Nodal line generation of straight bevel gear

Abstract

A method overcomes the defects associated with generating a tooth surface of a spur bevel gear (50) by relative rotation about a root line (54), and vice versa involves generating a spur bevel gear flank surface about an instantaneous axis of rotation coincident with a pitch line (57) of the spur bevel gear (50).

Description

TECHNICAL FIELD

[0001] The present invention relates to bevel gears, and in particular to the manufacture of straight bevel gear tooth flank surfaces by the generating method. BACKGROUND

[0002] Figure 1 One example of a straight bevel gear 2 is shown having a plurality of teeth 3, each tooth having a tooth tip surface 4, a root portion 5 and a pair of tooth flank surfaces 6. The area 7 between a pair of consecutive teeth is referred to as a tooth "slot" or tooth "space", where the root portion 5 coincides with the bottom of the tooth slot. For a pair of mating straight bevel gears (and most types of gears) (i.e. a gearset), typically one member of the pair (referred to as the pinion member) is smaller and has fewer teeth, while the larger mating member (referred to as the gear member) has more teeth. In most cases, the pinion member is the driving member of the gearset, and the gear member is the driven member of the gearset.

[0003] One method for producing bevel gears is the generating method. In the generating process, a rotating tool is fed to a predetermined depth within the workpiece. Once this depth is reached, the tool and workpiece are rolled together with a predetermined relative rolling motion (referred to as the generating roll), as if the workpiece were rotating in mesh with a theoretical generating gear whose teeth are represented by the stock removing surface of the tool. The profile shape of the teeth is formed by the relative motion of the tool and workpiece during the generating roll.

[0004] Straight bevel gears are typically manufactured using a mechanical double knife planer (e.g. US 842,455), interlocking cutters on a mechanical machine (e.g. US 2,567,273) or a single peripheral cutter on a free form CNC machine (such as US 7,364,391, the entire disclosure of which is incorporated herein by reference).

[0005] US 7,364,391 discloses a single side cutting method that rough cuts and finish cuts all of the first side surfaces of the teeth in a first step (e.g. Figure 16(a)) and then changes the position of the cutter to finish cut all of the second side surfaces of the teeth in a second step (e.g. Figure 16(b)). This two step method can be performed on a computer controlled multi-axis gear manufacturing machine such as the one disclosed in US 6,712,566, the entire disclosure of which is incorporated herein by reference. This two step method generates precise octoids and allows for flank shape modification. After heat treatment, the differential gear can be ground with a CBN grinding process in a similar manner to the cutting.

[0006] A suitable cutting tool for performing the above two step method is shown inFigure 17 A peripheral cutting tool 130, such as disclosed in US 6,712,566, is shown in FIG. 1, which illustrates the tool removably secured to a spindle 128 of a machine tool (not shown). The cutting tool 130 includes a head 132 having a plurality of stick blades 134. The tips of the cutting blades 134 trace out a blade tip circle, also referred to as a point diameter or point circle. A clamping block 136 is located above each stick blade. Figure 17 The tool in FIG. 1 has a top ring 138 located above the clamping block 136, which has integrated clamping screws 139.

[0007] The above cutting process must adjust the tool or blade movement to align with the dedendum angle of the spline. On a mechanical machine, the axis of the generating roll is also oriented collinearly with the dedendum line of the workpiece during the cutting of the spline. When a CNC freeform machine, such as disclosed in US 6,712,566, is used to manufacture a spur bevel gear with a single tool disk (one side at a time), the original process on a mechanical machine is effectively replicated, and the side generating is also around a momentary axis of rotation aligned with the workpiece dedendum line. If there is a dedendum angle not equal to zero, as in the case of a spur bevel gear, then the generated tooth surface that is relatively rotated around the dedendum line violates the law of gearing. Subsequently, such a generating setup causes the flank surface mismatch, which manifests as profile crowning and surface warping, and makes the surface significantly deviate from the conjugate surface. The result is small tooth contact and large motion transmission error. If the pinion member and the gear member do not roll on their pitch cones with the virtual generating gear plane during the manufacturing process, then the kinematic coupling condition between the pinion and the gear is not satisfied.

[0008] A spur bevel gear cut with the above method produces a generating mark that starts parallel to the dedendum line and then continues as a conical mark or line. However, in the prior art case of a spur bevel gear, the generating line does not all point to a point, such as, for example, at a point coinciding with the intersection between the pinion axis and the gear axis.

[0009] The generating mark (also referred to as a generating flat) is a result of the distance between two previous cutting blades in the head. As one blade passes along the face width of the gear to be cut, the generating motion rotates the gear, and the blade produces a warped surface along the face width. The next blade finds the gear rotated by an amount, and produces its own generating flat, which is adjacent to the generating flat produced by the previous blade.

[0010] The developable plane approximates the involute profile with a polygon. If the tool head has an infinite number of cutting blades, or is replaced by a grinding wheel, the profile will be involute, without any developable plane. Also, if the development rotation is infinitely slow and the tool RPM is infinitely high, the developable plane will effectively disappear.

[0011] In the past, spur gears were thought to have considerable motion error. The flank geometry is far from conjugate, but most spur gears are used for fairly simple applications. Today, manufacturers of high precision equipment like to use spur gears because of the reduced axial forces (compared to helical gears). Therefore, for spur gears, high power density, high efficiency, and low rolling noise become more important. SUMMARY

[0012] The present invention overcomes the deficiencies associated with developing a tooth surface by relative rotation about a base curve, and instead involves developing a spur gear tooth flank surface about an instantaneous axis of rotation coincident with a pitch line of the spur gear.

[0013] The present invention relates to a method of developing teeth on a bevel gear, the method comprising: providing a bevel gear workpiece having an axis of rotation, and providing a stock removal tool having an axis of rotation, wherein the stock removal tool has at least one stock removal surface arranged about the tool axis of rotation, and wherein each of the at least one stock removal surfaces has a tip. The tips of the at least one stock removal surfaces trace out a tip circle of the tool. The stock removal tool is rotated, and the stock removal tool is then engaged with the bevel gear workpiece to develop teeth on the bevel gear workpiece by rolling the stock 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 theoretical developed gear having teeth represented by the at least one stock removal surface of the tool.

[0014] The development is performed in accordance with a development setup comprising: positioning the stock removal tool relative to the bevel gear workpiece such that the tip circle of the tool is tangential to a base curve of the bevel gear workpiece; and positioning the stock removal tool relative to the bevel gear workpiece such that the instantaneous axis of rolling lies at a pitch line of the workpiece or at a pitch line of the theoretical developed gear during the development. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 An example of a spur bevel gear is shown.

[0016] Figure 2 A three-dimensional representation of a developed gear plane and a pinion pitch cone that does not roll on the developed gear plane is shown.

[0017] Figure 3Three-dimensional representation of a gear plane and gear pitch cone is shown, where the pitch cone does not roll on the gear plane.

[0018] Figure 4 Three-dimensional representation of a pinion pitch cone rolling on top of a virtual gear plane and a gear pitch cone rolling from below on a virtual gear plane.

[0019] Figure 5 Three-dimensional representation of a pinion rolling on top of a virtual gear and a gear rolling from below on a virtual gear.

[0020] Figure 6 Top view of a cutting machine setup is shown, where the cutter rolls on the root line of the gear.

[0021] Figure 7 Gear contact analysis of a spur bevel gear set is shown, where both the gear member and pinion member are generated by rolling on the root line of the respective member.

[0022] Figure 8 Gear contact analysis of a spur bevel gear set is shown, where both the gear member and pinion member are generated by rolling on the root line of the respective member, and profile crowning correction is applied.

[0023] Figure 9 Top view of a cutting machine setup is shown, where the cutter rolls on the pitch line of the gear.

[0024] Figure 10 Gear contact analysis of a spur bevel gear set is shown, where both the gear member and pinion member are generated by rolling on the pitch line of the respective member.

[0025] Figure 11 Gear contact analysis of a spur bevel gear set is shown, where both the gear member and pinion member are generated by rolling on the pitch line of the respective member, and length crowning is applied.

[0026] Figure 12 Gear contact analysis of a spur bevel gear set is shown, where both the gear member and pinion member are generated by rolling on the pitch line of the respective member, and length crowning and addendum modification is applied on both members.

[0027] Figure 13 Conical gear generation coordinate system is shown.

[0028] Figure 14(a) shows a gear member non-generated setup.

[0029] Figure 14(b) shows a pinion member special generated setup.

[0030] Figure 15 A comparison of the motion transmission error of a pair of involute straight bevel gears to a pair of generated straight bevel gears is shown.

[0031] Figures 16(a) and 16(b) show a two-step method for manufacturing straight bevel gears.

[0032] Figure 17 A peripheral cutting tool for performing the two-step method of Figures 16(a) and 16(b) is shown.

[0033] Figure 18 A straight bevel gear with exaggerated generated planes is shown.

[0034] Figure 19 A two-dimensional representation of straight bevel gear flanks with generated planes that are conical and parallel to the root line at the start, but whose extensions do not intersect at the intersection point is shown.

[0035] Figure 20 A two-dimensional representation of straight bevel gear flanks with generated planes that are parallel to an extended pitch line that intersects the intersection point of the pinion and the gear axis is shown. The generated planes do not intersect the intersection point.

[0036] Figure 21 A two-dimensional representation of straight bevel gear flanks with generated planes that are not parallel but conical and whose extensions extend to the intersection point between the pinion and the gear axis, where they intersect the extended pitch line is shown.

[0037] Figure 22 A two-dimensional representation of straight bevel gear flanks with generated planes that are not parallel but conical and whose extensions do not extend to the intersection point between the pinion and the gear axis is shown. DETAILED DESCRIPTION

[0038] The terms "invention," "the invention," and "the present invention" used in this specification are intended to refer broadly to all of the subject matter of this specification and any patent claims below. Statements containing these terms should be understood not to limit the subject matter described herein or to limit the meaning or scope of any patent claims below. Furthermore, this specification does not seek to describe or limit the subject matter covered by any claims in their specific forms or in relation to any particular embodiments. The subject matter should be understood by reference to the entire description of the application, the drawings, and any claims attached hereto. The present invention can be used in other constructions and can be practiced or implemented in various ways. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. It is further noted that the use of "including," "comprising," or "having" and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. Unless otherwise indicated herein, the use of letters such as A, B, C, etc., to denote various components is intended to denote various, like components in the description and / or drawings.

[0039] The details of the application will now be discussed with reference to the drawings, which are by way of example only. In the drawings, like reference numerals will refer to like features or components. The size and relative sizes of certain aspects or elements can be exaggerated for clarity or detailed explanation purposes. For better understanding and ease of observation, doors, housings, internals or externals, etc. can be omitted from the drawings.

[0040] The use of “including,” “having,” “containing,” and “comprising” and variations thereof herein are meant to encompass the items listed thereafter and equivalents thereof as well as additional items. Use of letters is for identification only and is not meant to denote that a component should be executed in a particular order. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise, and the term “and / or” includes one or more of the associated listed items, as well as their combination.

[0041] Although references in the following description to directions, such as upper, lower, upward, downward, rearward, bottom, top, front, rear, etc., can refer to directions in the drawings, this is only for convenience in

[0042] Figure 2 A pinion member pitch cone 10 is shown passing through a virtual developed gear plane 12 from above. The angle 9 between the pinion axis 21 and the developed gear plane 12 is equal to the pinion’s dedendum angle.

[0043] Figure 3 A gear member pitch cone 11 is shown passing through a virtual developed gear plane 12 from below. The angle 8 between the gear axis 16 and the developed gear plane 12 is equal to the gear’s dedendum angle. In operation of the pinion and gear ( Figure 4 ), the angle between the pinion axis 21 and the gear axis 16 must be equal to the shaft angle 15, which is the pinion’s pitch angle 13 plus the gear’s pitch angle 14. This means that, in operation, the pinion’s pitch angle rolls over the gear’s pitch angle, but in manufacturing, the dedendum angle rolls over the connected developed gear, which results in a conjugate mismatch of the flank surfaces.

[0044] Figure 4The pitch cone 10 of the pinion and the pitch cone 11 of the bevel gear are also shown. The disc 12 between them is a virtual developed gear plane. If the developed plane 12 is rotated around its axis 26, the cone above the disc 10 will rotate around its axis 21 and the cone below the disc 11 will rotate around its axis 16 and both cones will roll on the disc 12 without slipping. The ratio between the rotations of the cones is calculated as: Ratio = sin (pinion pitch cone angle 13) / sin (gear pitch cone angle 14).

[0045] In this case it is: Pinion pitch cone angle 13 + gear pitch cone angle 14 = shaft angle 15.

[0046] Only gear sets where the pitch cones roll on the developed gear plane without slipping satisfy the gear drive law and have conjugate bases.

[0047] Figure 5 A developed gear 17 is shown, which is the developed disc 12 after the teeth have been added ( Figure 4 ). The teeth and the grooves have a trapezoidal profile and taper from the outside towards the center 23. This is an exact bevel gear similar to the developed rack of an involute spur gear.

[0048] Figure 6 A prior art spur bevel gear development by rolling on the root line is shown. As an example, according to Figure 6 The gear set manufactured can have the following basic parameters: Number of teeth of pinion member = 15; Number of teeth of gear member = 17; Tooth face width = 20 mm; Profile offset = 0.0; Profile depth factor = 1.0; Root gap = 0.5 mm; Backlash = 0.1 mm; Pinion face angle = 51.40°; Gear face angle = 58.57°; Pinion fillet edge radius = 0.5 mm; Gear fillet edge radius = 0.5 mm; Pinion pressure angle = 20°; Gear pressure angle = 20°; Shaft angle = 90°; Gear outside pitch diameter = 100.00 mm; Outside peripheral cutter diameter 228.6 mm.

[0049] Figure 6A top view showing the generating setup in a cutting machine (e.g., US 6,712,566). The workpiece gear assembly 20 has a rotation axis 21 that intersects the generating gear axis 22 (which is the same as the axis of the cutting machine carriage) at point 23. The root line 24 of the gear 20 intersects the generating gear axis 22 and is perpendicular to it. A circular peripheral cutter 25 is adjusted such that the insert tip circle 25 is tangent to the root line 24. During the cutting and generating process, the cutter 25 rotates around its axis 26 (in... Figure 5 The tool (shown only as a point) rotates to perform the cutting action. Furthermore, the tool itself rotates about the generating gear axis 22, while the working gear rotates about its axis 21 (i.e., the generating roller) to generate the octagonal tooth profile. The rotation angle of the working gear is equal to the rotation angle of the generating gear multiplied by the number of teeth of the generating gear, and then divided by the number of teeth of the working gear. This setup (where the root line 24 is adjusted to coincide with the instantaneous rolling axis (i.e., the line where the two bodies contact each other and roll onto each other without slippage)) is consistent with prior art straight bevel gear manufacturing. Figure 6 In the instantaneous rolling axis, the rolling axis is in the generating plane and matches the Z-axis.

[0050] Figure 7 The text shows the data based on... Figure 6 Analysis of the tooth contact between the generated pinion and gear. The corrected surface 30 shows a deviation from the conjugate. A profile convexity 38 appears due to generation along the tooth root line. The tooth contact 31 (using a 0.006 mm thick dummy marker compound film) extends across the entire working area. This means that the areas above and below the contact 31 (areas 32 and 33) are lost due to mechanical and / or kinematic undercuts in the pinion component (area 32) and gear component (area 33). Even under high loads, the tooth contact does not extend into areas 32 and 33. Figure 7 In this example, 40% of the possible working profile has been lost. The contact ratio between adjacent teeth drops from the theoretical value of 1.35 to below 1.0, which means that the contact transition from one pair of teeth to the next cannot maintain any overlap, resulting in large effective transfer error, loud operation, and high load concentration. Figure 7 The motion transmission curves in Figure 34 show the motion transmission of three consecutive tooth pairs. The two gaps between the three parabolic curves 35, 36, and 37 also reflect a transmission error greater than 500 microradians.

[0051] Attempts to eliminate profile convexity by using cutting inserts with curved profiles do not work well, such as... Figure 8 As shown. Contour convexity 38 ( Figure 7 It was not eliminated, but only as Figure 8The reduction shown in 40 results in a negative length convexity 41 as a side effect. The resulting tooth contact 42 has poor shape and position, and motion transmission curves 43 show motion error curves 46, 47, and 48 greater than 500 microradians. The loss areas of working profiles 44 and 45 are the same as those before correction in regions 32 and 33. It seems impossible to achieve conjugate surfaces if the tooth flank surface is developed to apply rolling along the tooth root line. Conjugate tooth flank surfaces are needed as a starting point for developing advanced and optimized spur bevel gear designs.

[0052] Figure 9 The present invention solution for generating rolling on nodal lines is shown in the figure. Used to generate Figure 9 The straight bevel gear set has the characteristics of being designed for Figures 2 to 4 The tooth root line in the diagram is the same as the basic parameters listed for the gear set. This invention is applicable to the production of bevel gears from gear blanks (e.g., rough cutting) and the machining of the teeth of the rough-cut gears (e.g., grinding, finishing, etc.). A control program and a multi-axis computer-controlled gear manufacturing machine are also envisioned, having control instructions for executing the method of this invention.

[0053] Figure 9 A top view of the generating setup in the cutting machine is shown. The workpiece gear 50 has a rotation axis 51 that intersects the generating gear axis 52 (which is the same as the axis of the cutting machine carriage) at point 53. Point 53 also represents the X-axis of the generating system (perpendicular to the page orientation). The pitch line 57 of the gear 50 intersects the generating gear axis 52 at center point 53 in the generating gear coordinate system and is perpendicular to the generating gear axis. The insert tip circle (also called the tip diameter, point circle, or point circle) of the circular peripheral tool 55 is adjusted such that it is tangent to the root line 54. During the cutting and generating process, the tool 55 rotates around its axis 56 (in... Figure 9 The tool (shown only as a point in the diagram) rotates to perform the cutting action. Furthermore, the rotating tool itself rotates (i.e., moves) about the generating gear axis 52 (i.e., the generating roller) to generate the October tooth profile. This arrangement (where the root line 54 is tangent to the tool insert tip circle and the pitch line 57 is oriented to coincide with the instantaneous rolling axis (i.e., the line where the two bodies (workpiece and generating gear) contact each other and roll onto each other without slippage) is a result of the invention, where the instantaneous rolling axis is oriented separately from the tool circle. Figure 9 In the instantaneous rolling axis, the instantaneous rolling axis is in the developing plane (XZ) and matches the Z-axis.

[0054] The above discussion also applies to grinding. The outer tip of the grinding wheel's grinding surface delineates the tooth tip circle, dot diameter, or dot circle.

[0055] Figure 10 The text shows the data based on... Figure 9Tooth contact analysis of the generated pinion and gear. The corrected surface 60 showed no measurable deviation from the conjugate. As a result, proper generating at the pitch line leads to a conjugate correction with theoretically zero deviation 68. Tooth contact 61 (using a 0.006 mm thick dummy marker compound film) extends across the entire working area. Compared to the 40% loss in prior art tooth root generating methods, the loss areas 62 and 63 above and below contact 61 have been reduced to 28% of the lateral areas.

[0056] use Figure 10 The pitch line generating gear set fully achieves the theoretical contact ratio of 1.35 between adjacent teeth. The calculated motion transmission curves of the three consecutive tooth pairs 65, 66, and 67, shown in Figure 64, only show the transmission error varying within approximately 3 microradians. Figure 10 The conjugate tooth flank surface is a preferred starting point for developing advanced and optimized spur bevel gear designs.

[0057] Figure 11 This shows the effect after adding length convexity 71. Figure 10 Gear contact analysis of the gear set. The modified surface 70 shows the amount of trimming from the center of the tooth width towards the toe and heel. The contact area 72 is located between the toe and heel, but the profile convexity 73 remains approximately zero, which may result in edge contact along the tooth tip and root. The possibility of tip and / or edge contact is also reflected by the off-center average point 77 (optimal motion transmission point). The average point applies to the entire profile (in... Figure 11 The tooth contact pattern in the diagram extends along the inherent contour direction (a line or cross section), and is shown at any position. Motion transmission curve 75 shows the maximum transmission error 76, which is less than 10 microradians.

[0058] To maintain the conjugate tooth flank center 81 Figure 12 The correction 80 in the diagram receives the tooth tip and root trimmings, which are shown as profile convexity 82. The corrections along the tooth tip and root lines are raised and conjugate away from the tooth flank center. At the center of the tooth width, the tooth tip trimming amount 83 is shown, and the tooth root trimming amount 84 is shown. Figure 11 The tooth contact 85 in the middle was not significantly changed due to the trimming of the tooth crest and root, but Figure 10 The average point 77 in the middle has moved to Figure 12 The optimal center position is shown in Figure 86. The motion transmission curve shows a transmission error of approximately 20 microradians.

[0059] Figure 13An elevational view and a top view of the developable coordinate system of the present invention are shown. The elevational view shows the vector EX extending from the center of the developable gear to the center of the cutter, the cutter wheel diameter RW, and the vector RM extending from the center of the developable gear to the middle of the root at the dedendum. The cutter profile 90 is shown as an ellipse due to the tilt required for the correct pressure angle of the cutting workpiece. The axes X and Z of the developable system are also shown. The top view also shows the vectors EX, RW, and RM. In addition, the axes Y and Z are shown. The top view also has a simplified sketch of the workpiece 91 (gear member) to be developed. The pitch line 92 matches the Z axis of the developable system and lies in the developable plane. Figure 13 The current situation in the equation represents the development on the pitch line of the gear member.

[0060] Figures 14(a) and 14(b) show the inventive solution for two developable gear settings of a non-developable gear member and a special developed pinion gear member of a gear set. Figure 14(a) shows a top view of the setting in the cutting machine for cutting a non-developable gear member. The gear 100 has a rotation axis 101 which intersects the developable gear axis 102 (which is the same as the cutting machine carriage axis) at point 103. Point 103 also represents the X axis of the cutting system (oriented perpendicular to the page). The dedendum line 104 is the same as the Z axis 107 of the developable system, which is perpendicular to the developable gear axis 102 (Y axis). The circular peripheral cutter 105 is adjusted so that the insert tip circle (also called point diameter or point circle) is tangent to the dedendum 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 action. No additional rotation or movement is required to form the flank surfaces of the non-developable gear with straight profile. The gear member 100 is a non-developable member, and the pitch line 108 of the gear 100 oriented with the pitch angle 109 does not have to match the developable gear plane, but can be located anywhere in the Y-Z plane. The rationale for developing on the pitch line is established by the fact that the developed member (Figure 14(b)) uses the non-developable member as a developable gear.

[0061] Figure 14(b) shows a top view of the machine setup for a special involute pinion member mated with a non-involute gear member. Pinion 110 has a rotation axis 111 that intersects the involute gear axis 112 (which is the same as the cutting machine carriage axis) at point 113. Point 113 also represents the X-axis of the involute system (oriented perpendicular to the page). Angle 118 is the same as the shaft angle between the pinion member and the gear member. Thus, in the case where the shaft angle is not equal to 90°, the pinion axis will not match the Z-axis of the involute system 117. Circular peripheral cutter 115 is adjusted so that the blade tip circle (also known as the tip diameter or point circle) is tangent to the root line 114. During the cutting process, cutter 115 rotates about its axis 116 (shown only as a point in Figure 14(b)) to perform the cutting action. In addition, the cutter itself rotates (i.e., moves) about the involute gear axis 112 (i.e., the involute roll) in order to involute the modified involute tooth profile. The angle 119 between the pinion pitch line 120 and the involute gear axis 112 is equal to the pitch angle of the mating gear. The pinion is involuted on the pitch line of the conical involute gear, which coincides with the pinion pitch line 120. The involute gear 121, which normally has a 90° pitch angle (the angle between the Y-axis and the Z-axis of the involute system), is now conical and resembles the mating gear member.

[0062] Considering the coincident pitch lines of the pinion and the involute gear as described above, in those cases where the mating gear is non-involute and the involute gear for the pinion is conical, the pinion is involuted on the pitch line of the pinion, as shown in Figure 14(b). If one of the two gearset members is non-involute (Figure 14(a)), it is necessary to use the non-involute member as the involute gear for the other gearset member in order to achieve a conjugate gearset that rolls on the pitch line without slipping in operation. This is referred to as the kinematic coupling requirement. In this case, the ratio between the involute gear and the pinion is equal to the ratio given by the number of teeth of both the pinion and the involute gear.

[0063] The above discussion applies equally to grinding. The outer tip of the grinding wheel abrasive surface traces the tip circle, tip diameter, or point circle.

[0064] Figure 15 A comparison of the transmission error of a root line involute spur gearset (top graph) versus a pitch line involute spur gearset (bottom graph) is shown. The two graphs on top show the fast Fourier transform results for a root line involute spur gearset with gear torques of 10 Nm and 200 Nm. The first order of engagement shows the transmission error amplitude versus rotational frequency for the meshing teeth (100 RPM gear speed with 17 gear teeth and a meshing frequency of 100 17 / 60 = 28.333 Hz correlation). Higher orders of transmission error are shown for the second through seventh orders of engagement.

[0065] Figure 15 The two graphs at the bottom show the transmission error amplitudes for the first and higher orders of engagement. The low torque of 10 Nm represents the noise critical state of transmission. The transmission error amplitudes of the pitch line developed straight bevel gear set are in the range of 10% of the root line developed straight bevel gear set. The higher torque of 200 Nm represents the average operating torque of the straight bevel gear set. Even considering the surface deformation and tooth bending caused by the higher torque, the transmission error amplitudes of the seven orders of engagement of the pitch line developed gear set are only 50% on average compared to the root line developed gear set.

[0066] The conjugate tooth side center with fillets at the addendum and dedendum is the preferred basis for increasing power density, increasing efficiency, and reducing vibration and noise during operation. A method of addendum and / or dedendum filleting is disclosed in US 63 / 381,145, the entire disclosure of which is incorporated herein by reference. The present invention aims to solve the task of developing the straight bevel gear tooth side surface around the instantaneous rotation axis coinciding with the pitch line of the straight bevel gear. The transformation is equal for both the developed pinion member and the developed gear member. At the beginning, two main vectors of the cutting machine setup are described - the mean cone distance vector and the tool vector in its initial state are established: The mean cone distance vector RM0 from the machine center to the tooth surface at the dedendum: 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); where: HFpitch_heel is the dedendum height from the dedendum to the pitch line at the heel, HFpitch_toe is the dedendum height from the dedendum to the pitch line at the toe, HFpt is the dedendum height from the dedendum to the pitch line at the middle, DOMNheel is the normal module at the heel, DOMNtoe is the normal module at the toe, DPTHF is the depth factor, Fci is the gap factor, x is the profile shift factor, RM0 is the vector from the machine center to the tooth surface at the root, SI corresponds to the sign of the lower tooth side (-1) and the upper tooth side (+1), DARC is the deeper cut at the center due to the cutting arc, ALFA is the pressure angle of the respective gear, RMIR is the average conicity along the dedendum angle.

[0067] Tool vector radius RW0: RW0x = 0 (7); RW0y = DIAM / 2 (8); RW0z = 0 (9); where: RW0 is the tool vector radius from the tool center to the dedendum at the mean surface, DIAM is the tool diameter.

[0068] The initial tool axis is pointing in the Y-axis direction of the developable system. The tool axis matrix is representing the tool X-axis in the first column, the tool Y-axis (equal to the axis of rotation) in the second column, and the tool Z-axis in the third column. The tool axis matrix TKA0 is pointing the tool Y-axis in the positive X-axis direction of the developable system for the upper tooth side cutting and in the negative X-axis direction of the developable system for the lower tooth side cutting. TKA0 is established by rotating 90° around the X-axis of the developable system and then 90° around the Y-axis of the developable system: (10).

[0069] The following five transformation steps show a step-by-step approach to establish the average conicity vector, the tool vector radius, and the tool axis matrix, which positions the tool axis circle tangent to the dedendum cone of the straight bevel gear but reaches a virtual developable tooth plane aligned with the generatrix. Step 6 discloses the calculation of the actual cutting machine settings from the vector and tool matrix transformation results.

[0070] Step 1, the cutting edge normal vector is rotated to the disc angle: The initial cutting edge vector point in the X-axis direction: CNx = 1 (11); CNy = 0 (12); CNz = 0 (13).

[0071] Rotated around the Z-axis about the disc angle DPHIX, (14). CN0 = ROT0 x CN (15); where: CN is the initial cutting edge vector, CN0 is the cutting edge vector after the disk angle rotation, ROT0 is the rotation matrix for the tool insert disk angle, DPHIX is the tool disk angle.

[0072] Step 2, tool vector, cutting edge vector, and tool axis matrix rotation to tool angle position: Rotate tool angle PHIX about Z axis, (16) ; RW1 = ROT1 x RW0 (17) ; CN1 = ROT1 x CN0 (18) ; TKA1 = ROT1 x TKA0 (19) ; where: ROT1 is the rotation matrix for the tool pressure angle position, PHIX is tool angle = gear pressure angle + disk angle, RW1 is the tool vector after tool pressure angle rotation, CN1 is the cutting edge vector after tool pressure angle rotation, TKA1 is the tool axis matrix after tool pressure angle rotation.

[0073] Step 3, tool vector, cutting edge vector, and tool axis matrix rotation from perpendicular to pitch angle to perpendicular to root angle position: Rotate GAMMAroot - GAMMApitch about X axis, Pinion: GAMMApitch1 = arctan(sin(Shaft Angle) / (Z2 / Z1 + cos(Shaft Angle))) (20) ; Gear: GAMMApitch2 = Shaft Angle - GAMMApitch1 (21).

[0074] For the following derivations, GAMMApitch is used for both pinion and gear: GAMMAroot = GAMMApitch - arctan((HFpitch_heel - HFpitch_toe) / F (22) ; (23) ; RW2 = ROT2 x RW1 (24); CN2 = ROT2 x CN1 (25); TKA2 = ROT2 x TKA1 (26); where: ROT2 is the rotation matrix for the tool rotation from perpendicular to the pitch line to perpendicular to the root line, GAMMAroot is the root angle of the pinion or tooth member, GAMMApitch is the pitch angle of the pinion and tooth member, RW2 is the tool vector after rotation perpendicular to the root angle, CN2 is the cutting edge vector after GAMMAroot-GAMMApitch rotation, TKA2 is the tool axis matrix after GAMMAroot-GAMMApitch rotation.

[0075] Step 4, Pressure and Lead Angle Correction: Tooth side line (lead) mismatch caused by the change in the tool vector (and with it the cutting edge vector and tool axis matrix) perpendicular to the root line: The cutting edge vector must have no Z component, ANGYAX = arctan(CNz / CNx) (27).

[0076] Rotating about the Y axis of the developable system by approximately ANGYAX (ROT3) eliminates the tooth side line mismatch: (28); RW3 = ROT3 x RW2 (29); CN3 = ROT3 x CN2 (30); TKA3 = ROT3 x TKA2 (31); where: ROT3 is the rotation matrix for the tool rotation to eliminate the tooth side line mismatch, ANGYAX is the rotation to eliminate the Z component of the cutting edge vector, RW3 is the tool vector after rotation to eliminate the tooth side line mismatch, CN3 is the cutting edge vector after rotation to eliminate the tooth side line mismatch, TKA3 is the tool axis matrix after rotation to eliminate the tooth side line mismatch.

[0077] The cutting edge vector must be tilted by the gear pressure angle ALFA in the X-Y plane of the developable system; ANGZAX = ALFA - sign arctan(CNy / CNx) is the deviation of the cutting edge angle in the X-Y plane from ALFA (32).

[0078] Rotating about the Z axis of the develop system by about ANGZAX (ROT4) eliminates the profile mismatch: (33); RW4 = ROT4 x RW3 (34); CN4 = ROT4 x CN3 (35); TKA4 = ROT4 x TKA3 (36); ROT4 is the rotation matrix used to rotate the tool to eliminate the profile mismatch, ANGZAX is the rotation to eliminate the deviation of the cutting edge vector from ALFA in the X-Y plane, RW4 is the tool vector after rotation to eliminate the profile mismatch, CN4 is the cutting edge vector after rotation to eliminate the profile mismatch, TKA4 is the tool axis matrix after rotation to eliminate the profile mismatch.

[0079] Step 5, Rotate the tool to the space angle: The tool needs to be rotated in order to generate the correct slot width. For the upper cut, rotate the tool about the develop gear axis (Y in Figure 12 ) in the positive direction by one quarter pitch (360° / ZG / 4), plus corrections for backlash, profile shift, and profile shift.

[0080] For the lower cut, rotate the tool about the develop gear axis (Y in Figure 12 ) in the negative direction by one quarter pitch (360° / ZG / 4), plus corrections for backlash, profile shift, and profile 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); (41); RM5 = ROT5 x RM0 (42); RW5 = ROT5 x RW4 (43); CN5 = ROT5 x CN4 (44); TKA5 = ROT5 x TKA4 (45); where: SPLF is the tooth gap, DOMN is the normal modulus at the mean face, ZG is the number of teeth of the generated gear, DSPG1 is the D-space angle accounting for the tooth gap, DSPG2 is the D-space angle accounting for profile shift, DSPG3 is the D-space angle accounting for profile side shift, SPAG is the space angle, ROT5 is the rotation matrix for tool rotation to correct the space angle, RM5 is the vector from the machine center to the tooth midface at the dedendum after rotation to the space angle, RW5 is the tool vector path after rotation to the space angle, CN5 is the cutting edge vector after rotation to the space angle, TKA5 is the tool axis matrix after rotation to the space angle.

[0081] The space angle is half of the slot width taper (i.e., half of the slot width taper angle) and is established by the rotation of the tool center roll position about the generated gear axis while the workpiece is adjusted by the pitch cone tangent to the generated gear plane (X-Z plane).

[0082] Step 6, Machine Setup Calculation: The setup of the real manufacturing machine is 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) ; S = (53); XP = 0 (54); XB = EX5y (55); EM = 0 (56); RA = ZG / Z (57); in: EX5 is from Figure 12 The vector from the origin of the XYZ system to the tool center (the origin of the tool radius vector). ROOTA is the machine tooth root angle. Q0 is the center of the scroll position. J is the knife angle. I is the tilt angle. S is the radial distance from the machine center to the tool center. XP is the point where the machine center intersects the pinion and gear axis at the axis of the current component. XB is a sliding base. EM stands for Machine Offset. RA stands for rolling ratio. ZG is the number of teeth in the generating gear. Z is the current number of teeth on the gear.

[0083] Non-generating gears and special generating pinions.

[0084] In spiral bevel gears and quasi-hyperboloid gears, a method has been developed that allows for infeed cutting of gear components without any generating process, and generates the pinion component by using a virtual replica of the non-generating gear component as the generating gear. To achieve this, the tool is positioned to represent a tooth of the virtual generating gear, which rotates around the generating gear axis as the original planar generating gear. Prior art guidelines recommend applying this process only when the ratio between the pinion and gear is greater than three. The main advantage of this non-generating gear cutting is a 30% reduction in cutting time. For spur bevel gears, the cutting time savings can be as high as 50%. In the prior art, the combination of the non-generating gear and the specially generated pinion forming a conjugate pair is unknown for spur bevel gears. The inventors have discovered that to achieve a conjugate rolling spur bevel gear set in which the gears are non-generating, a special spatial angular rotation is required on the pinion and gear components. Therefore, the setup of the two components (pinion and gear) will change. The transformations in steps 1 to 4 are the same as those shown for generating gear sets. Steps 5, 5a, and 5b have been developed for the pinion component cutting setup, and steps 5c, 5d, and 5e have been developed for the non-generating gear component cutting setup.

[0085] Pinion member setting calculation for gear set with non-involute gear members.

[0086] The inventors found that a spatial angle rotation must be performed around the generating gear axis, where the spatial angle quantity must be converted from the pitch plane to the generating gear plane.

[0087] Step 5a, rotation of pinion axis: In this step, the pinion axis is rotated in the Y-Z plane to include the shaft angle between the negative Z axis and the pinion axis: (58); RMX = ROTX x RM0 (59); RWX = ROTX x RW4 (60); TKAX = ROTX x TKA4 (61).

[0088] Step 5b, rotation to spatial angle: The spatial angle quantity must be converted from the pitch plane to the generating gear plane; SPAGX = SPAG / sin(GAMMApitch G) (62).

[0089] The spatial angle rotation is around the generating gear axis Y: (63); RM5 = ROT5 x RMX (64) ; RW5 = ROT5 x RWX (65) ; TKA5 = ROT5 x TKAX (66).

[0090] Step 6a, machine setting calculation for pinion: Machine setting calculation according to equations (34) to (40), except for the machine dedendum angle and the roll ratio: ROOTA = 90°-SHAFTANG (67) ; RA = Z2 / Z1 (68) ; where: GAMMApitch G is the pitch angle of the gear member, Z1 is the number of teeth of the pinion, Z2 is the number of teeth of the gear.

[0091] Pinion member setting calculation for gear set with non-involute gear members.

[0092] Likewise, for non-involute gears, a spatial angle rotation must be performed around the axis of the generating gear, where the spatial angle quantity must be converted from the pitch plane to the generating gear plane.

[0093] Step 5c, rotation of the gear axis: Rotation of the gear vectors to match the gear axis with the Y axis of the generating system (generating gear system): (69) ; RMX = ROTX x RM0 (70) ; RWX = ROTX x RW4 (71) ; TKAX = ROTX x TKA4 (72).

[0094] Step 5d, spatial angle rotation: The spatial angle quantity must be converted from the pitch plane to the generating gear plane: SPAGX = SPAG / sin(GAMMApitch) ; Spatial angle rotation around the axis of the generating gear (Y axis): (73) ; RMY = ROTY x RMX (74) ; RWY = ROTY x RWX (75) ; TKAY = ROTY x TKAX (76).

[0095] Step 5e, spatial angle rotation: Inverse rotation of the gear vectors to match the gear pitch line with the Y axis of the generating system: (77) ; RM5 = ROTX x RMY (78) ; RW5 = ROTX x RWY (79) ; TKA5 = ROTX x TKAY (80).

[0096] Step 6b, machine setting calculation for non-involute gears: Machine setting calculation according to equations (34) to (40), except for the roll ratio: RA = 1 (81).

[0097] Figure 18 A spur bevel gear 19 is shown with exaggerated generating planes. Typically, a spur bevel gear has 100 or more planes. Figure 18The gear 219 in FIG. 2 has only three developable planes in order to more clearly show the creation of these planes. The developable planes in FIG. 2 are shown as dashed lines. The developable planes in FIG. 2 are shown as solid lines. Figure 18 The active blade 220 in the snapshot of FIG. 2 has just been marked as a dashed surface at the portion being cut. As the blade 220 moves in the direction of the V-cut, the gear rotates with a developable rotation about its axis 221. The result is that the profile lines 222 and 223 are not parallel. Thus, the developable plane surfaces 224 are warped. The blade 225 creates a developable plane 226 and has exited the gear surface. The developable rotation causes the gear to rotate so that the blade 227 contacts the gear at profile line 228 and travels to profile line 229 where the blade exits the gear surface. Again, the lines 228 and 229 are not parallel. During the development process, the cutter also moves and rotates in the directions 230, 231, and 232, as shown on the cutter blade 225, which controls the tooth profile geometry and determines where the instantaneous axis of rotation between the cutter plane and the work gear lies. This also determines where the instantaneous line of rotation between the developing gear and the work gear lies. Changes in the position and direction of the instantaneous line of rotation also change the direction 233 of the developable planes. The developable planes can be parallel to the dedendum line 234, or they can be tapered.

[0098] Figure 19 A two-dimensional representation of a straight bevel gear flank 240 is shown. The extended pitch line 243 intersects the intersection point of the pinion and gear axis 244. The developable planes 241 are tapered and start parallel to the dedendum line 242, but their extensions 254 do not intersect at the intersection point 244. The developable planes 241 near the pitch line are not parallel to the pitch line. Figure 19 The developable planes in FIG. 2 are created by developing on the dedendum line, which will result in an additional profile along the direction 230 in FIG. 2 between the cutting tool and the developed flank. Figure 18 The result is an angle 246 between the developable plane intersecting the addendum 247 and the addendum line 247. Depending on the design, the angle 246 can be between 2° and 6°.

[0099] Figure 20 A two-dimensional representation of a straight bevel gear flank 250 is shown. The developable planes 251 are all parallel to the extended pitch line 252, which intersects the intersection point of the pinion and gear axis 253. The developable planes do not intersect the intersection point 253. This developable plane characteristic is typically given for helical gears or face gears. Figure 20 The developable planes in FIG. 2 cannot be created by developing on the straight bevel gear pitch line of the present invention.

[0100] Figure 21A two-dimensional representation of a straight bevel gear flank 260 is shown. The developable planes 261 are not parallel in the direction of the tooth length but are conical, and their extensions 262 all point to the intersection 263 between pinion and gear axis, where they intersect the extended pitch line 264. Figure 21 The developable planes in the straight bevel gear are produced by developing on the pitch line.

[0101] Figure 22 A two-dimensional representation of a straight bevel gear flank 270 is shown. The developable planes 271 are not parallel but are conical, and their extensions 275 do not point to the intersection 273 between pinion and gear axis. The straight bevel gear with these developable planes is developed around a line between the root line 272 and the pitch line 274.

[0102] While the application has been described with reference to preferred embodiments, it is to be understood that the application is not limited to the details of the embodiments. The application is intended to include modifications that are obvious to those skilled in the art without departing from the spirit and scope of the appended claims.

Claims

1. A method for generating or machining teeth on a bevel gear, the method comprising: Provide bevel gear workpieces with a rotation axis. A material removal tool with a rotation axis is provided, the material removal tool having at least one material removal surface arranged about the rotation axis of the tool, each of the at least one material removal surface having a tip, wherein the tip of the at least one material removal surface delineates the tooth tip circle of the tool. Rotate the material removal tool. The rotating material removal tool engages with the bevel gear workpiece. The teeth are generated on the bevel gear workpiece by causing the material removal tool and the workpiece to roll together in a predetermined relative rolling motion, wherein the predetermined relative rolling motion represents the rotation of the workpiece in meshing with a theoretically generated gear having teeth, wherein the teeth of the theoretically generated gear are represented by the at least one material removal surface of the tool. The unfolding is performed according to unfolding settings, which include: The material removal tool is positioned relative to the bevel gear workpiece, such that the addendum circle is tangent to the root line of the bevel gear workpiece. The material removal tool is positioned relative to the bevel gear workpiece, such that the instantaneous rolling axis is located at the pitch line of the workpiece during the generating process.

2. The generating method according to claim 1, characterized in that, The material removal tool includes a cutting tool having at least one cutting blade.

3. The generating method according to claim 1, characterized in that, The material removal tool includes a grinding wheel.

4. The generating method according to claim 1, characterized in that, The production or processing also includes providing length convexity to the teeth of the workpiece.

5. The generating method according to claim 1, characterized in that, The production or processing also includes providing profile convexity to the teeth of the workpiece, the profile convexity including at least one of tooth tip trimming and tooth root trimming.

6. The generating method according to claim 1, characterized in that, The bevel gear is a straight bevel gear.

7. The generating method according to claim 6, characterized in that, The straight bevel gear is the pinion component in a straight bevel gear set.

8. The generating method according to claim 7, characterized in that, The pinion component is paired with the non-generating gear component to form a conjugate gear set.

9. The generating method according to claim 1, characterized in that, As a result of the generating process, a generating plane is formed on the surface of the teeth of the generating gear. The generating plane is oriented in a conical manner along the length of the teeth, such that when the generating gear is positioned to mesh with a mating member having a rotational axis, the orientation of the generating plane points to the intersection between the rotational axis of the generating gear and the rotational axis of the mating member.

10. The generating method according to claim 9, characterized in that, The reference extension lines pointing from the unfolded plane intersect at the intersection point.

11. A gear set comprising a gear component and a mating pinion component, wherein, The gear component and the pinion component are each manufactured or processed by the method according to claim 1.

12. A gear set comprising a gear component and a mating pinion component, wherein, The gear component is non-generating, and the pinion component is manufactured or processed by the method according to claim 1.

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

14. A multi-axis computer-controlled gear manufacturing machine, the computer control having control instructions for executing the method according to claim 1.

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