Psychoacoustic gear tooth surface shape modification

Abstract

A method of producing a tooth surface on a gear tooth by controlled removal of stock material from a process gear with a tool, wherein the process gear and the tool are movable relative to each other along and / or around a plurality of axes. The tool and the process gear are engaged with each other and then moved relative to each other with a generating motion along and / or around the plurality of axes. Stock material is removed from the process gear to produce the tooth surface on the process gear. The generating motion along and / or around the plurality of axes includes a motion along and / or around at least one of the axes, wherein the motion is defined by a function having a primary component and a secondary component. The primary component defines a maximum tooth surface shape deviation magnitude for each tooth of the process gear, and the secondary component defines a modification to the tooth surface for each tooth of the process gear.

Description

TECHNICAL FIELD

[0001] The present invention relates to the manufacture of bevel gears by a generating method with a modification of the tooth surface in order to achieve a reduction of psychoacoustic noise of the gear set. BACKGROUND

[0002] In the production of gears, particularly bevel gears and hypoid gears, two machining processes are commonly used, namely a generating process and a non-generating process.

[0003] The generating machining process can be divided into two categories, face milling (intermittently tooth dividing) and face hobbing (continuously tooth dividing). In the generating face milling machining process, a rotating tool is fed to a predetermined depth within the workpiece. Once this depth is reached, the tool and the workpiece are rolled together with a predetermined relative rolling motion, referred to as generating roll, as if the workpiece were rotating in mesh with a theoretical generating gear whose teeth are represented by the material removed surface of the tool. The profile shape of the teeth is formed by the relative motion of the tool and the workpiece during the generating roll. Typically, the tool is a cup-shaped grinding wheel or a cutting tool comprising a disc-shaped tool head having a plurality of cutting inserts protruding from an end face of the tool head.

[0004] Generating grinding for ring bevel gears or pinions uses a grinding wheel as the teeth of a theoretical generating gear, while the workpiece rolls on the generating gear teeth to finish the profile and lead of the workpiece tooth surface. During the generating roll, a computer-controlled (e.g., CNC) free-form machine such as disclosed in U.S. Patent No. 6,712,566 (the entire disclosure of which is incorporated herein by reference) changes its axis positions by hundreds of steps, for example, each step is represented by up to three linear axis positions (e.g., X, Y, Z) and up to three rotational axis positions (e.g., tool C, workpiece A, pivot B) of the machine. When generating grinding of bevel gears and hypoid gears is performed, typically five axes are needed (the grinding wheel (e.g., axis C) rotates independently) which change their axis positions hundreds of times during the rolling of each tooth surface.

[0005] In the generating face hobbing machining process, the tool and the machined gear rotate in time relationship and the tool is rolled (e.g., from toe to heel) so that all tooth spaces are formed in a single generating roll of the tool. Upon reaching the heel, the generating roll is completed.

[0006] Non-generating machining processes, whether intermittent or continuous, are those processes in which the profile shape of the teeth on the workpiece is directly produced by the profile shape of the tool. The tool is fed into the workpiece and the profile shape on the tool is imparted to the workpiece. The concept of a theoretical generating gear in the form of a "crown gear" applies to non-generating machining processes without the use of a generating roll. A crown gear is a theoretical gear whose tooth surface is complementary to the tooth surface of the workpiece in a non-generating machining process. Thus, when forming the tooth surface on a non-generating workpiece, the cutting inserts on the tool represent the teeth of a crown gear.

[0007] The relationship between the workpiece and the generating gear can be defined by a set of parameters known as the basic machine settings. These basic settings link the dimensions and proportions of the generating gear and the workpiece and provide a common starting point for gear design, thereby unifying the design procedure among many models of machines. The basic settings completely describe the relative positioning between the tool and the workpiece at any instant.

[0008] The basic machine settings for forming gears are known in the art and a disclosure of these settings can be found in Goldrich's "CNC Generation of Spiral Bevel and Hypoid Gears: Theory and Practice" (The Gleason Works, Rochester, New York, 1990). In the present disclosure, the basic machine settings that represent the closest prior art known to the applicant are identified as follows: (1) Radial S, which is the distance between the cradle axis and the tool axis; (2) Inclination angle Pi, which defines the angle between the cradle axis and the tool axis; (3) Rotation angle Pj, which defines the orientation of the tool axis with respect to a fixed reference surface on the cradle; (4) Swing angle q, which defines the angular position of the tool about the cradle axis; (5) Root cone angle Σ, which represents the orientation of the workpiece holder with respect to the cradle axis; (6) Slide base Xb, which is the distance from the machine center to the apparent intersection of the workpiece and cradle axes; (7) Head setting Xp, which is the distance along the workpiece axis from the apparent intersection of the workpiece and cradle axes to a point at a fixed distance from the workpiece; (8) Workpiece offset Em, which defines the distance between the workpiece axis and the cradle axis; (9) Rotational position of the workpiece Wg; and (10) Rotational position of the tool Wt, which is used in the case of face hobbing. In addition, in a generating machining process, the ratio-of-roll Ra, which is the ratio of the workpiece rotation to the cradle rotation, must be known.

[0009] It is well known in the gear industry that the area of bearing contact between meshing tooth surfaces should be limited to keep the contact area within the boundaries of the teeth, thereby preventing the tooth surfaces from contacting at their edges, which can lead to tooth damage and / or gear failure.

[0010] In order to limit the area of tooth contact, it is necessary to modify the theoretically conjugate tooth surface by introducing a modification, such as "crowning", to limit the contact area in unloaded or loaded conditions, thereby being insensitive to inaccuracies such as gear housing tolerances, gear members and assemblies, and deflections. Thus, during rolling, the modified mating tooth surfaces generally contact each other at one point or along a line, rather than the entire tooth surface of the mating tooth surfaces contacting, unlike the theoretical case of a perfectly conjugate tooth surface and a transmission system with zero deflection and tolerance. Therefore, the mating tooth surface surfaces are only conjugate at that point or along that line. The contact is limited to an area of a certain size, such that the contact area will remain within the tooth boundaries despite the influence of actual deflections, tolerances, and loads.

[0011] However, for example in the case of crowning, motion errors are introduced by the non-conjugate members rolling into engagement with each other. And the motion errors generate noise.

[0012] In general, psychoacoustics studies sound perception. In recent years, psychoacoustic sound pattern optimization has received increasing attention, one area of research being the application of psychoacoustics to gear noise. For example, Brecher et al. conducted a theoretical study including providing respective different tooth surface variations between teeth and teeth to reduce tonal noise. Tonal noise was used as a psychoacoustic measure in order to judge how gear noise is received by the human ear and how it is evaluated by the brain. Even if sound pressure measurements or single tooth surface tests indicate that a particular gear set is noisy and annoying, the gear noise can be perceived as unobtrusive or inaudible.

[0013] One known type of inter-tooth tooth surface variation is topography scattering, which introduces a variation in helix angle and a variation in pressure angle on the tooth surface of the gear to be optimized. The amount of helix angle variation and the amount of pressure angle variation between teeth and teeth are different. In order to quantify the amount of helix angle variation and the amount of pressure angle variation between teeth and teeth, random distributions as well as normal distributions have been applied.

[0014] Applying the change in helix angle and the change in pressure angle by using the revised machine settings results in tooth thickness errors and tooth division errors. Controlling tooth thickness errors and tooth division errors becomes very difficult or even impossible in cases where the tooth surface shape is corrected differently from tooth to tooth and in cases where both tooth surfaces of one groove are ground at the same time (i.e., finished). There is also the disadvantage that a complete set of machine settings (i.e., base settings) for each tooth groove must be transferred to the machine and compiled into the part machining program. For example, for a seventeen (17) tooth pinion, this requires 17 times the amount of data processing and data storage and makes closed loop feedback such as coordinate measuring machines more complex because the closed loop feedback must be applied to 17 sets of base settings for the individual 17 tooth pinions.

[0015] Psychoacoustically optimized gear sets at the state of the art exhibit the mentioned tooth thickness errors and tooth division errors. These errors degrade the gear quality by several levels and negatively affect the load carrying capacity of the gear set.

[0016] The tooth surface shape scatter of psychoacoustically optimized gear sets at the state of the art also results in tooth surface angle point deviations between the teeth of a pinion or ring gear in the range of + / - 5 to + / - 10 microns. This degree of tooth surface shape deviation is unacceptable for most gear manufacturers because such deviations can cause the contact pattern between tooth pairs to change, which brings the risk of tooth angle load concentration. Tooth angle load concentration can cause the gear set under load to fail prematurely.

[0017] Surface scatter can degrade the harmonic frequency level in individual tooth surface tests and create sidebands in the frequency spectrum between the harmonic frequencies. Therefore, the noise level in a vehicle with a gear set with targeted surface scatter at the noise critical speed and under load will be difficult for a human driver to identify. However, surface scatter should not degrade the gear quality level with respect to division errors and runout errors, and it should not cause individual tooth surface shape errors that would cause the contact pattern from one pair of meshing teeth to the next pair of meshing teeth to be inconsistent. Furthermore, the targeted tooth surface shape deviation must be designed to avoid edge contact along the boundaries of the teeth. In the case of high load applications, edge contact can cause surface damage, which can lead to tooth breakage. Another goal of psychoacoustically motivated tooth surface shape scatter is to make the gear set insensitive to small changes in shaft position. For closed loop correction and ease of grinding machine input data processing, it is desirable for a pinion or ring gear to have only one set of base settings, rather than one set of settings for each tooth groove. SUMMARY

[0018] The invention includes a method of generating a tooth surface on a gear tooth by controlled removal of stock material from a work gear with a tool, wherein the work gear and the tool are movable relative to each other along and / or around a plurality of axes. The tool and the work gear are engaged with each other and then moved relative to each other with a generating motion along and / or around the plurality of axes. Stock material is removed from the work gear to generate the tooth surface on the work gear. Wherein the generating motion along and / or around the plurality of axes includes a motion along and / or around at least one of the axes, wherein the motion is defined by a function that includes a primary component and a secondary component. The primary component defines a maximum tooth surface shape deviation amplitude for each tooth of the work gear, and the secondary component defines a modification to the tooth surface for each tooth of the work gear. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 A six-axis freeform bevel gear grinding machine is shown schematically.

[0020] Figure 2 A three-dimensional view of a bevel gear tooth is shown.

[0021] Figure 3 A modified material removal along a tooth contact path is shown, showing a first order function, a sine function, and a third order function.

[0022] Figure 4 A coordinate measurement of one tooth with a sine secondary function is shown.

[0023] Figure 5 A normal distribution as a primary function is shown.

[0024] Figure 6 Is a simplified two-dimensional illustration of a pressure angle variation.

[0025] Figure 7 A split sine function is shown with different frequencies and amplitudes in two segments.

[0026] Figure 8 A secondary function of Figure 7 is shown, wherein the toe dwell segment and the heel dwell segment surround the center of the roll. DETAILED DESCRIPTION

[0027] The terms "application," "the application," and "the present application" used in this specification are intended to refer broadly to all of the subject matter of this specification and any patent claims below. Statements containing these terms should be understood not to limit the subject matter described herein or to limit the meaning or scope of any patent claims below. Furthermore, this specification does not seek to describe or limit the subject matter covered by any claims in any particular part, paragraph, statement, or drawing of this application. The subject matter should be understood by reference to the entire specification, all drawings, and any claims attached hereto. The application can use other configurations and can be practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting.

[0028] The use of "including," "having," and "containing" 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 merely for identification 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 intended to include the plural forms as well, unless the context clearly indicates otherwise, and the term "and / or" includes a combination of one or more of the associated items.

[0029] Although directions such as upper, lower, upward, downward, rearward, bottom, top, front, back, etc., can be referenced below in describing the drawings, these references are made relative to the figures (as viewed) for convenience. These directions are not intended to be taken literally unless specifically so stated, and are not intended to limit the present application in any manner. Additionally, terms such as "first," "second," "third," etc., are used herein for descriptive purposes only and are not intended to connote importance or significance to one or the other, unless specifically so stated.

[0030] Details of the application will now be discussed with reference to the drawings, which are by way of example only. In the drawings, like reference numerals or characters will be used to refer to like features or components. The size and relative sizes of certain aspects or elements can be exaggerated for clarity or detailed explanation purposes. For better understanding of the application, and to facilitate focusing on and observing, doors, housings, internals or external protections, etc. can be omitted from the drawings.

[0031] The correction of the application is applicable to workpiece gears manufactured by a formative method. If both components are formative, surface scattering can be applied to both components. In the case of a Formate bevel gear set with a formative pinion and a non-formative ring gear, the correction can only be applied to the formative pinion.

[0032] The modification of the present invention is applied at least in two levels. The primary and higher level controls the maximum amount of deviation of the individual tooth's face shape. The primary modification control is preferably defined by a cosine function or by a normal distribution. Other mathematical functions (e.g. higher order functions), a sine function or a random distribution can also be applied to the primary modification.

[0033] The secondary and lower level controls the modification of the individual tooth surface itself. The secondary can be defined as a first order function, a third order function and / or a sine function. In addition, other higher order functions as well as cosine functions, normal distributions or random distributions can be utilized. The secondary modification of each individual tooth is not made by a conventional helix angle correction and pressure angle correction, but by a roll position dependent function formed based on the center point of the tooth face. The center point formed modification does not introduce tooth thickness errors or tooth division errors.

[0034] The machining process modification of the present invention such as uniaxial or multi-axial motion available on computer controlled freeform bevel gear cutting or grinding machines (e.g. US 6,712,566) to superimpose the tooth face shape (by the basic set-up formation) with small modifications preferably in the single micron range. The main design scheme of such machines is shown in Figure 1 and includes a six-axis freeform bevel gear grinding machine with a monolithic column as the base structure. The linear motion axes are X, Y and Z which are preferably mutually perpendicular with respect to each other. The rotational motion axes are A, B and C. A is the workpiece spindle rotation, B is the swing axis (i.e. the pivot axis) that adjusts the correct angular tilt between the tool axis and the workpiece axis, and C is the tool spindle rotation. The modification is determined such that the average tooth face shape of all the teeth of the gear with the tooth face shape scatter will be the same as the gear without any modification. Due to the roll position dependency of the single tooth correction, the tooth division and tooth thickness between teeth will not change as long as the reference roll position is the same or close to the tooth center point.

[0035] In general, it is known that a change in the workpiece axis (A-axis) rotation angle only is equivalent to a change in the roll ratio. As shown in Figure 2 the three-dimensional view of a bevel gear tooth, the roll ratio modification results in a combined change of the helix angle and the pressure angle. The first order change of the A-axis rotation (dependent on the distance of the actual roll position to the center roll position) removes less material at the beginning roll position (heel-to-root in the figure) as required for machining the nominal tooth face surface. The modification starts at the beginning roll position (heel-to-root in the figure) and ends at the end roll position (toe-to-tip in the figure). There is no modification along the contact line through the midpoint of the tooth face. This amount becomes smaller as the roll angle moves from the beginning roll to the center roll and is zero along the contact line between the tool and the tooth face at the center roll position. The contact line between the beginning roll and the center roll is schematically shown in Figure 2In the middle. As the rolling motion progresses from the center to the end, more material than is required for the nominal tooth surface is removed proportionally. This is determined by... Figure 2 The corrected surface is defined by the helix angle correction line and the pressure angle correction line.

[0036] In this invention, one or more of the following machine motion corrections are preferably performed:

[0037] • A-axis angle correction (angular movement around workpiece axis A)

[0038] • Y-axis position correction (linear movement along a direction parallel to the pivot axis B, where the pivot axis B is located) Figure 1 (The machine configuration is vertical)

[0039] • X-axis position correction (linear movement along axis A).

[0040] Correct the markings on axes A, Y, and / or X. Figure 1 In the machine structure shown.

[0041] Figure 3 This illustrates the corrected material removal along the contact path and perpendicular to the tooth surface. Figure 3 The diagram illustrates the first-order transformation of the A-axis. Besides or alternative to this first-order transformation, one or more more complex functions can be implemented. For example, third-order functions and sine functions can be applied, and these functions are also... Figure 3 As shown in the image.

[0042] In the first step of this invention, the maximum correction amount for each individual tooth is calculated in a first-level calculation. Figure 5 The diagram illustrates a normal distribution as a first-order function, which determines the maximum correction amount for each tooth of the modified pinion or gear. At tooth number 1, the maximum correction amount has a large negative value. Between teeth, this amount gradually becomes positive until it reaches a large positive value at tooth number zm, which is at the top of the normal distribution curve. Increasing the number of teeth shows a decreasing correction until it reaches a large negative value at tooth number n+1, which is one tooth more than the last tooth and therefore equal to the first tooth.

[0043] The maximum correction for a specific tooth is calculated as a cosine function and / or a normal distribution. Figure 5 This symbolically illustrates how the tooth shape, defined by a normal distribution, varies between teeth. Figure 5 In the diagram, only the maximum variation for each tooth is shown.

[0044] The first-order cosine function type is: cos[φ].

[0045] The function should start at the first tooth with φ = - π and end at the last tooth plus 1 with φ = + π. At the average tooth number (n + 2) / 2 (not necessarily an integer), the variable φ should be zero.

[0046] According to these boundary conditions:

[0047] If zi = 1, then φ = - π

[0048] If zi = n + 1, then φ = + π

[0049] If zi = zm, then φ = 0

[0050] The cosine function becomes:

[0051] cos[φ] = cos[(n + 2) / (-2) · (2 π / n) + zi · (2 π / n)] (1)

[0052] where:

[0053] φ... variable of the cosine function

[0054] zi... actual tooth

[0055] zm... tooth number in the middle of the function = (n + 2) / 2

[0056] n... tooth number of the target gear

[0057] n + 1... tooth number at the end of the function

[0058] The amplitude of the cosine function in equation (1) varies from -1 to +1. In order to receive an amplitude with the desired correction amount Corr perpendicular to the tooth surface, in the case of a modified A-axis rotation, the cosine function must be multiplied by:

[0059] Corr / (cos β · cos α · RM · sin γ) (2)

[0060] where:

[0061] Corr... correction amount perpendicular to the tooth surface (user input)

[0062] β... helix angle of the component

[0063] α... pressure angle of the component

[0064] RM... average pitch

[0065] γ... root cone angle of the component

[0066] The maximum A-axis correction amount of the corresponding tooth becomes:

[0067] ΔA max(zj) = Corr / (cos β - cos a - RM - sin y) - cos [(n + 2) / (-2) - (2π / n) + zj - (2π / n)] (3)

[0068] where:

[0069] ΔA max (zj)... maximum A-axis correction amplitude of tooth zj

[0070] Normal distribution as a first order function type: e -η

[0071] where:

[0072] -η... variable of Euler function

[0073] For the current 13-tooth example, the function shall start at tooth number zj = 1, where ΔA max = 0.01463 as threshold value. The threshold value is controlled by the chosen 0.1 multiplier in the exponent, which in this example provides an Euler function amplitude of 1.463%. This creates the desired cut-off before the function travels to infinite zero value. It shall also end at tooth number zj = n + 1, where ΔA max = 0.01463 as threshold value.

[0074] The exponent -η evolves to -η = 0.1 - (zj - n / 2 - 1) 2 to satisfy the following boundary conditions:

[0075] where zj = 1 and n = 13 or n / 2 = 6.5, which becomes -η = -0.1 - (1 - 6.5 - 1) 2 = -4.225 Likewise, zj = n + 1 = 14 and n / 2 = 6.5, which becomes -η = 0.1 - (14 - 6.5 - 1) 2 = -4.225

[0076] At zj = n / 2 = 6.5, which becomes -η = 0

[0077] With these definitions, the normal distribution becomes:

[0078] e -0.1(zi-n / 2-1)2 (zj = 1 → e -0.1(6.5)2 = 0.01463) (4)

[0079] To achieve a positive maximum of 1.0 and a minimum of (-1.0 + 2 - 0.02732) = -0.945, the Euler function is multiplied by 2 and shifted by 1.0 along the ordinate direction:

[0080]

[0081] In order to receive an amplitude with the required correction Corr normal to the tooth surface, in the case of a modified A-axis rotation, the cosine function must be multiplied by the following item of equation 2:

[0082] Corr / (cosβ·cosα·RM·sinγ)

[0083] The maximum A-axis correction of the corresponding tooth becomes:

[0084] ΔA max (zj) = Corr / (cosβ·cosα·RM·sinγ)·[2·e -0.1(zi-n / 2-1)2 -1] (6)

[0085] It is worth noting that the two first order functions start at tooth number 1 and end at tooth number n+1. If the function were to end at the last tooth numbered n, the last tooth and the first tooth would receive the same correction, which is not ideal for scatter effects. In Figure 5 the function resulting from equation 5 is illustrated in the middle. This function will reach an amplitude of -1.0 in positive and negative infinity. In order to design a usable normal distribution, thresholds must be defined at the expected starting and ending points of the function.

[0086] The second order A-axis correction is preferably determined along the contact path of a single tooth and uses the first order inter-tooth magnitude ΔA max . Figure 3 Three exemplary functions are shown in the middle.

[0087] The first order function boundary conditions are:

[0088] qs≤ qj≤ qe

[0089] If qj = qs => amplitude, then ΔA(zj, qj) = +1.0

[0090] If qj = qe => amplitude, then ΔA(zj, qj) = -1.0

[0091] Under these boundary conditions, the second order first order function Figure 3 (zj, qj) becomes:

[0092] ΔA(zj, qj) = ΔA max (zj)·2·(qj - q0) / (qs - qe) (7)

[0093] Where:

[0094] ΔA(zj, qj)... longitudinal coordinate value δ of the second order function depending on the rolling position

[0095] The sine function boundary conditions are:

[0096] qs≤ qj≤ qe

[0097] If qj = qs = > amplitude, then ΔA(zi, qj) = 0.0

[0098] If qj = qe = > amplitude, then ΔA(zi, qj) = 0.0

[0099] If qj = q0 = > amplitude, then ΔA(zi, qj) = 0.0

[0100] Maximum amplitude between qs and q0 = > +1.0

[0101] Maximum amplitude between q0 and qe = > -1.0

[0102] With these boundary conditions, the second order sinusoidal function ( Figure 3 ) becomes:

[0103] ΔA(zi, qj) = ΔA max (zi) sin [2π · (qj - q0) / (qs - qe)] (8)

[0104] The third order function boundary conditions are:

[0105] qs≤ qj≤ qe

[0106] If qj = qs = > amplitude, then ΔA(zi, qj) = +1.0

[0107] If qj = qe = > amplitude, then ΔA(zi, qj) = -1.0

[0108] If qj = q0 = > amplitude, then ΔA(zi, qj) = 0.0

[0109] With these boundary conditions, the second order third order function ( Figure 3 ) becomes:

[0110] ΔA(zi, qj) = ΔA max (zi) π [8π(qj - q0) 3 / (qs - qe) 3 ] (9)

[0111] Where:

[0112] qs... start scroll position

[0113] q0... center scroll position

[0114] qe... end scroll position

[0115] Instead of combining the helix angle and pressure angle variation by modifying the A-axis position as described above, it is also possible that the pressure angle is varied alone and can be applied alone or in addition to the A-axis variation. The mechanism to generate the pressure angle variation requires a combination of Y-axis position and A-axis rotation modification as shown in the two-dimensional diagram in Figure 6 which shows a simplified representation in order to explain the pressure angle variation. This variation is achieved by a small rotation of the workpiece axis (A-axis) and a connected Y-axis movement. The Y-axis movement is calculated such that the tool profile follows the center line of the tooth space, thus achieving the pressure angle variation.

[0116] Similar to the above described individual A-axis modification, the first order function is the cosine function (eq. (10) and eq. (11)) and / or the normal distribution (eq. (12) and eq. (13)). In case of a pressure angle modification, two functions for the 1st order modification have to be defined, where one function is used for the A-axis modification and the other function is used for the Y-axis modification:

[0117] Cosine: ΔA* max (zj) = -RM - Δα - cos[(n + 2) / (-2) - (2π / n) + zj - (2π / n)] (11)

[0118] ΔY max (zj) = -RM - Δα - cos[(n + 2) / (-2) - (2π / n) + zj - (2π / n)] (11)

[0119] Normal distribution: ΔA* max (zj) = Δα - [2 - e -0.1(zi-n / 2-1)2 -1] (12)

[0120] ΔY max (zj) = -RM - Δα - [2 - e -0.1(zi-n / 2-1)2 -1] (13)

[0121] where:

[0122] Δα... angle correction amount of the pressure angle (user input)

[0123] ΔA* max (zj)... maximum A-axis modification amplitude of tooth zj

[0124] ΔY max (zj)... maximum Y-axis modification amplitude of tooth zj

[0125] For the individual pressure angle modification, the second order function can be a first order function, a sine function and / or a third order function. Here, only the example of the preferred sine function is given for both said axes A and Y:

[0126] ΔA*(zj, qj) = ΔA*max (zi) · sin [2π · (qj - q0) / (qs - qe)] (14)

[0127] ΔY(zi, qj) = ΔY max (zi) π sin [2π · (qj - q0) / (qs - qe)] (15)

[0128] where:

[0129] ΔA*(zi, qj)... longitudinal coordinate value dependent on secondary function at roll position

[0130] ΔY(zi, qj)... longitudinal coordinate value dependent on secondary function at roll position

[0131] An additional correction using the X-axis can be made as the only correction or in combination with the A-axis correction and / or the Y-axis correction. Similar to the above-mentioned separate A-axis correction, the primary function is a cosine function (equation (16)) and / or a normal distribution (equation (17)).

[0132] Cosine: ΔX max (zi) = ΔX · cos [(n + 2) / (-2) · (2π / n) + zi · (2π / n)] (16)

[0133] Normal distribution: ΔX max (zi) = ΔX · [2 · e -0.1(zi-n / 2-1)2 -1] (17)

[0134] where:

[0135] ΔX... X-axis correction amount (user input)

[0136] ΔX max (zi)... maximum X-axis correction amplitude of tooth zi

[0137] The secondary function can be a first-order function, a sine function and / or a third-order function. Here, only the most preferred example of a sine function is shown.

[0138] ΔX(zi, qj) = ΔX max (zi) · sin [2π · (qj - q0) / (qs - qe)] (18)

[0139] where:

[0140] ΔX(zi, qj)... longitudinal coordinate value dependent on secondary function at roll position

[0141] Preferably according to equation (15), the Y-axis correction can also be made as the only correction. Similar to the separate X-axis correction described above, the first order function is a cosine function (equation (16)) and / or a normal distribution (equation (17)). The second order function can be a first order function, a sine function and / or a third order function.

[0142] In order to provide a second order tooth constraint function which can be optimized and adjusted in its amplitude and its wavelength, the following equation (19) was developed. This equation is only applicable for a sinusoidal tooth surface shape correction:

[0143] qm= (qs+ qe) / 2

[0144] qs≤ qj< qm= >f = f Toe (user input); Amp = A Toe (user input)

[0145] qm≤ qj< qe= >f = f Heel (user input); Amp = A Heel (user input)

[0146] ΔA(zi, qj) = ΔA max (zi) · Amp · sin [2πf · (qj-qm) / (qs-qe)] (19)

[0147] wherein:

[0148] qm... average rolling position

[0149] tToe... toe section frequency

[0150] fHeel... heel section frequency

[0151] f... actual frequency

[0152] AToe... amplitude of the toe section

[0153] AHeel... amplitude of the heel section

[0154] Amp... actual amplitude

[0155] The visualization of the control parameters for the wavelength and the amplitude is shown in Figure 7 which shows a plot with a split sine function. The first half of this function starts at qs and ends at qm. The amplitude of this first half function is 0.6 and the frequency is 0.8 (extended wavelength). The second half of this function starts at qm and ends at qe. The amplitude of this second half function is 1.3 and the frequency is 1.2 (reduced wavelength). Figure 7 The plot of the amplitude and the frequency of the standard sine function is based on the definition of an amplitude of 1.0 and a frequency of 1 / (2π) (equal to a wavelength of 2π).

[0156] Between toe and mean face, the frequency factor f Toe is 0.8 (longer wavelength). Between mean face and heel, the frequency factor f Heel is 1.2 (shorter wavelength). At this time, an average rolling position is introduced. In the case of a hypoid pinion, the central rolling position is not at the geometric center of the tooth surface. The average rolling position can ensure that the secondary modification function is more centered.

[0157] Preferably, a pause is introduced at the center of the secondary function and preferably at a position adjacent to the center of the secondary function. The amplitude of the secondary function at the mean face (center of the face width) at the center of the rolling position of the generating roll is zero. In coordinate measurement, the grid center point is used to determine the inter-tooth indexing error. In most practical cases, the grid center point does not exactly match the center of the rolling position, but has a slightly different position. In order to avoid the introduction of inter-tooth indexing errors, it is preferred that the amplitude of the secondary function at the position of the measurement grid center point is zero. This is preferably achieved by a toe pause section and a heel pause section. Figure 8 A toe pause section ΔToe between the rolling center (mean face) and the toe and a heel pause section ΔHeel between the rolling center and the heel are shown. When machining within the two pause sections, the secondary function is effectively switched off and no modification of the tooth surface surface is machined (the amplitude of the secondary function within the pause sections is zero). The preferred amount of the toe pause section and the heel pause section is between 0° and 4° of the roll.

[0158] Equation (19) can be applied to the individual A-axis modification (equation (8)), to the pressure angle modification (equations (14) and (15)) and to the X-axis modification (equation (18)).

[0159] Figure 4 An example of a sinusoidal tooth surface shape modification of a generated bevel pinion is shown, which is represented on a symbolic three-dimensional tooth with a 9x5 surface point measurement grid.

[0160] Figure 4 The basic data of the bevel gear set to which the pinion shown in Fig. 6 belongs are as follows:

[0161]

[0162] In the example, the grinding wheel is rotated around the axis C Figure 1) rotates and moves relative to the workpiece so as to engage the tooth surface of the workpiece (e.g., the opposing tooth surface of the tooth slot) with the tool. The grinding wheel and the workpiece move relative to each other in a generating motion (i.e., rolling), wherein the workpiece rolls relative to the grinding wheel (representing the teeth of a theoretical generating gear) to finish the profile and lead of the tooth surface of the workpiece. During the generating roll, a computer-controlled (e.g., CNC) freeform machine (e.g., Figure 1 ) changes its axis positions to guide the grinding wheel and the workpiece along appropriate motion paths relative to each other to perform the generating roll to produce the desired tooth surface modification. In Figure 4 , the tooth surface modification is introduced by a modification of the A-axis (workpiece axis in Figure 1 ) which is defined by a normal distribution as a first order function and a sinusoidal function as a second order function. An example of such A-axis modification is defined by equation (8).

[0163] Figure 4 The conventions used in

[0164] are consistent with the standard outputs of gear metrology. The contact path is from the heel root to the toe top on concave tooth surfaces and from the heel top to the toe root on convex tooth surfaces. The flat plane is the nominal tooth surface and the wobble surface represents the modified surface. A sinusoidal function can be identified along the contact path. Along the contact line direction, all modification values are equal, which forms a three-dimensional modification function.

[0164] Figure 4 The modification is shown to be zero at the tooth surface center and at the entry and exit points. The maximum tooth surface shape deviation amplitude is marked as the amplitude of the sinusoidal function in Figure 4 . Despite the considerable sinusoidal function amplitude of 10 microns, the corner point deviation has the desired low amount between 0 microns and 3 microns. The tooth contact sweeps along the contact path from the entry to the exit. The instantaneous contact area is a line or an elongated ellipse oriented along the contact line direction. The effective contact length along the contact path direction under light load is between the maximum and minimum points of the sinusoidal function (the area with hash marks in the upper graph marked as concave tooth surface). The effective contact area covers only about 50% of the tooth surface. The reason is that the adjacent tooth pairs carry the load before and after these transition points. In the case of the sinusoidal function modification, the tooth meshing impact (marked in Figure 4 ) occurs in the area of zero slope. Other functions, like the first order modification, show a slope in the impact area that worsens the impact condition. The sinusoidal tooth shape change compared to the nominal tooth shape changes the impact timing between tooth and tooth without worsening the impact condition. This provides the best conditions to achieve a reduction in psychoacoustic noise without causing indexing errors or edge contact with reduced strength, except for the fact that the tooth surface center point remains unmodified at all times.

[0165] The preferred results of the manufacturing method of the present invention are achieved when the maximum amount of primary tooth spacing control follows a normal distribution and the secondary control of individual tooth correction follows a sinusoidal function. The sinusoidal secondary correction results in only a very small tooth corner point deviation within a 5-micrometer range, twice the deviation of prior art methods. Furthermore, the secondary correction is driven by a rolling position relative to the center rolling position or relative to any selected rolling position (e.g., the average rolling position). This means that the original tooth surface will exist at the center rolling position (or the average rolling position). Because the tooth spacing (or pitch) and tooth thickness are measured at the tooth center point, the machining method of the present invention does not introduce any indexing or tooth thickness errors.

[0166] right Figure 4 Further research has shown that a sine function oriented along the contact path direction (=the direction of contact motion) will reduce the risk of edge contact and compensate for minor misalignment between pinions and gears.

[0167] Although the invention has been discussed in relation to modifications along the A, Y, and / or X directions of motion, it is also applicable to the B and / or Z directions of motion. For bevel gear grinding, the tool rotation about axis C is independent of all other motions, and the generating method does not depend on the rotational motion along axis C. Therefore, the invention is not applicable to motion along axis C.

[0168] Although the method of the present invention has been described in relation to grinding, the modified tooth surface shape of the present invention can be produced using other generating processes (such as solid cutting, scraping, and grinding). Furthermore, the method of the present invention is applicable to machining processes that simultaneously machine two opposing tooth surface surfaces of a tooth groove or machining only one tooth surface surface of a tooth groove at a time.

[0169] While the invention has been described with reference to preferred embodiments, it should be understood that the invention is not limited to its details. The invention is intended to include modifications that will be obvious to those skilled in the art without departing from the spirit and scope of the appended claims.

Claims

1. A method for producing a tooth surface on a gear tooth by controlled removal of raw material from a machined gear using a tool, the machined gear and the tool being movable relative to each other along and / or about a plurality of axes, the method comprising: Engage the tool with the machining gear. The tool and the machining gear are moved relative to each other in a generating motion along and / or around the plurality of axes. The raw material is removed from the machining gear to create a tooth surface on the machining gear. The generating motion along and / or around the plurality of axes includes motion along and / or around at least one of the axes, the motion being defined by a function comprising a first-order component and a second-order component, the first-order component defining the maximum tooth surface shape deviation of each tooth of the machined gear, and the second-order component defining the correction of the tooth surface of each tooth of the machined gear. The secondary component is determined along the contact path of each tooth of the processed gear, and the determination of the secondary component includes the inter-tooth quantity value obtained from the primary component.

2. The method according to claim 1, wherein, The first-order component includes at least one of the cosine function and the normal distribution.

3. A method for creating a tooth surface on a gear tooth by controlled removal of raw material from a machined gear using a tool, the method comprising: A gear manufacturing machine is provided, the machine having multiple axes and including a workpiece mandrel rotatable about a workpiece axis A and a tool mandrel rotatable about a tool axis C, the workpiece mandrel and the tool mandrel being movable relative to each other along at least one of linear axes X, Y and Z and about a pivot axis B. A workpiece is provided on the workpiece mandrel. A tool is provided on the tool mandrel. Engage the tool with the machining gear. The tool and the machining gear are moved relative to each other in a generating motion, the generating motion including generating rolling along and / or around the plurality of axes. The raw material is removed from the machining gear to create a tooth surface on the machining gear. The generating motion along and / or around the plurality of axes includes a corrective motion along and / or around at least one of the axes, the corrective motion being defined by a function comprising a first-order component and a second-order component, the first-order component defining the maximum tooth surface shape deviation magnitude for each tooth of the machined gear, and the second-order component defining the correction to the tooth surface of each tooth of the machined gear. The secondary component is determined along the contact path of each tooth of the processed gear, and the determination of the secondary component includes the inter-tooth quantity value obtained from the primary component.

4. The method according to claim 3, wherein, The corrective motion includes motion along and / or around at least one of the following: Angular motion around workpiece axis A, The linear motion X along the workpiece axis A, and Linear motion Y along a direction parallel to the pivot axis B.

5. The method according to claim 4, wherein, The linear motion Y is along the vertical direction.

6. The method according to claim 3, wherein, The first-order component includes at least one of the cosine function and the normal distribution.

7. The method according to claim 3, wherein, The inter-tooth magnitude is applied to a tooth constraint correction function, which includes at least one of the following: First-order function sine function, and Third-order function.

8. The method of claim 3, further comprising introducing a pause segment in the secondary component, the pause segment being located at least at the center of the rolling position of the generated rolling, wherein, Within the pause segment, the amplitude of the secondary component is zero.

9. The method according to claim 8, wherein, The pause includes at least one of a toe pause section and a heel pause section, wherein the toe pause section is located between the center of the rolling position and the toe end of the tooth, and the heel pause section is located between the center of the rolling position and the heel end of the tooth.

10. The method according to claim 9, wherein, Each of the toe pause section and the heel pause section extends between 0° and 4° of the rolling radius.

11. The method according to claim 3, wherein, The tool includes a grinding wheel.

12. The method according to claim 3, wherein, The first-order component includes a normal distribution, and the second-order component includes a sine function.

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