Tooth face shape design method of helical gear

Abstract

To design a tooth face shape which can secure a load capacity of a tooth face while setting contact stress on a contact line to allowable contact stress or lower.SOLUTION: In an entire length contact region in which a contact line exists while extending from a tooth tip up to a tooth root out of a reference tooth face being a tooth face at which the tooth faces line-contact with one another in a non-load state, relative curvature radii of the tooth faces in a plurality of division points included in the contact line differ from one another, and therefore, contact stresses of the plurality of division points when loads are applied on the tooth faces differ from one another. In the entire length contact region, a modification region and a modification amount when modifying the tooth faces for deforming the reference tooth face to a concave direction so that the contact stress exceeding the allowable contact stress becomes the allowable contact stress or less are decided on the basis of a distribution of the contact stress on the contact line when a load larger than a load in a tooth face design specification is applied to the tooth face of the reference tooth face as a whole, and the allowable contact stress being a limit value of the contact stress which takes into account tooth face damage.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a method for designing the tooth flank form of a helical gear. [Background technology]

[0002] Involute tooth profiles have the advantages of being unaffected by changes in the center distance, easy tooling, and knowledge based on a large amount of research and proven results. However, in recent years, machining precision has improved dramatically, making it possible to create complex shapes, and attempts have been made to design tooth profiles other than involute tooth profiles. As one of these, attempts have been made to design tooth profiles that incorporate meshing between convex and concave tooth surfaces, whereas involute tooth profiles contact each other. In the past, there were VBB tooth profiles and trochoid tooth profiles, but recent tooth profiles that look similar to involute tooth profiles include the Cornu tooth profile (Patent Document 1) and the sine tooth profile (Non-Patent Document 2). It has been found that such tooth profiles have a non-uniform contact stress distribution on the tooth surface, and include areas with higher contact stress than involute tooth surfaces.

[0003] Deforming a portion of the gear tooth flank that is in line contact under no load to meet a specific purpose is called tooth flank modification. Conventionally, various types of tooth flank modification have been used, including "tooth contact" tooth flank modification, which takes into account the machining and assembly errors of helical gears, "tooth deflection" tooth flank modification, which takes into account the deflection of the teeth due to load and the initial biting when the gears start to mesh, and "vibration" tooth flank modification, which takes into account vibration caused by tooth bending and elastic deformation.

[0004] In Patent Document 1, which concerns "tooth deflection" tooth surface modification of helical gears, three-dimensional bias tooth surface modification is applied to the tooth surfaces outside the complete contact line region of long-face-width helical / double-helical gears that have a reference tooth surface with an involute curve as a tooth profile and transmit high loads, so that corner contact does not occur at the tip or root of the tooth width end due to "tooth deflection". The complete contact line region has a width of an integer multiple of the contact line pitch in the tooth width direction on the tooth surface of the gear. Patent Document 1 states that by applying bias tooth surface modification to the tooth surfaces outside the complete contact line region, it is possible to transmit power by meshing smoothly without generating large shocks at the start and end of meshing. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Patent No. 2965913 [Non-patent literature]

[0006] [Non-Patent Document 1] Research on Gears, Yokendo, edited by Masao Naruse, 1962, pp.77-133. [Non-Patent Document 2] Sine tooth gear design system, (2022.12), Amtec Corporation website, http: / / www.amtecinc.co.jp / new-catalogue / 32.seigen-hagata.htm [Non-Patent Document 3] Design of Cylindrical Gears, Kinki Gear Forum, Taiga Publishing, (1979), pp.134,147. [Non-Patent Document 4] JIGMA Gear College (Master Course) Text, edited by the Japan Gear Manufacturers Association, (2022), p64-66. Summary of the Invention [Problem to be solved by the invention]

[0007] When there is no load, the tooth flank of one gear and the tooth flank of the other gear come into contact along a curve, and this contact curve is called the contact line. Here, we will call the tooth flank that makes linear contact when there is no load the "reference tooth flank." Among the tooth flanks of helical gears with parallel axes, there are gears in which the relative curvature of the tooth flank along the contact line changes significantly. For such gear tooth flanks, even if the load per unit length of the contact line (hereinafter referred to as "line load") is constant, the contact stress (Hertzian stress) on the contact line will vary greatly.

[0008] If the contact stress on the tooth surface exceeds the allowable contact stress determined by the tooth material, damage to the tooth surface such as pitting will occur. For this reason, in gears where the relative curvature of the tooth surface along the contact line changes significantly, particular attention must be paid to areas with high contact stress. [Means for solving the problem]

[0009] The present invention provides a method for designing the tooth flank shape of a helical gear, in which, within the extent of a reference tooth flank, which is a tooth flank where tooth flanks are in line contact with each other under no load, within a full-length contact region where a contact line extends from the tooth tip to the tooth root, the relative radii of curvature of the tooth flank at multiple division points included in the contact line are different from one another, and therefore the contact stresses at the multiple division points when a load is applied to the tooth flank are different from one another.

[0010] Based on the distribution of contact stress on the contact line when a load greater than the load of the gear design specifications is applied to the entire tooth surface of the reference tooth surface within the full-length contact area, and the allowable contact stress, which is the limit value of the contact stress taking into account damage to the tooth surface, a modification area and modification amount are determined for the tooth surface modification that deforms the reference tooth surface in a concave direction so that the contact stress exceeding the allowable contact stress becomes equal to or less than the allowable contact stress.The tooth surface shape is then designed by modifying the reference tooth surface based on the determined modification area and modification amount.

[0011] The amount of modification can be determined so that within the modification region, the distribution of contact stress after tooth surface modification includes a flat distribution of contact stress along a limit line indicating the allowable contact stress. The load that is greater than the load of the gear design specification can be made greater than the load of the gear design specification by the amount of reduction when the load on the entire tooth surface is reduced by the tooth surface modification relative to the reference tooth surface.

[0012] The tooth surface modification curve specified by the determined modification area and modification amount can be a first tooth surface modification curve in which the distribution of the modification amount is convex in the central area of ​​the tooth height, a second tooth surface modification curve in which the distribution of the modification amount is inclined relative to the tooth height direction, or a third tooth surface modification curve in which the first tooth surface modification curve and the second tooth surface modification curve are added together. Effect of the Invention

[0013] According to the present invention, it is possible to design a tooth flank shape that can ensure the load capacity of the tooth flank while keeping the contact stress on the contact line below the allowable contact stress. [Brief description of the drawings]

[0014] [Figure 1] FIG. 2 is a diagram illustrating the full-length contact area and the contact length changing area on the tooth surface of a helical gear. [Diagram 2] FIG. 2 is a diagram showing a contact stress distribution in a reference tooth profile, a contact stress distribution when tooth surface modification according to the present embodiment is performed, and a modification curve of the tooth surface. [Diagram 3] FIG. 13 is a diagram showing the contact stress distribution of an unmodified reference tooth profile when different loads are applied. [Figure 4] FIG. 1 is a diagram showing an example of the estimated results of contact stress distribution, sum of line loads, and maximum Hertz stress for a reference tooth profile and a modified tooth profile. [Diagram 5] FIG. 1 is a diagram showing an example of a calculation result of contact stress distribution before and after performing tooth surface modification including "tooth contact" tooth surface modification. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] The tooth flank profile design method of this embodiment is targeted at helical gears, and designs the final tooth flank (tooth flank profile) by modifying the tooth flank with respect to a reference tooth flank. Here, the reference tooth flank is the tooth flank with which the helical gear makes line contact along a curve when no load is applied.

[0016] (Tooth surface area where tooth surface modification is performed) The tooth surface is modified in at least a portion of the overall contact area, which will be described later.

[0017] The contact line on the reference tooth surface of a helical gear is inclined with respect to the tooth trace line. When helical gears are rotated, looking at the tooth profile of one of the helical gears, the contact line is generated from the tooth tip at one end of the face width, and as the helical gear rotates, the contact line moves toward the center of the face width and extends from the tooth tip to the tooth root. As shown in Figure 1, the region from the tooth tip at one end of the face width to where the contact line extends to the tooth root is called the "contact length change region" (the hatched region on the left side in Figure 1).

[0018] After the contact line extends from the tooth tip to the tooth root, the contact line moves from one end of the face width to the other end as the helical gear rotates, while still extending from the tooth tip to the tooth root. Figure 1 shows an example of the contact line, with the arrow indicating the direction of movement of the contact line. Here, the region where the contact line moves in the face width direction when it extends from the tooth tip to the tooth root is called the "full length contact area". The full length contact area is the contact area of ​​the tooth surface excluding the contact length changing area.

[0019] When the contact line passes through the full-length contact area and reaches the tooth tip at the other end of the face width, as the helical gear rotates, the contact line moves toward the tooth base at the other end of the face width, shortening the length of the contact line and finally disappearing. The region from when the length of the contact line starts to shorten until it disappears is also the "contact length change region" (the hatched region on the right side in Figure 1). As shown in Figure 1, the tooth flank of the tooth profile has contact length change regions at both ends in the face width direction, and the full-length contact region exists between the two contact length change regions.

[0020] In the "helical" gear to which the present invention is applied, the relative curvature of the tooth flank changes along the contact line. The shape analysis of the relative curvature can be performed based on the contents described in Non-Patent Document 1. Examples of tooth profiles in which the relative curvature of the tooth flank changes significantly along the contact line include the Cornu spiral tooth profile (Patent No. 4376938, etc.) and the sine tooth profile, and even in an involute tooth profile with a large gear ratio, there are areas where the relative curvature of the tooth flank changes significantly depending on the conditions.

[0021] (Design method for tooth surface modification) A method for designing the tooth flank shape of a helical gear will be described. In this embodiment, the tooth flank is modified with respect to the reference tooth flank for the contact line within the above-mentioned full-length contact area, and the final tooth flank (tooth flank shape) is designed.

[0022] In the design of tooth surface modifications that take into account surface pressure, the first step is to apply a specific load, such as a design specification value, to the tooth surface and estimate the distribution of contact stress (Hertzian stress) that occurs along the contact line within the entire contact area.

[0023] There are several methods for calculating tooth surface contact stress, including using the Hertz contact stress theory by assuming a load per unit length of the contact line (line load), and using simulations such as the finite element method or boundary element method to calculate contact stress. Either method can be used to estimate the distribution of contact stress along the contact line. Here, we will explain the former method, the method of using the Hertz contact stress theory by assuming a line load.

[0024] In the Hertz contact stress theory, which deals with contact between cylinders, the length of the cylinder is considered to be sufficiently long. In contrast, in the tooth flank shape targeted in this embodiment, the change in the relative curvature of the tooth flank along the contact line of the tooth flank is large. However, in this case, this Hertz contact stress theory is considered to be valid as a zeroth approximation value for the gear tooth flank.

[0025] If the contact line is divided into fine intervals, the Hertzian contact stress at each interval can be expressed by equation (1).

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[0026] According to equation (1), the line load P l and the relative radius of curvature R n By calculating the contact stress P n In the evaluation of the load capacity of the tooth surface of a helical gear, there is an example (Non-Patent Document 3) where the line load of the tooth surface of the helical gear is set to a constant value. Following this example, here, the line load P l is assumed to be constant within the entire contact area.

[0027] Allowable contact stress P of helical gear tooth surface 0MAX and contact stress P n Based on the distribution of the contact stress, the modification area and the modification amount of the tooth surface are determined. Here, the allowable contact stress P 0MAX is determined by the material and heat treatment of the helical gear.

[0028] The mechanism by which the load capacity is improved by tooth surface modification will be explained using Figures 2 and 3. In the schematic diagrams of Figures 2 and 3, the tooth surface modification is applied to a partial area of ​​the tooth surface, but in reality, the tooth surface modification for the purpose of improving the surface pressure is applied over a wide area of ​​the tooth surface to make the modification curve a smooth curve.

[0029] Conventionally, there have been performed "tooth contact" tooth surface modification that takes into account machining errors and assembly errors of helical gears, "tooth deflection" tooth surface modification that takes into account tooth deflection due to load and initial engagement, and "vibration" tooth surface modification that takes into account vibration due to tooth bending and elastic deformation. Here, it goes without saying that the above-mentioned conventional tooth surface modification can be performed in addition to the "surface pressure" tooth surface modification in this embodiment. In actual tooth surface modification, at least the "tooth contact" tooth surface modification is taken into account, and the modification area and modification amount for the "surface pressure" tooth surface modification are designed taking into account the entire tooth profile.

[0030] Since the tooth flanks of the gear, pinion and rack share a common contact line, once the rack tooth flank or tooth profile is determined, the tooth flanks or tooth profiles of the gear and pinion are also determined. Once the tooth profile curve of the cross section perpendicular to the straight tooth trace of the rack is determined, the rack tooth flank is determined. For this reason, rack tooth profile modification has the same meaning as tooth flank modification.

[0031] In the first stage of designing tooth surface modification, the contact stress distribution on the tooth surface is obtained. If no load is applied to the tooth surface, no contact stress will occur, so in actual design, a load F0 higher than the gear specifications is desired and a load F0 is applied to the gear tooth surface. In this sense, the "desired load F0" is applied to the entire tooth surface.

[0032] Figure 2 shows the distribution of contact stress in a rack reference tooth profile when a load F0 is applied to the entire tooth flank, the distribution of contact stress when the same load F0 is applied to a tooth profile after the tooth flank has been modified (hereinafter referred to as the "modified tooth profile"), and a curve (modification curve) showing the modification area and amount of modification of the tooth flank. In Figure 2, the horizontal axis indicates the position in the rack tooth profile direction from the tooth tip to the tooth root, and the vertical axis indicates contact stress. In the modification curve shown in Figure 2, the modification area is specified by the horizontal axis, and the modification amount is specified by the vertical axis.

[0033] Modifying a tooth flank means deforming a part of the tooth flank with respect to a reference tooth profile. In the tooth flank modification of the present invention, the position of the tooth flank of the modified tooth profile is shifted toward the inside of the tooth from the position of the tooth flank of the reference tooth profile.

[0034] In the contact stress distribution of the reference tooth profile shown in Fig. 2, the contact stress P n is the allowable contact stress P 0MAX In this embodiment, at least the contact stress P n is the allowable contact stress P 0MAX For the area higher than the above, the contact stress P nm is the allowable contact stress P 0MAX In the modification of the tooth surface, the modification area of ​​the tooth surface is determined, and the modification amount of the tooth surface at each division point on the contact line included in the modification area is also determined.

[0035] The modified area of ​​the tooth surface is the contact stress P of the reference tooth profile. n Among the distribution of contact stress P n is the allowable contact stress P 0MAX It is necessary to include a region where the stress is higher than the contact stress exceeding region (hereinafter referred to as the "contact stress exceeding region"). In actual design, depending on the purpose, the modification region of the tooth surface may be made approximately the same as the contact stress exceeding region, but generally the modification region of the tooth surface is made to be a wider region than the contact stress exceeding region. Making the modification region of the tooth surface wider than the contact stress exceeding region can also increase the load capacity of the entire tooth surface. In the modification curve shown in Figure 2, the modification region of the tooth surface is set to be a little wider than the contact stress exceeding region, prioritizing ease of understanding of the explanation of the principle of tooth surface modification.

[0036] The amount of tooth surface modification Δδ is the contact stress P of the reference tooth profile. n and allowable contact stress P 0MAX Specifically, the larger the contact stress difference is, the larger the modification amount Δδ of the tooth surface is made, and the smaller the contact stress difference is, the smaller the modification amount Δδ of the tooth surface is made.

[0037] At each point on the contact line, the contact stress ΔP that needs to be reduced by tooth surface modification n is expressed by equation (2).

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[0038] Tooth surface modification reduces contact stress by ΔP n The relationship between the amount of modification Δδ and the amount of reduction in contact stress must be calculated. An example of how to calculate this relationship will be described later. l There is research that suggests that the amount of approach between the tooth flanks is roughly proportional to the amount of approach between the tooth flanks. In order to clearly show how tooth flank modification works, let us assume that the proportionality constant K is also known, and as shown in equation (3), the amount of change in line load ΔP l It is assumed that the amount of tooth modification Δδ is proportional to the amount of tooth modification. In other words, the amount of approach between the tooth flanks changes due to tooth modification, but this change in the amount of approach is considered to have the same effect as the change in the amount of approach due to a change in line load.

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[0039] Contact stress P n and line load P l and the relative curvature of the tooth surface R n Since the relationship is given by equation (1), the reduction in contact stress at each segment of the contact line ΔP n The decrease in line load ΔP l is known, and by using equation (3), the tooth surface modification amount Δδ at each division point can be obtained.

[0040] The load applied to the entire tooth surface of the unmodified (reference tooth surface) is F0, and the line load per unit length of the contact line is P l By modifying the tooth surface, the contact stress in the modified area P n is the allowable contact stress P 0MAX Contact stress P is lower than nm And the line load P l is the amount of change ΔP l The load on the entire tooth surface that is borne by the modified area is reduced by ΔF0. However, if we look at the area other than the modified area (unmodified area), the contact stress P n is the allowable contact stress P 0MAX The contact stress Pn There is some margin. Therefore, the load on the entire tooth surface is increased to (F0 + ΔF0), which is the load on the entire tooth surface of the non-finished (reference tooth surface) by the amount ΔF0 by which the load on the entire tooth surface is reduced by tooth surface finishing. At this time, the line load increases slightly in both the finished area and the non-finished area. In the state where the load (F0 + ΔF0) is applied to the non-finished tooth surface (reference tooth surface), the tooth surface load is reduced by approximately ΔF0 due to tooth surface finishing, and the applied load becomes (F0 + ΔF0 - ΔF0). In this way, with the total line load value, which is the load on the entire finished tooth surface, maintained at the same value as the total line load value of the reference tooth surface, the contact stress P nm can be made less than or equal to the allowable contact stress P 0MAX as follows.

[0041] Fig. 3 shows the contact stress distribution (broken line and solid line) of the non-finished reference tooth profile. When the desired load F0 is applied, in the contact stress distribution shown by the broken line in Fig. 3, the maximum contact stress greatly exceeds the allowable contact stress P 0MAX . Therefore, the load F L applied to the entire reference tooth surface is set to a value (F L < F0) smaller than "the load F0 applied to the entire desired tooth surface", so that the maximum contact stress is less than or equal to the allowable contact stress P 0MAX . The solid line in Fig. 3 is the contact stress distribution when a load F L smaller than the load F0 is applied.

[0042] As described above, the relationship between the tooth surface finishing amount Δδ and the tooth surface contact stress has an important role, and it is necessary to estimate this relationship. This relationship can be obtained by simulation using the finite element method or the like. In this sense, the method shown below is an example of an estimation method.

[0043] When the contact length between the cylindrical surfaces with radii R1 and R2 is l and the load on the cylinder is P, according to Hertz's contact stress theory, the maximum Hertz stress (contact stress) P0 at the contact part is expressed by Equation (4), where the Young's modulus of the two cylinders is E i , and the Poisson's ratio is v i .

Equation

[0044] The contact stress P0 at any point on the contact line with a relative radius of curvature R is the allowable contact stress P 0MAX The line load at the division point P is calculated as follows. l (P l =P / l) is the relative curvature of the tooth surface at the division point (1 / R) and the allowable contact stress P 0MAX Using this, it can be expressed as equation (5).

[0045]

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[0046] Uniform line load P lEVEN The amount of modification Δδ of the tooth flank is determined based on the above. As described above, the tooth flank modification in this embodiment is to make the reference tooth flank into a recessed shape.

[0047] By the way, the load P l When a load is applied, the teeth approach each other, and there is a phenomenon in which the tooth surface appears to be elastically deformed and recessed, and this approach amount is known as the elastic approach amount δ. In the relationship between the load and the elastic approach amount, if the amount of elastic approach amount is eliminated by tooth surface modification, the load will be eliminated by the tooth surface modification, so the elastic approach amount can be replaced with the tooth surface modification amount. In other words, when a tooth surface modification amount Δδ is applied, the load ΔP that causes a change in the elastic approach amount Δδ is l It can be considered that the line load is reduced by the amount of

[0048] As a result of research into the elastic approach of gear tooth flanks, there is a document (Non-Patent Document 4) that introduces an evaluation formula by Lundberg, Foppl, Conry, etc. Among these, the Conry formula is simple and does not include the relative curvature of the tooth flank, but since the relative curvature of the tooth flank handled in this invention changes significantly along the contact line, the relative curvature part in the Lundberg and Foppl formula is incorporated into the Conry formula to create a new formula (6).

[0049] These research results are believed to represent the relationship when the length of the contact line is sufficiently long and the relative curvature of the tooth surface on the contact line is uniform. However, here we will use the results of these researches on the amount of elastic approach because we believe that the calculations are meaningful if they can be used as the zeroth approximation in successive approximations and can be treated qualitatively.

[0050]

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[0051] On the tooth surface of a helical gear, the line load P l Following the example where is assumed to be constant, we also assume here that the line load is constant. In that case, equation (6) becomes equation (7).

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[0052] Line load difference ΔP l The tooth surface modification amount Δδ is determined by the above equation, and the tooth surface modification amount Δδ can be expressed by the equation (8).

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[0053] Fig. 4 shows the allowable contact stress P for the reference tooth surface and modified tooth surface of a helical gear. 0MAX 200 [Kgf / mm 2 ], the load acting on the contact line (sum of line loads) and the characteristics of the distribution of contact stress (Hertzian stress) are shown. In Fig. 4, A shows the contact stress distribution when a load F0 is applied to the entire tooth surface of the reference tooth profile, and B shows the maximum contact stress on the reference tooth surface when the load F0 is applied to the entire tooth surface of the reference tooth profile, and 0MAX In order to reduce the load on the entire tooth surface to F0, the load F L C shows the contact stress distribution when the contact stress distribution is equal to the overall allowable contact stress P 0MAX The tooth surface is modified to have the following distribution, and the contact stress distribution is shown when the same load F0 as the reference tooth surface is applied to the entire modified tooth surface.

[0054] As an example of a trial calculation, in contact stress distribution A where the total linear load (2162 [Kgf]) is applied to the entire tooth surface, the maximum contact stress (229 [Kgf / mm 2 ]) is the assumed allowable contact stress P 0MAX (200 [Kgf / mm 2 ]) is greater than the maximum contact stress of 200 [Kgf / mm 2 In order to make the value smaller than 1609 [Kgf / mm], it is necessary to reduce the total line load on the entire tooth surface. 2 ] and the maximum contact stress is reduced to 197 [Kgf / mm 2 ], the contact stress distribution is contact stress distribution B.

[0055] By adjusting the amount of tooth surface modification, the sum of the line loads becomes the same as that of contact stress distribution A (2162 [Kgf]), and the maximum contact stress becomes the same as that of contact stress distribution B (197 [Kgf / mm 2 ]) the contact stress distribution when designed is contact stress distribution C.

[0056] Comparing contact stress distribution B and contact stress distribution C, the maximum contact stress is almost the same value (197 [Kgf / mm 2 ]) and the sum of the line loads is 1609 [Kgf] for the unmodified tooth surface (contact stress distribution B) and 2162 [Kgf] for the modified tooth surface (contact stress distribution C), which shows that the load capacity is greatly improved by the tooth surface modification.

[0057] On gear tooth surfaces, "tooth contact" tooth surface modification is generally performed to deal with machining errors and center distance errors. It is considered natural that the "surface pressure" tooth surface modification of the present invention is used in combination with other tooth surface modifications such as "tooth contact" tooth surface modification. Figure 5 shows an example of the results of a trial calculation of contact stress distribution when "tooth contact" tooth surface modification is performed in addition to the "surface pressure" tooth surface modification of this embodiment. In Figure 5, the lower diagram shows the relative radius of curvature and contact stress distribution in the tooth profile before tooth surface modification, and the upper diagram shows the modification curve and contact stress distribution in the tooth profile after tooth surface modification. As shown in Figure 5, by performing tooth surface modification, the contact stress on the contact line can be increased to the allowable contact stress P 0MAX It is possible to distribute the load along the tooth surface and improve the load capacity (sum of the line load) on the tooth surface.

[0058] In the example of FIG. 4, the tooth surface modification curve is a tooth surface modification curve (hereinafter referred to as "first tooth surface modification curve") in which the distribution of the tooth surface modification amount is convex in the central region of the tooth height, but various tooth surface modification curves can be set according to the characteristics of the tooth profile. Specifically, in addition to the first tooth surface modification curve of a convex shape, a tooth surface modification curve (hereinafter referred to as "second tooth surface modification curve") in which the distribution of the tooth surface modification amount is inclined with respect to the tooth height direction can be set. In the second tooth surface modification curve, the tooth surface modification amount increases continuously from the tooth base to the tooth tip, or the tooth surface modification amount increases continuously from the tooth tip to the tooth base. Furthermore, as in the modification curve in the example of FIG. 5, a tooth surface modification curve (hereinafter referred to as "third tooth surface modification curve") in which the first tooth surface modification curve and the second tooth surface modification curve are added together can also be set.

Claims

1. A method for designing a tooth flank form of a helical gear, comprising the steps of: Among the reference tooth flanks, which are tooth flanks that come into line contact with each other under no load, within the entire contact region where the contact line extends from the tooth tip to the tooth root, the relative radii of curvature of the tooth flanks at multiple division points included in the contact line are different from each other, and therefore the contact stresses at the multiple division points when a load is applied to the tooth flanks are different from each other, Based on the distribution of the contact stress on the contact line when a load greater than the load of the gear design specifications is applied to the entire tooth surface of the reference tooth surface within the full length contact area, and on the allowable contact stress which is the limit value of the contact stress taking into consideration damage to the tooth surface, a modification area and a modification amount are determined when performing tooth surface modification to deform the reference tooth surface in a concave direction so that the contact stress exceeding the allowable contact stress becomes equal to or less than the allowable contact stress, A method for designing a tooth flank shape, comprising the steps of: modifying the reference tooth flank based on the determined modification area and modification amount, thereby designing a tooth flank shape.

2. 2. A method for designing a tooth flank shape according to claim 1, characterized in that the modification amount is determined so that within the modification area, a flat contact stress distribution along a limit line indicating the allowable contact stress is included in the distribution of contact stress after tooth flank modification.

3. 2. The method for designing a tooth flank profile according to claim 1, wherein the load that is greater than the load in the gear design specifications is greater than the load in the gear design specifications by an amount that is reduced when the load on the entire tooth flank is reduced by tooth flank modification with respect to the reference tooth flank.

4. A method for designing a tooth flank shape according to any one of claims 1 to 3, characterized in that the tooth flank modification curve specified by the determined modification area and modification amount is a first tooth flank modification curve of a type in which the distribution of the modification amount is convex in the central area of ​​the tooth height, a second tooth flank modification curve of a type in which the distribution of the modification amount is inclined with respect to the tooth height direction, or a third tooth flank modification curve of a type obtained by adding the first tooth flank modification curve and the second tooth flank modification curve.

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