Pitch line generation for straight-tooth bevel gears

Abstract

A method that overcomes the drawbacks associated with creating the tooth surface of a straight bevel gear (50) using relative rotation around the root line (54), and instead aims to create the flank surface of a straight bevel gear (50) around an instantaneous axis of rotation that coincides with the pitch line (57) of the straight bevel gear (50).

Description

[Technical Field]

[0001] This invention relates to bevel gears, and more particularly to the manufacture of flank surfaces of straight-toothed bevel gears by a manufacturing method. [Background technology]

[0002] Figure 1 shows an example of a straight bevel gear 2 having multiple teeth 3, each tooth having a top land 4, a root portion 5, and a pair of tooth flank surfaces 6. The region 7 between a pair of consecutive teeth is known as a tooth "slot" or "space," and the root portion 5 coincides with the bottom of the tooth slot. In the case of a mating pair (i.e., a gear pair) of straight bevel gears (and most types of gears), one member of the pair is usually smaller and has fewer teeth (known as the pinion member) than the larger mating member (known as the gear member) which has more teeth. In most cases, the pinion member is the driving member, and the gear member is the driven member of the gear pair.

[0003] One process for manufacturing bevel gears is the generation process. In the generation process, a rotating tool is fed into the workpiece to a predetermined depth. Once this depth is reached, the tool and workpiece roll together in a predetermined relative rolling motion known as the generation roll, as if the workpiece were rotating in mesh with a theoretical generation gear, and the teeth of the theoretical generation gear are represented by the material removal surface of the tool. The tooth contour shape is formed by the relative motion of the tool and workpiece in the generation roll.

[0004] Straight bevel gears are generally manufactured using two mechanical tool planes (e.g., U.S. Patent No. 842,455), interlocking cutters on a mechanical machine (e.g., U.S. Patent No. 2,567,273), or a single peripheral cutter on a freeform CNC machine (e.g., U.S. Patent No. 7,364,391, the entire disclosure of which is incorporated herein by reference).

[0005] U.S. Patent No. 7,364,391 discloses a one-sided cutting process in which, in a first step (e.g., Figure 16(a)), all first sides of the teeth are rough-cut and then finished, and then in a second step (e.g., Figure 16(b)), the cutter is repositioned to finish-cut all second flanks of the teeth. The two-step process may be performed on a computer-controlled multi-axis gear manufacturing machine, such as the one disclosed in U.S. Patent No. 6,712,566, the entire disclosure of which is incorporated herein by reference. The two-step process creates an accurate octoid and allows for flank morphology modification. After heat treatment, the differential gear can be ground in a CBN grinding process in a manner similar to cutting.

[0006] A suitable cutting tool for performing the two-step process described above is shown in Figure 17, which shows a peripheral cutting tool 130 detachably fixed to a spindle 128 of a machine tool (not shown), such as disclosed in U.S. Patent No. 6,712,566. The cutting tool 130 comprises a cutter head 132 having a plurality of stick blades 134. The tips of the cutting blades 134 form a tip circle, which is also known as a point diameter or point circle. A clamp block 136 is positioned above each stick blade. The cutter in Figure 17 has a top ring 138 above the clamp block 136, which has an integrated clamp screw 139.

[0007] The cutting process described above requires that the movement of the cutter or blade be adjusted to align with the root angle of the tooth slot. In the case of a mechanical machine, the axis of the generating roll during slot cutting is also oriented collinearly with the root line of the workpiece. When manufacturing a straight bevel gear with a single cutter disc (one flank at a time) using a CNC freeform machine (as disclosed in U.S. Patent No. 6,712,566), the original process for a mechanical machine is effectively replicated, and flank generation is also around an instantaneous axis of rotation aligned with the root line of the workpiece. When a root angle that is not equal to zero exists, as in the case of a straight bevel gear, the generation of the tooth surface with relative rotation around the root line violates the gear ring law. As a result, such a generation configuration causes misalignment of the flank surface, which is shown as tooth profile crowning and surface warping, and causes the surface to deviate significantly from the conjugate plane. Consequently, tooth contact is reduced and motion transmission errors are increased. The kinematic coupling conditions between the pinion and the gear are not met if the pinion and gear members do not roll on their pitch cones together with the virtual gear plane during the manufacturing process.

[0008] A straight bevel gear machined using the method described above forms a generative mark that begins parallel to the tooth root and is followed by a tapered mark or line. However, in the prior art of straight bevel gears, the generatrix does not all point to a single point, such as the point that coincides with the intersection between the pinion shaft and the gear shaft.

[0009] The generative mark, also known as the generative plane, is the result of the distance between two preceding cutting blades in a cutter head. As one blade passes along the width of the gear being cut, the generative motion rotates the gear, and the blade forms a curved surface along the width of the gear. The next blade finds the gear that has been rotated by a certain amount and creates its own generative plane next to what the previous blade created.

[0010] The generating plane approximates an involute contour with polygons. If the cutter head has an infinite number of cutting edges or is replaced by a grinding wheel, the contour becomes an involute without a generating plane. Also, if the generating rotation is infinitely slow and the cutter RPM is infinitely high, the generating plane effectively disappears.

[0011] Traditionally, straight bevel gears have been recognized as having fairly large motion errors. Although the Frank geometric shape is far from conjugate, most straight bevel gears were used in fairly simple applications. Today, manufacturers of high-precision equipment prefer to use straight bevel gears due to their lower axial force (compared to curved bevel gears). Therefore, high power density, high efficiency, and low rolling noise become more important for straight bevel gears. [Overview of the project]

[0012] This invention overcomes the drawbacks associated with creating tooth surfaces by relative rotation around the root line and instead aims to create flank surfaces of straight bevel gears around an instantaneous axis of rotation that coincides with the pitch line of the straight bevel gear.

[0013] The present invention relates to a method for creating or machining teeth on a bevel gear, comprising: providing a bevel gear workpiece having a rotating axis; and providing a material removal tool having a rotating axis, wherein the material removal tool has at least one material removal surface arranged around the tool's rotating axis, and each of the at least one material removal surface has a tip. The tip of the at least one material removal surface traces the tip circle of the tool. The material removal tool is rotated and then engages with the bevel gear workpiece to create teeth on the bevel gear workpiece by rolling the material removal tool and the workpiece together in a predetermined relative rolling motion, the predetermined relative rolling motion representing the workpiece rotating in mesh with a theoretically generated gear having teeth, the teeth of the theoretically generated gear represented by at least one material removal surface of the tool.

[0014] The generation is carried out according to a generation configuration, which includes positioning a material removal tool relative to a bevel gear workpiece such that the tip circle of the tool is in contact with the root line of the bevel gear workpiece, and positioning the material removal tool relative to the bevel gear workpiece such that the instantaneous rolling axis during generation is located on the pitch line of the workpiece or the pitch line of the theoretically generated gear. [Brief explanation of the drawing]

[0015] [Figure 1] An example of a straight-toothed bevel gear is shown. [Figure 2] This shows the generator gear plane and a three-dimensional representation of a pinion pitch cone that does not roll on the generator gear plane. [Figure 3] The three-dimensional representation of the generator gear plane and the gear pitch cone is shown, and the pitch cone does not roll on the generator gear plane. [Figure 4] This is a three-dimensional representation of a pinion pitch cone rolling on top of a virtual gear generation plane and a gear pitch cone rolling from below on the same virtual gear generation plane. [Figure 5] This shows a three-dimensional representation of a pinion rolling on top of a virtual generator gear and a gear rolling from below on the same virtual generator gear. [Figure 6] This shows a top view of a cutting machine configuration in which a cutter rolls along the root line of a gear tooth. [Figure 7] This shows an analysis of the tooth contact area of ​​a straight-toothed bevel gear pair, which is created by both the gear member and the pinion member rolling on the tooth root line of each member. [Figure 8] This shows an analysis of the tooth contact area of ​​a straight bevel gear pair, created by both the gear and pinion members rolling on the root lines of their respective teeth, with tooth profile crowning correction applied. [Figure 9] This shows a top view of a cutting machine configuration in which a cutter rolls along the pitch line of a gear. [Figure 10] This shows an analysis of the tooth contact area of ​​a straight-toothed bevel gear pair, created by the rolling of both the gear and pinion components along their respective pitch lines. [Figure 11]Shows a tooth contact analysis of a straight bevel gear pair that is generated by both the gear member and the pinion member rolling on their respective pitch lines, and to which length crowning is applied. [Figure 12] Shows a tooth contact analysis of a straight bevel gear pair that is generated by both the gear member and the pinion member rolling on their respective pitch lines, and to which length crowning and tip relief are applied for both members. [Figure 13] Shows a bevel gear generation coordinate system. [Figure 14(a)] Shows a non-generating configuration of a gear member. [Figure 14(b)] Shows a special generating configuration of a pinion member. [Figure 15] Shows a comparison of motion transmission errors between a root line generated straight bevel gear pair and a pitch line generated straight bevel gear pair. [Figure 16(a)] Shows a two-stage process for manufacturing a straight bevel gear. [Figure 16(b)] Shows a two-stage process for manufacturing a straight bevel gear. [Figure 17] Shows a peripheral cutting tool for carrying out the two-stage process of Figures 16(a) and 16(b). [Figure 18] Shows a straight bevel gear having an exaggerated generating plane. [Figure 19] Shows a two-dimensional representation of straight bevel gear flanks having tapered generating planes starting parallel to the root line, the extensions of which do not intersect at the intersection point. [Figure 20] Shows a two-dimensional representation of straight bevel gear flanks having generating planes parallel to an extended pitch line that intersects the intersection point between the pinion and the gear shaft. The generating planes do not intersect the intersection point. [Figure 21] Shows a two-dimensional representation of straight bevel gear flanks having tapered, non-parallel generating planes, the extensions of which extend to the intersection point between the pinion and the gear shaft and intersect the extended pitch line there. [Figure 22] Shows a two-dimensional representation of straight bevel gear flanks having tapered, non-parallel generating planes, the extensions of which do not extend to the intersection point between the pinion and the gear shaft. [Modes for carrying out the invention]

[0016] As used herein, the terms “invention,” “the invention,” and “the present invention” are intended to broadly refer to all the subject matter herein and any of the following claims. Statements containing these terms should not be understood as limiting the subject matter described herein or the meaning or scope of any of the following claims. Furthermore, this specification does not attempt to describe or limit the subject matter covered by any of the claims in any particular part, paragraph, description, or drawing of this application. The subject matter should be understood by referring to this entire specification, all drawings, and any of the following claims. The present invention is capable of other configurations and can be practiced or executed in various ways. It should also be understood that the expressions and terms used herein are for illustrative purposes only and should not be considered limiting.

[0017] Herein, the details of the present invention will be considered with reference to the accompanying drawings illustrating the invention, merely as examples. In the drawings, similar features or components are referred to by similar reference numerals. The size and relative size of specific embodiments or elements may be exaggerated for clarity or for detailed explanatory purposes. Doors, casings, internal or external protective coverings, etc., may be omitted from the drawings for better understanding and clarity of the present invention.

[0018] The use of “includes,” “have,” and “equip,” and their variations, herein means to include the items and their equivalents listed thereafter, as well as any additional items. The use of letters to identify elements of a method or process is for identification purposes only and does not mean to indicate that the elements should be performed in a particular order. Where herein used, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless otherwise specified in the context, and the term “and / or” includes any and all combinations of one or more related listed items.

[0019] In the following descriptions of the drawings, directions such as top, bottom, upward, downward, rear, base, top, front, and back may be referred to, but these are for convenience only and refer to the drawings (as they are typically seen). These directions are not intended to be taken literally or to limit the invention in any way. In addition, terms such as “first,” “second,” and “third” are used herein for illustrative purposes only and are not intended to indicate or imply any importance or significance unless expressly stated otherwise.

[0020] Figure 2 shows the pinion member pitch cone 10 penetrating the virtual generating gear plane 12 from above. The angle 9 between the pinion shaft 21 and the generating gear plane 12 is equal to the tooth root angle of the pinion.

[0021] Figure 3 shows a gear member pitch cone 11 penetrating the virtual generating gear plane 12 from below. The angle 8 between the gear shaft 16 and the generating gear plane 12 is equal to the root angle of the gear. In the operation of the pinion and gear (Figure 4), the angle between the pinion shaft 21 and the gear shaft 16 must be equal to the shaft angle 15, which is the pinion pitch angle 13 plus the gear pitch angle 14. This means that during operation, the pinion pitch angle rolls over the gear pitch angle, but during the manufacturing process, the root angle rolls over the connecting generating gear, which results in a mismatch of the flank faces from conjugate.

[0022] Figure 4 also shows the pitch cone 10 of the bevel pinion and the pitch cone 11 of the bevel gear. The disk 12 between them is the virtual generating gear plane. As the generating plane 12 rotates around its axis 26, the cone 10 on the disk rotates around its axis 21, and the cone 11 below the disk rotates around its axis 16, with both cones rolling on the disk 12 without sliding. The ratio between the rotations of the cones is calculated as follows: Ratio = sin(pinion pitch cone angle 13) / sin(gear pitch cone angle 14) in this case: Pinion pitch cone angle 13 + Gear pitch cone angle 14 = Shaft angle 15

[0023] Only gear pairs in which the pitch cone rolls without sliding on the generating gear plane satisfy the gear ring law and have a conjugate base.

[0024] Figure 5 shows the generating gear 17, which is the generating disk 12 (Figure 4) after the teeth have been added. The teeth and slots have a trapezoidal contour and taper from the outside towards the center 23. This is a precise bevel gear, similar to the generating rack of an involute cylindrical gear.

[0025] Figure 6 shows the creation of a conventional straight-tooth bevel gear by rolling along the tooth root line. As an example, a gear pair manufactured according to Figure 6 may have the following basic parameters: Number of teeth on the pinion component = 15 Number of teeth on the gear component = 17 Surface=20mm Contour shift = 0.0 Contour depth coefficient = 1.0 Tooth gap = 0.5 mm Backlash = 0.1mm Pinion face angle = 51.40° Gear surface angle = 58.57° Fillet edge radius pinion = 0.5 mm Fillet edge radius gear = 0.5 mm Pressure angle pinion = 20° Pressure angle gear = 20° Shaft angle = 90° Outer pitch diameter gear = 100.00 mm Peripheral cutter diameter: 228.6 mm

[0026] Figure 6 shows a top view of the generating configuration in a cutting machine (e.g., U.S. Patent No. 6,712,566). The workpiece gear member 20 has a rotation axis 21 that intersects the generating gear axis 22 (which is the same as the cutting machine cradle axis) at point 23. The tooth root line 24 of the gear 20 intersects the generating gear axis 22 and is perpendicular to the generating gear axis. The circular peripheral cutter 25 is adjusted so that the tip circle 25 is tangent to the tooth root line 24. During the cutting and generating process, the cutter 25 rotates around its axis 26 (shown only as a point in Figure 5) to perform the cutting motion. Furthermore, the cutter itself rotates around the generating gear axis 22, while the work gear rotates around its axis 21 (i.e., the generating roll) to generate the octoid flank contour. The work gear rotation angle is equal to the generating gear rotation angle multiplied by the number of teeth of the generating gear and divided by the number of teeth of the work gear. This configuration, in which the tooth root line 24 is adjusted to coincide with the instantaneous rolling axis (i.e., the line along which both bodies are in contact with each other and roll against each other without slippage), is consistent with the manufacturing of conventional straight-tooth bevel gears. In Figure 6, the instantaneous rolling axis lies in the generating plane and coincides with the Z-axis.

[0027] Figure 7 shows an analysis of the tooth contact area of ​​the pinion and gear created according to Figure 6. The relative tooth surface error surface 30 indicates the deviation from conjugate. Tooth profile crowning 38 occurs as a result of creation on the tooth root line. The tooth contact area 31 (using a virtual marking compound film with a thickness of 0.006 mm) extends across the entire working area. This means that the upper and lower parts of the contact area 31 (areas 32 and 33) are lost due to mechanical and / or kinematic undercuts in the pinion member (area 32) and gear member (area 33). Even under high load, the tooth contact area cannot extend into areas 32 and 33. In this example in Figure 7, 40% of the possible working contour is lost. The contact ratio between adjacent teeth drops from a theoretical value of 1.35 to less than 1.0, meaning that the contact transition from one pair of teeth to the next cannot maintain the overlap, leading to large effective transmission errors, large motion, and high load concentration. The motion transmission graph 34 in Figure 7 shows the motion transmission of three consecutive tooth pairs. The two gaps between the three parabolic curves 35, 36, and 37 also reflect that the transmission error is greater than 500 microradians.

[0028] Attempts to eliminate tooth profile crowning by using a cutting blade with a curved profile are unsuccessful, as shown in Figure 8. Tooth profile crowning 38 (Figure 7) is not eliminated but only reduced as shown in 40 of Figure 8, with the side effect of creating negative length crowning 41. The resulting tooth contact area 42 is poorly formed and positioned, and the motion transmission graph 43 shows motion error curves 46, 47, and 48 that are greater than 500 microradians. The loss areas of the working profiles 44 and 45 are identical to the areas 32 and 33 before correction. It appears impossible to achieve a conjugate surface when flank surface creation applies rolling along the tooth root line. A conjugate flank surface is needed as a starting point for the development of highly optimized straight bevel gear designs.

[0029] A solution of the present invention for generating rolls on the pitch line is shown in Figure 9. The straight-toothed bevel gear pair used to create Figure 9 has the same basic parameters as those enumerated for the root-line generating gear pairs in Figures 2 to 4. The present invention is applicable to manufacturing bevel gears from gear blanks (e.g., rough cutting) and machining the teeth of rough-cut gears (e.g., grinding, finish cutting). A control program having control commands for carrying out the method of the present invention and a multi-axis computer-controlled gear manufacturing machine are also intended.

[0030] Figure 9 shows a top view of the generation configuration in the cutting machine. The workpiece gear 50 has a rotating axis 51 that intersects the generation gear axis 52 (identical to the cutting machine cradle axis) at point 53. Point 53 also symbolizes the X axis of the generation system (oriented perpendicular to the page). The pitch line 57 of the gear 50 intersects the generation gear axis 52 at the center point 53 in the generation gear coordinate system and is perpendicular to the generation gear axis. The tip circle (also known as the tip circle, point diameter, or point circle) of the circular peripheral cutter 55 is adjusted to be tangent to the tooth root line 54. During the cutting and generation process, the cutter 55 rotates around its axis 56 (shown only as a point in Figure 9) to perform the cutting action. Furthermore, the rotating cutter itself rotates (i.e., moves) around the generation gear axis 52 (i.e., the generation roll) to generate the octoid tooth flank contour. In this configuration, the root line 54 is tangent to the tip circle of the cutter blade, and the pitch line 57 is oriented to coincide with the instantaneous rolling axis (i.e., the line along which both bodies (workpiece and generator gear) are in contact with each other and roll against each other without slipping). This configuration is a result of the present invention, in which the instantaneous rolling axis is separated from the orientation of the cutter circle. In Figure 9, the instantaneous rolling axis lies in the generator plane (XZ) and coincides with the Z axis.

[0031] The above discussion also applies to polishing. The outer tip of the polishing surface of the polishing wheel traces a tip circle, a point diameter, or a point circle.

[0032] Figure 10 shows the analysis of the tooth contact area of ​​the pinion and gear created according to Figure 9. The relative tooth surface error surface 60 shows no measurable deviation from the conjugate. As a result, accurate creation on the pitch line results in a conjugate relative tooth surface error with a theoretically zero deviation 68. The tooth contact area 61 (using a virtual marking compound film with a thickness of 0.006 mm) extends across the entire working area. The loss areas 62 and 63 above and below the contact area 61 are reduced to 28% of the flank area compared to a 40% loss with the conventional tooth root line creation method.

[0033] A theoretical contact ratio of 1.35 between adjacent teeth is fully achieved in the pitch-line generating gear pair shown in Figure 10. The calculated motion transmission graph 64 for the three consecutive tooth pairs 65, 66, and 67 shows transmission errors with variations of only about 3 microradians. The conjugate flank faces in Figure 10 are a favorable starting point for the development of highly optimized straight-tooth bevel gear designs.

[0034] Figure 11 shows the tooth contact analysis of the gear pair from Figure 10 after length crowning 71 has been added. The relative tooth surface error surface 70 shows the amount of clearance from the center of the face width toward the toe and heel. The contact area 72 is localized between the toe and heel, but the tooth profile crowning 73 is still about zero, which is likely to result in marginal contact along the apex and root. The likelihood of apex and / or marginal contact is also reflected by the non-center mean point 77 (point of optimal motion transmission). The mean point is applied to the entire contour (a line or cross section extending in the contour direction within the tooth contact pattern in Figure 11) and is shown at arbitrary locations. The motion transmission graph 75 shows the maximum transmission error 76 of less than 10 microradians.

[0035] To preserve the conjugate flank center 81, the relative tooth surface error 80 in Figure 12 underwent crown and root relief, indicated as tooth profile crowning 82. The relative tooth surface error along the crown and root lines was lifted, leaving the flank center conjugate. At the center of the face width, the crown relief amount 83 and root relief amount 84 are indicated. The tooth contact area 85 in Figure 11 did not visually change due to the crown and root relief, but the average point 77 in Figure 10 moved to the optimal center position 86 in Figure 12. The motion transmission graph shows a transmission error 88 of approximately 20 microradians.

[0036] Figure 13 shows a front view and a top view of the generating coordinate system for the present invention. The front view shows vector EX extending from the generating gear center to the cutter center, cutter radius vector RW, and vector RM extending from the generating gear center to the mid-face of the tooth root. The cutter profile 90 is shown as an ellipse due to its inclination required to cut the workpiece at a precise pressure angle. The axes X and Z of the generating system are also shown. The top view also shows vectors EX, RW, and RM. The axes Y and Z are also shown. The top view also has a simplified sketch of the workpiece 91 (gear member) to be generated. The pitch line 92 coincides with the Z axis of the generating system and lies in the generating plane. In this case in Figure 13, it represents generation on the pitch line of the gear member.

[0037] Solutions of the present invention for two generating gear configurations for non-generating gear members and special generating pinion members of a gear pair are shown in Figures 14(a) and 14(b). Figure 14(a) shows a top view of the configuration in a cutting machine for cutting a non-generating gear member. Gear 100 has a rotation axis 101 that intersects the generating gear axis 102 (identical to the cutting machine cradle axis) at point 103. Point 103 also symbolizes the X axis (oriented perpendicular to the page) of the cutting system. The root line 104 is identical to the Z axis 107 of the generating system, which is perpendicular to the generating gear axis 102 (Y axis). The circular peripheral cutter 105 is adjusted so that its tip circle (also known as the point diameter or point circle) is tangent to the root line 104. During the cutting process, the cutter 105 rotates around its axis 106 (shown only as a point in Figure 14(a)) to perform the cutting operation. No additional rotation or movement is required to form the flank surface of a non-generating gear with a linear contour. The gear member 100 is a non-generating member, and the pitch line 108 of the gear 100, oriented at a pitch angle 109, does not need to coincide with the generating gear plane, but can be located anywhere in the YZ plane. The principle of generation on the pitch line is established by the fact that the generated member (Figure 14(b)) uses the non-generating member as a generating gear.

[0038] Figure 14(b) shows a top view of the mechanical configuration of a special generating pinion member that meshes with a non-generating gear member. The pinion 110 has a rotation axis 111 that intersects the generating gear axis 112 (which is the same as the cutting machine cradle axis) at point 113. Point 113 also symbolizes the X axis of the generating system (oriented perpendicular to the page). Angle 118 is the same as the shaft angle between the pinion member and the gear member. Therefore, the pinion axis does not coincide with the Z axis of the generating system 117 if the shaft angle is not equal to 90°. The circular peripheral cutter 115 is adjusted so that the tip circle (also known as the tip circle, point diameter, or point circle) is tangent to the tooth root line 114. During the cutting process, the cutter 115 rotates around its axis 116 (shown only as a point in Figure 14(b)) to perform the cutting motion. Furthermore, the cutter itself rotates (i.e., moves) around the generating gear axis 112 (i.e., the generating roll) to create a modified involute tooth flank contour. The angle 119 between the pinion pitch line 120 and the generating gear axis 112 is equal to the pitch angle of the meshing gear. The pinion is generated on the pitch line of a conical generating gear that coincides with the pinion pitch line 120. The generating gear 121, which generally has a pitch angle of 90° (the angle between the Y and Z axes of the generating system), is conical here and resembles a meshing gear member.

[0039] Assuming that the pitch lines of the pinion and the generating gear coincide as described above, the pinion is generated on its pitch line when no meshing gear is generated and the generating gear of the pinion is conical, as shown in Figure 14(b). When one of two gear pair members is a non-generating gear (Figure 14(a)), the non-generating gear member must be used as the generating gear of the other gear pair member in order to achieve a conjugate gear pair that rolls smoothly on the pitch line during operation. This is called the kinematic coupling requirement. In this case, the ratio between the generating gear and the pinion is equal to the ratio given by the number of teeth on both the pinion and the generating gear.

[0040] The above discussion also applies to polishing. The outer tip of the polishing surface of the polishing wheel traces a tip circle, a point diameter, or a point circle.

[0041] Figure 15 shows a comparison of the transmission error of a root-line generated straight-tooth bevel gear pair (top figure) compared to a pitch-line generated straight-tooth bevel gear pair (bottom figure). The two graphs above show the Fast Fourier Transform results of root-line generated straight-tooth bevel gear pairs with gear torques of 10 Nm and 200 Nm. The first meshing order indicates the amplitude of the transmission error of the meshing teeth as it increases with the rotational frequency (a gear speed of 100 RPM with 17 gear teeth corresponds to a meshing frequency of 100... * (Related to 17 / 60 = 28.333 Hz). Higher-order transmission errors are 2 次 ~7 次 This is expressed by the degree of interlocking.

[0042] The two graphs at the bottom of Figure 15 show the transmission error amplitude for meshing orders of 1st order and above. The low torque of 10 Nm represents the noise critical state of transmission. The transmission error amplitude of pitch-line generated straight-tooth bevel gear pairs is within 10% of the root-line generated version. The higher torque of 200 Nm represents the average operating torque of straight-tooth bevel gear pairs. Even considering the surface deformation and tooth bending caused by the higher torque, the transmission error amplitude for 7th meshing order of pitch-line generated gear pairs is only 50% on average compared to root-line generated gear pairs.

[0043] Conjugate flank centers with relief at the apex and root are a preferred basis for improving power density, efficiency, and reducing vibration and noise during operation. Methods for providing relief at the apex and / or root are disclosed in U.S. Patent Application Publication No. 63 / 381,145, the entire disclosure of which is incorporated herein by reference. The present invention aims to solve the problem of creating flank surfaces of a straight bevel gear around an instantaneous axis of rotation that coincides with the pitch line of the straight bevel gear. The transformations are equal for the created pinion member and the created gear member. First, two main vectors describing the cutting machine configuration, the mean conical distance vector and the cutter radius vector, are established in their initial state: The mean conical distance vector RM0 from the machine center to the interdental surface of the tooth root is: HFpitch_heel=DOMNheel *(DPTHF+Fcl-x) (1) HFpitch_toe=DOMNtoe * (DPTHF+Fcl-x) (2) HFpt=(HFpitch_heel+HFpitch_toe) / 2 (3) RM0x=sign * (HFpt+DARC) * tan(ALFA) (4) RM0y = HFpt + DARC (5) RM0z=RMIR (6) Here, HFpitch_heel... The root of the tooth from the root to the pitch line in the heel. HFpitch_toe... The root of the tooth from the root to the pitch line in the toe. HFpt...the root of the tooth in the intermediate surface from the tooth root to the pitch line. DOMNheel...Normal module in heals DOMNtoe...Normal module in Tou DPTHF...Depth coefficient Fcl...Gap coefficient x...Contour shift coefficient RM0... Vector from the mechanical center to the interdental surface at the tooth root. SI... Lower flank sign (-1), upper flank sign (+1) DARC... Deeper cutting at the center using a cutter arc. ALFA... Pressure angle of each gear RMIR... Mean cone distance along the root angle

[0044] Cutter radius vector RW0: RW0x=0 (7) RW0y = DIAM / 2 (8) RW0z=0 (9) Here, RW0...Cutter radius vector from the center of the cutter to the root of the tooth on the intermediate surface. DIAM...Cutter diameter

[0045] The initial cutter axis points in the Y-axis direction of the generating system. The cutter axis matrix represents the cutter X-axis in the first column, the cutter Y-axis (axis of equal rotation) in the second column, and the cutter Z-axis in the third column. Cutter axis matrix TKA0 points in the positive X-axis direction of the generating system for upper flank cutting and in the negative X-axis direction of the generating system for lower flank cutting. TKA0 is established by a 90° rotation around the X-axis of the generating system, followed by a 90° rotation around the Y-axis of the generating system.

[0046]

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[0047] The following five transformation steps illustrate a stepwise approach to establishing the mean cone distance vector, cutter radius vector, and cutter axis matrix, which position the cutter axis circle tangentially to the root cone of a straight-tooth bevel gear and further align with the pitch line to arrive at a virtual generating gear plane. Step 6 discloses the calculation of the actual cutting machine settings from the vector and cutter matrix transformation results.

[0048] Step 1, Rotate the cutting edge normal vector to the dish angle: Initial cutting end vector point in the X-axis direction CNx=1 (11) CNy=0 (12) CNz=0 (13)

[0049] Rotation around the Z-axis with the dish angle DPHIX as the center.

[0050]

number

[0051] CN0 = ROT0 x CN (15) Here, CN...Initial cutting edge vector CN0...Cutting edge vector after dish angle rotation ROT0...Cutter blade dish angle rotation matrix DPHIX...Cutter dish angle

[0052] Step 2: Rotation of the cutter radius vector, cutting edge vector, and cutter axis matrix relative to the cutter angular position: Rotation around the Z-axis due to cutter angle PHIX

[0053]

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[0054] RW1 = ROT1 x RW0 (17) CN1 = ROT1 x CN0 (18) TKA1 = ROT1 x TKA0 (19) Here, ROT1... Rotation matrix of cutter pressure angle position PHIX...Cutter angle = Gear pressure angle + Dish angle RW1...Cutter radius vector after cutter pressure angle rotation CN1...Cutting edge vector after cutter pressure angle rotation TKA1...Cutter axis matrix after cutter pressure angle rotation

[0055] Step 3: Rotation of the cutter radius vector, cutting edge vector, and cutter axis matrix from a direction perpendicular to the pitch angle to a direction perpendicular to the root angle orientation: Rotation around the X-axis using GAMMAroot-GAMMApitch Pinion: GAMMApitch1 = arctan(sin(shaft angle) / (Z2 / Z1+cos(shaft angle))) (20) Gear: GAMMApitch2 = shaft angle - GAMMApitch1 (21) In the following derivation, GAMMApitch is commonly used for pinions and gears: GAMMAroot=GAMMApitch-arctan((HFpitch_heel-HFpitch_toe) / F (22)

[0056]

number

[0057] RW2 = ROT2 x RW1 (24) CN2 = ROT2 x CN1 (25) TKA2 = ROT2 x TKA1 (26) Here, ROT2... Rotation matrix of cutter rotation from a direction perpendicular to the pitch line to a direction perpendicular to the root line. GAMMAroot...Root angle of a pinion or gear component GAMMApitch...Pitch angle of pinion and gear components RW2...Cutter radius vector after rotation, perpendicular to the root angle. CN2...Cutting edge vector after GAMMAroot-GAMMApitch rotation TKA2...Cutter axis matrix after rotation of GAMMAroot-GAMMApitch

[0058] Step 4, Correction of pressure angle and lead angle: Flank line (lead) mismatch caused by changes in the cutter radius vector perpendicular to the root line (and the resulting cutting edge vector and cutter axis matrix): The cutting edge vector must not have a Z component. ANGYAX = arctan(CNz / CNx) (27)

[0059] The rotation of the generation system around the Y-axis, centered on ANGYAX(ROT3), eliminated the Franck line mismatch:

[0060]

number

[0061] RW3 = ROT3 x RW2 (29) CN3 = ROT3 x CN2 (30) TKA3 = ROT3 x TKA2 (31) Here, ROT3... Rotation matrix for cutter rotation to eliminate flank line mismatch. ANGYAX... Rotation that eliminates the Z component of the cutting edge vector. RW3... Rotated cutter radius vector to eliminate flank line mismatch CN3... Rotated cutting edge vector to eliminate flank line mismatch TKA3... Rotated cutter axis matrix to eliminate flank line mismatch

[0062] The cutting edge vector must be inclined by the gear pressure angle ALFA within the XY plane of the generation system.

[0063] ANGZAX=ALFA-sign * arctan(CNy / CNx)... Deviation of cutting edge angle in the XY plane from ALFA (32)

[0064] Rotation of the generation system centered around ANGZAX(ROT4) around the Z-axis eliminates contour discrepancies:

[0065]

number

[0066] RW4 = ROT4 x RW3 (34) CN4 = ROT4 x CN3 (35) TKA4 = ROT4 x TKA3 (36) ROT4... Rotation matrix for cutter rotation to eliminate contour mismatch. ANGZAX... Rotation to eliminate cutting edge vector deviation from ALFA in the XY plane RW4...Post-rotation cutter radius vector for eliminating contour mismatch CN4...Post-rotation cutting edge vector for eliminating contour mismatch TKA4...Post-rotation cutter axis matrix for eliminating contour mismatch

[0067] Step 5: Rotate the cutter to the spatial angle: Rotation of the cutter is required to generate an accurate slot width. In the case of up-cutting, the cutter is rotated in the positive direction around the generating gear axis (Y in FIG. 12) by 1 / 4 pitch (360° / ZG / 4), with corrections added to account for backlash, contour shift, and contour side shift.

[0068] In the case of down-cutting, the cutter is rotated in the negative direction around the generating gear axis (Y in FIG. 12) by 1 / 4 pitch (360° / ZG / 4), with corrections added to account for backlash, contour shift, and contour side shift. DSPG1=SPLF / 4 / RMIR...(37) DSPG2=-atan(x * DOMN * tan(ALFA) / RMIR)...(38) DSPG3=-sign * Y1 / 2 * DOMN / RMIR...(39) SPAG=360° / ZG / 4+DSPG1+DSPG2+DSPG3 (40)

[0069] [Formula]

[0070] RM5=ROT5xRM0 (42) RW5=ROT5xRW4 (43) CN5=ROT5xCN4 (44) TKA5=ROT5xTKA4 (45) Wherein, SPLF...Backlash DOMN...Normal module in the intermediate plane ZG...Number of teeth on the generating gear DSPG1...D-space angle considering backlash DSPG2...D-space angle considering contour shift DSPG3...D-space angle considering contour side shift SPAG...spatial angle ROT5... Rotation matrix for cutter rotation to correct spatial angles RM5...Vector from the mechanical center after spatial angular rotation to the interdental surface at the tooth root. RW5...Cutter radius vector after rotation to spatial angle CN5...Cutting edge vector after rotation to spatial angle TKA5...Cutter axis matrix after rotation to spatial angle

[0071] The spatial angle is half the slot width taper (i.e., half the slot width taper angle) and is established by the rotation of the cutter center roll position around the generator gear axis, while the workpiece is adjusted by a pitch cone in a tangential direction with respect to the generator gear plane (XZ plane).

[0072] Step 6, Machine settings calculation: The actual settings for the manufacturing machine are calculated from the mathematical transformation results as follows: EX5x = RM5x - RW5x (46) EX5y = RM5y - ​​RW5y (47) EX5z = RM5z - RW5z (48) ROOTA=GAMMAroot(49) Q0 = arctan(EX5x / EX5z) (50) J=Q0+arctan(TKA5(1,2) / TKA5(3,2)) (51) I = arccos(TKA5(2,2)) (52)

[0073]

number

[0074] XP=0 (54) XB = EX5y (55) EM=0 (56) RA = ZG / Z (57) Here, EX5...The vector from the origin of the XYZ system in Figure 12 to the center of the cutter (origin of the cutter radius vector) ROOTA...Mechanical root angle Q0...Center of the roll position J...Swivel angle I...Inclination angle S...Radial distance from the machine center to the cutter center XP...Machine center relative to the intersection of the pinion and gear axis on the axis of the current component. XB...Sliding base EM...Machine offset RA...Rolling Ratio ZG...Number of teeth on the generating gear Z...Current number of teeth on the gear

[0075] Non-generating gears, special generating pinions: A method has been developed for curved bevel gears and hypoid gears that allows gear members to be plunge-cut without a generation process, and for the pinion member to be generated by using a virtual replica of the non-generating gear member as the generating gear. To achieve this, the cutter is positioned to represent one tooth of the virtual generating gear that rotates around the generating gear axis like the original planar generating gear. Conventional art rules recommend that this process be applied only when the ratio between the pinion and the gear is greater than 3. The main advantage of this non-generating gear cutting is the reduction in cutting time by only 30%. In the case of straight bevel gears, the saving in cutting time can be as much as 50%. The combination of a non-generating gear and a special generating pinion that forms a conjugate pair is not known with respect to conventional straight bevel gears. The inventors have found that in order to achieve a conjugate rolling straight bevel gear pair in which the gear is not generated, it is necessary to apply a special spatial angular rotation to the pinion and gear members. As a result, the settings of both the pinion and gear members are changed. The transformations in steps 1-4 are identical to those shown for the generating gear pair. Steps 5, 5a, and 5b were developed for the pinion member cutting configuration, and steps 5c, 5d, and 5e were developed for the non-generating gear member cutting configuration.

[0076] The calculation for setting the pinion element for a set using non-generating gear elements is: The inventors have discovered that spatial angular rotation must be performed around the generating gear axis, and that the spatial angular quantity must be converted from the pitch plane to the generating gear plane:

[0077] Step 5a, rotation of the pinion shaft: In this step, the pinion axis is rotated in the YZ plane so that the shaft angle between the negative Z axis and the pinion axis is included:

[0078]

number

[0079] RMX=ROTXxRM0 (59) RWX = ROTX x RW4 (60) TKAX=ROTXxTKA4 (61)

[0080] Step 5b, Rotation to spatial angle: The spatial angle quantity must be converted from the pitch plane to the generator plane. SPAGX=SPAG / sin(GAMMApitch G) (62)

[0081] The spatial angular rotation is around the generating gear axis Y:

[0082]

number

[0083] RM5 = ROT5 x RMX (64) RW5 = ROT5 x RWX (65) TKA5 = ROT5 x TKAX (66)

[0084] Step 6a, Calculation of pinion machine settings: Except for the tooth root angle and roll ratio of the machine, the machine settings are calculated according to equations (34) to (40): ROOTA=90°-SHAFTANG (67) RA = Z² / Z¹ (68) Here, GAMMApitch G... Pitch angle of gear components Z1...Number of teeth on the pinion Z2...Number of teeth on the gear

[0085] The gear member setting calculation for a set using non-generated gear members is: Even for non-generating gears, spatial angular rotation must be performed around the generating gear axis, and the spatial angular quantity must be converted from the pitch plane to the generating gear plane.

[0086] Step 5c, rotation of the gear shaft: Rotation of the gear vector to align the gear axis with the Y-axis of the generating system (generating gear system):

[0087]

number

[0088] RMX=ROTXxRM0 (70) RWX = ROTX x RW4 (71) TKAX=ROTXxTKA4 (72)

[0089] Step 5d, spatial angle rotation: Spatial angular quantities must be converted from the pitch plane to the generator plane: SPAGX = SPAG / sin(GAMMApitch)

[0090] Spatial angular rotation around the generator gear axis (Y-axis):

[0091]

number

[0092] RMY = ROTY x RMX (74) RWY = ROTY x RWX (75) TKAY=ROTYxTKAX (76)

[0093] Step 5e, Spatial Angle Rotation: Reverse rotation of the gear vector to align the gear pitch line with the Y-axis of the generation system:

[0094]

number

[0095] RM5 = ROTX x RMY (78) RW5 = ROTX x RWY (79) TKA5=ROTXxTKAY (80)

[0096] Step 6b, Calculation of machine settings for non-generating gears: Except for the roll ratio, perform the machine setting calculations according to equations (34) to (40): RA=1 (81)

[0097] Figure 18 shows a straight bevel gear 19 with exaggerated generating planes. Generally, straight bevel gears have more than 100 planes. The gear 219 in Figure 18 has only three generating planes to more clearly show the formation of these planes. In the snapshot of Figure 18, the portion of the generating plane that the active cutting tool 220 is just cutting is marked as a dotted line surface. As the cutting tool 220 moves in the direction of the Vcut, the gear rotates in a generating rotation around its axis 221. As a result, contour lines 222 and 223 are not parallel. Therefore, a warp occurs in the generating plane surface 224. The cutting tool 225 forms a generating plane 226, extending from the tooth surface. The generating rotation rotates the gear such that the cutting tool 227 contacts the gear at contour line 228 and moves to contour line 229, which extends from the tooth surface. Also, lines 228 and 229 are not parallel. During the generation process, the cutter is also moved and rotated in directions 230, 231, and 232 shown on the cutter blade 225, which controls the geometric shape of the tooth profile and determines where the instantaneous axis of rotation between the cutter plane and the workpiece gear is located. This also determines where the instantaneous line of rotation between the generating gear and the workpiece gear is located. Changes in the position and direction of the instantaneous line of rotation also change the direction 233 of the generating plane. The generating plane may be parallel to the tooth root line 234 or it may be tapered.

[0098] Figure 19 shows a two-dimensional representation of the flank 240 of a straight-tooth bevel gear. The extended pitch line 243 intersects the intersection of the pinion and the gear shaft 244. The generating plane 241 is tapered and begins parallel to the root line 242, but its extensions 254 do not intersect at the intersection 244. The generating plane 241 near the pitch line is not parallel to the pitch line. The generating plane in Figure 19 is created by generation on the root line, which results in an additional contour that slides between the cutting tool and the generated flank in the direction 230 in Figure 18. As a result, an angle 246 is created between the generating plane intersecting the tip 247 and the tip line 247. The angle 246 can be 2° to 6° depending on the design.

[0099] Figure 20 shows a two-dimensional representation of the flank 250 of a straight-toothed bevel gear. All of the generating planes 251 are parallel to the extended pitch line 252 that intersects the intersection of the pinion and the gear shaft 253. The generating planes do not intersect the intersection 253. Such generating plane characteristics are typically given to bevel gears or face gears. The generating planes in Figure 20 cannot be formed by the pitch line generation of the straight-toothed bevel gear of the present invention.

[0100] Figure 21 shows a two-dimensional representation of a straight-toothed bevel gear flank 260. The generating planes 261 are not parallel but tapered in the direction of the tooth length, and all of their extensions 262 point to the intersection 263 between the pinion and the gear shaft, where they intersect with the extended pitch line 264. The generating planes in Figure 21 are created by generating along the pitch line.

[0101] Figure 22 shows a two-dimensional representation of the straight-toothed bevel gear flank 270. The generating plane 271 is not parallel but tapered, and its extension 275 does not point to the intersection 273 between the pinion and the gear shaft. Straight-toothed bevel gears having these generating planes are generated around the line between the root line 272 and the pitch line 274.

[0102] While the present invention has been described with reference to preferred embodiments, it should be understood that the present invention is not limited to these specific embodiments. The present invention is intended to include modifications that would be obvious to those skilled in the art, to which the subject matter belongs, without departing from the spirit and scope of the appended claims.

Claims

1. A method for manufacturing or machining teeth on a bevel gear, wherein the method is: To provide a bevel gear workpiece having a rotating shaft, To provide a material removal tool having a rotating axis, wherein the material removal tool has at least one material removal surface arranged around the tool's rotating axis, each of the at least one material removal surface has a tip, and the tip of the at least one material removal surface traces a tip circle of the tool. Rotating the material removal tool, Engaging the rotating material removal tool with the bevel gear workpiece, The method involves creating teeth on a bevel gear workpiece by rolling the material removal tool and the workpiece together in a predetermined relative rolling motion, wherein the predetermined relative rolling motion represents the workpiece rotating in mesh with a theoretically generated gear having teeth, and the teeth of the theoretically generated gear are represented by the at least one material removal surface of the tool. The aforementioned creation is carried out according to the creation configuration, and the creation configuration is, Positioning the material removal tool relative to the bevel gear workpiece such that the tip circle is in contact with the tooth root line of the bevel gear workpiece, A generation method comprising positioning the material removal tool with respect to the bevel gear workpiece such that the instantaneous rolling axis during generation is located on the pitch line of the workpiece.

2. The material removal tool includes a cutting tool having at least one cutting edge, according to claim 1.

3. The material removal tool comprises a polishing wheel, according to claim 1, the method for creating materials as described above.

4. The manufacturing or machining further comprises providing length crowning to the teeth of the workpiece, according to claim 1.

5. The method for creating a tooth according to claim 1, further comprising providing the tooth of the workpiece tooth with a crowning that includes at least one of a vertex relief and a root relief.

6. The method for creating a gear according to claim 1, wherein the bevel gear is a straight-toothed bevel gear.

7. The manufacturing method according to claim 6, wherein the straight-toothed bevel gear is a pinion member of a pair of straight-toothed bevel gears.

8. The gear generation method according to claim 7, wherein the pinion member is paired with a non-generating gear member to form a conjugate gear pair.

9. The creation method according to claim 1, wherein as a result of the creation, a creation plane is manufactured on the surface of the teeth of the created gear, and the creation plane is tapered along the length of the teeth such that when the created gear is arranged in mesh with a mating member having a rotation axis, the orientation of the creation plane is directed toward the intersection between the rotation axis of the created gear and the rotation axis of the mating member.

10. The generation method according to claim 9, wherein a reference extension line directed from the generation plane intersects at the intersection.

11. A gear pair comprising a gear member and a fitting pinion member, wherein the gear member and the pinion member are each manufactured or machined by the method described in claim 1.

12. A gear pair comprising a gear member and a fitting pinion member, wherein the gear member is non-manufactured and the pinion member is manufactured or machined by the method described in claim 1.

13. A control program having control commands for controlling a multi-axis computer-controlled gear manufacturing machine to perform the method according to claim 1, when executed on the machine.

14. A multi-axis computer-controlled gear manufacturing machine, wherein the computer control has control commands for performing the method according to claim 1.

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