Independent pinion and gear profile shift for bevel gears

Abstract

Machining or producing teeth on a pinion member (50) with a first tool and on a mating gear member (51) with a second tool. The pinion member is positioned relative to the first tool so as to introduce a profile shift (55) on the teeth of the pinion member during the machining or producing of the pinion member with the first tool. The gear member is positioned relative to the second tool so as to introduce a profile shift (56) on the teeth of the gear member during the machining or producing of the gear member with the second tool. The sum of the profile shift on the teeth of the pinion member and the profile shift on the teeth of the gear member equals a non-zero amount.

Description

INDEPENDENT PINION AND GEAR PROFILE SHIFT FOR BEVEL GEARS Field of the Invention

[0001] The present invention is directed to the manufacture of gears, particularly bevel and hypoid gears, such as by cutting, wherein the pinion member of a gearset has a low number of teeth. Background of the Invention

[0002] In the production of gears, especially bevel and hypoid gears, two types of processes are commonly employed, generating processes and non-generating processes. Either process can be divided into two categories, face milling (intermittent indexing) where one tooth slot is formed with each plunge of the tool, and face hobbing (continuous indexing) wherein the tool and workpiece rotate in a timed relationship and the tool is fed to depth thereby forming all tooth slots in a single plunge of the tool.

[0003] 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, the teeth of the theoretical generating gear being represented by the stock removing surfaces of the tool. The profile shape of the tooth is formed by relative motion of the tool and workpiece during the generating roll.

[0004] Non-generating processes are those in which the profile shape of a tooth on a workpiece is produced directly from the profile shape on the tool. The tool is fed into the workpiece and the profile shape on the tool is imparted to the workpiece. No generating roll is employed.

[0005] It is known to manufacture bevel and hypoid gears utilizing a cutting tool that is rotatable about an axis of rotation and comprises a generally circular cutter head and a plurality of cutting blades (e.g. stick-type cutting blades) projecting from a face of the cutter head. Examples of such cutters include US 6,120,217 and 4,575,285. The cutting blades are arranged in the cutter head for face milling or face hobbing as is known to the artisan. It is also known to utilize peripheral cutters for manufacturing bevel gears, such cutting tools may comprise inserted stick-type cutting blades, or the cutting tool may be a solid cutter. Suitable machines for carrying out face milling and face hobbing processes include computer-controlled multi-axis gear manufacturing machines such as that disclosed in US 6,712,566, the entire disclosure of which is hereby incorporated by reference.

[0006] One method for manufacturing straight bevel gears, such as differential gears for example, is disclosed in U.S.7,364,391, the entire disclosure of which is hereby incorporated by reference, and comprises a single side cutting process which roughs out and finish cuts all the first flanks of the teeth in a first step and then changes the position of the cutter in order to finish cut all the second flanks of the teeth in a second step. 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 two-step process generates precise involutes (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.

[0007] In the manufacture of bevel and hypoid gears as well as straight bevel gears (e.g. differential gears), particularly by cutting, if the number of teeth of the pinionmember is low, for example below 10 or even below 18, the pinion member may develop a severe undercut which can eliminate a large portion of the tooth profile in particular at the toe area (small diameter area). In turn, the undercut can weaken the tooth root and also reduce the flank contact area. As a result, the root bending stress and the surface stress are high, and the bevel gear pair (i.e., gear member and mating pinion member) has only a fraction of the load carrying capacity compared to a bevel gear pair (i.e., gearset) without undercut.

[0008] One way to avoid the negative effects of undercut is with the introduction of a profile shift wherein the tooth is shifted toward the tool, or away from the tool, by a certain amount during gear cutting. The profile shift coefficient is usually designated by the symbol “X” and in order to determine the amount of profile shift, X is multiplied by the normal module mn of the gear, resulting in the amount of profile shift.

[0009] In bevel and hypoid gears as well as straight bevel gears, a so called V0 profile shift is known. V0 profile shift means that the pinion member profile shift coefficient, X1, and the gear member profile shift coefficient, X2, have the same absolute amount but opposite signs (X1 = -X2 or X1 + X2 = 0). In cylindrical gears the V0 profile shift prevents a change of the center distance between pinion and gear. In bevel gears this is analogous to preventing a shaft angle change. This means that a positive profile shift in both members of a bevel gearset would change the shaft angle Σ by: (^^^^1 + ^^^^2) ∗ ^^^^^^^^Σ = ^^^^

[0010] If a bevel gearset is designed with a shaft angle of 90°, any profile shift which is not a V0 shift will result in a shaft angle unequal to 90° which is not permissible. This is the primary reason why the state-of-the-art bevel gear design calculation and manufacturing systems strictly apply the V0 profile shift.

[0011] A side effect of the V0 profile shift is the fact that although a “healthier” pinion profile can be achieved (if X1 is positive), the profile of the mating gear teeth takes an adverse effect due to negative profile shift. Even a gear member with three times the number of pinion member teeth, for example, will develop undercut from a certain amount of negative profile shift. This means, in turn, the amount of V0 profile shift is limited to the point where the lost root area on the gear teeth above the root fillet (or above the undercut) increases visibly (as best seen at 42 in Figure 6) and diminishes the improvement in the pinion teeth profiles.

[0012] This is especially significant when the number of pinion and gear teeth is equal (miter gears), or if the ratio is near one, like it is in the case of differential gears. Miter gears therefore never receive a profile shift and differential gears only show very small positive pinion profile shift coefficient (for example X1 = +0.15) because the gear profile will develop undercut with the corresponding negative profile shift coefficient (for example X2 = -0.15). Gearsets with larger ratios and a pinion tooth count below 18 also require profile shift and, in this case, only a limited V0 profile shift is possible. Summary of the Invention

[0013] The present invention comprises a method of machining or producing teeth on a pinion member with a first tool and on a mating gear member with a second tool with the pinion member having an axis of rotation and the gear member having an axis of rotation. The pinion member and the gear member, when in mesh, form a gearset, with the axis of rotation of the pinion member and the axis of rotation of the gear member defining a shaft angle of the gearset. Prior to machining or producing, the pinion member is positioned relative to the first tool so as to introduce a profile shift on the teeth of the pinion member during the machining or producing of the pinion member with the first tool. Also prior to machining or producing, the gear member is positioned relative to the second tool so as to introduce a profile shift on the teeth of the gearmember during the machining or producing of the gear member with the second tool. Wherein the sum of the profile shift on the teeth of the pinion member and the profile shift on the teeth of the gear member equals a non-zero amount. The pinion member is machined or produced with the first tool and the gear member is machined or produced with the second tool. Wherein subsequent to the machining or producing of the pinion member and the gear member, the pinion member and the gear member are rotatable in mesh with one another, and when in mesh, the pinion axis of rotation and the gear axis of rotation are oriented with respect to one another at an angle equal to the shaft angle. The shaft angle after the machining or producing is the same as a shaft angle of a reference or nominal gearset comprising the pinion member and the gear member machined or produced without the non-zero sum amount of profile shift. Brief Description of the Drawings

[0014] Figure 1 illustrates the effect of profile shift.

[0015] Figure 2 shows the analysis results of a straight bevel miter gearset with no profile shift coefficients (X1 = 0 and X2 = 0).

[0016] Figure 3 shows the analysis results of a straight bevel miter gearset with a V0 profile shift coefficient (X1 = 0.7 and X2 = -0.7).

[0017] Figure 4 shows the analysis results of a straight bevel miter gearset with a pinion profile shift coefficient of X1 = 0.7 and a gear profile shift coefficient of X2 = 0.7.

[0018] Figure 5 shows the analysis results of a straight bevel gearset with a ratio of 2.9 with no profile shift.

[0019] Figure 6 shows the analysis results of a straight bevel gearset with a ratio of 2.9 with a V0 profile shift. The pinion profile shift coefficient is X1 = +0.7 and the gear profile shift coefficient is X2 = -0.7.

[0020] Figure 7 shows the analysis results of a straight bevel gearset with a ratio of 2.9 with a pinion profile shift coefficient of X1 = +0.7 and a gear profile shift coefficient of X2 = +0.7.

[0021] Figure 8 shows the outline in a cross-sectional view of pinion member and a gear member of a gearset.

[0022] Figure 9 shows an enlarged view of a portion of Figure 8.

[0023] Figure 10 shows a parallel profile shift, applied to the gearset in Figure 5. The pinion profile shift coefficient is X1 = 0.15 and the gear profile shift coefficient is X2 = 0.

[0024] Figure 11 shows a parallel profile shift, applied to the gearset in Figure 5. The pinion profile shift coefficient is X1 = 0.5 and the gear profile shift coefficient is also X2 = 0.5.

[0025] Figure 12 shows the outline in a cross-sectional view of a pinion member 90 and a gear member 91 (solid lines). Detailed Description

[0026] 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 scopeof 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.

[0027] 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.

[0028] 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.

[0029] 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.

[0030] The effect of profile shift is shown in Figure 1. Tooth image 1 (left) shows a tooth without any profile shift. The addendum 2 and the dedendum 3 split the tooth profile at the pitch line. A standard tooth profile usually has an addendum 2 of 1 ∗ mn and a dedendum 3 of 1.2 ∗ mn.

[0031] Tooth image 7 (center) has a profile shift of 0.3 ∗ mn. Addendum 8 has increased by 0.3 ∗ mn and dedendum 9 has decreased by 0.3 ∗ mn compared to tooth 1. The root thickness 10 of the tooth has increased versus root thickness 4 and the tip thickness 11 has reduced versus tip thickness 5. The undercut tendency of tooth 1 in region 4 is eliminated in tooth 7 (region 10).

[0032] A negative profile shift is shown in tooth image 13 (right). The addendum 14 has decreased by 0.3 ∗ mnand the dedendum 15 has increased by 0.3 ∗ mncompared to tooth 1. The root thickness 16 of tooth 13 has been reduced and the tip thickness 17 has increased compared to tooth 1. There is a visible undercut in the region of root thickness 16.

[0033] As indicated above, the left profile in Figure 1 has no profile shift. The profile in the center of Figure 1 has a positive profile shift coefficient of X = 0.3. In practice thismeans the tooth is shifted towards the manufacturing tool by 0.3 ∗ mn (X ∗ mn) and themanufacturing tool is shifted away from the work axis by the same amount. That way the tooth depth stays the same, but the tooth is now at a larger diameter. As a result, the tooth becomes thicker in the root and thinner at the tip. The right-side graphic in Figure 1 shows a negative profile shift coefficient of X = -0.3. The tooth is shifted away from the manufacturing tool by 0.3 ∗ mn and the manufacturing tool is shifted towards the work axis by the same amount. That way the tooth depth stays the same but the tooth is now at a smaller diameter, which makes the tooth thinner in the root and thicker at the tip.

[0034] Figure 1 shows the position of the pitch circle is unchanged, with respect to zero profile shift, regardless of whether the profile shift coefficient is positive or negative. The tooth reference circle shifts in accordance with the respective profile shift so that the tooth thickness, dZ, at the reference circle is kept constant in all profile shifted cases, which happens automatically in cylindrical gear hobbing where the same hob is used to cut gears with different profile shifts. The negative profile shift weakens the root of the tooth and also causes undercut, while the positive profile shift reduces or eliminates undercut.

[0035] Figure 2 shows the analysis results of a straight bevel miter gearset (Ratio = 1) with no profile shift coefficient (X1 = 0 and X2 = 0). The Ease-Off surface 20 to the left represents the consolidated length and profile crowning of a pair of meshing teeth. To the right in Figure 2, the tooth contact area 21 and the active working profile 22 is shown. The lost tooth area 23 consists partially of the root fillet radius and partially of kinematic undercut of the gear tooth. The lost area 24 represents kinematic undercut of the pinion tooth.

[0036] Figure 3 shows the analysis results of a straight bevel miter gearset with a V0 profile shift coefficient (X1 = 0.7 and X2 = -0.7). To the right in Figure 3, the tooth contact area 25 and the active working profile 26 are shown. The lost area 27 has doubled compared to 23 and also the lost area 28 increased versus 24. In the case of this example miter gearset, the V0 profile shift had a negative influence on the tooth profiles of pinion and gear.

[0037] Figure 4 shows the analysis results of a straight bevel miter gearset with a pinion profile shift coefficient of X1 = 0.7 and a gear profile shift coefficient of X2 = 0.7. The active working profile 30 increased by about 36% versus 24. Accordingly, the lost areas 31 and 32 do not contain any undercut anymore. The tooth contact 29 spread out in profile direction and the effective contact ratio (the average number of teeth which transmit load) increase by about 36%. A gearset according to Figure 4 will have areduced root bending stress and a reduced flank surface stress compared to the gearset versions in Figures 2 and 3.

[0038] Figure 5 shows the analysis results of a straight bevel gearset with a ratio of 2.9 with no profile shift. The tooth contact 36 is very small in profile direction. The number of pinion teeth is 12, which would require a profile shift in order to increase the active working area 37, which is only about 50% of the available profile. The lost areas 38 and 39 are large due to physical pinion undercut and kinematic undercut in the gear.

[0039] Figure 6 shows the analysis results of a straight bevel gearset with a ratio of 2.9 with a V0 profile shift. The pinion profile shift coefficient is X1 = +0.7 and the gear profile shift coefficient is X2 = -0.7. The tooth contact 40 has the same size as 36. The active working profile 41 increased slightly compared to 37 and the lost area 43 is significantly reduced, compared to 39. The lost area 42 increased by the same amount, the lost area 43 reduced. It can be observed in the example of Figure 5 and Figure 6 that the effect of the V0 profile shift improves the profiles of one member and deteriorates the profile of the mating member.

[0040] Figure 7 shows the analysis results of a straight bevel gearset with a ratio of 2.9 with a pinion profile shift coefficient of X1 = +0.7 and a gear profile shift coefficient of X2 = +0.7. The positive profile shift in both members increased the tooth contact 44 in profile direction and accordingly doubled the active working profile 45 compared to 37. The lost areas 46 and 47 are reduced versus 38 and 39. A gearset according to Figure 7 will have a reduced root bending stress and a reduced flank surface stress compared to the gearset versions in Figures 5 and 6.

[0041] Because a change of the shaft angle of a given design is not permissible, the inventor developed a profile shift which is parallel to the respective pitch line. The parallel pinion profile shift 55 shown in Figure 8 shifts the pinion axis 52 to location 61. The parallel gear profile shift 56 shifts the gear axis 53 to location 62. As a result, thecrossing point 54 between pinion axis 52 and gear axis 53 shifts to location 63. Test calculations showed that the parallel profile shift is limited to small profile shift coefficients.

[0042] Figure 8 shows the outline in a cross-sectional view of pinion 50 and a gear 51. Pinion axis 52 and gear axis 53 intersect at crossing point 54. The common pitch line of pinion and gear is line 57. Before the profile shift, the pitch line is also identical to the reference pitch line, which divides the profile of both members into the addendum and dedendum. A positive pinion profile shift 55 and a positive gear profile shift 56 are applied parallel to their common pitch line 57. The positive profile shift means that the cutting tool moves away from the respective member and increases their diameters. The pinion pitch line is still line 57, but the new profile dividing reference pitch line is now line 58. The gear pitch line is still line 57, but the new reference pitch line of the gear is now 59. In order to mate and roll pinion and gear, which have now increased diameters, the reference pitch lines 58 and 59 have to be moved back to the location of the original pitch line 57. This move can only be accomplished with a parallel shift of the pinion axis 52 with the amount 68 (which is the same amount, but the opposite direction of 55) to location 61 (distance “a” in Figure 9), and with a parallel shift of the gear axis 53 with the amount 69 (which is the same amount but the opposite direction of 56) to location 62 (distance “b” in Figure 9). In the new axis location, crossing point 54 moved to location 63.

[0043] Figure 9 shows an enlarged and detailed view of area 64 of Figure 8. Crossing point 54 moved to location 63. The offset coordinates from 54 to 63 are “d” in the vertical direction and “c” in the horizontal direction. Because the crossing points are the origin of pinion and gear and determine their location and the location of their teeth, the offset coordinates have to be calculated in order to position pinion and gear correctly relative to each other in order to mesh and roll both members after the profile shift:

[0044] (^^^^1 + ^^^^2)^^^^^^^^ = ^^^^ + ^^^^ (1)

[0045] ^^^^ = ^^^^^^^^ tan^^^^ =tan^^(2) 1^^2c …horizontal offset a … vertical shift of pinion member axis b … vertical shift of gear member axis

[0046] rearranging (1): ^^^^ = (^^^^1 + ^^^^2)^^^^^^^^ − ^^^^ (3)^^^^

[0047] plugging (3) into (2):(^^^^1+^^^^2)^^^^^^^^−^^^^tan ^^^^ = ta(4) 1n ^^^^2

[0048] (4) rearranged: ^^^^� 1 1 (^^^^1+^^^^2 )^^^^^^^^^^^^^^^^^^^^^^^^+^^^^^^^^^^^^^^^^� =^^^^^^^^^^^^(5) 12^^^^2

[0049] (5) solving for a: ^^^^ = (^^^^1+^^^^2)^^^^^^^^(6)

[0050] from (2): ^^^^ = ^^^^tan^^^^1

[0051] ^^^^ = (^^^^2 ∗ ^^^^^^^^) − ^^^^ (7)where: γ1 … pinion member pitch angle γ2 … gear member pitch angle mn… normal module d … vertical offset

[0052] Figure 10 shows a parallel profile shift, applied to the gearset in Figure 5. A pinion profile shift coefficient of X1 = 0.15 and a gear profile shift coefficient of X2 = 0 was applied. The tooth contact 70 looks similar to 36, but the active working profile 71 is larger than 37. The lost area 73 is only about 50% of 39 and the lost area 72 has about the same size as 38. In summary, the parallel pinion profile shift achieved a noticeable improvement by increasing the active working profile.

[0053] Figure 11 shows a parallel profile shift, applied to the gearset in Figure 5. The pinion profile shift coefficient is X1 = 0.5 and the gear profile shift coefficient is also X2 = 0.5. The tooth contact 75 is significantly smaller than 36, and the active working profile 76 is less than half of 37. The lost area 77 is slightly smaller than 38, but the lost area 78 has increased. Large profile shift coefficients may reverse the positive effect of increasing the active working profile, which is attributed to the fact that the pinion pitch line 58 does not pass through the crossing point 54 of the pinion axis 52 and the gear axis 53. Also, gear pitch line 56 does not pass through the crossing point 54 between pinion axis 52 and the gear axis 53. The reason is the departure from the kinematic coupling condition between pinion and gear. Figure 11 shows a significant degradation of the tooth contact and an increase of the lost area (compared to the baseline in Figure 5).

[0054] In another embodiment, it was discovered that a proportional profile shift could be realized by allowing a change of the shaft angle. This is done after a previous pre- correction of the shaft angle, such that the resulting shaft angle is equal to the nominal and required shaft angle. This is achieved in two steps. In step 1 the shaft angle is pre- corrected before the profile shift is applied as discussed below with reference to Figure 12.

[0055] Figure 12 shows the outline in a cross-sectional view of pinion 90 and gear 91 (drawn with solid lines). Pinion axis 92 and gear axis 93 intersect in crossing point 94 and include the nominal shaft angle Σ1. In a first step, before the profile shift is applied, apre-corrected shaft angle Σ2is calculated based on the desired profile shifts of pinion and gear. The desired pinion profile shift 95 is used at the outer cone distance ROUT to calculate an angle xϕ1:

[0056] ^^^^ = ^^^^^^^^^^^^^^^^^^^^^^^^^^^1∗^^^^^^^^^^^^1 ^�^^^^^^^^^^^^^^^^� (8)to pre- corrected position 97. The original pinion pitch line 99 moves to location 100. The rotated pinion is drawn with dashed lines.

[0058] The desired gear profile shift 96 is used at the outer cone distance ROUT to calculate an angle xϕ2:

[0059] ^^^^ = ^^^^^^^^^^^^^^^^^^^^2∗^^^^^^^^^^^^2 ^^^^^^^^�^^^^^^^^^^^^^^^^� (9)

[0060] The gear axis 93 is then rotated around 94 about angle xϕ2to the pre-corrected position 98. The original gear pitch line 99 moves to location 101. The rotated gear outline is drawn with dotted lines.

[0061] The pre-corrected shaft angle between pinion and gear is:

[0062] Σ2 = Σ1 − ^^^^^^^^1 − ^^^^^^^^2 (10)where: Σ1… initial and final required shaft angle Σ2… temporary shaft angle for pre-correction

[0063] After the pre-correction of the shaft angle, the initial pitch angles γ1I and γ2I are now meaningless. New pitch angles, γ1and γ2, have to be calculated according to the kinematic rule of cones rolling without slippage:

[0064] ^^^^1^^^^^^^^^^^^ ^^^^1^^^^2=sin^^^^(11) 2

[0065] with: ^^^^2 = Σ2 − ^^^^1 (12)

[0066] (12) plugged in (11) and solved for γ1: ^^^^sin(Σ2)1= ^^^^^^^^^^^^^^^^^^^( )� (13) ^^^^2+cos Σ2�where: Z1… pinion number of teeth Z2… gear number of teeth

[0067] After the pre-correction of shaft angle and pitch angles, the pinion and gear profile shifts are applied in a second step. The pinion profile shift 95 (X1*mn) will increase the pinion diameter and create reference pitch line 100. The pinion axis is now rotated counterclockwise by the angle xϕ1 to the original location 92, which rotates the pinion reference pitch line 100 to the location of the original pitch line 99.

[0068] The gear profile shift 96 (X2*mn) will increase the gear diameter and create reference pitch line 101. The gear axis is now rotated clockwise by the angle xϕ2 to the original location 93, which rotates the gear reference pitch line 101 to the location of the original pitch line 99.

[0069] After the application of the profile shifts to the gearset with a pre-corrected shaft angle and corrected pitch angles, the nominal shaft angle Σ1 has returned in combination with the desired profile shift.

[0070] To summarize the above, for the pre-correction, the nominal shaft angle Σ1 is reduced by xϕ1 and xϕ2 (equations (8) and (9)), resulting in a smaller shaft angle Σ2 (in case of positive profile shift coefficients X1 and X2). After this, the original pitch angle γ1I and γ2I do not apply anymore. New pitch angles γ1 and γ1 have to be calculated (equations (12) and (13)). At this point, a gearset with the correct number of teeth and a pre-corrected shaft angle and with a pitch angle, adjusted to the pre-corrected shaft angle, is the result. In step 2 the pinion and gear profile shifts are applied which move the pinion reference pitch line 100 away from the common pitch line 99. Also, the gear reference pitch line 101 is moved away from the common pitch line 99. In order to achieve congruent pinion and gear reference pitch lines 100 and 101, the pinion is rotated around crossing point 94 counterclockwise about the angle xϕ1. The gear is rotated around crossing point 94 clockwise about the angle xϕ2. As a result, the nominal and required shaft angle Σ1is re- established. The pitch lines of pinion and gear are not congruent anymore, but the reference pitch lines of pinion and gear are congruent and match line 99.

[0071] With this two-step approach, an angular profile shift, which is proportional along the face width (direction ROUT) with the distance from the crossing point 94, is the result. A proportional profile shift is adjusted to the changing tooth depth between toe 102 and heel 103. The profile shifts of pinion and gear can be chosen individually and independently. There are no significant negative side effects which would limit the amounts of proportional pinion and gear profile shifts.

[0072] It would seem that by reducing the shaft angle by xϕ1+ xϕ2, then calculating the new pitch angles and after that adding xϕ1+ xϕ2to the reduced shaft angle, one wouldarrive at the same tooth proportions as if the angular profile shift was never applied. However, the inventor discovered that the pre-corrected pitch angles are maintained when the angular profile shift is added. The reason is that the generating ratio (number of generating gear teeth divided by the number of work gear teeth) remains when the profile shift is added, and the nominal shaft angle is established. The pre-correction of the shaft angle in the first step (if X1+X2 >0) reduces the mean diameter of pinion and gear, which also reduces the module. The profiles of pinion and gear will already benefit from the module reduction because fine pitch teeth have less undercut tendency than course pitch teeth. The angular profile shift in the second step will then change the tooth profile according to Figure 1. Figure 4 and Figure 7 show the results of using the proportional profile shift.

[0073] While the invention has been discussed and illustrated with respect to straight bevel gears, the invention applies equally to spiral bevel gears and hypoid bevel gears. Additionally, while cutting tools and cutting methods have been discussed, the invention likewise contemplates grinding from solid as well as finishing methods and related tools such as grinding and hard skiving. The invention is applicable to generated and non- generated gears including those gearsets where one member is a generated member and the mating member is a non-generated member.

[0074] 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

CLAIMS What is claimed is:

1. A method of machining or producing teeth on a pinion member with a first tool and on a mating gear member with a second tool, said pinion member having an axis of rotation and said gear member having an axis of rotation, said method comprising: positioning said pinion member relative to said first tool so as to introduce an amount of profile shift on the teeth said pinion member during the machining or producing of the pinion member with the first tool, positioning said gear member relative to said second tool so as to introduce an amount of profile shift on the teeth of said gear member during the machining or producing of the gear member with the second tool, wherein the sum of the profile shift on the teeth of the pinion member and the profile shift on the teeth of the gear member equals a non-zero amount, machining or producing said pinion member with said first tool, machining or producing said gear member with said second tool, wherein subsequent to the machining or producing of the pinion member and the gear member, said pinion member and said gear member being rotatable in mesh with one another and forming said gearset having a common pitch line, and when in mesh, the pinion axis of rotation and the gear axis of rotation intersecting at a crossing point and being oriented with respect to one another at a predetermined shaft angle, wherein said predetermined shaft angle after the machining or producing is the same as a shaft angle of a reference gearset comprising said pinion member and said gear member machined or produced without said non-zero sum amount of profile shift.

2. The method of claim 1 wherein the profile shift of said pinon comprises shifting the pinion in a direction and by an amount wherein a reference pitch line of the shifted pinion is spaced from the common pitch line of the gearset, said pinion reference pitch line and said gearset common pitch line being parallel to one another.

3. The method of claim 2 wherein the axis of rotation of the pinion is shifted by an amount equal to the amount of pinion profile shift but in a direction opposite to the pinion shifting direction.

4. The method of claim 1 wherein the profile shift of said gear comprises shifting the gear in a direction and by an amount wherein a reference pitch line of the shifted gear is spaced from the common pitch line of the gearset, said gear reference pitch line and said gearset common pitch line being parallel to one another.

5. The method of claim 4 wherein the axis of rotation of the gear is shifted by an amount equal to the amount of gear profile shift but in a direction opposite to the gear shifting direction.

6. The method of claim 1 wherein prior to said profile shift positioning on the teeth of said pinion member and said profile shift positioning on the teeth of said gear member, a pre-corrected shaft angle is determined based on the amount profile shift of the pinion member and the amount of profile shift of the gear member.

7. The method of claim 6 wherein subsequent to the profile shift positioning of the pinion member and gear member, the axis of the pinion member is rotated aboutthe crossing point of the gearset axes and the axis of the gear member is rotated about the crossing point of the gearset axes so as to orient the axis of the pinion member relative to the axis of the gear member at said predetermined shaft angle.

8. The method of claim 1 wherein said gearset comprises a bevel gear set.

9. The method of claim 8 wherein said bevel gear set comprises straight bevel gears, spiral bevel gears or hypoid bevel gears.

10. The method of claim 1 wherein said first tool comprises a cutting tool or a grinding tool, and said second tool comprise a cutting tool or a grinding tool.

11. The method of claim1 wherein said machining or producing the pinion member comprises a cutting process or a grinding process, and said machining or producing the gear member comprises a cutting process or a grinding process.

12. The method of claim1 wherein said machining or producing the pinion member comprises a generating or a non-generating process, and said machining or producing the gear member comprises a generating or a non-generating process.

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