Manufacture of gears with addendum and / or root modification

Abstract

A method of making a tooth profile surface on a workpiece. The method includes providing a gear cutting tool and rotating the gear cutting tool about an axis of rotation. The cutting tool and the workpiece engage each other and roll together according to the generating roll to create a contoured surface of the tooth. The generating roll includes a first roll ratio and a second roll ratio, where the first roll ratio and the second roll ratio are different from each other, and one of the first roll ratio and the second roll ratio results in a contoured section being formed on the tooth profile surface.

Description

Field of the Invention

[0001] The present invention relates to gears, in particular to the manufacture of straight bevel gears, and to providing relief at the tip and / or root of the tooth surface of a gear. Background Art

[0002] In the production of gears, especially bevel gears, two machining processes are generally employed, namely the generating process and the non-generating process. Each process can be divided into two categories, face milling (intermittent indexing) and face hobbing (continuous indexing). In face milling, each entry of the tool forms a tooth space, and in face hobbing, the tool and the workpiece rotate in a timed relationship and the tool is fed to a certain depth so that all tooth spaces are formed in a single entry of the tool.

[0003] In the generating process, a rotating tool is fed to a predetermined depth into the workpiece. Once this depth is reached, the tool and the workpiece roll together with a predetermined relative rolling motion (called generating roll), as if the workpiece were rotating in mesh with a theoretical generating gear, the teeth of which are represented by the surface removed by the blank of the tool. The profile shape of the tooth is formed by the relative motion of the tool and the workpiece during the generating roll.

[0004] The non-generating process refers to those processes in which the profile shape of the teeth on the workpiece is directly produced by 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. Generating roll is not employed.

[0005] Differential gears are generally straight bevel gears with a small number of teeth. Differential gears generally have a coarse pitch (″pitch″ is the distance between similar equally spaced tooth surfaces along a given line or curve), and generally have a pressure angle of about 25° or higher. The term ″coarse pitch″ is used when the number of teeth relative to the gear diameter is small. For example, 10 teeth on a gear with a diameter of 100 mm (module = 100 / 10 = 10 mm) are considered to be a coarse pitch, while 10 teeth on a gear with a diameter of 30 mm (module = 30 / 10 = 3 mm) are considered to be a fine pitch. Those skilled in the art generally consider teeth (or gears) with a module less than 5 mm to be ″fine pitch″, while teeth (or gears) with a module of 5 mm or greater are considered to be ″coarse pitch″.

[0006] Figure 1 An example of a straight bevel gear differential gear 2 with a plurality of teeth 4 is shown, where each tooth has a tooth tip surface 6, a tooth root portion 8, and a pair of tooth flank surfaces 10. The region 11 between a pair of consecutive teeth is called the tooth ″space″ or tooth ″slot″, where the tooth root portion 8 coincides with the bottom of the tooth space.

[0007] The differential gears have been cut by various methods. Figure 2 Fig. shows the cutting of straight bevel gears using a pair of tilted rotary cutters 12, 14 (commonly referred to as the upper cutter and the lower cutter respectively), the pair of tilted rotary cutters having cutting blades 16 for cutting tooth spaces in a workpiece 18. The cutter 12 is capable of rotating about an axis 22, and the cutter 14 is capable of rotating about an axis 20. In the generating process on a conventional mechanical cradle-type machine, the tilted cutters 12, 14 are typically fed to a predetermined depth in the workpiece, and the generating roll of the machine cradle (not shown) starts in a manner synchronized with the rotation of the workpiece 18 to form the tooth profile surfaces 24, 26. The rotating cutting blades 16 effectively interlock to cut the same tooth space simultaneously (e.g., US2,567,273).

[0008] Figure 3 and Figure 4 Fig. shows an example of a tool and method for manufacturing a straight bevel gear differential gear using a large circular cutter 30, the large circular cutter having a cutter diameter of, for example, 18 inches, 21 inches or 25 inches (460 mm, 535 mm or 635 mm). For example, see US 2,267,181, the entire disclosure of which is incorporated herein by reference. As Figure 3 seen, the cutting blades 32 are oriented on the outer periphery of the cutter body 34 and are grouped into roughing blades, semi-finishing blades and finishing blades. The cutter operates in a single indexing process and makes only one rotation when cutting a complete tooth space of the gear 38. In a conventional cutting process, the cutter is positioned at the toe end of the tooth space and moves from the toe to the heel during the roughing and semi-finishing portions of the cycle. When the cutter reaches the heel end of the tooth space, all the roughing blades and semi-finishing blades have been used. The cutter then moves back to the toe end to finish the tooth space with the finishing blades during a co-directional cutting process. There is a large space 36 between the last finishing blade and the first roughing blade, which allows the machine to index the workpiece to the next tooth space position without the cutter having to stop rotating and without a cutter retraction movement. The tool material is preferably high-speed steel, and the surface speed applied is typically between 20 m / min and 40 m / min, which makes this cutting process a broaching process.

[0009] The fact that one cutter rotation completes one slot and includes the indexing time makes the circular broaching process discussed above very fast. Compared with using a pair of tilted rotary cutting tools ( Figure 2Compared with the straight bevel gear cutting carried out by [[ID=]], the cutting time of the circular broaching process is only a fraction (e.g., 15% to 20%) of that of the interlocking rotary tool process, where the rotary cutting blades of the pair of inclined rotary cutting tools are effectively interlocked to cut the same tooth space using the same high-speed steel tool material.

[0010] The disadvantages of the circular broaching process are that the workpiece tooth profile is formed in a profile cutting process that cannot produce the precise figure-eight tooth shape for conjugate meshing with low motion error. Another disadvantage is that the circular broaching blade profile is circular rather than involute or involute approximation. Yet another disadvantage of circular broaching is the lack of available degrees of freedom for flank shape correction. Profile cutting using a circular blade profile produces a certain amount of length crowning (i.e., in the direction of tooth length). The selection of the tooth surface profile curvature radius can produce profile crowning. The profile (i.e., tooth height, root-to-tip direction) crowning must be large enough to mask the kinematic inaccuracies present due to the profile cutting process. It is almost impossible to fine-tune the tooth surface to optimize the rolling performance without redefining the cutting edge profile and manufacturing a new cutter.

[0011] After heat treatment, the tooth surfaces of gears cut by the circular broaching process are not hard-finished but are used with the deformations from the heat treatment process. This is sufficient for most practical applications. However, with the increasing demand of electric vehicle drivetrain manufacturers for high power density and quiet operation, the need for hard-finishing operations has become a requirement in many applications.

[0012] Another manufacturing method for differential gears that achieved an industrial breakthrough in the 1970s is forging. In forging, a billet with a temperature above 2,000°F (1,093°C) is pressed in a hard steel die. The die has the negative shape of the toothed side of the differential gear. The holes and the back side of the forged part are machined after the forging process. Some forging processes incorporate calibration as a finishing process. Calibration is carried out after forging to improve the surface finish as well as the tooth transposition quality. Nowadays, forging has achieved high-quality differential gears with a highly cost-effective manufacturing process. The advantages of forging are low manufacturing cost, high integrity of the produced parts in terms of bending and impact, and the ability to apply modifications such as placing reinforcing webs at the toe and heel tooth roots, as in Figure 5As seen in the gear set of, for example, the stiffening web includes a pinion 40 and a side gear 42 (sometimes referred to as the "gearing" members of a differential gear set). Some drawbacks are that the stiffening web limits the elastic bending of the teeth, which can lead to surface damage (such as pitting) under high load conditions and also cause cracks in the tooth roots. Additionally, due to the presence of the stiffening web, the tooth root line is not straight or curved, making it impossible to machine with any prior art gear machining processes. For example, machining must be carried out through a slow process using a ball nose end mill and a multi-axis machining center.

[0013] The forged gear has a scale, which is a thin outer layer with a higher hardness and a different steel structure. The forged scale also causes surface damage under high loads. The forged gear has a certain tooth thickness variation between the first part and the last part of the die tool life. This variation results in a change in backlash after assembly, which cannot be controlled. The forged differential gear is too tight at the beginning of the die tool life, which reduces efficiency. At the end of the die tool life, the forged gear has too much backlash, which causes a clicking noise and excessive driveline backlash.

[0014] Another method for manufacturing a straight bevel gear differential gear is disclosed in U.S. 7,364,391, the entire disclosure of which is incorporated herein by reference, and the method includes a single-side cutting process that rough cuts and finish cuts all first sides of the teeth in a first step (such as FIG. 6(a)), and then changes the position of the cutter in a second step (such as FIG. 6(b)) to finish cut all second sides of the teeth. This two-step process can be carried out on a computer-controlled multi-axis gear manufacturing machine, such as the computer-controlled multi-axis gear manufacturing machine disclosed in US 6,712,566, the entire disclosure of which is incorporated herein by reference. This two-step process produces an accurate involute (figure-eight shape) and allows modification of the flank shape. After heat treatment, the differential gear can be ground with a CBN grinding process in a manner similar to cutting. Compared with the circular broaching or forging discussed above, this two-step process has various advantages, especially for differentials used in an electric vehicle driveline. The drawback of this two-step process is that, for differential gears, the productivity is lower compared to circular broaching or forging.

[0015] A suitable cutting tool for performing the above two-step process is shown in Figure 7 and Figure 7 shows a peripheral cutting tool 50 removably fixed to the spindle 48 of a machine tool (not shown), such as, for example, the one disclosed in US 6,712,566. The cutting tool 50 includes a tool head 52 having a plurality of stick blades 54. Clamping blocks 56 are located above each stick blade. Figure 7The cutting tool therein has a top ring 58 located above the clamping block 56, and the top ring has an integrated clamping screw 59.

[0016] High power density and low rolling noise are the main requirements for electric vehicle differential gears. Conventional differential gears of the prior art (whether cut by circular broaching, forged, or cut by a two-step process) generally have a large-profile drum shape, which results in large motion errors (300 μrad to 2,000 μrad) and a low effective contact ratio (ε γ below 1.0). SUMMARY OF THE INVENTION

[0017] The present invention relates to a method of manufacturing teeth on a workpiece, the teeth having a tooth profile surface that includes a tip portion and a root portion, a toe end, a heel end, and a face width extending between the toe end and the heel end. The method includes providing a gear cutting tool and rotating the gear cutting tool about a rotational axis. The cutting tool and the workpiece are engaged with each other and roll together according to generating rolling to produce the profile surface of the teeth. The generating rolling includes a first rolling ratio and a second rolling ratio, wherein the first rolling ratio and the second rolling ratio are different from each other, and one of the first rolling ratio and the second rolling ratio causes a modified section to be formed on the tooth profile surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 An example of a differential gear is shown.

[0019] Figure 2 An interlocking arrangement of a pair of inclined cutting tools for cutting tooth grooves in a workpiece, which is a view of a circular broach in the process of cutting the tooth grooves of a differential gear.

[0020] Figure 3 A circular broach is shown.

[0021] Figure 4 It is an image of a circular broach for cutting the grooves of a differential gear.

[0022] Figure 5 A cross-sectional view of a forged differential gear set is shown.

[0023] Figures 6(a) and 6(b) show a two-step process for manufacturing straight bevel gears.

[0024] Figure 7 An outer peripheral cutting tool for performing the two-step process of Figures 6(a) and 6(b) is shown.

[0025] Figure 8 An example of the motion error and tooth contact of a differential gear pair is shown.

[0026] Figure 9 A contact analysis of a differential gear pair without a profile drum is shown.

[0027] Figure 10 Shows a cutting insert profile with a straight end modification.

[0028] Figure 11 Shows a cutting insert profile with a curved end modification.

[0029] Figure 12 Shows the contact analysis of a differential gear pair cut using the insert end modification.

[0030] Figure 13 Shows a cutting insert profile with a straight protrusion.

[0031] Figure 14 Shows a cutting insert profile with a curved protrusion.

[0032] Figure 15 Shows the contact analysis of a differential gear pair cut using the protruding insert.

[0033] Figure 16 Shows the tip modification using the modified hob ratio tip section.

[0034] Figure 17 Shows the contact analysis of a differential gear pair cut using the modified hob ratio section. Detailed Description

[0035] The terms "invention", "the invention", and "this invention" as used in this specification are intended to refer broadly to all of the subject matter of this specification and any of the following patent claims. Statements containing these terms should not be construed as limiting the subject matter described herein or the meaning or scope of any of the appended patent claims. Additionally, this specification does not seek to describe or limit the subject matter covered by any claim to any particular portion, paragraph, statement, or drawing of this application. The subject matter should be understood by reference to the entire specification, all of the drawings, and any appended claims. The invention can use other configurations and can be practiced or implemented in various ways. Also, it should be understood that the language and terminology used herein are for descriptive purposes and should not be regarded as limiting.

[0036] Details of the invention will now be discussed with reference to the drawings, which illustrate the invention by way of example only. In the drawings, like reference numerals will refer to like features or components. For purposes of clarity or detailed explanation, the size and relative size of certain aspects or elements may be exaggerated.

[0037] As used herein, the use of "comprising", "having", "including", and variations thereof are intended to cover the items listed hereinafter and their equivalents as well as additional items. The use of letters or numbers to identify elements of a method or process is for identification purposes only and does not imply that the elements should be performed in a particular order. As used herein, the singular forms "a", "an", and "the" are also intended to include the plural forms 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.

[0038] Although the following may refer to directions such as upper, lower, upward, downward, backward, bottom, top, front, rear, etc. when describing the drawings, for convenience, these references are made with respect to the drawings (as normally observed). These directions are not intended to be taken literally or to limit the invention in any way. Additionally, unless expressly stated, terms such as "first", "second", "third", etc. are used herein for descriptive purposes and are not intended to indicate or imply importance or significance.

[0039] Figure 8 An Ease-Off diagram of an example of a prior art differential gear pair is shown at the top. Ease-Off represents tooth flank shape modifications, such as length crowning and profile crowning, which are required to prevent edge contact under load and in the case of deflection and manufacturing tolerances. The Ease-Off amplitude along the marked profile section represents the profile crowning of the example gear set. This profile crowning corresponds to the kinematic error shown in the middle of Figure 8 The kinematic error is represented by three consecutive parabolas (the three consecutive parabolas represent three pairs of consecutive tooth engagements). The rated kinematic error value is the distance from the top line to the intersection of the parabolas. In this example, the rated kinematic error is 900 μrad. A large kinematic error will in turn increase the operating noise and reduce the power density. To reduce the kinematic error, the profile crowning must be reduced, which results in an almost conjugate profile. The tooth contact pattern is shown below the kinematic error diagram. The tooth contact is located at the center between the root end and the tip end of the tooth.

[0040] Figure 9 An Ease-Off diagram of a differential gear pair with an almost conjugate profile section is shown at the top. To provide a small amount of profile crowning, the profile is intentionally made not completely conjugate. A conjugate tooth profile has no crowning in the profile direction, which would result in a kinematic error of zero. Figure 9 The almost conjugate profile in Figure 9 results in a kinematic error of 10 μrad. The lack of a meaningful Ease-Off on the tooth profile in Figure 9 results in edge contact at the tooth tip surfaces of the pinion and the gear under load and in the case of deflection. The bottom part of

[0041] To avoid edge contact between the meshing teeth, tip relief can be implemented on the pinion teeth and the gear teeth. As Figure 10 shown, a cutting blade with a straight end modification can be applied to achieve tip relief. Figure 10 The cutting edge profile with the tip at the top and the blade end at the bottom is shown. This end modification starts at HKOW from the tip and has an angle DKOW. The starting point HKOW and the blade modification angle DKOW are selected to achieve the desired tip relief on the cut teeth. An example of a suitable machine for grinding the cutting blade to produce the modification under discussion is the Blade Profile Grinder (BPG) commercially available from The Gleason Works, Rochester, New York.

[0042] As Figure 11 shown, a circular end modification is also possible. This end modification has a starting point (at HKOW from the tip) and a blade modification radius RKOW. The starting point HKOW and the blade modification radius RKOW are selected to achieve the desired tip relief on the cut teeth.

[0043] Figure 12 The Ease - Off diagram of a differential gear pair with the pinion cutting blade and the gear cutting blade having blade end modifications is shown at the top. Since the tip follows the root line of the corresponding gear, and since the tip (face angle) of the differential gear tapers relative to the root line due to the tapered depth teeth of the straight bevel gear, the pinion blade end modification produces a modification segment that is larger at the heel and decreases in magnitude towards the toe (compared with Figure 9 ). There is a position between the center and the toe where the modification is zero. The modification at the tip of the Ease - Off is produced by the gear cutting blade, and the modification at the root is produced by the pinion cutting blade. Figure 12 The intermediate motion error is 240 μrad because the profile section "cuts" through a part of the modification area. The bottom figure shows the tooth contact pattern.

[0044] Another method of producing modifications at the tip and root ends of the Ease - Off is to use a blade with a protrusion as Figure 13 shown, which shows the profile of a cutting blade with a straight protrusion. This protrusion has a starting point (at HPRW from the tip) and a protrusion angle DALW relative to the cutting edge. The starting point HKOW and the protrusion angle DALW are selected to achieve the desired root relief on the cut teeth.

[0045] It is also possible to apply as Figure 14The curved projection shown, which shows the profile of a cutting blade with a circular projection. The projection has a starting point (at HPRW from the tip of the cutting edge) and a projection radius DPRW. The starting point HKOW and the projection radius DPRW are selected to achieve the desired root relief on the cutting tooth.

[0046] As Figure 15 shown (compared with Figure 9 ), the projection provides almost uniform relief along the face width on both sides of the Ease-Off. However, root relief is not desirable as it weakens the root of the tooth and reduces the power density. The motion error generated by the projection blade is 310 μrad. All blade modifications (such as blade end relief and projection) require complex blade profile modifications, which is a customized development for a specific gear set design. After the task of designing a specific blade modification (end relief or projection) has been completed, blade or cutter head reinforcement (as typically done for straight bevel gears) cannot be carried out.

[0047] Figure 16 A cross-sectional view of a differential gear profile is shown. The straight line represents the cutting edge profile of the cutting blade, which is straight without any modification. The two solid lines represent the cutting blades that generate the tooth profile, where a specific tooth has the correct (i.e., theoretical) roll ratio. The "roll ratio" is the ratio of the number of teeth in the theoretical generating gear to the number of teeth in the gear being cut. At the starting point of the tip relief, the roll ratio changes, and the dashed line shows the effect of the modified roll ratio, with the marked relief section. The tooth profile (e.g., involute) of a straight bevel gear is typically generated with a constant roll ratio. The method of the present invention is based on the change from a constant roll ratio to a modified roll ratio at a specific rolling position.

[0048] Figure 16 Schematically shows how the cutting blade profile generates an involute tooth profile (solid cutting edge line) with a first (e.g., constant) roll ratio and how it generates tip relief (dashed cutting edge line) with a second (e.g., modified) roll ratio. The "modified" second roll ratio is a modification relative to the first roll ratio. The modified roll ratio starts at the starting point of the modification ( Figure 16 ), and it ends at the tip of the tooth (or slightly higher, at the rolling position where the machine kinematics causes the generating roll to end). When the machining process moves the cutter blade from the tip to the root of the tooth, this end position is usually called the starting roll position. In available cutting processes, rolling from the root to the tip or from the tip to the root is possible. The modified roll ratio can be constant (different from the constant first roll ratio), or it can be calculated as a higher-order function according to the rolling position. For example, the corresponding polynomial can be written in the form of a Taylor series development:

[0049] RA = RA0·{1 - (c / 2!)·Δq - (d / 3!)·Δq2 -(e / 4!)·Δq 3 -(f / 6!)·Δq 4 …} (1)

[0050] Δq = q - q T

[0051] Condition: (q S <q T ) → {q S ≤q≤q T}

[0052] Condition: (q S >q T ) → {q T ≤q≤q S}

[0053] Wherein:

[0054] RA... Effective rolling ratio [-]

[0055] RA0... Base rolling ratio [-]

[0056] c... First-order coefficient [1 / (°)]

[0057] d... Second-order coefficient [1 / (°) 2

[0058] e... Third-order coefficient [1 / (°)3]

[0059] f... Fourth-order coefficient [1 / (°) 4

[0060] Δq... Rolling ratio difference [°]

[0061] q... Actual rolling position [°]

[0062] q T ... Tooth tip modification start position [°]

[0063] q S ... Tooth tip rolling position (tooth tip modification end position) [°]

[0064] Alternatively, for example, the modified rolling ratio can be determined by a general high-order polynomial, spline function, circular function, or elliptic function.

[0065] The tooth tip modification start position and the magnitudes of the coefficients are obtained through calculation or experiment to produce a desired modification amount in the desired region.

[0066] Figure 17 ​​An Ease-Off diagram of a differential gear pair (i.e., a gear member and a pinion member) manufactured with a modified roll ratio segment is shown at the top. The modification at the tip of the Ease-Off diagram is the result of the tip modification of the gear member, and the modification at the root of the Ease-Off diagram is the result of the tip modification of the pinion member. These modifications are larger at the heel and smaller at the toe, but they exist along the entire face width. The variation of the modification amplitude along the tooth width is caused by the direction of the generating marks, which have an angle slightly different from the face angle of the corresponding member. For straight bevel gears, this has practical advantages, as it results in small motion errors and also provides good protection against edge contact towards the heel. Under high loads, the contact extends towards the heel. The modified roll ratio segment provides the following desirable combination: a differential gear that rolls quietly under low loads and protection against edge contact under both low and high loads.

[0067] The results of the tip modifications on the pinion and gear teeth are shown in Figure 17 (compared with Figure 9 ). These modifications are almost uniform and look similar to the Figure 15 boss modifications in. The resulting motion error is 13 μrad. The advantage of the tip modification (which gets larger towards the heel and smaller towards the toe) is that when a load is applied, the contact area moves towards the heel, and thus a larger modification amount is desired at the heel. This ensures that the modification amount in the middle of the face results in a low motion error amplitude. The advantage of the tip modification relative to the root modification (boss) is that there is no weakening of the tooth root, and the modified roll ratio will not require any expensive blade modifications and can be optimized or changed only by changing the corresponding machining parameters. The bottom figure shows the tooth contact pattern for this example.

[0068] Although the method of the present invention has been discussed and illustrated with reference to gear tip modifications, the present invention is equally applicable to generating gear root modifications. Additionally, the modified roll ratio can be further modified by adjusting the machine settings (including cutter tilt, rotation, and / or cutter reference height) during generating rolling. For example, a defined second-order combination of cutter tilt and rotation can be used to cause a torsional motion of the cutter in order to balance the modification effect between the heel and toe on the tooth.

[0069] Furthermore, the method of the present invention also considers grinding. The grinding wheel is considered a cutting tool with undefined cutting edges.

[0070] Although the present invention has been described with reference to the preferred embodiments, it should be understood that the present invention is not limited to its details. Without departing from the spirit and scope of the appended claims, the present invention is intended to include modifications that are obvious to those skilled in the art.

Claims

1. A method of manufacturing teeth on a workpiece, the teeth having a tooth profile surface that includes a tip portion and a root portion of the tooth, a toe end, a heel end, and a face width extending between the toe end and the heel end, the method comprising: rotating a gear cutting tool about a rotational axis, engaging the cutting tool and the workpiece, rolling the cutting tool and the workpiece together according to generating rolling to produce the profile surface of the tooth, wherein the generating rolling includes a first roll ratio and a second roll ratio, wherein the first roll ratio and the second roll ratio are different from each other, and one of the first roll ratio and the second roll ratio causes a modified section to be formed on the tooth profile surface.

2. The method according to claim 1, wherein the modified section includes a modified section located at the tip portion of the tooth profile surface.

3. The method according to claim 1, wherein the modified section includes a modified section located at the root portion of the tooth profile surface.

4. The method according to claim 1, wherein the first roll ratio is a constant.

5. The method according to claim 1, wherein the second roll ratio is a constant.

6. The method according to claim 1, wherein one of the first roll ratio and the second roll ratio is defined as a higher-order function.

7. The method according to claim 1, wherein the tooth profile surface is an involute.

8. The method according to claim 1, wherein the modified section extends along the entire face width of the tooth.

9. The method according to claim 1, wherein the modified section is larger at the heel end of the tooth than at the toe end of the tooth.

10. The method according to claim 1, wherein the gear cutting tool includes a grinding wheel or a plurality of cutting blades.

11. The method according to claim 1, wherein one of the first roll ratio and the second roll ratio causes the modified section formed on the tooth profile surface to be further modified by adjusting machine settings during the generating rolling.

12. The method according to claim 11, wherein the machine settings include at least one of cutter tilt, cutter rotation, and cutter reference height.

13. The method according to claim 1, wherein the workpiece includes at least one of a gear member and a pinion member in a gear pair.

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