Pitch line generation of straight bevel gears

Abstract

A method that overcomes the deficiencies associated with generating the tooth surfaces of straight bevel gears (50) with a relative rotation around the root line (54) and instead is directed to generating straight bevel gear flank surfaces around an instant axis of rotation which coincides with the pitch line (57) of the straight bevel gear (50).

Description

PITCH LINE GENERATION OF STRAIGHT BEVEL GEARSField of the Invention

[0001] The present invention is directed to bevel gears and in particular to the manufacture of straight bevel gear flank surfaces by a generating method.Background of the Invention

[0002] Figure 1 illustrates one example of a straight bevel gear 2 having a plurality of teeth 3 with each tooth having a topland 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” with the root portion 5 coinciding with the bottom of the tooth slot. For a mating pair (i.e. a gearset) of straight bevel gears (and most types of gears) it is usual that one member of the pair is smaller and has fewer teeth (known as the pinion member) than the larger mating member having more teeth (known as the gear member). In most cases, the pinion member is the driving member and the gear member is the driven member of the gearset.

[0003] One process for producing bevel gears is a generating process. In a generating process, a rotating tool is fed into the workpiece to a predetermined depth. Once this depth is reached, the tool and workpiece are then rolled together in a predetermined relative rolling motion, known as the generating roll, as though the workpiece were rotating in mesh with a theoretical generating gear, with the teeth of the theoretical generating gear being represented by the stock removing surfaces of the tool. Theprofile shape of the tooth is formed by relative motion of the tool and workpiece during the generating roll.

[0004] Straight bevel gears have been commonly manufactured with mechanical two tool planers (US 842,455 for example), interlocking cutters on mechanical machines (US 2,567,273 for example) or single peripheral cutters on free-form CNC machines (such as US 7,364,391 the entire disclosure of which is hereby incorporated by reference).

[0005] US 7,364,391 discloses a single side cutting process which roughs out and finish cuts all the first flanks of the teeth in a first step (Figure 16(a) for example), and then changes the position of the cutter in order to finish cut all the second flanks of the teeth in a second step (Figure 16(b) for example). The two-step process may be carried out on a computer-controlled multi-axis gear manufacturing machine such as that disclosed in US 6,712,566, the entire disclosure of which is hereby incorporated by reference. The two-step process generates precise octoids and allows for flank form modifications. After heat treatment it is possible to grind the differential gears with a CBN grinding process in a similar manner as cutting.

[0006] A suitable cutting tool for carrying out the above-discussed two-step process is illustrated in Figure 17 which shows a peripheral cutting tool 130 removably secured to a spindle 128 of a machine tool (not shown) such as that disclosed in US 6,712,566 for example. The cutting tool 130 comprises a cutter head 132 with a plurality of stick blades 134. The tips of the cutting blades 134 describe a blade tip circle, which is also known as a point diameter or a point circle. A clamp block 136 is located above each stick blade. The cutter in Figure 17 has a top ring 138 above the clamp blocks 136 with integrated clamp screws 139.

[0007] The aforementioned cutting processes must adjust the cutter or blade movement to be aligned with the root angle of the tooth slots. For mechanicalmachines, the axis of the generating roll during the cutting of a slot is also oriented collinear to the root line of the workpiece. When CNC free-form machines (such as that disclosed in US 6,712,566) are used to manufacture straight bevel gears with a single cutter disk (one flank at a time), the original process on the mechanical machines is effectively duplicated and the flank generation is also around an instant axis of rotation which is aligned to the workpiece root line. If a dedendum angle not equal zero is present, as in the case of straight bevel gears, generating the tooth surfaces with a relative rotation around the root line violates the Law of Gearing. Subsequently, such a generating setup causes flank surface mismatch which shows as profile crowning and surface warping and makes the surfaces deviate significantly from a conjugate surface. The result is a small tooth contact and a large motion transmission error. The kinematic coupling condition between pinion and gear is not fulfilled if pinion member and gear member do not roll on their pitch cones with the virtual generating gear plane in the manufacturing process.

[0008] Straight bevel gears cut with the above-mentioned methods create generating marks which begin parallel to the root line and then continue as tapered marks or lines. However, in the state-of-the-art cases of straight bevel gears, the generating lines are not pointing all at one point, such as, for example, at the point which coincides with the crossing point between the pinion and gear axes.

[0009] Generating marks, also called generating flats, are the result of the distance between two preceding cutting blades in the cutter head. While one blade passes along the face width of the gear to be cut, the generating motion rotates the gear, and the blade creates a warped surface along the face width. The following blade finds the gear rotated by a certain amount and creates its own generating flat, next to the one the previous blade created.

[0010] The generating flats approximate the involute profile with a polygonal. If the cutter head had an infinite number of cutting blades, or was replaced by a grindingwheel, then the profile would be an involute without any generating flats. Also, if the generating rotation was infinitely slow and the cutter RPM was infinitely high, then the generating flats would effectively disappear.

[0011] In the past, it was accepted that straight bevel gears had a rather large motion error. The flank geometry was far away from conjugate, but most straight bevel gears were used for rather simple applications. Today, manufacturers of high precision equipment like to use straight bevel gears due to the reduced axial forces (compared with spiral bevel gears). Therefore, high power density, high efficiency and low rolling noise become more important for straight bevel gears.Summary of the Invention

[0012] The present invention overcomes the deficiencies associated with generating the tooth surfaces with a relative rotation around the root line and instead is directed to generating straight bevel gear flank surfaces around an instant axis of rotation which coincides with the pitch line of the straight bevel gear.

[0013] The invention is directed to a generating method of producing or machining teeth on a bevel gear comprising providing a bevel gear workpiece having an axis of rotation and providing a stock-removing tool having an axis of rotation with the stockremoving tool having at least one stock-removing surface arranged about the tool axis of rotation and with each of the at least one stock-removing surface having a tip. The at least one stock-removing surface tip describing a tip circle of the tool. The stockremoving tool is rotated and then engages the bevel gear workpiece to generate teeth on the bevel gear workpiece by rolling the stock-removing tool and workpiece together in a predetermined relative rolling motion, with the predetermined relative rolling motion representing the workpiece rotating in mesh with a theoretical generating gear havingteeth, with the teeth of the theoretical generating gear being represented by the at least one stock-removing surface of the tool.

[0014] The generating is carried out in accordance with a generating setup comprising positioning the stock-removing tool relative to the bevel gear workpiece whereby the tip circle of the tool is tangent to a root line of the bevel gear workpiece, and, positioning the stock-removing tool relative to the bevel gear workpiece whereby an instantaneous rolling axis during the generating is located at the pitch line of the workpiece or at the pitch line of the theoretical generating gear.Brief Description of the Drawings

[0015] Figure 1 illustrates an example of a straight bevel gear.

[0016] Figure 2 illustrates a three-dimensional representation of a generating gear plane and a pinion pitch cone not rolling on the generating gear plane.

[0017] Figure 3 shows a three-dimensional representation of a generating gear plane and a gear pitch cone with the pitch cone not rolling on the generating gear plane.

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

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

[0020] Figure 6 illustrates a top view of a cutting machine setup where the cutter rolling on the root line of the gear.

[0021] Figure 7 shows tooth contact analysis of a straight bevel gearset where both gear and pinion members are generated by rolling on the root line of the respective member.

[0022] Figure 8 shows tooth contact analysis of a straight bevel gearset where both gear and pinion members are generated by rolling on the root line of the respective member and with a profile crowning correction applied.

[0023] Figure 9 illustrates a top view of a cutting machine setup with the cutter rolling on the pitch line of the gear.

[0024] Figure 10 is a tooth contact analysis of a straight bevel gearset where both gear and pinion members are generated by rolling on the pitch line of the respective member.

[0025] Figure 11 shows tooth contact analysis of a straight bevel gearset where both gear and pinion members are generated by rolling on the pitch line of the respective member and with a length crowning applied.

[0026] Figure 12 shows tooth contact analysis of a straight bevel gearset where both gear and pinion members are generated by rolling on the pitch line of the respective member and with length crowning and a tip relief applied on both members.

[0027] Figure 13 illustrates a bevel gear generating coordinate system.

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

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

[0030] Figure 15 shows a comparison of motion transmission error of a root line generated versus a pitch line generated straight bevel gear pair.

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

[0032] Figure 17 shows a peripheral cutting tool for carrying out the two-step process of Figures 16(a) and 16(b).

[0033] Figure 18 shows a straight bevel gear with exaggerated generating flats.

[0034] Figure 19 shows a two-dimensional representation of a straight bevel gear flank having generating flats that are tapered and start parallel to the root line, but their extensions do not intersect at the crossing point.

[0035] Figure 20 shows a two-dimensional representation of a straight bevel gear flank having generating flats parallel to the extended pitch line, which intersects with the crossing point of pinion and gear axis. The generating flats do not intersect with the crossing point.

[0036] Figure 21 shows a two-dimensional representation of a straight bevel gear flank having generating flats that are not parallel but tapered and their extensions extend to the crossing point between pinion and gear axis, where they meet with the extended pitch line.

[0037] Figure 22 shows a two-dimensional representation of a straight bevel gear flank having generating flats that are not parallel but tapered and their extensions do not extend to the crossing point between pinion and gear axis.Detailed Description of the Preferred Embodiment

[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 not be understood 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 any particular part, paragraph, statement or drawing of the application. The subject matter should be understood by reference to the entire specification, all drawings and any claim below. The invention is capable of other constructions and of being practiced or being carried out in various ways. Also, it is understood that the phraseology and terminology used herein is for the purposes of description and should not be regarded as limiting.

[0039] The details of the invention will now be discussed with reference to the accompanying drawings which illustrate the invention by way of example only. In the drawings, similar features or components will be referred to by like reference numbers. The size and relative sizes of certain aspects or elements may be exaggerated for clarity or detailed explanation purposes. For a better understanding of the invention and ease of viewing, doors, casings, internal or external guarding, etc. may have been omitted from the drawings.

[0040] The use of “including”, “having” and “comprising” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. The use of letters to identify elements of a method or process is simply for identification and is not meant to indicate that the elements should be performed 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 any and all combinations of one or more of the associated listed items.

[0041] Although references may be made below to directions such as upper, lower, upward, downward, rearward, bottom, top, front, rear, etc., in describing the drawings, these references are made relative to the drawings (as normally viewed) for convenience. These directions are not intended to be taken literally or limit the present invention in any form. In addition, terms such as “first", “second”, “third”, etc., are used to herein for purposes of description and are not intended to indicate or imply importance or significance unless explicitly stated.

[0042] Figure 2 shows a pinion member pitch cone 10 which penetrates through a virtual generating gear plane 12 from above. The angle 9 between the pinion axis 21 and the generating gear plane 12 is equal to the root angle of the pinion.

[0043] Figure 3 shows a gear member pitch cone 11 which penetrates through the virtual generating gear plane 12 from below. The angle 8 between the gear axis 16 and the generating gear plane 12 is equal to the root angle of the gear. In the operation of pinion and gear (Figure 4), the angle between pinion axis 21 and gear axis 16 has to be equal to the shaft angle 15, which is the pinion pitch angle 13 plus the gear pitch angle 14. This means that in the operation, the pitch angle of the pinion rolls on the pitch angle of the gear, but in the manufacturing process the root angles roll on the connecting generating gear which leads to a flank surface mismatch from conjugate.

[0044] Figure 4 also shows the pitch cone 10 of a bevel pinion and the pitch cone 11 of a bevel gear. The disk 12 between them is the virtual generating gear plane. If the generating plane 12 rotates around its axis 26, cone 10 above the disk will rotate around its axis 21 and cone 11 below the disk will rotate around its axis 16 and both cones will roll without sliding on the disk 12. The ratio between the rotation of the cones is calculated as:Ratio = sin(pinion pitch cone angle 13) / sin(gear pitch cone angle 14)In this case it is:Pinion pitch cone angle 13 + gear pitch cone angle 14 = shaft angle 15

[0045] Only a gearset where the pitch cones roll without sliding on the generating gear plane fulfills the Law of Gearing and has a conjugate basis.

[0046] Figure 5 shows a generating gear 17, which is the generating disk 12 (Figure 4) after teeth have been added. The teeth and slots have a trapezoidal profile and are tapered from the outside towards the center 23. This is the exact bevel gear analogue to the generating rack of involute cylindrical gears.

[0047] The state-of-the-art straight bevel gear generation by rolling on the root line is shown in Figure 6. As an example, a gearset manufactured according to Figure 6 may have the following basic parameters:Number of teeth of pinion member = 15Number of teeth of gear member = 17Face with = 20mmProfile shift = 0.0Profile depth factor = 1.0Root clearance = 0.5mmBacklash = 0.1mmPinion face angle = 51.40°Gear face angle = 58.57°Fillet edge radii pinion = 0.5mmFillet edge radii gear = 0.5mmPressure angle pinion = 20°Pressure angle gear = 20°Shaft angle = 90°Outer pitch diameter gear = 100.00mmPeripheral cutter diameter 228.6mm

[0048] Figure 6 represents a top view of the generating setup in a cutting machine (e.g. US 6,712,566). Work piece gear member 20 has a rotational axis 21 which intersects with the generating gear axis 22 (which is identical to the cutting machine cradle axis) at point 23. The 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, such that the blade tip circle 25 it is tangent to the root line 24. During the cutting and generating process, the cutter 25 rotates around its axis 26 (only shown as a dot in Figure 5) to perform a cutting action. In addition, the cutter itself rotates around the generating gear axis 22 while the work gear rotates around its axis 21 (i.e., the generating roll) in order to generate an octoid flank profile. The work gear rotation angle is equal the generating gear rotation angle times the number of generating gear teeth, divided by the number of work gear teeth. This setup where the root line 24 is adjusted to coincide with the instantaneous rolling axis (i.e. the line where both bodies contact each other and roll onto each other without slippage) is consistent with the state-of-the-art straight bevel gear manufacturing. In Figure 6, the instantaneous rolling axis is in the generating plane and matches the Z-axis.

[0049] A tooth contact analysis of a pinion and a gear, generated according to Figure 6 is shown in Figure 7. The Ease-Off surface 30 shows the deviations from conjugate. As a result of the generation on the root line, a profile crowning 38 occurs. The tooth contact 31 (using a virtual marking compound film of ,006mm thickness) extends over the entire working area. This means that above and below the contact 31 (areas 32 and 33) are lost due to mechanical and / or kinematic undercut in the pinion member (area 32) and in the gear member (area 33). Even under high load, the tooth contact cannot spread into the areas 32 and 33. 40% of the possible working profile has been lost in the present example of Figure 7. The contact ratio between neighboring teeth dropsfrom the theoretical value 1.35 below 1.0, which means the contact transition from one pair of teeth to the next cannot maintain any overlap which leads to large effective transmission errors, loud operation 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 parabola shaped curves 35, 36 and 37 also reflect that the transmission error is larger than 500 microradians.

[0050] An attempt to eliminate the profile crowning by using cutting blades with curved profile does not work well as shown in Figure 8. The profile crowning 38 (Figure 7) is not eliminated but only reduced as shown at 40 in Figure 8 and a negative length crowning 41 as a side effect was created. The resulting tooth contact 42 is poorly shaped and positioned and the motion transmission graph 43 shows motion error curves 46, 47 and 48 larger than 500 microradians. The lost areas of working profile 44 and 45 are identical to the areas 32 and 33 before the correction. It appears to be not possible to achieve a conjugate surface if the flank surface generation applies a rolling on the root line. A conjugate flank surface is required as a starting point for the development of an advanced and optimized straight bevel gear design.

[0051] The inventive solution of a generating rolling on the pitch line is shown in Figure 9. The straight bevel gearset which was used to create Figure 9 has the same basic parameters as listed for the root line generated gearset in Figures 2 through 4. The invention is applicable to producing bevel gears from a gear blank (e.g., rough cutting) and to machining the teeth of a rough-cut gear (e.g., grinding, finish cutting, etc.). A control program and a multi-axis computer-controlled gear manufacturing machine having control instructions for carrying out the inventive method are also contemplated.

[0052] Figure 9 shows a top view of the generating setup in the cutting machine. Work piece gear 50 has a rotational axis 51 which intersects with the generating gear axis 52 (which is identical to the cutting machine cradle axis) at point 53. Point 53 also symbolizes the X axis (oriented perpendicular to the page) of the generating system.The pitch line 57 of gear 50 intersects with the generating gear axis 52 in the generating gear coordinate system at center point 53 and is perpendicular to the generating gear axis. The blade tip circle (also known as the tip circle, point diameter or point circle) of the circular peripheral / cutter 55 is adjusted such that it is tangent to the root line 54. During the cutting and generating process, the cutter 55 rotates around its axis 56 (only shown as a dot in Figure 9) to perform a cutting action. In addition, the rotating cutter itself is rotated (i.e. moved) around the generating gear axis 52 (i.e., the generating roll) in order to generate an octoid tooth flank profile. This setup where the root line 54 is tangent to the cutter blade tip circle and the pitch line 57 is oriented to coincide with the instantaneous rolling axis (i.e. the line where both bodies (workpiece and generating gear) contact each other and roll onto each other without slippage) is a result of the invention wherein the instantaneous rolling axis is separate from the orientation of the cutter circle. In Figure 9, the instantaneous rolling axis is in the generating plane (X-Z) and matches the Z-axis.

[0053] The above discussion applies equally to grinding. The outer tip of the grinding wheel abrasive surface describes a tip circle, point diameter or point circle.

[0054] A tooth contact analysis of a pinion and a gear, generated according to Figure 9 is shown in Figure 10. The Ease-Off surface 60 shows no measurable deviations from conjugate. As a result, the correct generation on the pitch line results in a conjugate Ease-Off with theoretically zero deviations 68. The tooth contact 61 (using a virtual marking compound film of .006mm thickness) extends over the entire working area.The lost areas 62 and 63 above and below the contact 61 have been reduced to 28% of the flank area, compared to 40% loss with the state-of-the-art root line generation method.

[0055] The theoretical contact ratio between neighboring teeth of 1.35 is achieved in full with the pitch line generated gearset of Figure 10. The calculated motion transmission graph 64 of the three consecutive tooth pairs 65, 66 and 67 only shows atransmission error having a variation within about 3 microradians. The conjugate flank surface of Figure 10 is a preferred starting point for the development of an advanced and optimized straight bevel gear design.

[0056] Figure 11 shows the tooth contact analysis of the gearset of Figure 10 after a length crowning 71 was added. The Ease-Off surface 70 shows a relief amount from the center of the face width towards toe and heel. The contact area 72 is localized between toe and heel but the profile crowning 73 is still about zero which will likely result in edge contact along the top and the root. The likelihood of top and / or edge contact is also reflected by the non-centered mean point 77 (point of optimal motion transmission). The mean point applies for the entire profile (line or section extending in the profile direction within the tooth contact pattern in Figure 11) and is shown in an arbitrary location. The motion transmission graph 75 shows a maximal transmission error 76 which is below 10 microradians.

[0057] In order to preserve a conjugate flank center 81 , the Ease-Off 80 in Figure 12 received a top and root relief which is shown as a profile crowning 82. The Ease-Off along the top line and the root line is lifted up and leaves the flank center conjugate. At the center of the face width, the top relief amount 83 is shown and the root relief amount 84 is shown. The tooth contact 85 in Figure 11 did not visibly change due to the top and root relief but the mean point 77 in Figure 10 has moved to the optimal center location 86 in Figure 12. The motion transmission graph shows a transmission error 88 of about 20 microradians.

[0058] Figure 13 shows a front view and a top view of a generating coordinate system for the present invention. The front view shows the vector EX extending from the generating gear center to the cutter center, the cutter radius vector RW, and the vector RM extending from the generating gear center to the midface at the root. The cutter silhouette 90 is shown as an ellipse, due to its inclination required to cut the correct pressure angle of the work piece. The axes X and Z of the generating system are alsoshown. The top view also shows the vectors EX, RW and RM. Also, the axes Y and Z are shown. The top view also has a simplified sketch of the work piece 91 (gear member) to be generated. The pitch line 92 matches the Z-axis of the generating system and lies in the generating plane. The present case in Figure 13 represents generating on the pitch line of the gear member.

[0059] The inventive solution of two generating gear setups for a non-generated gear member and a special generated pinion member of a gearset is shown in Figures 14(a) and 14(b). Figure 14(a) shows a top view to the setup in the cutting machine for cutting the non-generated gear member. Gear 100 has a rotational axis 101 which intersects with the generating gear axis 102 (which is 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 with 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 such that the blade 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 (only shown as a dot in Figure 14(a)) to perform a cutting action. There are no additional rotations or movements required to form the flank surfaces of a non-generated gear which have a straight profile. The gear member 100 is a non-generated member and the pitch line 108 of gear 100, oriented at pitch angle 109, doesn’t have to match the generating gear plane but can lie anywhere in the Y-Z plane. The principle of generating on the pitch line is established by the fact that the generated member (Figure 14(b)) uses the non-generated member as a generating gear.

[0060] Figure 14(b) shows a top view onto the machine setup of the special generated pinion member which mates the non-generated gear member. Pinion 110 has a rotational axis 111 which intersects with the generating gear axis 112 (which is identical to the cutting machine cradle axis) at point 113. Point 113 also symbolizes the X axis (oriented perpendicular to the page) of the generating system. The angle 118 isidentical to the shaft angle between pinion and gear members. The pinion axis will therefore not match the Z-axis of the generating system 117 in the case of a shaft angle not equal to 90°. The circular peripheral cutter 115 is adjusted such that the blade tip circle (also known as the tip circle, point diameter or point circle) is tangent to the root line 114. During the cutting process, the cutter 115 rotates around its axis 116 (only shown as a dot in Figure 14(b)) to perform a cutting action. In addition, the cutter itself is rotated (i.e. moved) around the generating gear axis 112 (i.e. , the generating roll) in order to generate a modified involute tooth flank profile. The angle 119 between the pinion pitch line 120 and the generating gear axis 112 is equal to the pitch angle of the mating gear. The pinion is generated on the pitch line of the conical generating gear which is coincident with the pinion pitch line 120. The generating gear 121, which commonly has a 90° pitch angle (angle between Y-axis and Z-axis of the generating system) is now conical and resembles the mating gear member.

[0061] Given the coincident pitch lines of pinion and generating gear as discussed above, the pinion is generated on the pitch line of the pinion in those cases where the mating gear is non-generated and the generating gear for the pinion is conical as shown in Figure 14(b). If one of the two gearset members is non-generated (Figure 14(a)), it is necessary to use the non-generated member as the generating gear for the other gearset member in order to achieve a conjugate gearset which rolls in operation on the pitch line without slippage. This is referred to as the kinematic coupling requirement. In this case, the ratio between the generating gear and the pinion is equal to the ratio given by the tooth count of both the pinion and the generating gear.

[0062] The above discussion applies equally to grinding. The outer tip of the grinding wheel abrasive surface describes a tip circle, point diameter or point circle.

[0063] Figure 15 shows the comparison of transmission errors of a root line generated straight bevel gearset (top graphics) versus a pitch line generated straight bevel gearset (bottom graphics). The two graphics on top show the fast Fourier transformation resultsof a root line generated straight bevel gearset with a gear torque of 10Nm and 200Nm. The first mesh order shows the transmission error amplitude of the meshing teeth with the frequency of the rotation (a gear speed of 100RPM with 17 gear teeth relates to a mesh frequency 100*17 / 60 = 28.333Hz). Higher order transmission errors are shown with the 2ndto 7thmesh order.

[0064] The two graphics at the bottom of Figure 15 show the transmission error amplitudes of the first and higher mesh orders. The low torque of 10Nm represents the noise critical state of a transmission. The transmission error amplitudes of the pitch line generated straight bevel gearset are in the range of 10% of the root line generated version. The higher torque of 200Nm represents an average operation torque of the straight bevel gearset. Even considering the surface deformation and tooth bending caused by the higher torque, the transmission error amplitudes of the seven mesh orders of the pitch line generated gearset is on average only 50% compared to the root line generated gearset.

[0065] A conjugate flank center with reliefs at top and root is the preferred basis for improved power density, improved efficiency and reduced vibration and noise during the operation. A method of top and / or root relief is disclosed in US 63 / 381 ,145 the entire disclosure of which is hereby incorporated by reference). The present invention is directed to solve the task of generating straight bevel gear flank surfaces around an instant axis of rotation which coincides with the pitch line of the straight bevel gear. The transformations are equal for the generated pinion member as well as the generated gear member. At the beginning, the two major vectors, describing the cutting machine setup, the mean cone distance vector and the cutter radius vector are established in their initial state:

[0066] Mean cone distance vector RMO from machine center to tooth midface at root:HFpitch_heel = DOMNheel*(DPTHF+Fcl-x) (1)HFpitchJoe = DOMNtoe*(DPTHF+Fcl-x) (2)HFpt = (HFpitch_heel+HFpitchJoe) / 2 (3)RMOx = sign*(HFpt+DARC)*tan(ALFA) (4)RMOy = HFpt+DARC (5)RMOz = RMIR (6)Where:HFpitch heel... dedendum at heel from root to pitch line HFpitchJoe... dedendum at toe from root to pitch line HFpt... dedendum at midface from root to pitch line DOMNheel... normal module at heelDOMNtoe... normal module at toeDPTHF... depth factorFcl... clearance factor x... profile shift factorRMO... vector from machine center to tooth midface at rootSI... sign for lower flank (-1), sign for upper flank (+1)DARC... deeper cutting at center due to cutter arcALFA... pressure angle of respective gearRMIR... mean cone distance along root angle

[0067] Cutter radius vector RWO:RWOx = 0 (7)RWOy = DIAM / 2 (8)RWOz = 0 (9)Where:RWO. .. cutter radius vector from center of cutter to tooth root at midfaceDIAM... cutter diameter

[0068] Initial cutter axis points in Y-axis direction of generating system. Cutter axis matrix represents in first column cutter X-axis, in second column cutter Y-axis (equal axis of rotation) and in third column cutter Z-axis. Cutter axis matrix TKAO with cutter Y- axis pointing in positive X-axis direction of generating system for upper flank cutting and in negative X-axis direction of generating system for lower flank cutting. TKAO is established by a 90° rotation around X-axis of generating system, followed by a 90° rotation around the Y-axis of the generating system.

[0069] The following five transformation steps show a step-by-step approach to establish a mean cone distance vector, a cutter radius vector and a cutter axes matrix which position the cutter axis circle tangential to the straight bevel gear root cone yet arrive at a virtual generating gear plane which is aligned with the pitch line. Step 6 discloses the calculation of real cutting machine settings from the vectors and cutter matrix transformation results.

[0070] Step 1 , rotation of cutting edge normal vector to dish angle:Initial cutting edge vector points in X-axis directionCNx = 1 (11)CNy = 0 (12)CNz = 0 (13)

[0071] Rotation round Z-axis about dish angle DPHIXCNO = ROTO x CN (15)Where:CN... initial cutting edge vectorCNO... cutting edge vector after dish angle rotationROTO... rotation matrix for cutter blade dish angleDPHIX... cutter dish angle

[0072] Step 2, rotation of cutter radius vector, cutting edge vector and cutter axis matrix to cutter angle position:Rotation about Z-axis by cutter angle PH IXRW1 = ROT1 x RWO (17)CN1 = ROT1 x CNO (18)TKA1 = ROT1 x TKAO (19)Where:ROT1... rotation matrix for 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

[0073] Step 3, rotation of cutter radius vector, cutting edge vector and cutter axis matrix from perpendicular to pitch angle to perpendicular to root angle orientation:Rotation about X-axis by GAMMAroot-GAMMApitchPinion: GAMMApitchl = arctan(sin(Shaft Angle) / (Z2 / Z1+cos(Shaft Angle))) (20)Gear: GAMMApitch2 = Shaft Angle-GAMMApitchl (21)

[0074] For the following derivations GAMMApitch is generically used for pinion and gear:GAMMAroot = GAMMApitch-arctan((HFpitch_heel-HFpitch_toe) / F (22)RW2 = ROTZ x RW1 (24)CN2 = ROT2 x CN1 (25)TKA2 = ROT2 x TKA1 (26)Where:ROT2... rotation matrix for cutter rotation from perpendicular to pitch line to perpendicular to root lineGAMMAroot... root angle of pinion or gear memberGAMMApitch... pitch angle of pinion and gear memberRW2... cutter radius vector after rotation perpendicular to root angleCN2... cutting edge vector after GAMMAroot-GAMMApitch rotationTKA2... cutter axis matrix after GAMMAroot-GAMMApitch rotation

[0075] Step 4, correction of pressure and lead angle:Flank line (lead) mismatch, caused by to the change of cutter radius vector perpendicular to the root line (and cutting edge vector and cutter axis matrix with it):Cutting edge vector must not have a Z-componentANGYAX = arctan(CNz / CNx) (27)

[0076] Rotation around Y-axis of generating system about ANGYAX (ROT3) eliminated flank line mismatch:RW3 = ROTS x RW2 (29)CN3 = ROT3 x CN2 (30)TKA3 ROT3 x TKA2 (31)Where:ROTS... rotation matrix for cutter rotation to eliminate flank line mismatchANGYAX... rotation to eliminate cutting edge vector Z-componentRW3... cutter radius vector after rotation to eliminate flank line mismatchCN3... cutting edge vector after rotation to eliminate flank line mismatchTKA3... cutter axis matrix after rotation to eliminate flank line mismatch

[0077] Cutting edge vector must be inclined in X-Y-plane of the generating system by the gear pressure angle ALFA.ANGZAX = ALFA - sign*arctan(CNy / CNx) ...deviation of cutting edge angle in X-Y-plane from ALFA (32)

[0078] A rotation around the Z-axis of the generating system about ANGZAX (ROT4) eliminates profile mismatch:RW4 = ROT4 x RW3 (34)CN4 = ROT4 x CN3 (35)TKA4 = ROT4 x TKA3 (36)ROT4... rotation matrix for cutter rotation to eliminate profile mismatchANGZAX... rotation to eliminate cutting edge vector deviation from ALFA in X-Y-planeRW4... cutter radius vector after rotation to eliminate profile mismatchCN4... cutting edge vector after rotation to eliminate profile mismatchTKA4... cutter axis matrix after rotation to eliminate profile mismatch

[0079] Step 5, rotation of cutter to space angle:The rotation of the cutter is required in order to generate the correct slot width. For the upper cutting, the cutter is rotated around the generating gear axis (Y in Figure 12) in positive direction by a quarter pitch (3607ZG / 4), plus corrections to consider backlash, profile shift and profile side shift.

[0080] For the lower cutting, the cutter is rotated around the generating gear axis (Y in Figure 12) in negative direction by a quarter pitch (3607ZG / 4), plus corrections to consider backlash, profile shift and profile 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)RMS = ROTS x RMO (42)RW5 = ROTS x RW4 (43)CN5 = ROTS x CN4 (44)TKA5 = ROTS x TKA4 (45)Where:SPLF... backlashDOMN... normal module at midfaceZG... number of teeth of generating gearDSPG1... D space angle considering backlashDSPG2... D space angle considering profile shiftDSPG3... D space angle considering profile side shiftSPAG... space angleROTS... rotation matrix for cutter rotation to correct space angleRMS... vector from machine center to tooth midface at root after space angle rotationRW5... cutter radius vector after rotation to space angleCN5... cutting edge vector after rotation to space angleTKA5... cutter axis matrix after rotation to space angle

[0081] The space angle is one-half of the slot width taper (i.e. one-half of the slot width taper angle) and is established with a rotation of the cutter center roll position around the generating gear axis, while the work is adjusted with the pitch cone tangentially to the generating gear plane (X-Z-plane).

[0082] Step 6, Machine setting calculation:The settings of the real manufacturing machine are calculated from the mathematical transformation results as follows:Where:EX5... Vector from origin of X-Y-Z system in Figure 12 to center of cutter (origin of cutter radius vector)ROOTA... machine root angleQO... center of roll positionJ... swivel angle1... tilt angle5... radial distance machine center to cutter centerXP... machine center to crossing point of pinion and gear axis at current member’s axisXB... sliding baseEM... machine offsetRA... ratio of rollZG... number of teeth generating gearZ... number of teeth current gear

[0083] Gear Non-Generated gear special generated pinion:

[0084] In spiral bevel and hypoid gears a method has been developed which allows the gear member to be plunge cut without any generating process and the pinion member to be generated by using a virtual duplicate of the non-generated gear member as a generating gear. In order to accomplish this, the cutter is positioned to represent one tooth of the virtual generating gear which rotates like the original plane generating gear around the generating gear axis. The state-of-the-art rule recommends this process be applied only when the ratio between pinion and gear is greater than three. The major advantage of this non-generated gear cutting is the cutting time which is reduced by 30%. For a straight bevel gear, the cutting time savings would even be up to 50%. The combination of a non-generated gear and a special generated pinion which form a conjugate pair is not known for straight bevel gears in the state-of-the-art. The inventor discovered that the application of a special space angle rotation for the pinion and gear members is required to achieve a conjugate rolling straight bevel gear set where the gear is non-generated. Consequently, the settings of both members, pinion and gear will change. The transformations of steps 1 through 4 are identical as shown for a generated gearset. Step 5, step 5a and step 5b have been developed for the pinion member cutting setup and steps 5c, 5d and 5e were developed for the nongenerated gear member cutting setup.

[0085] Pinion member setting calculation for set with a non-generated gear member:

[0086] The inventor discovered that the space angle rotation has to be performed around the generating gear axis, where the space angle amount has to be converted from the pitch plane to the generating gear plane:

[0087] Step 5a, rotation of the 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:RMX = ROTX x RM0 (59)RWX = ROTX x RW4 (60)TKAX = ROTX x TKA4 (61)

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

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

[0090] Step 6a, machine setting calculation for pinion:Machine setting calculation according to equation (34) to (40) except machine root angle and ratio of roll:ROOTA = 90°-SHAFTANG (67)RA = Z2 / Z1 (68)Where:GAMMApitch G... pitch angle of the gear memberZ1... number of teeth pinionZ2... number of teeth gear

[0091] Gear member setting calculation for set with non-generated gear member:

[0092] Also for the non-generated gear, the space angle rotation has to be performed around the generating gear axis, where the space angle amount has to be converted from the pitch plane to the generating gear plane.

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

[0094] Step 5d, space angle rotation:The space angle amount has to be converted from the pitch plane to the generating gear plane:SPAGX = SPAGZsin(GAMMApitch)Space angle rotation around the generating gear axis (Y-axis):RMY = ROTY x RMX (74)RWY = ROTY x RWX (75)TKAY = ROTY x TKAX (76)

[0095] Step 5e, space angle rotation:Back rotation of gear vectors to match the gear pitch line with the Y-axis of the generating system:RM 5 = ROTX x RM Y (78)RW5 = ROTX x RWY (79)TKA5 = ROTX x TKAY (80)

[0096] Step 6b, machine setting calculation for non-generated gear:Machine setting calculation according to equation (34) to (40) except ratio of roll:RA = 1 (81)

[0097] Figure 18 shows a straight bevel gear 19 which has exaggerated generating flats. Commonly a straight bevel gear has 100 or more flats. Gear 219 in Figure 18 has only three generating flats in order to show more clearly the creation of these flats. The part of the generating flat which the active blade 220 is just cutting in the snapshot of Figure 18 is marked as a dotted surface. While blade 220 moves in the direction of Vcut, the gear rotates with the generating rotation around its axis 221. The result is that profile lines 222 and 223 are not parallel. The generating flat surface 224 is therefore warped. Blade 225 created generating flat 226 and has exited the tooth surface. The generating rotation rotates the gear such that blade 227 contacts the gear at profile line 228 and travels to profile line 229 where it exits the tooth surface. Also, lines 228 and 229 are not parallel. During the generating process the cutter is also moved and rotated in the directions 230, 231 and 232, shown on 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 is located. This also determines where the instantaneous line of rotation between the generating gear and the work gear is located. A change in the location and direction of the instantaneous line of rotation also changes the direction 233 of the generating flats. The generating flats can be parallel to the root line 234, or they can be tapered.

[0098] Figure 19 shows a two-dimensional representation of a straight bevel gear flank 240. The extended pitch line 243 intersects with the crossing point of pinion and gear axis 244. The generating flats 241 are tapered and start parallel to the root line 242, but their extensions 254 do not intersect at the crossing point 244. The generating flats 241 close to the pitch line are not parallel to the pitch line. The generating flats in Figure 19are created by generating on the root line which will cause an additional profile sliding in direction 230 in Figure 18 between the cutting tool and the generated flank. The result is angle 246 between the generating flat which meets the tip 247 and the tooth tip line 247. The angle 246 can be between 2° and 6° depending on the design.

[0099] Figure 20 shows a two-dimensional representation of a straight bevel gear flank 250. The generating flats 251 are all parallel to the extended pitch line 252, which intersects with the crossing point of pinion and gear axis 253. The generating flats do not intersect with crossing point 253. Such a generating flat characteristic is typically given for beveloid gears or face gears. The generating flats in Figure 20 cannot be created by the inventive straight bevel gear pitch line generation.

[0100] Figure 21 shows a two-dimensional representation of a straight bevel gear flank 260. The generating flats 261 are not parallel but tapered in the tooth length direction and their extensions 262 all point at the crossing point 263 between pinion and gear axis, where they meet with the extended pitch line 264. The generating flats in Figure 21 are created by generating on the pitch line.

[0101] Figure 22 shows a two-dimensional representation of a straight bevel gear flank 270. The generating flats 271 are not parallel but tapered and their extensions 275 do not point at the crossing point 273 between pinion and gear axis. A straight bevel gear with these generating flats is generated around a line which is between the root line 272 and the pitch line 274.

[0102] While the invention has been described with reference to preferred embodiments it is to be understood that the invention is not limited to the particulars thereof. The present invention is intended to include modifications which would be apparent to those skilled in the art to which the subject matter pertains without deviating from the spirit and scope of the appended claims.

Claims

CLAIMSWhat is claimed is:

1. A generating method of producing or machining teeth on a bevel gear, said method comprising: providing a bevel gear workpiece having an axis of rotation, providing a stock-removing tool having an axis of rotation, said stock-removing tool having at least one stock-removing surface arranged about the tool axis of rotation, with each of said at least one stock-removing surface having a tip, with the at least one stock-removing surface tip describing a tip circle of the tool, rotating said stock- removing tool, engaging said rotating stock-removing tool and said bevel gear workpiece, generating said teeth on the bevel gear workpiece by rolling said stock-removing tool and said workpiece together in a predetermined relative rolling motion, with said predetermined relative rolling motion representing the workpiece rotating in mesh with a theoretical generating gear having teeth, with the teeth of the theoretical generating gear being represented by the at least one stock-removing surface of said tool, wherein said generating is carried out in accordance with a generating setup comprising: positioning said stock-removing tool relative to said bevel gear workpiece whereby said tip circle is tangent to a root line of said bevel gear workpiece, and positioning said stock-removing tool relative to said bevel gear workpiece whereby an instantaneous rolling axis during said generating is located at the pitch line of said workpiece.

2. The generating method of claim 1 wherein said stock-removing tool comprises a cutting tool having at least one cutting blade.

3. The generating method of claim 1 wherein said stock-removing tool comprises a grinding wheel.

4. The generating method of claim 1 wherein the producing or machining further includes providing the workpiece teeth with length crowning.

5. The generating method of claim 1 wherein the producing or machining further includes providing the workpiece teeth with profile crowning comprising at least one of top relief and root relief.

6. The generating method of claim 1 wherein said bevel gear is a straight bevel gear.

7. The generating method of claim 6 wherein said straight bevel gear is a pinion member of a straight bevel gearset.

8. The generating method of claim 7 wherein said pinion member is paired with and a non-generated gear member to form a conjugate gearset.

9. The generating method of claim 1 wherein as a result of said generating, generating flats are produced on the surface of the teeth of the generated gear, said generating flats being oriented in a tapered manner along the length of said teeth such that when the generated gear is placed in mesh with a mating member having an axis of rotation, the orientation of the generating flats are directed toward a crossing point between the axis of rotation of the generated gear and the axis of rotation of the mating member.

10. The generating method of claim 9 wherein reference extension lines directed from said generating flats meet at said crossing point.

11. A gearset comprising a gear member and a mating pinion member, wherein said gear member and said pinion member are each produced or machined by the method of claim 1.

12. A gearset comprising a gear member and a mating pinion member, wherein said gear member is non-generated and said pinion member is produced or machined by the method of claim 1.

13. Control program having control instructions, which, when executed on a multi-axis computer-controlled gear manufacturing machine, controls the machine for carrying out the method of claim 1.

14. A multi-axis computer-controlled gear manufacturing machine, the computer control having control instructions for carrying out the method of claim 1.

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