 and the shift small wheel is developed
As shown in FIG. 1, a coordinate system S 1 、S g1 、S i Fixedly connected with the first virtual shift gear shaper cutter 2, the first shift disc-shaped grinding wheel 1, the second virtual shift gear shaper cutter 3 and the shift small wheel respectively (i=2, 3 respectively represents the coordinate system or tooth surface parameters of the second virtual shift gear shaper cutter 3 and the shift small wheel), S p 、S t Is an auxiliary coordinate system. Three motion relationships exist during grinding: the first indexed disc wheel 1 at angular velocity omega 1 Z around the first virtual indexing gear shaper cutter 2 1 The axial swing simulates the rotation of the first virtual displacement gear shaper cutter 2 and the angular velocity omega between the second virtual displacement gear shaper cutter 3 and the displacement small wheel i Around axis Z i Is rotated to form an generating motion, and omega i ＝ω 1 m i1 ，m i1 The gear ratio of the first virtual shift gear shaper cutter 2, the second virtual shift gear shaper cutter 3 and the shift pinion; the projections of the center distance between the first virtual shift gear shaper cutter 2 and the first shift disc-shaped grinding wheel 1 in the X-axis and Z-axis directions are E respectively g1 And L g1 Z of the first virtual shift gear shaper cutter 2 1 The shaft and the end surface of the first deflection disc-shaped grinding wheel 1 form a helix angle beta, the first deflectionThe disc-shaped grinding wheel 1 is positioned to be parallel to the Z of the first virtual displacement gear shaper cutter 2 1 An axial feed motion; variable position abrasive disc at angular velocity omega g1 High-speed rotation constitutes cutting motion.
Tooth surface equation of the first virtual shift pinion 2:
the section parameters of the first virtual shift gear shaper cutter 2 are shown in fig. 2, R p1 、R b1 Respectively representing the reference circle radius and the base circle radius, θ, of the first virtual shift gear shaper cutter 2 1 Represents the rotation angle parameter of the gear, theta b1 Represents the central angle lambda corresponding to 1/2 of the tooth groove width on the base circle 1 Representing the rotation angle, p, of the involute of the end surface of the first virtual shift gear shaper cutter 2 around the axis 1 Representing the spiral motion parameters. At S 1 In the coordinate system, the tooth surface of the first virtual shift pinion 2 is represented by the following formula:
D＝θ b1 +θ 1 ±λ 1 ，/>
θ b1 ＝π/(2N 1 )-(tanα t -α t )-(xm n ·tanα t )/R p1 ，N 1 representing the number of teeth, alpha, of the first virtual indexing gear shaper cutter 2 t Represents the end face pressure angle of the virtual shift gear shaper cutter, xm n Indicating the amount of displacement.
Tooth surface equation of the first indexing dish wheel 1:
the profile line of the modified abrasive disk is the end surface section line of the virtual modified gear shaper cutter, so the tooth surface of the modified abrasive disk is an involute surface of revolution, L is the same time g1 =0. As shown in fig. 1 and 3, θ g1 Is the angle parameter of the curved surface of the grinding wheel 1, M t1 、M pt 、M g1p Coordinate system S 1 To a coordinate system S t Coordinate system S t To a coordinate system S p Coordinate system S p To a coordinate system S g1 Coordinate transformation matrix of (2), at S g1 In the first position-changing disc-shaped grinding wheelThe bit vector and unit normal vector of 1 are represented by the following formulas:
R g1 (θ 1 ,λ 1 ,θ g1 )＝M g1p (θ g1 )M pt M t1 R 1 (θ 1 ,λ 1 )，n g1 (θ 1 ,λ 1 ,θ g1 )＝L g1p (θ g1 )L pt L t1 n 1 (θ 1 ,λ 1 )
tooth surface equation of the second virtual shift pinion 3 and shift pinion:
the second virtual shift gear shaper cutter 3 and shift small wheel generating coordinate system is shown in fig. 4, S m 、S n L is an auxiliary coordinate system 0 Representing the center distance phi of the first virtual shift gear shaper cutter 2 and the second virtual shift gear shaper cutter 3 i ＝φ g1 m i1 In S i In the coordinate system, the tooth surface equations of the second virtual shift pinion 3 and the shift pinion are expressed by the following formulas:
R i (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝M in M nm M m1 (φ g1 )M 1t M tg1 (L g1 )R g1 (θ 1 ,λ 1 ,θ g1 )
f 1 (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝n g1 ν 1 ＝0
f 2 (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝n g1 ν 2 ＝0
n i (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝L in L nm L m1 (φ g1 )L 1t L tg1 (L g1 )n g1 (θ 1 ,λ 1 ,θ g1 )
above simultaneous cancellation parameter θ g1 Can use R i (θ 1 ,λ 1 ,φ g1 ,L g1 ) The tooth surfaces of the second virtual shift pinion 3 and the shift pinion are shown.
ν 1 ＝[0 0 1]，
ν 1 、ν 2 The center speed of the grinding wheel 1, the second virtual shift gear shaper cutter 3 and the relative speeds of the shift small wheel and the grinding wheel 1 are respectively.
Tooth surface equation of the second indexing dish wheel 4:
the profile line of the modified abrasive disk is the end surface section line of the virtual modified gear shaper cutter, so the tooth surface of the modified abrasive disk is an involute surface of revolution, L is the same time g2 =0. As shown in fig. 3 and 5, the coordinate system S 2 And a coordinate system S g2 S is fixedly connected with the second virtual shift gear shaper cutter 3 and the second shift disc-shaped grinding wheel 4 respectively p 、S t As an auxiliary coordinate system, the projections of the center distances between the second virtual shift gear shaper cutter 3 and the second shift disc-shaped grinding wheel 4 in the X-axis and Z-axis directions are E respectively g2 And L g2 Z of the second virtual shift gear shaper cutter 3 2 The shaft is formed with the end face of the second deflection disc-shaped grinding wheel 4Helix angle beta, theta g2 Is the angle parameter of the curved surface of the grinding wheel 2, M t2 、M pt 、M g2p Coordinate system S 2 To a coordinate system S t Coordinate system S t To a coordinate system S p Coordinate system S p To a coordinate system S g2 Coordinate transformation matrix of (2), at S g2 The position vector and unit normal vector of the second indexed dish wheel 4 are represented by:
R g2 (θ 2 ,θ g2 ,λ 2 ,φ g2 )＝M g2p (θ g2 )M pt M t2 R 2 (θ 2 ,λ 2 ,φ g2 )n g1 (θ 2 ,θ g2 ,λ 2 ,φ g2 )＝L g1p (θ g2 )L pt L t1 n 1 (θ 2 ,λ 2 ,φ g2 )
θ 2 ＝-θ 1 m 21 ，m 21 is the gear ratio of the first virtual shift gear shaper cutter 2 and the second virtual shift gear shaper cutter 3
λ 2 ＝-λ 1 ，φ g2 ＝m 21 φ g1
θ b2 ＝π/(2N 2 )-(tanα t -α t )-(xm n ·tanα t )/R p2 ，N 2 Representing the number of teeth, R, of the second virtual shift gear shaper cutter 3 p2 The pitch circle radius of the second virtual shift pinion 3 is shown.
Generating a motion process of the non-orthogonal offset shifting bevel gear:
as shown in fig. 6, the axis of the second virtual shift pinion 3 is not parallel to and does not intersect with the axis of the non-orthogonal offset shift bevel gear, and has an offset angle gamma m And an offset distance E, which is set to be equal to,L 1 the center distance between the second virtual shift slotting cutter 3 and the non-orthogonal offset helical tooth surface gear is shown. Three motion relationships exist during grinding: the second deflection abrasive disc 4 at an angular velocity omega 2 Z around the second virtual indexing gear shaper cutter 3 2 The axial rotation and swing simulate the rotation of the second virtual displacement gear shaper cutter 3, and the non-orthogonal offset displacement helical gear is driven at the angular speed omega 4 Around axis Z 4 Is rotated to form an generating motion, and omega 4 ＝ω 2 m 42 ，m 42 The gear ratio of the gear with the inclined tooth surface is offset and shifted in a non-orthogonal way for the second virtual shift gear shaper cutter 3; a second indexed dish wheel 4 to be parallel to the Z of the second virtual indexed gear shaper cutter 3 2 An axial feed motion; variable position abrasive disc at angular velocity omega g2 High-speed rotation constitutes cutting motion.
Shift tooth surface equation of non-orthogonal offset helical tooth surface gear:
coordinate system S 2 And a coordinate system S 4 S is fixedly connected with the second virtual shift gear shaper cutter 3 and a non-orthogonal offset bevel gear surface gear respectively m 、S t 、S k 、S r 、S n In order to assist in the coordinate system, is the gear ratio of the second virtual shift slotting cutter 3 and the non-orthogonal offset helical tooth surface gear. At S 4 In the coordinate system, the tooth surface equation of the non-orthogonal offset helical tooth surface gear is expressed by the following formula:
R 4 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝M 4n M nr M rk M km M m2 M 2t M tg2 (L g2 )R g2 (θ 2 ,θ g2 ,λ 2 ,φ g2 )
n 4 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝L 4n L nr L rk L km L m2 L 2t L tg2 (L g2 )n g2 (θ 2 ,θ g2 ,λ 2 ,φ g2 )
f 3 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝n g2 ν 3 ＝0
f 4 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝n g2 ν 4 ＝0
above simultaneous cancellation parameter θ g2 Can use R 4 (θ 2 ,λ 2 ,φ 4 ,L g2 ) Representing the tooth flanks of a non-orthogonally offset helical gear.
ν 3 、ν 4 The center speed of the grinding wheel 2 and the relative speeds of the non-orthogonal offset helical gear and the grinding wheel 2 are respectively.
Firstly, according to the motion relation of two virtual shift gear shaping cutters and the tooth surface parameters of a first virtual shift gear shaping cutter 2, deriving the tooth surface equation of a first shift gear shaping wheel 1, deriving the tooth surface equation of a second virtual shift gear shaping cutter 3 and a shift pinion, deriving the tooth surface equation of a second shift gear shaping wheel 4 according to the tooth surface equation of the second virtual shift gear shaping cutter 3, and finally deriving the shift tooth shape of a non-orthogonal shift gear with an oblique tooth surface according to the motion relation of the second virtual shift gear shaping cutter 3 and the tooth surface equation of the second shift gear shaping wheel 4. The shift pinion and the non-orthogonal offset shift helical gear thus generated may constitute a non-orthogonal offset shift helical gear pair. The gear pair with the non-orthogonal offset deflection bevel gear surface is processed by adopting the deflection disc-shaped grinding wheel, so that the structure is simple, and the gear surface with higher precision can be obtained.
The invention provides a non-orthogonal offset bevel gear pair with a disc-shaped grinding wheel, wherein if a positive-displacement bevel gear and a negative-displacement bevel gear are processed by the disc-shaped grinding wheel respectively, the obtained negative-displacement bevel gear and positive-displacement bevel gear can form the non-orthogonal offset bevel gear pair. The non-orthogonal offset bevel gear pair is processed by adopting the offset disc-shaped grinding wheel, so that the gear pair has a simple structure, is convenient to design, manufacture and repair, is not limited by design parameters of a face gear, and can obtain a tooth face with higher precision. The invention is mainly used for generating the shift tooth profile of the non-orthogonal offset helical gear pair, and provides a technical method for processing the non-orthogonal offset shift helical gear pair.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (9)
1. The method for generating the shift tooth form of the non-orthogonal offset helical gear pair by the disc-shaped grinding wheel is characterized by comprising the following steps of: the method comprises the steps of machining a deflection small wheel by using a first deflection disc-shaped grinding wheel, machining a non-orthogonal deflection bevel gear by using a second deflection disc-shaped grinding wheel, simulating the generating motion of the first virtual deflection gear shaper and the deflection small wheel by the rotation and the swinging of the first deflection disc-shaped grinding wheel around the first virtual deflection gear shaper, simulating the generating motion of the second virtual deflection gear shaper and the non-orthogonal deflection bevel gear by the rotation and the swinging of the second deflection disc-shaped grinding wheel around the second virtual deflection gear shaper, enabling the first deflection disc-shaped grinding wheel and the second deflection disc-shaped grinding wheel to rotate to form cutting motions, enabling the center of the first deflection disc-shaped grinding wheel to reciprocate along an axis parallel to the first virtual deflection gear shaper to form feeding motions, and enabling the center of the second deflection disc-shaped grinding wheel to reciprocate along an axis parallel to the second virtual deflection gear shaper to form feeding motions.
2. The method for generating the shift tooth form of the non-orthogonal offset helical gear pair by using the disc-shaped grinding wheel according to claim 1, wherein the method comprises the following steps of: the first virtual shift gear shaper cutter and the second virtual shift gear shaper cutter have the same modulus, the same end face pressure angle and the same position vector of the second virtual shift gear shaper cutter and the shift small wheel, if the first virtual shift gear shaper cutter is positively shifted, the second virtual shift gear shaper cutter and the shift small wheel are negatively shifted, the non-orthogonal offset bevel gear is positively shifted, and the generated negative shift small wheel and the positive shift non-orthogonal offset bevel gear form a pair of non-orthogonal offset bevel gear pairs.
3. The method for generating the shift tooth form of the non-orthogonal offset helical gear pair by using the disc-shaped grinding wheel according to claim 1, wherein the method comprises the following steps of: the specific process of the generating motion of the first virtual shift gear shaper cutter, the second virtual shift gear shaper cutter and the shift small wheel is as follows: coordinate system S 1 、S g1 、S i Fixedly connected with the first virtual shift gear shaper, the first shift disc-shaped grinding wheel, the second virtual shift gear shaper and the shift small wheel respectively, wherein i=2, 3 respectively represent coordinate systems or tooth surface parameters of the second virtual shift gear shaper and the shift small wheel, S p 、S t To assist the coordinate system, three motion relationships exist during grinding: the first indexing disc wheel has an angular velocity omega 1 Z around the first virtual indexing gear shaper cutter 1 The rotary pendulum of the shaft, the rotation of the first simulated virtual shift gear shaper cutter and the second virtual shift gear shaper cutter and the shift small wheel are driven at the angular velocity omega i Around axis Z i Is rotated to form an generating motion, and omega i ＝ω 1 m i1 ，m i1 For the gear ratio of the first virtual shift gear shaper, the second virtual shift gear shaper and the shift pinion, the projections of the center distances of the first virtual shift gear shaper and the first shift disc grinding wheel in the X-axis and Z-axis directions are E respectively g1 And L g1 Z of first virtual shift gear shaper cutter 1 The shaft and the end face of the first deflection abrasive disk form a helix angle beta, and the first deflection abrasive disk is parallel to the Z of the first virtual deflection gear shaper cutter 1 Axial feed movement, indexing the disc wheel at angular velocity omega g1 High-speed rotation constitutes cutting motion.
4. A method of generating a shifted profile of a non-orthogonally offset helical face gear pair with a grinding wheel according to claim 3, wherein: the tooth surface equation of the first virtual shift gear shaper cutter is:
in the section parameters of the first virtual shift gear shaper cutter, R p1 、R b1 Respectively representing the reference circle radius and the base circle radius theta of the first virtual shift gear shaper cutter 1 Represents the rotation angle parameter of the gear, theta b1 Represents the central angle lambda corresponding to 1/2 of the tooth groove width on the base circle 1 Representing the rotation angle, p, of the involute of the end surface of the first virtual shift gear shaper cutter around the axis 1 Representing the spiral motion parameters, at S 1 In the coordinate system, the tooth surface of the first virtual shift pinion is represented by the following formula:
D＝θ b1 +θ 1 ±λ 1 ，/>
θ b1 ＝π/(2N 1 )-(tanα t -α t )-(xm n ·tanα t )/R p1 ，N 1 representing the number of teeth, alpha, of the first virtual indexing gear shaper cutter t Represents the end face pressure angle of the virtual shift gear shaper cutter, xm n Indicating the amount of displacement.
5. The method for generating the shift tooth form of the non-orthogonal offset helical gear pair by using the disc-shaped grinding wheel according to claim 4, wherein the method comprises the following steps of: the tooth surface equation of the first deflection abrasive disc is:
the generating line of the first deflection grinding wheel is the end surface section line of the first virtual deflection gear shaper cutter, so that the tooth surface of the first deflection grinding wheel is an involute rotating curved surface, and L g1 ＝0，θ g1 Is the angle parameter of the curved surface of the grinding wheel 1, M t1 、M pt 、M g1p Coordinate system S 1 To a coordinate system S t Coordinate system S t To a coordinate system S p Coordinate system S p To a coordinate system S g1 Coordinate transformation matrix of (2), at S g1 The position vector and unit normal vector of the first indexed disc wheel 1 are represented by the following formulas:
R g1 (θ 1 ,λ 1 ,θ g1 )＝M g1p (θ g1 )M pt M t1 R 1 (θ 1 ,λ 1 )，n g1 (θ 1 ,λ 1 ,θ g1 )＝L g1p (θ g1 )L pt L t1 n 1 (θ 1 ,λ 1 )
6. the method for generating the shift tooth form of the non-orthogonal offset helical gear pair by using the disc-shaped grinding wheel according to claim 5, wherein the method comprises the following steps of: the tooth surface equation of the second virtual shift gear shaper cutter and the shift small wheel is as follows:
in the generating coordinate system of the second virtual shift gear shaper cutter and the shift small wheel, S m 、S n L is an auxiliary coordinate system 0 Representing the center distance phi of the first virtual shift gear shaper cutter 2 and the second virtual shift gear shaper cutter 3 i ＝φ g1 m i1 In S i In the coordinate system, the tooth surface equations of the second virtual shift pinion and the shift pinion are represented by the following formulas:
R i (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝M in M nm M m1 (φ g1 )M 1t M tg1 (L g1 )R g1 (θ 1 ,λ 1 ,θ g1 )
f 1 (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝n g1 ν 1 ＝0
f 2 (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝n g1 ν 2 ＝0
n i (θ 1 ,λ 1 ,θ g1 ,φ g1 ,L g1 )＝L in L nm L m1 (φ g1 )L 1t L tg1 (L g1 )n g1 (θ 1 ,λ 1 ,θ g1 )
above simultaneous cancellation parameter θ g1 Can use R i (θ 1 ,λ 1 ,φ g1 ,L g1 ) Representing tooth surfaces of the virtual second virtual shift pinion and the shift pinion;
ν 1 ＝[0 0 1]，
ν 1 、ν 2 the center speed of the first deflection grinding wheel, the second virtual deflection gear shaper cutter, the deflection small wheel and the relative speed of the first deflection grinding wheel are respectively.
7. The method for generating the shift tooth form of the non-orthogonal offset helical gear pair by using the disc-shaped grinding wheel according to claim 6, wherein the method comprises the following steps of: the tooth surface equation of the second virtual deflection abrasive disc is:
the generating line of the second virtual deflection grinding wheel is the end surface section line of the virtual deflection gear shaper cutter, so that the tooth surface of the second virtual deflection grinding wheel is an involute rotating curved surface, and L g2 =0, coordinate system S 2 And a coordinate system S g2 Fixedly connected with a second virtual shift gear shaping cutter and a second shift disc-shaped grinding wheel respectively, S p 、S t The projections of the center distance between the second virtual shift gear shaper cutter and the second shift disc grinding wheel in the X-axis and Z-axis directions are E respectively g2 And L g2 Z of the second virtual shift gear shaper cutter 2 The shaft and the end face of the second deflection disc-shaped grinding wheel form a helix angle beta, theta g2 Is the angle parameter of the curved surface of the second deflection disc-shaped grinding wheel, M t2 、M pt 、M g2p Coordinate system S 2 To a coordinate system S t Coordinate system S t To a coordinate system S p Coordinate system S p To a coordinate system S g2 Coordinate transformation matrix of (2), at S g2 The position vector and unit normal vector of the second indexed dish wheel 4 are represented by:
R g2 (θ 2 ,θ g2 ,λ 2 ,φ g2 )＝M g2p (θ g2 )M pt M t2 R 2 (θ 2 ,λ 2 ,φ g2 )
n g1 (θ 2 ,θ g2 ,λ 2 ,φ g2 )＝L g1p (θ g2 )L pt L t1 n 1 (θ 2 ,λ 2 ,φ g2 )
θ 2 ＝-θ 1 m 21 ，m 21 is the gear ratio of the first virtual shift gear shaper cutter to the second virtual shift gear shaper cutter
λ 2 ＝-λ 1 ，φ g2 ＝m 21 φ g1 ；
θ b2 ＝π/(2N 2 )-(tanα t -α t )-(xm n ·tanα t )/R p2 ，N 2 Representing the number of teeth of the second virtual shift gear shaper cutter, R p2 Representing the pitch circle radius of the second virtual shift gear shaper cutter;
8. the method for generating the shift tooth form of the non-orthogonal offset helical gear pair by using the grinding wheel according to claim 7, wherein the method comprises the following steps of: the motion process of the generating non-orthogonal offset deflection oblique tooth surface gear is as follows:
the second virtual shift gear shaping cutter shaft line is not parallel to and is not intersected with the gear shaft line of the non-orthogonal offset shift bevel gear surface and has an offset angle gamma m And an offset E, L 1 Representing the center distance between the second virtual shift gear shaper cutter and the non-orthogonal offset helical gear, wherein three motion relations exist during grinding: the second deflection disc wheel is at angular velocity omega 2 Z around the second virtual indexing gear shaper cutter 2 The axial rotation and swing simulate the rotation of a second virtual displacement gear shaper cutter and the angular speed omega of a non-orthogonal offset displacement helical gear 4 Around axis Z 4 Is rotated to form an generating motion, and omega 4 ＝ω 2 m 42 ，m 42 For the gear ratio of the second virtual shift gear shaper and the non-orthogonal offset shift bevel gear, the second shift disk is parallel to the Z of the second virtual shift gear shaper 2 Axial feeding movement, angular speed of the indexing disc-shaped grinding wheelDegree omega g2 High-speed rotation constitutes cutting motion.
9. The method for generating the shift tooth form of the non-orthogonal offset helical gear pair by using the disc-shaped grinding wheel according to claim 8, wherein the method comprises the following steps of: the shift tooth surface equation of the non-orthogonal offset helical tooth surface gear is as follows:
coordinate system S 2 And a coordinate system S 4 Respectively fixedly connected with a second virtual shift gear shaper cutter and a non-orthogonal offset helical gear, S m 、S t 、S k 、S r 、S n To assist the coordinate system, phi 4 ＝φ g2 m 4g2 ，m 4g2 For the gear ratio of the second virtual shift slotting cutter and the non-orthogonal offset helical face gear, at S 4 In the coordinate system, the tooth surface equation of the non-orthogonal offset helical tooth surface gear is expressed by the following formula:
R 4 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝M 4n M nr M rk M km M m2 M 2t M tg2 (L g2 )R g2 (θ 2 ,θ g2 ,λ 2 ,φ g2 )
n 4 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝L 4n L nr L rk L km L m2 L 2t L tg2 (L g2 )n g2 (θ 2 ,θ g2 ,λ 2 ,φ g2 )
f 3 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝n g2 ν 3 ＝0
f 4 (θ 2 ,θ g2 ,λ 2 ,φ 4 ,L g2 )＝n g2 ν 4 ＝0
above simultaneous cancellation parameter θ g2 By R 4 (θ 2 ,λ 2 ,φ 4 ,L g2 ) Representing tooth surfaces of a non-orthogonally offset helical tooth face gear;
ν 3 、ν 4 respectively the secondThe center speed of the variable-position disc-shaped grinding wheel, the relative speed of the non-orthogonal offset helical gear and the second variable-position disc-shaped grinding wheel;
ν 3 ＝[0 0 1]，
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