Method for generating modified tooth profile of disc-shaped grinding wheel for generating non-orthogonal offset skew tooth surface gear pair

Abstract

The application provides a method for generating a modified tooth profile of a non-orthogonal offset skew tooth surface gear pair by using a disc-shaped grinding wheel, and belongs to the technical field of gear machining. First, the tooth surface equation of the modified disc-shaped grinding wheel is derived according to the motion relationship of two virtual modified gear shaping cutters and the tooth surface parameters of the virtual modified gear shaping cutters. Then, the tooth surface equations of the virtual modified gear shaping cutters and the modified pinion are derived. Next, the tooth surface equation of the modified disc-shaped grinding wheel is derived according to the tooth surface equation of the virtual modified gear shaping cutters. Finally, the modified tooth profile of the non-orthogonal offset skew tooth surface gear is derived according to the motion relationship of the virtual modified gear shaping cutters and the non-orthogonal offset skew tooth surface gear and the tooth surface equation of the modified disc-shaped grinding wheel. The generated modified pinion and the non-orthogonal offset modified skew tooth surface gear can form a non-orthogonal offset modified skew tooth surface gear pair. The non-orthogonal offset modified skew tooth surface gear pair is machined by using the modified disc-shaped grinding wheel, so that the non-orthogonal offset modified skew tooth surface gear pair has a simple structure and a high-precision tooth surface.

Description

Technical Field

[0001] This invention relates to the field of gear machining technology, and in particular to a method for generating non-orthogonal offset helical gear pairs using a disc-shaped grinding wheel. Background Technology

[0002] Helical gear pairs have important applications in the aerospace field, especially in helicopter transmission systems. Current research on helical gear pairs mostly focuses on orthogonal or orthogonally offset helical gear pairs, neglecting the research on the most complex and universally applicable non-orthogonal offset modified helical gear pairs.

[0003] Common machining methods for face gears include gear shaping, gear hobbing, and gear grinding. The principle of face gear machining with a gear shaper is highly consistent with the meshing principle of face gear transmissions, and it forms the theoretical foundation for subsequent research on face gear tooth surfaces, profile modification, hobbing, and grinding. Based on the principle of face gear shaping, Litvin et al. laid the foundation for the meshing theory of point-contact face gear transmissions and elaborated in detail the conditions for root undercut and tip sharpening of face gears. NorthStar Aerospace in Canada has also successfully developed a CNC face gear shaper, realizing the shaping of face gears. Chinese scholars have conducted research on machining interference, tooth surface design, and meshing simulation, and have mastered the gear shaping technology for orthogonal face gears.

[0004] Gear grinding is a key technology for achieving high surface accuracy in face gears. Litvin et al. proposed a method for grinding face gears using worm gears, but the grinding wheel dressing equipment and cutting tools are relatively complex. Dr. Stadtfeld of Gleason Corporation in the United States proposed methods for grinding face gears using disc-shaped grinding wheels and straight-edged cutting tools. Due to the advantages of disc-shaped grinding wheels, such as simple structure, convenient design, manufacturing, and dressing, and easy implementation of machine tool movements, domestic scholars have conducted in-depth research on them.

[0005] The precision of gear pairs generated by gear shapers with non-orthogonal offset modified helical tooth surfaces is not high. In addition, worm grinding wheels are complex to manufacture, difficult to dress, and their tooth surfaces are affected by singularities, making them unsuitable for face gear pairs with certain parameters. Summary of the Invention

[0006] The purpose of this invention is to provide a method for generating non-orthogonal offset helical gear pairs using a disc-shaped grinding wheel, solving the technical problems of low precision in generating non-orthogonal offset helical gear pairs using gear shapers, as well as the complexity of worm grinding wheel manufacturing, difficulty in dressing, and the influence of singularities on the tooth surface, making it unsuitable for face gear pairs with certain parameters. Using a modified disc-shaped grinding wheel to process non-orthogonal offset helical gear pairs not only offers a simple structure, convenient design, manufacturing, and dressing, and is not limited by the face gear design parameters, but also yields high-precision tooth surfaces.

[0007] This invention proposes a method for generating modified tooth profiles in non-orthogonal offset helical gear pairs using disc-shaped grinding wheels. If modified pinions and non-orthogonal offset helical gears are machined using positive and negative modified disc-shaped grinding wheels respectively, the resulting negative modified pinion and positive modified non-orthogonal offset helical gear can constitute a non-orthogonal offset modified helical gear pair. Using modified disc-shaped grinding wheels to machine non-orthogonal offset modified helical gear pairs not only offers a simple structure and convenient design, manufacturing, and dressing, but is also not limited by the design parameters of the face gear, and can achieve high-precision tooth surfaces. This invention is mainly used for generating modified tooth profiles in non-orthogonal offset helical gear pairs, providing a technical method for machining non-orthogonal offset modified helical gear pairs.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A method for generating non-orthogonal offset helical gear pairs using disc-shaped grinding wheels involves machining a modified pinion with a first modified disc-shaped grinding wheel and machining the non-orthogonal offset helical gear with a second modified disc-shaped grinding wheel. The generating motion of the first virtual modified gear shaper and the modified pinion is simulated by the oscillation of the first modified disc-shaped grinding wheel around a first virtual modified gear shaper, and the generating motion of the second virtual modified gear shaper and the non-orthogonal offset helical gear with a second virtual modified gear shaper is simulated by the oscillation of the second modified disc-shaped grinding wheel around a second virtual modified gear shaper. Both the first and second modified disc-shaped grinding wheels rotate to form the cutting motion. The center of the first modified disc-shaped grinding wheel reciprocates along an axis parallel to the first virtual modified gear shaper to form the feed motion, and the center of the second modified disc-shaped grinding wheel reciprocates along an axis parallel to the second virtual modified gear shaper to form the feed motion.

[0010] Furthermore, the first virtual modified gear shaper cutter and the second virtual modified gear shaper cutter have the same module and the same end face pressure angle. The second virtual modified gear shaper cutter and the modified pinion have the same position vector. If the first virtual modified gear shaper cutter is positively modified, then the second virtual modified gear shaper cutter and the modified pinion are negatively modified. The non-orthogonal offset helical gear is positively modified, and the resulting negatively modified pinion and the positively modified non-orthogonal offset helical gear form a pair of non-orthogonal offset modified helical gear pairs.

[0011] Furthermore, the specific process of the generating motion of the first virtual modified gear cutter and the second virtual modified gear cutter with the modified pinion is as follows: coordinate systems S1, S g1 S i These are respectively fixedly connected to the first virtual modified gear hobbing cutter, the first modified disc grinding wheel, the second virtual modified gear hobbing cutter, and the modified pinion. i = 2, 3 represent the coordinate system or tooth surface parameters of the second virtual modified gear hobbing cutter and the modified pinion, respectively. S p S tTo assist the coordinate system, three motion relationships exist during grinding: the first modified disc grinding wheel oscillates around the Z1 axis of the first virtual modified gear shaper with an angular velocity ω1; the rotation of the first simulated virtual modified gear shaper; and the rotation of the second virtual modified gear shaper and the modified small wheel with an angular velocity ω1. i Around axis Z i The rotation constitutes the unfolding motion, and ω i =ω1m i1 m i1 The gear ratios of the first virtual modified gear hobbing cutter, the second virtual modified gear hobbing cutter, and the modified pinion are given. The projections of the center distance between the first virtual modified gear hobbing cutter and the first modified disc grinding wheel in the X and Z axes are respectively E. g1 and L g1 The Z1 axis of the first virtual modified gear hobbing cutter forms a helix angle β with the end face of the first modified disc grinding wheel. The first modified disc grinding wheel feeds in a direction parallel to the Z1 axis of the first virtual modified gear hobbing cutter, and the modified disc grinding wheel moves at an angular velocity ω. g1 High-speed rotation constitutes the cutting motion.

[0012] Furthermore, the tooth surface equation of the first virtual modified gear shaper is:

[0013] In the cross-sectional parameters of the first virtual displacement gear cutter, R p1 R b1 Let θ1 and θ2 represent the pitch circle radius and base circle radius of the first virtual modified gear shaper, respectively, and let θ1 represent the gear rotation angle parameter. b1 Let λ represent the central angle corresponding to half the tooth groove width on the base circle, λ1 represent the rotation angle of the involute end face of the first virtual displacement gear shaper around the axis, and p1 represent the helical motion parameters. In the S1 coordinate system, the tooth surface of the first virtual displacement gear shaper is represented by the following formula:

[0014] D = θ b1 +θ1±λ1,

[0015] θ b1 =π / (2N1)-(tanα) t -α t )-(xm n ·tanα t ) / R p1 N1 represents the number of teeth of the first virtual displacement gear cutter, α t The xm represents the end face pressure angle of the virtual displacement gear hobbing cutter. n Indicates displacement.

[0016] Furthermore, the tooth surface equation of the first displaced disc grinding wheel is:

[0017] The feed line of the first modified disc grinding wheel is the end face section of the first virtual modified gear shaper. Therefore, the tooth surface of the first modified disc grinding wheel is an involute surface of revolution. At this time, L g1 =0, θ g1 M represents the angular parameters of the surface of grinding wheel 1. t1 M pt M g1p From coordinate system S1 to coordinate system S t Coordinate system S t To coordinate system S p Coordinate system S p To coordinate system S g1 The coordinate transformation matrix in S g1 In the first displacement disc grinding wheel 1, the position vector and unit normal vector are expressed by the following formula: R g1 (θ1,λ1,θ g1 ) = M g1p (θ g1 M pt M t1 R1(θ1,λ1), n g1 (θ1,λ1,θ g1 ) = L g1p (θ g1 )L pt L t1 n1(θ1,λ1)

[0018] Furthermore, the tooth surface equations of the second virtual modified gear shaper and the modified pinion are as follows:

[0019] In the coordinate system formed by the second virtual modified gear shaper and the modified small gear, S m S n As an auxiliary coordinate system, L0 represents the center distance between the first virtual modified gear hobbing cutter 2 and the second virtual modified gear hobbing cutter 3, and φ i =φ g1 m i1 In S i In the coordinate system, the tooth surface equations of the second virtual modified gear shaper and the modified pinion are expressed by the following formula:

[0020] R i (θ1,λ1,θ g1 ,φ g1 ,L g1 ) = M in M nm M m1 (φ g1 M 1t M tg1 (L g1 )R g1 (θ1,λ1,θg1 )

[0021] f1(θ1,λ1,θ g1 ,φ g1 ,L g1 ) = n g1 ν 1 =0

[0022] f2(θ1,λ1,θ g1 ,φ g1 ,L g1 ) = n g1 ν 2 =0

[0023] n i (θ1,λ1,θ g1 ,φ g1 ,L g1 ) = L in L nm L m1 (φ g1 )L 1t L tg1 (L g1 )n g1 (θ1,λ1,θ g1 )

[0024] Eliminating the parameter θ in the above equations g1 R can be used i (θ1,λ1,φ g1 ,L g1 () represents the tooth surface of the virtual second virtual modified gear cutter and the modified pinion;

[0025] ν 1 =[0 0 1],

[0026] ν 1 ν 2 These are the center speed of the first modified disc grinding wheel, the relative speed of the second virtual modified gear cutter and the modified small wheel with the first modified disc grinding wheel, respectively.

[0027] Furthermore, the tooth surface equation of the second virtual displacement disc grinding wheel is:

[0028] The feed curve of the second virtual modified disc grinding wheel is the end face section of the virtual modified gear shaper. Therefore, the tooth surface of the second virtual modified disc grinding wheel is an involute surface of revolution. At this time, L g2 =0, coordinate system S2 and coordinate system S g2S is respectively fixedly connected to the second virtual displacement gear hobbing cutter and the second displacement disc grinding wheel. p S t As an auxiliary coordinate system, the projections of the center distance between the second virtual displacement gear hobbing cutter and the second displacement disc grinding wheel in the X and Z axes are respectively E g2 and L g2 The Z2 axis of the second virtual displacement gear hobbing cutter forms a helix angle β with the end face of the second displacement disc grinding wheel. g2 M is the angle parameter of the second displacement disc-shaped grinding wheel surface. t2 M pt M g2p From coordinate system S2 to coordinate system S t Coordinate system S t To coordinate system S p Coordinate system S p To coordinate system S g2 The coordinate transformation matrix in S g2 In the process, the position vector and unit normal vector of the second displacement disc grinding wheel 4 are expressed by the following formula:

[0029] R g2 (θ2,θ g2 ,λ2,φ g2 ) = M g2p (θ g2 M pt M t2 R2(θ2,λ2,φ g2 )

[0030] n g1 (θ2,θ g2 ,λ2,φ g2 ) = L g1p (θ g2 )L pt L t1 n1(θ2,λ2,φ g2 )

[0031] θ2=-θ1m 21 m 21 It is the tooth ratio between the first virtual displacement gear cutter and the second virtual displacement gear cutter.

[0032] λ2=-λ1,φ g2 =m 21 φ g1 ;

[0033] θ b2 =π / (2N2)-(tanα) t -α t )-(xm n ·tanα t ) / R p2N2 represents the number of teeth of the second virtual displacement gear cutter, R p2 This indicates the pitch circle radius of the second virtual modified gear hobbing cutter;

[0034] Furthermore, the motion process of generating a non-orthogonal offset modified helical gear is as follows:

[0035] The axis of the second virtual modified gear shaper is neither parallel nor intersecting with the axis of the non-orthogonal offset modified helical gear, and has a phase misalignment angle γ. m Let E be an offset distance, and L1 represent the center distance between the second virtual modified gear shaper and the non-orthogonal offset helical gear. During grinding, there are three motion relationships: the second modified disc grinding wheel oscillates around the Z2 axis of the second virtual modified gear shaper with an angular velocity ω2, simulating the rotation of the second virtual modified gear shaper, and forms a generating motion with the rotation of the non-orthogonal offset helical gear around the Z4 axis with an angular velocity ω4, where ω4=ω2m. 42 m 42 The gear ratio between the second virtual modified gear shaper and the non-orthogonal offset modified helical gear is given. The second modified disc grinding wheel feeds in a direction parallel to the Z2 axis of the second virtual modified gear shaper, and the modified disc grinding wheel moves at an angular velocity ω. g2 High-speed rotation constitutes the cutting motion.

[0036] Furthermore, the equation for the modified tooth surface of a non-orthogonal offset helical gear is:

[0037] Coordinate systems S2 and S4 are respectively fixedly connected to the second virtual modified gear shaper and the non-orthogonal offset helical gear. m S t S k S r S n As an auxiliary coordinate system, Given the tooth ratio of the second virtual modified gear shaper and the non-orthogonal offset helical gear, the tooth surface equation of the non-orthogonal offset helical gear in the S4 coordinate system is expressed by the following equation:

[0038] R4(θ2,θ g2 ,λ2,φ4,L g2 ) = M 4n M nr M rk M km M m2 M 2t M tg2 (L g2 )R g2 (θ2,θ g2 ,λ2,φ g2 )

[0039] n4(θ2,θ g2 ,λ2,φ4,L g2 ) = L 4n L nr L rk L km L m2 L 2t L tg2 (L g2 )n g2 (θ2,θ g2 ,λ2,φ g2 )

[0040] f3(θ2,θ g2 ,λ2,φ4,L g2 ) = n g2 ν 3 =0

[0041] f4(θ2,θ g2 ,λ2,φ4,L g2 ) = n g2 ν 4 =0

[0042] Eliminating the parameter θ in the above equations g2 Using R4(θ2,λ2,φ4,L) 2g ) represents the tooth surface of a non-orthogonal offset helical gear;

[0043] ν 3 ν 4 These are the center speed of the second modified disc grinding wheel and the relative speed between the non-orthogonal offset helical gear and the second modified disc grinding wheel, respectively.

[0044] ν 3 =[0 0 1],

[0045]

[0046] The present invention, by adopting the above-described technical solution, has the following beneficial effects:

[0047] This invention first derives the tooth surface equation of the modified disc grinding wheel based on the kinematic relationship between two virtual modified gear shapers and their tooth surface parameters. Then, it derives the tooth surface equations of the virtual modified gear shaper and the modified pinion. Next, it derives the tooth surface equation of the modified disc grinding wheel based on the tooth surface equation of the virtual modified gear shaper. Finally, it derives the modified tooth profile of the non-orthogonal offset helical gear based on the kinematic relationship between the virtual modified gear shaper and the non-orthogonal offset helical gear, and the tooth surface equation of the modified disc grinding wheel. The modified pinion and the non-orthogonal offset helical gear generated in this way can constitute a non-orthogonal offset helical gear pair. Using a modified disc grinding wheel to machine a non-orthogonal offset helical gear pair not only results in a simple structure but also produces a high-precision tooth surface. Attached Figure Description

[0048] Figure 1 This is a diagram illustrating the motion process of the virtual modified gear cutter and the modified pinion in this invention.

[0049] Figure 2 This is a cross-sectional parameter diagram of the virtual displacement gear cutter of the present invention;

[0050] Figure 3 This is a coordinate system diagram of the two grinding wheels of the present invention;

[0051] Figure 4 This is a coordinate system diagram of the virtual displacement gear cutter and displacement pinion of the present invention;

[0052] Figure 5 This is a coordinate transformation diagram of the virtual displacement gear hobbing cutter to the displacement disc grinding wheel of the present invention;

[0053] Figure 6 This is a diagram illustrating the motion process of the virtual modified gear shaper and the non-orthogonal offset modified helical gear of the present invention.

[0054] In the attached diagram, 1-first modified disc grinding wheel, 2-first virtual modified gear shaper, 3-second virtual modified gear shaper, 4-second modified disc grinding wheel, 5-non-orthogonal offset modified helical gear. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. However, it should be noted that many details listed in the specification are merely to provide the reader with a thorough understanding of one or more aspects of the present invention, and these aspects of the invention can be implemented even without these specific details.

[0056] like Figure 1-2As shown, the method for generating a non-orthogonal offset helical gear pair using a disc-shaped grinding wheel involves machining the offset pinion with a first offset disc-shaped grinding wheel 1 and machining the non-orthogonal offset helical gear 5 with a second offset disc-shaped grinding wheel 4. The generating motion of the first virtual offset gear shaper 2 and the offset pinion is simulated by the oscillation of the first offset disc-shaped grinding wheel 1 around the first virtual offset gear shaper 2; the generating motion of the second virtual offset gear shaper 3 and the non-orthogonal offset helical gear 5 is simulated by the oscillation of the second offset disc-shaped grinding wheel 4 around the second virtual offset gear shaper 3. The high-speed rotation of the offset disc-shaped grinding wheel constitutes the cutting motion, and the reciprocating movement of the center of the offset disc-shaped grinding wheel along the axis parallel to the virtual offset gear shaper constitutes the feed motion. The first virtual offset gear shaper 2 and the second virtual offset gear shaper 3 have the same module and the same end-face pressure angle. The second virtual modified gear cutter 3 and the modified pinion have the same position vector. Therefore, if the first virtual modified gear cutter 2 is positively modified, the second virtual modified gear cutter 3 and the modified pinion are negatively modified. The non-orthogonal offset helical gear is positively modified, and the generated negatively modified pinion and the positively modified non-orthogonal offset helical gear form a pair of non-orthogonal offset modified helical gear 5.

[0057] The motion process of generating the second virtual displacement gear cutter 3 and the displacement pinion.

[0058] like Figure 1 As shown, coordinate systems S1 and S2 are... g1 S i Each of the following components is fixedly connected to the first virtual modified gear hobbing cutter 2, the first modified disc grinding wheel 1, the second virtual modified gear hobbing cutter 3, and the modified pinion (i = 2, 3 represent the coordinate system or tooth surface parameters of the second virtual modified gear hobbing cutter 3 and the modified pinion, respectively). p S t As an auxiliary coordinate system, three motion relationships exist during grinding: the first modified disc grinding wheel 1 oscillates around the Z1 axis of the first virtual modified gear shaper 2 with an angular velocity ω1, simulating the rotation of the first virtual modified gear shaper 2; and it moves with the second virtual modified gear shaper 3 and the modified small wheel with an angular velocity ω. i Around axis Z i The rotation constitutes the unfolding motion, and ω i =ω1m i1 m i1 The gear ratio of the first virtual modified gear hobbing cutter 2 to the second virtual modified gear hobbing cutter 3 and the modified pinion; the projections of the center distance between the first virtual modified gear hobbing cutter 2 and the first modified disc grinding wheel 1 in the X and Z axes are respectively E g1 and L g1 The Z1 axis of the first virtual modified gear hobbing cutter 2 forms a helix angle β with the end face of the first modified disc grinding wheel 1. The first modified disc grinding wheel 1 feeds in a direction parallel to the Z1 axis of the first virtual modified gear hobbing cutter 2; the modified disc grinding wheel moves at an angular velocity ω. g1 High-speed rotation constitutes the cutting motion.

[0059] The tooth surface equation of the first virtual modified gear shaper 2:

[0060] The cross-sectional parameters of the first virtual displacement gear cutter 2 are as follows: Figure 2 As shown, R p1 R b1 θ1 represents the pitch circle radius and base circle radius of the first virtual modified gear shaper 2, respectively, and θ1 represents the gear rotation angle parameter. b1 Let λ represent the central angle corresponding to half the tooth groove width on the base circle, λ1 represent the rotation angle of the involute on the end face of the first virtual displacement gear shaper 2 around the axis, and p1 represent the helical motion parameters. In the S1 coordinate system, the tooth surface of the first virtual displacement gear shaper 2 is represented by the following formula:

[0061] D = θ b1 +θ1±λ1,

[0062] θ b1 =π / (2N1)-(tanα) t -α t )-(xm n ·tanα t ) / R p1 N1 represents the number of teeth of the first virtual displacement gear cutter 2, α t The xm represents the end face pressure angle of the virtual displacement gear hobbing cutter. n Indicates displacement.

[0063] The tooth surface equation of the first modified disc grinding wheel 1:

[0064] The feed curve of the modified disc grinding wheel is the end face section of the virtual modified gear shaper. Therefore, the tooth surface of the modified disc grinding wheel is an involute surface of revolution. At this time, L g1 =0. For example... Figure 1 and Figure 3 As shown, θ g1 M represents the angular parameters of the surface of grinding wheel 1. t1 M pt M g1p From coordinate system S1 to coordinate system S t Coordinate system S t To coordinate system S p Coordinate system S p To coordinate system S g1 The coordinate transformation matrix in S g1 In the first displacement disc grinding wheel 1, the position vector and unit normal vector are expressed by the following formula:

[0065] R g1 (θ1,λ1,θ g1 ) = M g1p (θ g1 Mpt M t1 R1(θ1,λ1), n g1 (θ1,λ1,θ g1 ) = L g1p (θ g1 )L pt L t1 n1(θ1,λ1)

[0066] The tooth surface equations of the second virtual modified gear shaper 3 and the modified pinion:

[0067] The second virtual gear shaping cutter 3 and the small gear shaping wheel are converted into a coordinate system as follows: Figure 4 As shown, S m S n For the auxiliary coordinate system, L0 represents the center distance between the first virtual modified gear hobbing cutter 2 and the second virtual modified gear hobbing cutter 3, and φ i =φ g1 m i1 In S i In the coordinate system, the tooth surface equations of the second virtual modified gear shaper 3 and the modified pinion are expressed by the following formula:

[0068] R i (θ1,λ1,θ g1 ,φ g1 ,L g1 ) = M in M nm M m1 (φ g1 M 1t M tg1 (L g1 )R g1 (θ1,λ1,θ g1 )

[0069] f1(θ1,λ1,θ g1 ,φ g1 ,L g1 ) = n g1 ν 1 =0

[0070] f2(θ1,λ1,θ g1 ,φ g1 ,L g1 ) = n g1 ν 2 =0

[0071] n i (θ1,λ1,θ g1 ,φ g1 ,L g1 ) = Lin L nm L m1 (φ g1 )L 1t L tg1 (L g1 )n g1 (θ1,λ1,θ g1 )

[0072] Eliminating the parameter θ in the above equations g1 R can be used i (θ1,λ1,φ g1 ,L g1 ) represents the tooth surface of the second virtual modified gear cutter 3 and the modified pinion.

[0073] ν 1 =[0 0 1],

[0074] ν 1 ν 2 These are the center speed of grinding wheel 1, the relative speed of the second virtual shift cutter 3 and the shifted small wheel with grinding wheel 1, respectively.

[0075] The tooth surface equation of the second displacement disc grinding wheel 4:

[0076] The feed curve of the modified disc grinding wheel is the end face section of the virtual modified gear shaper. Therefore, the tooth surface of the modified disc grinding wheel is an involute surface of revolution. At this time, L g2 =0. For example... Figure 3 and Figure 5 As shown, coordinate system S2 and coordinate system S g2 It is respectively fixedly connected to the second virtual displacement gear hobbing cutter 3 and the second displacement disc grinding wheel 4, S p S t As an auxiliary coordinate system, the projections of the center distance between the second virtual displacement gear hobbing cutter 3 and the second displacement disc grinding wheel 4 in the X-axis and Z-axis directions are respectively E g2 and L g2 The Z2 axis of the second virtual displacement gear hobbing cutter 3 forms a helix angle β with the end face of the second displacement disc grinding wheel 4. g2 M represents the angular parameters of the two curved surfaces of the grinding wheel. t2 M pt M g2p From coordinate system S2 to coordinate system S t Coordinate system S t To coordinate system S p Coordinate system S p To coordinate system S g2 The coordinate transformation matrix in Sg2 In the process, the position vector and unit normal vector of the second displacement disc grinding wheel 4 are expressed by the following formula:

[0077] R g2 (θ2,θ g2 ,λ2,φ g2 ) = M g2p (θ g2 M pt M t2 R2(θ2,λ2,φ g2 )n g1 (θ2,θ g2 ,λ2,φ g2 ) = L g1p (θ g2 )L pt L t1 n1(θ2,λ2,φ g2 )

[0078] θ2=-θ1m 21 m 21 It is the tooth ratio between the first virtual displacement gear cutter 2 and the second virtual displacement gear cutter 3.

[0079] λ2=-λ1,φ g2 =m 21 φ g1

[0080] θ b2 =π / (2N2)-(tanα) t -α t )-(xm n ·tanα t ) / R p2 N2 represents the number of teeth of the second virtual displacement gear cutter 3, R p2 This indicates the pitch circle radius of the second virtual displacement gear cutter 3. ,

[0081] The motion process of generating a non-orthogonal offset modified helical gear:

[0082] like Figure 6 As shown, the axis of the second virtual modified gear cutter 3 is not parallel to and does not intersect with the axis of the non-orthogonal offset modified helical gear, and has a phase angle γ. mAnd an offset distance E, L1 represents the center distance between the second virtual modified gear shaper 3 and the non-orthogonal offset helical gear. During grinding, three motion relationships exist: the second modified disc grinding wheel 4 oscillates around the Z2 axis of the second virtual modified gear shaper 3 at an angular velocity ω2, simulating the rotation of the second virtual modified gear shaper 3, and forms a generating motion with the rotation of the non-orthogonal offset helical gear around the Z4 axis at an angular velocity ω4, where ω4 = ω2m. 42 m 42 The gear ratio between the second virtual modified gear shaper 3 and the non-orthogonal offset modified helical gear; the second modified disc grinding wheel 4 feeds in a direction parallel to the Z2 axis of the second virtual modified gear shaper 3; the modified disc grinding wheel moves at an angular velocity ω g2 High-speed rotation constitutes the cutting motion.

[0083] Equation of modified tooth surface for non-orthogonal offset helical gears:

[0084] Coordinate systems S2 and S4 are respectively fixedly connected to the second virtual modified gear shaper 3 and the non-orthogonal offset helical gear. m S t S k S r S n As an auxiliary coordinate system, Let be the tooth ratio of the second virtual modified gear shaper 3 and the non-orthogonal offset helical gear. In the S4 coordinate system, the tooth surface equation of the non-orthogonal offset helical gear is expressed by the following equation:

[0085] R4(θ2,θ g2 ,λ2,φ4,L g2 ) = M 4n M nr M rk M km M m2 M 2t M tg2 (L g2 )R g2 (θ2,θ g2 ,λ2,φ g2 )

[0086] n4(θ2,θ g2 ,λ2,φ4,L g2 ) = L 4n L nr L rk L km L m2 L 2t L tg2 (L g2 )n g2 (θ2,θ g2 ,λ2,φ g2)

[0087] f3(θ2,θ g2 ,λ2,φ4,L g2 ) = n g2 ν 3 =0

[0088] f4(θ2,θ g2 ,λ2,φ4,L g2 ) = n g2 ν 4 =0

[0089] Eliminating the parameter θ in the above equations g2 R4(θ2,λ2,φ4,L) can be used. g2 ) represents the tooth surface of a non-orthogonal offset helical gear.

[0090] ν 3 ν 4 These are the center speed of grinding wheel 2 and the relative speed between the non-orthogonal offset helical gear and grinding wheel 2, respectively.

[0091] , , ,

[0092] First, based on the kinematic relationship between the two virtual modified gear shapers and the tooth surface parameters of the first virtual modified gear shaper 2, the tooth surface equation of the first modified disc grinding wheel 1 is derived. Then, the tooth surface equations of the second virtual modified gear shaper 3 and the modified pinion are derived. Next, based on the tooth surface equation of the second virtual modified gear shaper 3, the tooth surface equation of the second modified disc grinding wheel 4 is derived. Finally, based on the kinematic relationship between the second virtual modified gear shaper 3 and the non-orthogonal offset helical gear, and the tooth surface equation of the second modified disc grinding wheel 4, the modified tooth profile of the non-orthogonal offset helical gear is derived. The modified pinion and the non-orthogonal offset helical gear generated in this way can constitute a non-orthogonal offset helical gear pair. Using a modified disc grinding wheel to machine a non-orthogonal offset helical gear pair not only results in a simple structure but also produces a high-precision tooth surface.

[0093] This invention proposes a method for generating modified tooth profiles in non-orthogonal offset helical gear pairs using disc-shaped grinding wheels. If modified pinions and non-orthogonal offset helical gears are machined using positive and negative modified disc-shaped grinding wheels respectively, the resulting negative modified pinion and positive modified non-orthogonal offset helical gear can constitute a non-orthogonal offset modified helical gear pair. Using modified disc-shaped grinding wheels to machine non-orthogonal offset modified helical gear pairs not only offers a simple structure and convenient design, manufacturing, and dressing, but is also not limited by the design parameters of the face gear, and can achieve high-precision tooth surfaces. This invention is mainly used for generating modified tooth profiles in non-orthogonal offset helical gear pairs, providing a technical method for machining non-orthogonal offset modified helical gear pairs.

[0094] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for generating a non-orthogonally offset helical gear pair using a disc-shaped grinding wheel, characterized in that: A first modified disc grinding wheel is used to machine a modified pinion, and a second modified disc grinding wheel is used to machine a non-orthogonal offset modified helical gear. The generating motion of the first virtual modified gear shaper and the modified pinion is simulated by the oscillation of the first modified disc grinding wheel around the first virtual modified gear shaper. The generating motion of the second virtual modified gear shaper and the non-orthogonal offset modified helical gear is simulated by the oscillation of the second modified disc grinding wheel around the second virtual modified gear shaper. Both the first and second modified disc grinding wheels rotate to form the cutting motion. The center of the first modified disc grinding wheel reciprocates along an axis parallel to the first virtual modified gear shaper to form the feed motion. The center of the second modified disc grinding wheel reciprocates along an axis parallel to the second virtual modified gear shaper to form the feed motion. The specific processes of the generating motion of the first and second virtual gear shaping cutters with the gear shaping pinion are as follows: Coordinate systems S1, S2, S3, S4, S5, S6, S7, S8, S9, S1, S1, S9, S1, S1, S2, S1, S2, S3, S1, S2, S3, S4 ... g1 S i It is respectively fixedly connected to the first virtual modified gear hobbing cutter, the first modified disc grinding wheel, the second virtual modified gear hobbing cutter, and the modified pinion. S represents the coordinate system of the second virtual modified gear hobbing cutter and the modified gear, respectively. p S t To assist the coordinate system, three motion relationships exist during grinding: First, the first modified disc grinding wheel oscillates around the Z1 axis of the first virtual modified gear shaper with an angular velocity ω1, simulating the rotation of the first virtual modified gear shaper, and moves with the second virtual modified gear shaper and the modified small wheel with an angular velocity ω. i Around axis Z i The rotation constitutes the unfolding motion, and , The first virtual modified gear hobbing cutter has a tooth ratio of 1 to 2 virtual modified gear hobbing cutter and 2 modified gear small wheel. The second type has the projections of the center distance between the first virtual modified gear hobbing cutter and the first modified disc grinding wheel in the X and Z axes respectively as E. g1 and L g1 The first virtual modified gear hobbing cutter's Z1 axis forms a helix angle β with the end face of the first modified disc grinding wheel. The first modified disc grinding wheel feeds in a direction parallel to the Z1 axis of the first virtual modified gear hobbing cutter. Alternatively, the first modified disc grinding wheel feeds at an angular velocity ω. g1 High-speed rotation constitutes the cutting motion; The motion process of generating a non-orthogonal offset modified helical gear is as follows: The axis of the second virtual modified gear shaper is neither parallel nor intersecting with the axis of the non-orthogonal offset modified helical gear, and has a phase misalignment angle γ. m And an offset distance E, L1 represents the center distance between the second virtual modified gear shaper and the non-orthogonal offset helical gear. During grinding, there are three motion relationships: First, the second modified disc grinding wheel oscillates around the Z2 axis of the second virtual modified gear shaper at an angular velocity ω2, simulating the rotation of the second virtual modified gear shaper, which, together with the rotation of the non-orthogonal offset helical gear around the Z4 axis at an angular velocity ω4, constitutes a generating motion. , The first type is the gear ratio between the second virtual modified gear shaper and the non-orthogonal offset modified helical gear. The second type involves the second modified disc grinding wheel feeding in a direction parallel to the Z2 axis of the second virtual modified gear shaper. The third type involves the second modified disc grinding wheel moving at an angular velocity ω. g2 High-speed rotation constitutes the cutting motion.

2. The method for generating a non-orthogonally offset helical gear pair using a disc-shaped grinding wheel according to claim 1, characterized in that: The first virtual modified gear shaper cutter and the second virtual modified gear shaper cutter have the same module and the same end face pressure angle. The second virtual modified gear shaper cutter and the modified pinion have the same position vector. If the first virtual modified gear shaper cutter is positively modified, then the second virtual modified gear shaper cutter and the modified pinion are negatively modified. The non-orthogonal offset helical gear is positively modified. The negatively modified pinion and the positively modified non-orthogonal offset helical gear form a pair of non-orthogonal offset modified helical gear pairs.

3. The method for generating a non-orthogonally offset helical gear pair using a disc-shaped grinding wheel according to claim 1, characterized in that: The tooth surface equation of the first virtual modified gear shaper is: In the cross-sectional parameters of the first virtual displacement gear cutter, R p1 R b1 Let θ1 and θ2 represent the pitch circle radius and base circle radius of the first virtual modified gear shaper, respectively, and let θ1 represent the gear rotation angle parameter. b1 Let λ represent the central angle corresponding to half the tooth groove width on the base circle, λ1 represent the rotation angle of the involute end face of the first virtual displacement gear shaper around the axis, and p1 represent the helical motion parameters. In the S1 coordinate system, the tooth surface of the first virtual displacement gear shaper is represented by the following formula: ， ， , This indicates the number of teeth on the first virtual displacement gear cutter. This indicates the end face pressure angle of the virtual displacement gear hobbing cutter. Indicates displacement.

4. The method for generating a non-orthogonally offset helical gear pair using a disc-shaped grinding wheel according to claim 3, characterized in that: The equation for the tooth surface of the first modified disc grinding wheel is: The feed line of the first modified disc-shaped grinding wheel is the end face section of the first virtual modified gear shaper. Therefore, the tooth surface of the first modified disc-shaped grinding wheel is an involute surface of revolution. θ g1 The angle parameters of the surface of the first displacement disc grinding wheel (1) are: , , From coordinate system S1 to coordinate system S t Coordinate system S t To coordinate system S p Coordinate system S p To coordinate system S g1 The coordinate transformation matrix in S g1 In the first displacement disc grinding wheel (1), the position vector and unit normal vector are expressed by the following formula: ， ， ， 。 5. The method for generating a non-orthogonally offset helical gear pair using a disc-shaped grinding wheel according to claim 4, characterized in that: The tooth surface equations of the second virtual modified gear shaper and the modified pinion are as follows: In the coordinate system formed by the second virtual modified gear shaper and the modified small gear, S m S n As an auxiliary coordinate system, L0 represents the center distance between the first virtual modified gear hobbing cutter (2) and the second virtual modified gear hobbing cutter (3). In S i In the coordinate system, the tooth surface equations of the second virtual modified gear shaper and the modified pinion are expressed by the following formula: Eliminating parameters in the above equations Available This represents the tooth surface of the virtual second virtual modified gear cutter and the modified pinion; ， ， ， ， , These are the center speed of the first modified disc grinding wheel, the relative speed of the second virtual modified gear cutter and the modified small wheel with the first modified disc grinding wheel, respectively.

6. The method for generating a non-orthogonally offset helical gear pair using a disc-shaped grinding wheel according to claim 5, characterized in that: The tooth surface equation of the second virtual displacement disc grinding wheel is: The feed curve of the second virtual modified disc grinding wheel is the end face section of the second virtual modified gear shaper. Therefore, the tooth surface of the second virtual modified disc grinding wheel is an involute surface of revolution. Coordinate system S2 and coordinate system S g2 S is respectively fixedly connected to the second virtual displacement gear hobbing cutter and the second displacement disc grinding wheel. p S t As an auxiliary coordinate system, the projections of the center distance between the second virtual displacement gear hobbing cutter and the second displacement disc grinding wheel in the X and Z axes are respectively E g2 and L g2 The Z2 axis of the second virtual displacement gear hobbing cutter forms a helix angle β with the end face of the second displacement disc grinding wheel. g2 The angle parameters of the second displacement disc-shaped grinding wheel surface. , , From coordinate system S2 to coordinate system S t Coordinate system S t To coordinate system S p Coordinate system S p To coordinate system S g2 The coordinate transformation matrix in S g2 In the middle, the position vector and unit normal vector of the second displacement disc grinding wheel (4) are expressed by the following formula: , It is the tooth ratio between the first virtual displacement gear cutter and the second virtual displacement gear cutter. ， ； , R represents the number of teeth of the second virtual displacement gear cutter. p2 This indicates the pitch circle radius of the second virtual modified gear hobbing cutter; ， ， 。 7. The method for generating a non-orthogonally offset helical gear pair using a disc-shaped grinding wheel according to claim 1, characterized in that: The equation for the modified tooth surface of a non-orthogonal offset helical gear is: Coordinate systems S2 and S4 are respectively fixedly connected to the second virtual modified gear shaper and the non-orthogonal offset helical gear. m S t S k S r S n As an auxiliary coordinate system, , Given the tooth ratio of the second virtual modified gear shaper and the non-orthogonal offset helical gear, the tooth surface equation of the non-orthogonal offset helical gear in the S4 coordinate system is expressed by the following equation: Eliminating parameters in the above equations ,use This refers to the tooth surface of a non-orthogonally offset helical gear. , These are the center speed of the second modified disc grinding wheel and the relative speed between the non-orthogonal offset helical gear and the second modified disc grinding wheel, respectively. ， ， ， ， ， ， 。

Images