A method for processing a line contact tapered spiral bevel gear pair

Abstract

This invention discloses a machining method for a line-contact tapered spiral bevel gear pair. Based on the principle of conjugate tooth surface forming, the method defines that the production surface used for machining the large gear tooth surface is consistent with that used for machining the small gear tooth surface. The large gear tooth surface is machined using a forming method, while the small gear tooth surface is machined using a generating method. The method includes: establishing a meshing motion model of the spiral bevel gear pair to determine the relative motion and spatial position relationship between the large and small gear tooth surfaces during meshing transmission; establishing a small gear cutting model, and based on the aforementioned relative motion and spatial position relationship, obtaining the production surface of the small gear and the relative motion and spatial position relationship of the small gear tooth surface during the tooth generating process, and deriving the production surface equation and the small gear tooth surface equation; using a spiral bevel gear machining cutter as the generating cutter for machining the small gear, with the cutting surface of the cutter forming the production surface of the small gear during machining. This machining method can realize the machining of line-contact tapered spiral bevel gear pairs while also having economical machining efficiency.

Description

Technical Field

[0001] This invention pertains to the field of bevel gear machining technology, specifically relating to a machining method for a line-contact tapered spiral bevel gear pair. This method is applicable to the machining of spiral bevel gears and quasi-hypoid gear pairs. Background Technology

[0002] Spiral bevel gears are used to transmit power and motion across intersecting and staggered shafts, and are key mechanical transmission components in equipment manufacturing, transportation, engineering machinery, aerospace, and military equipment. However, during the machining of tapered spiral bevel gears, the limitations imposed by the cutter head structure and the cutting motion of mechanical machine tools make it difficult to achieve line contact conjugate meshing. Currently, the design is mainly based on the "local conjugate principle," aiming at local point contact on the tooth surface and utilizing stress-deformation factors to achieve local conjugate meshing contact transmission in the gear pair. However, the tooth profile design theory and manufacturing technology based on the local conjugate principle are still limited by the relatively small contact area in improving the tooth surface load-bearing capacity and service life.

[0003] With the continuous development of CNC machining technology, the processing and manufacturing of spiral bevel gears has evolved from mechanical machine tools to special CNC machine tools and CNC machining centers, which makes it possible to process line contact involute spiral bevel gear pairs with a larger contact area. At present, the existing line contact involute spiral bevel gear pair processing technology has the following problems: (1) Based on additive manufacturing technology, line contact spiral bevel gear pairs with arbitrary tooth shapes can be processed; however, the processing efficiency is too low, and the tooth surface accuracy and strength cannot be guaranteed. (3) Based on free surface processing technology, the cutting path of the ball end mill can be rationally planned, and line contact spiral bevel gear pairs with arbitrary tooth shapes can be accurately processed; however, the processing efficiency is very low, and it is difficult to apply industrially. (3) Using the tooth surface generation line of the spherical involute spiral bevel gear as the cutting edge of the tool, and the reverse motion of the tooth surface generation motion as the cutting motion, the tooth surface of the arc bevel gear can be cut; however, this cutting edge is not easy to process, and the processed gear has a large tooth shape error. Summary of the Invention

[0004] In view of the above-mentioned prior art, in order to apply the line contact conjugate tooth surface to practice, this invention proposes a machining method for line contact tapered tooth spiral bevel gear pairs, aiming to realize the design and manufacturing of line contact tapered tooth conjugate tooth surface pairs, while having economical machining efficiency.

[0005] To address the aforementioned technical problems, this invention proposes a machining method for a line-contact tapered spiral bevel gear pair. The pinion tooth surface is machined using a generating method, while the large gear tooth surface is machined using a forming tool with a linear cutting edge. In this invention, the production surface used for machining the large gear tooth surface is defined to be consistent with that used for machining the pinion tooth surface. The generating machining of the pinion tooth surface includes the following steps:

[0006] Step 1: Establish the meshing motion model of the spiral bevel gear pair: Based on the principle of conjugate tooth surfaces, determine the relative motion and spatial position relationship between the tooth surfaces of the large gear and the small gear during the meshing transmission process;

[0007] Step 2: Establish the pinion gear cutting model: Based on the relative motion and spatial position relationship between the large gear tooth surface and the small gear tooth surface during the meshing transmission process, obtain the production surface of the small gear and the relative motion and spatial position relationship between the small gear tooth surface during the cutting generation process, and derive the production surface equation and the small gear tooth surface equation.

[0008] Step 3: Use the spiral bevel gear machining cutter as the generating cutter for machining the small gear. During machining, the cutting surface of the cutter forms the production surface for machining the small gear.

[0009] Furthermore, the machining method for the line contact tapered spiral bevel gear pair described in this invention includes:

[0010] Step 1, the specific process of establishing the meshing motion model of the spiral bevel gear pair is as follows:

[0011] Establish coordinate system S1 and coordinate system S with the vertex O1 of the small wheel pitch cone as the origin. p Establish coordinate system S2 and coordinate system S with the vertex O2 of the large wheel cone as the origin. g ;

[0012] In coordinate system S2, the position vector of the larger gear tooth surface is represented as r2, and in coordinate system S1, the position vector of the smaller gear tooth surface that meshes with the larger gear tooth surface is r1.

[0013]

[0014] In equation (1), M 12 The transformation matrix from coordinate system S2 to coordinate system S1 is used to characterize the spatial positional relationship between the tooth surfaces of the large and small gears during meshing transmission; f 12 The meshing equation between the tooth surfaces of the large gear and the small gear is used to characterize the relative motion between the tooth surfaces of the large gear and the small gear during meshing transmission.

[0015] Z F1 Z represents the distance from the vertex O1 of the small wheel's pitch cone to the intersection point H1 of the small wheel's axis. F2 E represents the distance from the apex O2 of the large wheel's pitch cone to the intersection point H2 of the large wheel's axis; d η is the offset distance; η is the axis intersection angle; and These represent the meshing angles of the small wheel and the large wheel, respectively. z1 and z2 are the number of teeth on the small wheel and the large wheel, respectively.

[0016] The specific process of establishing the pinion gear cutting model in step 2 is as follows:

[0017] 2-1) Parameter definition, including:

[0018] The pitch cone of the gear is π c The vertex of the production wheel cone is O. c The vertex of the cone-shaped production wheel is O. ac The intersection point of the axis of the generating wheel is H. c ;

[0019] The small wheel cone is π. p The vertex of the pinion cone is O1, and the intersection of the pinion axis is H1;

[0020] The top surface of the cutter head is π. t ; Cutter head, cutter top surface π t The center point is O t Passing through the center point O t The vertical line is O d O t ;

[0021] Let node P be the line passing through node P and the axis of the producing wheel, and intersect the pitch cone π of the producing wheel. c The intersection point is K, and the vertical line O d O t With planar KO c P intersects at point O. d ;

[0022] 2-2) Establish a coordinate system, including:

[0023] With the apex O of the production wheel cone c Establish a coordinate system S for the circle. c , where z c The axis coincides with the axis of the production wheel, y c The axis is perpendicular to the plane KO c P;

[0024] The coordinate system S c Along the z c The coordinate system S is obtained by translating a distance l in the negative direction of the axis. f Coordinate system S f The origin is O f x f The axis passes through point O d ;

[0025] With center point O t Establish a coordinate system S for the circle. t , where z t The axis is perpendicular to the top surface of the cutter head (π). t y t The axis is parallel to the y-axis c axis;

[0026] Establish the origin as O o coordinate system S o The coordinate system S o Origin o With coordinate system S t dot O t Overlap, where z o axis and z c Parallel to the axis and with the z t The included angle between the axes is T;

[0027] 2-3) Define the radial and angular tool positions of the cutter head:

[0028] Origin O f With the origin O o The distance S represents the radial tool position of the tool head; the straight line O f O o With line O f O d The included angle q represents the angular tool position of the tool head;

[0029] 2-4) Define the machining parameters for the small wheel:

[0030] Radial tool position S of the cutter head; angular tool position q of the cutter head; origin O c and origin O f The distance between them, l; z o axis and z t The included angle T of the axes;

[0031] 2-5) Equation of the production surface:

[0032] Let coordinate system S t The position vector r of the cutting surface of the cutter head in the middle t Coordinate transformation to coordinate system S c In the process, the equation of the production surface is obtained as follows:

[0033] r c =M ct (S,q,l,T)·r t (2)

[0034] In equation (2), r c M represents the position vector of the production surface. ct Represents coordinate system S t To coordinate system S c The transformation matrix;

[0035] 2-6) Equation of pinion tooth surface:

[0036] Replace the position vector r2 of the large gear tooth surface in equation (1) with the position vector r of the production surface in equation (2). cObtain the position vector r of the cutting surface of the cutter head. t The equation for the pinion tooth surface is as follows:

[0037]

[0038] In equation (3), M 2c Represents coordinate system S c The transformation matrix M to coordinate system S2 12 M 2c and M ct Together they are used to characterize the spatial relationship between the cutting surface of the cutter head and the tooth surface of the pinion gear during the tooth generation process;

[0039] f 1t The meshing equation between the cutting surface of the cutter head and the tooth surface of the pinion is used to characterize the relative motion between the cutting surface of the cutter head and the tooth surface of the pinion during the tooth generation process.

[0040] 2-7) Based on the meshing motion model of the spiral bevel gear pair and the pinion cutting model, realize the generating process of the pinion.

[0041] Compared with the prior art, the beneficial effects of the present invention are:

[0042] (1) Based on the principle of conjugate tooth surface forming of gear transmission, the machining of line contact gradually decreasing spiral bevel gears can be realized.

[0043] (2) The machining of large wheels is not limited by special machine tools for spiral bevel gears, and can also be carried out by conventional CNC machine tools that meet the requirements of machining freedom.

[0044] (3) Compared with existing additive manufacturing technology, it can guarantee tooth surface strength; compared with freeform surface processing technology, it can guarantee processing efficiency. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the meshing motion model of the spiral bevel gear pair in the processing method of the present invention;

[0046] Figure 2 This is a schematic diagram of the small gear cutting process in this invention;

[0047] Figure 3 This is the coordinate system for small gear tooth cutting in this invention;

[0048] Figure 4 This is a schematic diagram of the large wheel cutting process in this invention;

[0049] Figure 5 This is a schematic diagram of a three-dimensional model of the line contact spiral bevel gear pair of the present invention. Detailed Implementation

[0050] This invention proposes a machining method for a line-contact tapered spiral bevel gear pair. The design concept is as follows: based on the principle of conjugate tooth surface forming, the large gear tooth surface of the spiral bevel gear pair is set as the production surface of its paired small gear tooth surface. The relative motion and spatial position relationship between the production surface and the small gear tooth surface during the tooth-cutting and generating process are completely consistent with the relative motion and spatial position relationship between the large gear tooth surface and the small gear tooth surface during the meshing transmission process. Based on this, a small gear cutting model is established. Based on the production surface, the required cutting tools for machining the small and large gears are selected. This method enables the machining of the line-contact tapered spiral bevel gear pair while maintaining economical machining efficiency.

[0051] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention.

[0052] This invention proposes a machining method for a line-contact tapered spiral bevel gear pair. The large gear tooth surface of the spiral bevel gear pair is defined as the generating surface of its mating small gear tooth surface. Furthermore, the relative motion and spatial position relationship between this generating surface and the small gear tooth surface during the tooth generation process are completely consistent with the relative motion and spatial position relationship between the large gear tooth surface and the small gear tooth surface during the meshing transmission process. In other words, the generating surface used for machining the small gear tooth surface is defined to be consistent with the generating surface used for machining the small gear tooth surface. In this invention, the small gear tooth surface is machined using a spiral bevel gear cutter head with high machining efficiency. The cutting surface of the cutter head during machining forms the generating surface used for machining the small gear. In this invention, the large gear tooth surface is machined using a forming tool with a linear cutting edge. During machining, the cutting edge of the tool and the large gear tooth surface are in line contact. The cutting edge of the tool forms the generating surface, i.e., the large gear tooth surface, during the machining motion of the machine tool, thereby machining the large gear tooth surface.

[0053] In this invention, the following design is required for the small wheel to be manufactured using the generating method:

[0054] Step 1: Establish the meshing motion model of the spiral bevel gear pair: Based on the principle of conjugate tooth surfaces, determine the relative motion and spatial position relationship between the tooth surfaces of the large and small gears during the meshing transmission process; specific contents include:

[0055] Determine the relative motion and spatial relationship between the tooth surfaces of the large and small gears during the meshing transmission process. Establish Figure 1 The meshing motion model of the spiral bevel gear pair shown is illustrated, in which coordinate system S1 and coordinate system S2 are established with the vertex O1 of the small gear pitch cone as the origin. p Establish coordinate system S2 and coordinate system S with the vertex O2 of the large wheel cone as the origin. g Z F1 Z represents the distance from the vertex O1 of the small wheel's pitch cone to the intersection point H1 of the small wheel's axis. F2 E represents the distance from the apex O2 of the large wheel's pitch cone to the intersection point H2 of the large wheel's axis; d η is the offset distance; η is the axis intersection angle; and These represent the meshing angles of the small wheel and the large wheel, respectively, and their relationship satisfies the expression... z1 and z2 represent the number of teeth on the pinion and sprocket, respectively. In coordinate system S1, the position vector of the pinion tooth surface, which meshes conjugately with the sprocket tooth surface, is r1. In coordinate system S2, the position vector of the sprocket tooth surface is represented as r2.

[0056]

[0057] In equation (1), M 12 The transformation matrix from coordinate system S2 to coordinate system S1 is used to characterize the spatial positional relationship between the tooth surfaces of the large and small gears during meshing transmission; f 12 The equation representing the meshing between the tooth surfaces of the large and small gears is used to characterize the relative motion between the tooth surfaces of the large and small gears during meshing transmission.

[0058] Step 2: Establish the pinion gear cutting model: Based on the relative motion and spatial position relationship between the large gear tooth surface and the pinion tooth surface during the meshing transmission process, obtain the relative motion and spatial position relationship between the pinion's generating surface and the pinion tooth surface during the cutting and generating process.

[0059] The small gear cutting process is as follows: Figure 2 As shown, the large gear tooth surface of the spiral bevel gear pair is set as the generating surface of its paired small gear tooth surface, so that the relative motion and spatial position relationship between the generating surface and the small gear tooth surface during the tooth generating process is completely consistent with the relative motion and spatial position relationship between the large gear and the small gear tooth surface during the meshing transmission process; at the same time, the spiral bevel gear machining cutter head is used as the generating milling cutter for machining the small gear, and the cutting surface of the cutter head during machining forms the generating surface of the small gear.

[0060] Establish the coordinate system for small gear cutting machining as follows: Figure 3 As shown, where π c , π p and π t These represent the feed wheel cone, the small wheel cone, and the cutter head top surface, respectively; O1, O c and O ac H1 and H represent the vertex of the small wheel pitch cone, the vertex of the feed wheel pitch cone, and the vertex of the feed wheel surface cone, respectively; c These are the intersection points of the small wheel axis and the feed wheel axis, respectively; P is a node, and the straight line passing through node P and the feed wheel axis intersects the feed wheel pitch cone π. c The intersection point is K, and the cone of the production wheel is π. t Center point O t vertical line O d O t With planar KO c P intersects at point O. dThe apex O of the production wheel segment cone. c Establish a coordinate system S for the circle. c , where z c The axis coincides with the axis of the production wheel, y c The axis is perpendicular to the plane KO c P; the coordinate system S c Along the z c The coordinate system S is obtained by translating a distance l in the negative direction of the axis. f Coordinate system S f The origin is O f x f The axis passes through point O d That is, the apex O of the production wheel cone. c and coordinate system S f Origin O f The distance between them is l; with center point O t Establish a coordinate system S for the circle. t , where z t The axis is perpendicular to the top surface of the cutter head (π). t y t The axis is parallel to the y-axis c Axis; establish origin as O o coordinate system S o The coordinate system S o Origin o With coordinate system S t dot O t Overlap, where z o axis and z c Parallel to the axis and with the z t The angle between the axes is T. Coordinate system S f Origin f With coordinate system S o Origin o The distance between them is S, representing the radial tool position of the tool head; coordinate system S f Origin f With coordinate system S o Origin o Connect, coordinate system S f Origin f With point O d Connection, O f O o With O f O d The included angle between them is q, representing the angular tool position of the tool head. The coordinate system S... t The position vector r of the cutting surface of the cutter head in the middle t Coordinate transformation to coordinate system S c From this, the equation of the production surface can be obtained as follows:

[0061] r c=M ct (S,q,l,T)·r t (2)

[0062] In equation (2), r c M represents the position vector of the production surface. ct Represents coordinate system S t To coordinate system S c The transformation matrix.

[0063] Replace the position vector r2 of the large gear tooth surface in equation (1) with the position vector r of the production surface in equation (2). c The position vector r of the cutting surface of the cutter head can be obtained. t The equation for the pinion tooth surface is as follows:

[0064]

[0065] In equation (3), M 2c Represents coordinate system S c The transformation matrix M to coordinate system S2 12 M 2c and M ct Together, they are used to characterize the spatial relationship between the cutting surface of the cutter head and the tooth surface of the pinion during the tooth generation process; f 1t The equation representing the meshing between the cutting surface of the cutter head and the tooth surface of the pinion is used to characterize the relative motion between them during the gear generating process. The spiral bevel gear machining cutter head is used as the generating cutter for machining the pinion, and the cutting surface of the cutter head forms the generating surface of the machined pinion.

[0066] In this invention, the large wheel gear cutting process is as follows: Figure 4 As shown, a forming tool with a linear cutting edge is used to machine the tooth surface of the large wheel. During the machining process, the cutting edge of the tool and the tooth surface of the large wheel are in line contact and the cutting surface of the tool is always tangent to the tooth surface of the large wheel. The cutting edge of the tool forms the forming surface for machining the small wheel, i.e. the tooth surface of the large wheel, during the machining motion of the machine tool.

[0067] To verify that the method of this invention can realize the machining of line contact tapered spiral bevel gear pairs, this embodiment establishes a three-dimensional model of the line contact spiral bevel gear pair based on the model provided in the method of this invention. The basic parameters include: number of teeth of the pinion z1 = 13, number of teeth of the gear z2 = 43, large end module 4mm, and offset distance E. d =20mm, shaft angle η=90°. First, based on the meshing motion model of the spiral bevel gear pair, Z is calculated. F1 =18.702mm, Z F2= -4.307mm. Then, based on the pinion gear cutting model, S = 80.945mm, q = 74.562°, T = 17.253°, and l = 5.765mm were calculated. Finally, the above data were substituted into the production surface equation and pinion gear tooth surface equation established in this invention, and the three-dimensional model of the line contact spiral bevel gear pair was obtained as follows. Figure 5 As shown.

[0068] Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many modifications under the guidance of the present invention without departing from the spirit of the present invention, and these modifications are all within the protection scope of the present invention.

Claims

1. A method for machining a line-contact tapered spiral bevel gear pair, wherein the tooth surface of the smaller gear is machined by generating method and the tooth surface of the larger gear is machined by forming method, characterized in that: The generating surface used for machining the large gear tooth surface is defined to be consistent with the generating surface used for machining the small gear tooth surface. The generating process of the small gear tooth surface includes the following steps: Step 1: Establish the meshing motion model of the spiral bevel gear pair: Based on the principle of conjugate tooth surfaces, determine the relative motion and spatial position relationship between the tooth surfaces of the large gear and the small gear during the meshing transmission process; Step 2: Establish the pinion gear cutting model: Based on the relative motion and spatial position relationship between the large gear tooth surface and the small gear tooth surface during the meshing transmission process, obtain the production surface of the small gear and the relative motion and spatial position relationship between the small gear tooth surface during the cutting generation process, and derive the production surface equation and the small gear tooth surface equation. Step 3: Use the spiral bevel gear machining cutter as the generating cutter for machining the small gear. During machining, the cutting surface of the cutter forms the production surface for machining the small gear.

2. The machining method for the line contact tapered spiral bevel gear pair according to claim 1, characterized in that: The specific process of establishing the meshing motion model of the spiral bevel gear pair in step 1 is as follows: Establish coordinate system S1 and coordinate system S with the vertex O1 of the small wheel pitch cone as the origin. p Establish coordinate system S2 and coordinate system S with the vertex O2 of the large wheel cone as the origin. g ; In coordinate system S2, the position vector of the larger gear tooth surface is represented as r2, and in coordinate system S1, the position vector of the smaller gear tooth surface that meshes with the larger gear tooth surface is r1. In equation (1), M 12 The transformation matrix from coordinate system S2 to coordinate system S1 is used to characterize the spatial positional relationship between the tooth surfaces of the large and small gears during meshing transmission; f 12 The meshing equation between the tooth surfaces of the large gear and the small gear is used to characterize the relative motion between the tooth surfaces of the large gear and the small gear during meshing transmission. Z F1 Z represents the distance from the vertex O1 of the small wheel's pitch cone to the intersection point H1 of the small wheel's axis. F2 E represents the distance from the apex O2 of the large wheel's pitch cone to the intersection point H2 of the large wheel's axis; d This is the offset distance; η is the angle between the axes; and These represent the meshing angles of the small wheel and the large wheel, respectively. z1 and z2 are the number of teeth on the small wheel and the large wheel, respectively.

3. The machining method for the line contact tapered spiral bevel gear pair according to claim 2, characterized in that: The specific process of establishing the pinion gear cutting model in step 2 is as follows: 2-1) Parameter definition, including: The pitch cone of the gear is π c The vertex of the production wheel cone is O. c The vertex of the cone-shaped production wheel is O. ac The intersection point of the axis of the generating wheel is H. c ; The cone of the small wheel is π. p The vertex of the pinion cone is O1, and the intersection of the pinion axis is H1; The top surface of the cutter head is π. t ; Cutter head, cutter top surface π t The center point is O t Passing through the center point O t The vertical line is O d O t ; Let node P be the line passing through node P and the axis of the producing wheel, and intersect the pitch cone π of the producing wheel. c The intersection point is K, and the vertical line O d O t With planar KO c P intersects at point O. d ; 2-2) Establish a coordinate system, including: With the apex O of the production wheel cone c Establish a coordinate system S for the circle. c , where z c The axis coincides with the axis of the production wheel, y c The axis is perpendicular to the plane KO c P; The coordinate system S c Along the z c The coordinate system S is obtained by translating a distance l in the negative direction of the axis. f Coordinate system S f The origin is O f x f The axis passes through point O d ; With center point O t Establish a coordinate system S for the circle. t , where z t The axis is perpendicular to the top surface of the cutter head (π). t y t The axis is parallel to the y-axis c axis; Establish the origin as O o coordinate system S o The coordinate system S o Origin o With coordinate system S t dot O t Overlap, where z o axis and z c Parallel to the axis and with the z t The included angle between the axes is T; 2-3) Define the radial and angular tool positions of the cutter head: Origin O f With the origin O o The distance S represents the radial tool position of the tool head; the straight line O f O o With line O f O d The included angle q represents the angular tool position of the tool head; 2-4) Define the machining parameters for the small wheel: Radial tool position S of the cutter head; angular tool position q of the cutter head; origin O c and origin O f The distance between them, l; z o axis and z t The included angle T of the axes; 2-5) Equation of the production surface: Let coordinate system S t The position vector r of the cutting surface of the cutter head in the middle t Coordinate transformation to coordinate system S c In the process, the equation of the production surface is obtained as follows: r c =M ct (S,q,l,T)·r t (2) In equation (2), r c M represents the position vector of the production surface. ct Represents coordinate system S t To coordinate system S c The transformation matrix; 2-6) Equation of pinion tooth surface: Replace the position vector r2 of the large gear tooth surface in equation (1) with the position vector r of the production surface in equation (2). c Obtain the position vector r of the cutting surface of the cutter head. t Equation of the pinion tooth surface: In equation (3), M 2c Represents coordinate system S c The transformation matrix M to coordinate system S2 12 M 2c and M ct Together they are used to characterize the spatial relationship between the cutting surface of the cutter head and the tooth surface of the pinion gear during the tooth generation process; f 1t The meshing equation between the cutting surface of the cutter head and the tooth surface of the pinion is used to characterize the relative motion between the cutting surface of the cutter head and the tooth surface of the pinion during the tooth generation process. 2-7) Based on the meshing motion model of the spiral bevel gear pair and the pinion cutting model, realize the generating process of the pinion.

4. The machining method for the line contact tapered spiral bevel gear pair according to claim 1, characterized in that: The large gear tooth surface is machined using a forming method, which employs a forming tool with a linear cutting edge.

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