JP6205600B2 - Involute spur gear with a curved tooth profile - Google Patents

Description

  The present invention relates to a spur gear that is resistant to wear and has low noise.

Spur gears are widely used as mechanical elements.
Until now, in spur gears, as described in Non-Patent Document 1, Patent Document 1 and the like, “Tooth profile deformation and impact due to load have generated noise, and tooth profile correction as relief has been made as a reduction method” It has been. Here, the tooth profile correction is a linear correction that cuts teeth. However, the relationship between the noise generation mechanism and the tooth profile correction when the gear is a rigid body or when there is no deformation such as a light load is unclear. The inventor analyzed the case where the gear is a rigid body and is not affected by deformation. First, analysis software was developed to analyze the transition of contact points between the front and rear tooth profiles, and a simulation was performed. As a result, we found a different noise factor system. Further, it has been found that the conventional straight tooth profile correction is effective in reducing noise due to this cause system, but is insufficient. Furthermore, we found that tooth profile correction with a special curve is effective for noise reduction. That is, it was concluded that “noise is generated due to the corner angle when absorbing the pitch error of the front and rear tooth profiles, and that the curved tooth profile correction is effective as a method for reducing the noise”.

JP-A-5-340463

Chotaro Naruse “Gear basics and design” published by Yokendo 1992

  According to the author's analysis, it was found that when there is a pitch error in the spur gear, the transition of the contact point from the tooth profile to the tooth profile is not performed smoothly, which has an adverse effect on wear and noise. Here, this transition mechanism is clarified by simulation, and the details of what is a problem are clarified. First, analysis software developed to elucidate the movement mechanism is described. Next, the movement mechanism is clarified, and the cause of adverse effects on wear and noise is clarified. Specifically, the locus of the tooth profile and the contact point is clarified, and the angular velocity ratio, slip rate, relative curvature, etc. at each contact point are obtained and the characteristics are clarified. If there is no tooth profile error, it can be explained simply based on the involute tooth profile meshing theory. The contact point moves linearly while maintaining a constant angular velocity ratio on a straight line, and the transition of the contact point from the tooth profile to the tooth profile is also smooth. When there is a tooth profile error, the contact point moves non-linearly on the curve, and the transition of the contact point from the tooth profile to the tooth profile is not performed smoothly. Except for the moment when the contact point from the tooth profile to the tooth profile shifts, adjacent tooth profiles do not contact at the same time, and the actual meshing rate is 1. In addition, the contact point locus region is deviated, and the corner of the tooth tip is generated. What is important here is that the pitch error is absorbed around the corner, and the transition of the contact point from the tooth profile to the tooth profile is performed without impact. However, it shows infinite slip rate and infinite relative curvature around the corner, and generates wear and noise. Next, the movement mechanism when there is a straight tooth profile correction will be clarified, and it will be shown that the wear and noise are reduced but insufficient.

  First, analysis software was developed to elucidate the transfer mechanism of contact points. The content is the calculation of various amounts on the tooth profile, contact point trajectory, and contact point trajectory for adjacent tooth profile pairs. The contact point of the involute tooth profile when there is no pitch error, tooth profile correction, or the like can be obtained from a mathematical formula. However, it is not easy to obtain contact points when there is a pitch error, tooth profile correction, etc. over the entire region of the contact point locus line, and numerical analysis is used here.

  FIG. 1 is an explanatory diagram showing design criteria, where 101 is a gear 1, 102 is a gear 2, 103 is a gear 1 axis, 104 is a gear 2 axis, 105 is a design reference plane (XY plane), and 106 is a design reference point. P and 107 represent a stationary coordinate system (X, Y, Z). Here, the tooth profile, the contact point trajectory line and the various quantities on the line that mainly mesh with the design reference point on the design reference plane are mainly handled.

  FIG. 2 is an explanatory diagram showing the configuration of adjacent tooth forms of two pairs (m, n), where 201 is a tooth form 1m, 202 is a tooth form 2m, 203 is a tooth form 1n, 204 is a tooth form 2n, and 205 is a tooth form m pair. 206 is a pair of tooth profiles, 207 is a pitch error, 208 is a root circle 1, 209 is a tip circle 1, 210 is a root circle 2, 211 is a tip circle 2, 212 is rotated, and 213 is an original tooth profile 1m. Represent. As shown in FIG. 2, a pair of adjacent tooth forms (m, n) are considered, and a pitch error 207 is given to the tooth form 1 m 201 of the m set 205. Then, the set of tooth profiles 2 (tooth profile 2m202, tooth profile 2n204) is rotated 212 and brought into contact with the tooth profile 1. In this case, the tooth surface is generally in contact with any of m and n groups (tooth profile m pair 205, tooth profile n pair 206). If the tooth profile drawn with rotation and the locus of the contact point are obtained, the transition mechanism of the contact point can be clarified. Various quantities are evaluation values, such as an angular velocity ratio, a slip ratio of 1, 2 and a relative curvature. At the time of transition of the contact point, that is, when the contact of the n set (tooth profile n pair 206) is finished and the transition to the m set (tooth profile m pair 205) is made, the mechanism is intuitively grasped including whether or not to make a shocking transition. It ’s difficult. As will be described later, in actuality, when shifting from the n set to the m set, a corner hit occurs, and the pitch error and the like are absorbed thereby to shift. Therefore, it is not to say that the transition is shocking. However, since angular contact occurs, the angular velocity ratio changes when shifting, one of the slip rates becomes infinite, and the relative curvature also becomes infinite.

The solution method of the contact point in the analysis software is shown. The tooth profile 1G1 and the tooth profile 2G2 can be expressed by the following formulas using the tooth profile variable v and the rotation angle φ as variables. Further, the tooth profile normal 1n1 and the tooth profile normal 2n2 can be expressed by the following mathematical expressions. Here, G1, G2, n1, and n2 are vectors.
(Equation 1)
G1 = G1 (v1, φ1)
(Equation 2)
G2 = G2 (v2, φ2)
(Equation 3)
n1 = n1 (v1, φ1),
(Equation 4)
n2 = n2 (v2, φ2)
The conditional expression of the contact point can be expressed by the following expression.
(Equation 5)
G1 = G2
(Equation 6)
n1 = n2
In the above equations, scalar three conditional expressions are finally given to four variables. Therefore, the following equation for the contact point is obtained. The contact point can be obtained by calculation with m and n pairs, but the contact point first becomes the actual contact point. Here, Q is a vector.
(Equation 7)
Q = Q (φ1)
Since it is difficult to find the solution of this equation, the actual solution is obtained by numerical calculation. Numerical calculation requires third-order calculations, but this software has developed an algorithm that converges with second-order calculations. As a result, significant time savings were achieved.

Although the angular velocity ratio is generally constant, it changes at the time of transition of the contact point, so it is necessary to obtain a solution. Next, the solution of the angular velocity ratio in the analysis software is shown. FIG. 3 is an explanatory view showing a general solution of the angular velocity ratio, 301 is a tooth profile normal, 302 is a tooth profile normal 2, 303 is an intersection point P2, 304 is a contact point Q, 305 is a contact point Q2, and 306 is a distance r1. , 307 is a distance r2, 308 is a radius rg1, 309 is a radius rg2, 310 is an angular velocity ω1, 311 is an angular velocity ω2, and 312 is a gear center line. The angular velocity ratio is obtained from the following equation with reference to FIG. This indicates that it is determined by the position of the contact point and the tooth surface normal N301 direction, and finally by the position of the intersection of the tooth surface normal N and the gear center line O12 (312). Initially, this position is constant at the design reference point P106, but when the contact point moves, the position changes to P2 (106) because the position of the contact point and the tooth surface normal direction change, and the angular velocity ratio finally changes. To do. Here, the common tooth surface normal when one side is around a corner follows the other tooth surface normal.
(Equation 8)
ω = ω1 / ω2 = rg2 / rg1 = r2 / r1

The simulation diagram of the tooth profile and the contact point trajectory shows the tooth profile drawn with the rotation and the trajectory of the contact point. From this figure, the transition mechanism of contact points can be clarified. FIG. 4 is a diagram of a simulation tooth surface, and 401 represents the tooth surface. Table 1 shows the basic specifications of the gears used in the simulation. The tooth profile is a general involute tooth profile. Although the inclination (torsion angle) of the reference surface is zero, the same conclusion is obtained for a non-zero helical gear.

  FIG. 5 is a simulation diagram of the tooth profile and the locus of the contact point when there is no pitch error, 501 is tooth profile 1, 502 is tooth profile 2, 503 is (order 1), 504 is (order 2), and 505 is (order 3). ), 506 represents a pitch, 507 represents a contact point locus line, and 508 represents rotation. Here, (order 1) indicates that the order is 1. When there is no error, it can be explained simply based on the involute tooth meshing theory. Rotate adjacent pair of teeth (m, n). At the initial point, n sets of tooth forms are in contact with each other at the initial stage, and move in the order of the figures (order 1) 503 to (order 3) 505 with rotation. A characteristic when there is no pitch error is that there is a section (order 2) 504 in which m and n pairs simultaneously have contact points.

  FIG. 6 is a simulation diagram of the tooth profile and the locus of the contact point when there is a pitch error. When there is an error, the tooth profile at the time of transition of the contact point and the locus of the contact point are greatly different from those when there is no error. First, the locus region of the contact point is biased toward the tooth tip side. Secondly, the locus line of the contact point is bent halfway. Third, unlike the case where there is no pitch error, m and n sets do not have contact points at the same time except for the moment of transition. That is, it can be said that the substantial contact ratio is 1. FIG. 7 is a simulation diagram of the tooth profile and the locus of the contact point when the error sign is reversed. As shown in FIG. 7, when the error sign changes, the direction in which the locus region of the contact point is biased is reversed. Further, the bending direction is reversed, and a shape resembling rotational symmetry about the design reference point is shown.

  FIG. 8 is an explanatory diagram per corner, and 801 represents per corner. A major feature when there is a pitch error is that 801 per corner is generated at the time of transition of the contact point, thereby absorbing the pitch error. Moreover, FIG. 9 is explanatory drawing of 2 times contact, 901 represents 2 times contact. As shown in FIG. 9, the contact point 901 is contacted twice at the contact point of the mating tooth surface when the contact point is shifted. The following various quantities are calculated for the tooth profile shown in FIG. FIG. 10 is a characteristic diagram of the angular velocity ratio. As shown in FIG. 10, the angular velocity ratio at the time of transition of the contact point changes. As a result, torque fluctuation occurs. FIG. 11 is a characteristic diagram of the slip ratio. As shown in FIG. 11, the slip rate at the time of transition of the contact point changes. The slip ratio 1 is infinite and the other is 1. This is because the gear tip 1 speed direction and the contact point locus line direction coincide with each other and the slip rate 1 becomes infinite because the corners of the tooth tips on the tooth profile are in continuous contact. FIG. 12 is a characteristic diagram of relative curvature. As shown in FIG. 12, the relative curvature at the time of transition of the contact point is infinite. This is because the curvature of the corner points on the tooth profile 1 is infinite and the relative curvature is also infinite.

  As described above, in the area around the corner, the angular velocity ratio changes, the slip rate 1 becomes infinite, and the relative curvature becomes infinite. The fact that the relative curvature is infinite means that the stress at the contact point is infinite. Actually, the stress due to tooth contact considering the deformation of the corner is considered, but it is still a large value. The mating tooth surface per corner comes in contact twice by sliding in the opposite direction. These indicate that the tooth surface is scratched, worn, shavings, degreased, and the like, causing a large damage and a large noise factor. Although it seems that there is a difference in the degree of wear depending on the sliding direction of the contact point per corner, the sliding direction varies depending on the sign of the pitch error and the rotation direction.

Next, consider a case where straight tooth profile correction is applied. Linear tooth profile correction is added to reduce noise and the like. FIG. 13 is an explanatory diagram showing a tooth profile configuration for straight tooth profile correction, in which 1301 indicates a correction unit, 1302 indicates a cut region, 1303 indicates a tooth profile correction start point, and 1304 indicates a correction angle. The correction start point of the correction tooth profile is indicated by a position coefficient, and the direction is indicated by a correction angle. here,
(Equation 9)
Correction start point radius = tip circle radius-position factor * tooth right angle module

  FIG. 14 is a simulation diagram of the tooth profile and the locus of the contact point in the case of straight tooth profile correction, and 1401 represents (order 4). As shown in FIG. 14, a phenomenon such as a corner is observed even in the case of straight tooth correction, in the case where there is no correction of the tooth profile. At the joint of both curves at the starting point of the tooth profile correction, this area is referred to as the apex angle. In the figure, the transition from n normal contacts (order 1) 503 to m sets of contacts (order 4) 1401 through the order of apex angle (order 2) 504 and linear contact (order 3) 505 is performed. . The following various quantities are calculated for the tooth profile shown in FIG. The pitch error is absorbed mainly around the apex angle, and the contact point is shifted. The contact line trajectory line has a biased region. In this case as well, m and n sets do not have contact points at the same time except for the moment when the contact points are transferred from n set contact points to n set contact points. That is, the substantial meshing rate is 1. When the error sign changes, the direction in which the locus region of the contact point is biased is reversed. Further, the bending direction is reversed, and a shape resembling rotational symmetry about the design reference point is shown.

  FIG. 15 is a simulation diagram in the case where the contact point is transferred in the order of linear contact and corner contact per apex angle, and 1501 represents (order 5). When the pitch error is not sufficiently absorbed around the apex angle, the contact point is transferred from the normal contact to the apex angle through the linear contact and the angular contact. Here, the straight contact section is small. FIG. 15 shows the phenomenon when the correction angle is small. Here, the transition of the contact point is performed from normal contact (order 1) 503 to apex angle (order 2) 504, linear contact (order 3) 505, and per corner (order 4) 1401.

  FIG. 16 is an explanatory diagram per apex angle, and 1601 represents per apex angle. A major feature in the case of straight tooth profile correction is that, as shown in FIG. 16, 1601 per apex angle, per corner or the like occurs at the time of transition of the contact point, and thereby the pitch error is absorbed. Further, when the contact point is shifted, the contact point of the mating tooth surface contacts twice. FIG. 17 is a characteristic diagram of the angular velocity ratio. As shown in FIG. 17, the angular velocity ratio at the time of transition of the contact point changes. As a result, torque fluctuation occurs. FIG. 18 is a characteristic diagram of the slip ratio. As shown in FIG. 18, the slip ratio at the time of transition of the contact point changes greatly. Slip rate 1 is infinite and slip rate 2 is 1. This is because the corner points on the tooth profile are in continuous contact, so that the gear speed 1 direction matches the contact point locus line direction, and the slip ratio 1 becomes infinite. FIG. 19 is a characteristic diagram of relative curvature. As shown in FIG. 19, the relative curvature at the time of transition of the contact point is infinite. This is because the curvature of the corner points on the tooth profile is infinite and the relative curvature is also infinite.

  As described above, the angular velocity ratio varies around the apex angle or the area around the corner, the slip rate 1 becomes infinite, and the relative curvature becomes infinite. The fact that the relative curvature is infinite means that the stress at the contact point is infinite. Actually, the stress due to tooth contact considering the deformation of the corner is considered, but it is still a large value. The apex angle and the mating tooth surface around the corner come in contact twice by sliding in the opposite direction. These indicate that the tooth surface is scratched, worn, shavings, degreased, and the like, causing a large damage and a large noise factor.

  As described above, when the tooth profile is not corrected, noise and wear caused by the corners occur. An involute tooth profile that has been linearly corrected on the tooth tip side also has a certain effect on noise reduction and wear resistance compared to the case without tooth profile correction, but similar apex angles and corner hits occur. Insufficient for noise reduction and wear resistance.

  It is a problem to be solved by the present invention to avoid the apex angle and the corner angle and improve noise and wear.

  FIG. 20 is an explanatory diagram showing a tooth profile configuration for tooth profile correction by a specific curve, 2001 is an involute, 2002 is an arc, 2003 is a base circle, 2004 is a contact point Qb, 2005 is a center of curvature, 2006 is an arc radius, 2007 is Represents a circle passing through the center of the tooth. FIG. 23 is a simulation diagram of the locus of contact points.

  A means for solving the problem is to make the tooth profile an involute tooth profile whose tooth profile is modified to a specific curved shape on the tooth tip side. As shown in FIG. 20, when the starting point of the corrected tooth profile on the involute tooth profile is Qic1303, the tooth profile normal at the starting point is Nic301, and the intersection of the normal 301 and the base circle 2003 is Qb2004, the curvature at the starting point Qic1303 of the correction curve is shown. The curvature center Oc2005 is on the tooth profile normal Nic, and the curvature center Oc is defined between the start point Qic and the intersection point Qb. The correction tooth profile is a curve in which the distance between the correction tooth profile and the involute tooth profile before correction increases toward the tooth tip, and the correction tooth profile start point Qic1303 passes through the tooth center (rack center, pitch point in the case of zero displacement) and one gear shaft It is determined on the tooth tip side from the center circle 2007. Further, as shown in FIG. 23, the specifications of the curve-corrected tooth profile are changed from the contact of the tooth profile pair n (contact order (order 1) 503) to the contact of the tooth profile m (contact order (order 2) 504). The contact points on the n pairs of tooth profiles 1 when the contact is transferred to are determined on the tooth profile excluding the tooth tip. Similarly, the tooth profile 2 that meshes with the tooth profile 1 is corrected by a specific curve.

  According to the present invention, a spur gear excellent in noise reduction and wear resistance can be realized.

FIG. 1 is an explanatory diagram showing design criteria. (Problems to be solved by the invention) FIG. 2 is an explanatory diagram showing a pair of adjacent tooth profile configurations (m, n). (Task) FIG. 3 is an explanatory diagram showing a general solution for the angular velocity ratio. (Problems to be solved by the invention) FIG. 4 is a diagram of a simulation tooth surface. (Task) FIG. 5 is a simulation diagram of the tooth profile and the locus of the contact point when there is no pitch error. (Task) FIG. 6 is a simulation diagram of the tooth profile and the locus of the contact point when there is a pitch error. (Task) FIG. 7 is a simulation diagram of the tooth profile and the locus of the contact point when the error sign changes. (Task) FIG. 8 is an explanatory diagram per corner. (Task) FIG. 9 is an explanatory diagram of two-time contact. (Task) 10 is a characteristic diagram of the angular velocity ratio. (Task) FIG. 11 is a characteristic diagram of the slip ratio. (Task) FIG. 12 is a characteristic diagram of relative curvature. (Task) FIG. 13 is an explanatory diagram showing a tooth profile configuration for straight tooth profile correction. (Task) FIG. 14 is a simulation diagram of the tooth profile and the locus of the contact point in the case of straight tooth profile correction. (Task) FIG. 15 is a simulation diagram in the case where the contact point shifts in the order of linear contact and corner contact per apex angle. (Task) FIG. 16 is an explanatory diagram per apex angle. (Task) FIG. 17 is a characteristic diagram of the angular velocity ratio. (Task) FIG. 18 is a characteristic diagram of the slip ratio. (Task) FIG. 19 is a characteristic diagram of relative curvature. (Task) FIG. 20 is an explanatory diagram showing a tooth profile configuration for tooth profile correction by a specific curve. (Means for solving the problem) FIG. 21 is a simulation diagram of the trajectory of the contact point when cornering occurs. Example 1 FIG. 22 is an explanatory diagram for explaining the relationship between adjacent tooth forms of a pair of two pairs (m, n). Example 1 FIG. 23 is a simulation diagram of the locus of contact points. Example 1 FIG. 24 is a characteristic diagram of the angular velocity ratio. Example 1 FIG. 25 is a characteristic diagram of the slip ratio. Example 1 FIG. 26 is a characteristic diagram of relative curvature. Example 1 FIG. 27 is an explanatory diagram of a tooth profile when a large curve tooth profile correction is taken. (Example 2) FIG. 28 is an explanatory diagram of a tooth profile in the case of complex tooth profile correction. (Example 2)

  As described above, when there is a pitch error, a corner hit occurs when there is no tooth profile correction, and a vertex angle occurs when the straight tooth profile is corrected. In order to avoid these problems, an involute tooth profile in which the tooth tip side is modified with a specific curve is proposed here. A spur gear having this tooth form is a form for carrying out the invention. In the following description, arcs are mainly used as the modified tooth profile curve, but the same can be said for the general shape of a specific curve.

  As shown in FIG. 20, the tip of the corrected tooth profile on the involute tooth profile is Qic, the tooth profile normal at the start point is Nic, and the contact point between the normal and the basic circle When Qb is set, the curvature center Oc of the curvature at the contact point Qic of the correction curve is determined on the tooth profile normal Nic.

  Further, the center of curvature Oc is defined between the starting point Qic and the contact point Qb. The corrected tooth profile is a curve in which the distance between the corrected tooth profile and the involute tooth profile before correction increases toward the tooth tip. The starting point Qic of the correction tooth profile is determined on the tooth tip side from a circle passing through the center of the tooth (rack center, pitch point in the case of dislocation zero) and centered on one gear shaft.

  Further, as shown in FIG. 23, the contact point on the n pairs of tooth forms 1 when the contact moves from the contact tooth pair n to the next contact tooth pair m as shown in FIG. It is determined to be on the tooth profile excluding the tooth tip.

  Hereinafter, a detailed method of forming the tooth profile will be described with reference to FIG.

As described above, the starting point of the correction tooth profile on the involute tooth profile is Qic1303. The starting point Qic of the correction tooth profile is determined on the tooth tip side from a circle centering on one axis of the gear passing through the center of the tooth (rack center or pitch point in the case of zero displacement). In order to obtain the same pitch error absorption effect as in the case of straight tooth profile correction, the starting point is set on the root side compared to the case of straight tooth profile correction. The correction start point is indicated by a position coefficient. here,
(Equation 10)
Correction start point radius = tip circle radius-position factor * tooth right angle module

The tooth profile normal at the starting point is Nic301, and the contact point between the normal 301 and the base circle 2003 is Qb2004. The curvature center Oc2005 of the curvature at the start point Qic1303 of the correction curve is determined on the tooth profile normal Nic301. Thereby, the correction tooth profile becomes a curve in contact with the involute tooth profile. When the center of curvature Oc is set to a position other than the tooth profile normal line Nic, an apex angle is generated at the starting point Qic of the correction curve as in the case of straight tooth profile correction, which adversely affects noise and wear. The curvature radius is indicated by a curvature radius coefficient (in the case of an arc, an arc radius coefficient). here,
(Equation 11)
Modified curve curvature radius = curvature radius coefficient * involute tooth profile curvature radius

  The curvature center Oc2005 of the curvature at the start point Qic1303 of the correction curve is determined between the start point Qic and the contact point Qb2004. Thereby, the correction tooth profile becomes a curve inscribed in the involute tooth profile. When it is determined outside Qb, the pitch error cannot be absorbed, and an impact is generated when shifting to the next tooth, which adversely affects noise and wear. Further, the center of curvature Oc2005 is determined to be more than 1.5 times the module from the start point Qic1303 of the corrected tooth profile. Thereby, excessive tooth profile correction can be prevented.

  The corrected tooth profile is a curve in which the distance between the corrected tooth profile and the involute tooth profile before correction increases toward the tooth tip. This distance is a distance on a straight line contacting the basic circle of the gear 1. Specifically, the curve is an arc, an ellipse, a hyperbola, or the like. This absorbs pitch errors and prevents impact when moving to the next tooth.

  FIG. 21 is a simulation diagram of the trajectory of the contact point when cornering occurs. If the position coefficient is small and the circular arc radius coefficient is large, corner hitting occurs even in this case. This is a case where the pitch error cannot be absorbed. FIG. 21 shows an example of this case, and it can be seen that a corner hit occurs and the contact line locus line is bent.

The per corner can be achieved by optimizing the starting point Qic1303, the center of curvature Oc2005, and the like. That is, the starting point of the corrected tooth profile on the tooth profile and the radius of curvature of the correction curve are expressed as “the contact point on the n pairs of tooth profiles 1 when the contact is transferred from the contacting tooth profile pair n to the next contacting tooth profile pair m”. It is determined to be positioned on the tooth profile excluding the tooth tip. " FIG. 22 is an explanatory diagram for explaining the relationship between adjacent tooth profiles of a pair of two pairs (m, n). 2201 is a reference involute 1, 2202 is a modified involute 1, 2203 is a reference involute 2, 2204 is a modified involute 2, Corresponding correction involute error 2206 is the contact point locus line before correction, 2207 is the reference involute 1, 2208 is the corrected involute 1, 2209 is the reference involute 2, 2210 is the corrected involute 2, 2211 is the error correction, 2212 is the tooth profile center line . In FIG. 22, the reference involute indicates an involute tooth profile when the pitch error is zero and the tooth profile is not corrected. The corrected involute indicates an involute tooth profile that has undergone tooth profile correction. The errors include a reference involute pitch error ΔP1 (207) shown on the gear pair m side and an error ΔP2 (2205) due to the correction involute of the mating tooth profile. Here, “pitch error + partner curve error” is ΔP. The correction is performed by a correction involute shown on the gear pair n side, and the correction amount is ΔPc2211. Here, the condition for determining the contact point to be on the tooth profile excluding the tooth tip is to satisfy the following equation.
(Equation 12)
ΔP <ΔPc

  In order to give the starting point of the correction tooth profile and the correction curve curvature radius satisfying this condition, there are a method of obtaining from a solution of an equation, a method of obtaining by a numerical solution, a method of obtaining from a locus of a tooth profile and a contact point. In the case of the method of obtaining from the tooth profile and the locus of the contact point, various position coefficients and arc radius coefficients are given, the conditions are evaluated by simulation, and the starting point and the curvature center satisfying the conditions are selected. For example, it is NG in the case of FIG. 21, and OK in the case of FIG. At the time of design, the tolerance ΔP is given as an error ΔP. In production, it is possible to make an evaluation using image processing to determine whether the contact point at the time of transition is located on the tooth profile excluding the tooth tip by meshing with an actual or reference mating gear on the production line.

  FIG. 23 shows a simulation diagram of the tooth profile of a gear having a curved tooth profile satisfying the above various conditions and the locus of the contact point. The position coefficient, the arc radius coefficient, and the like have the same values for the gears 1 and 2 for simplicity, but the values for the gears 1 and 2 may be different.

  FIG. 24 is a characteristic diagram of the angular velocity ratio. As shown in FIG. 24, the angular velocity ratio at the time of transition of the contact point changes. As a result, torque fluctuations occur, but pitch errors are absorbed. Further, except for the moment when the contact point shifts from the n contact points to the m contact points, the m and n contact members do not have contact points at the same time. That is, the substantial meshing rate is 1.

  FIG. 25 is a characteristic diagram of the slip ratio. As shown in FIG. 25, the slip rate at the time of transition of the contact point changes. FIG. 26 is a characteristic diagram of relative curvature. As shown in FIG. 26, the relative curvature does not become infinite.

  At a contact point where the slip rate 1 is 1, the slip rate 2 is infinite. At this contact point, a normal line perpendicular to the contact point locus line passes through the two gear axes. Note that this phenomenon with an infinite slip rate of 2 is special, and as can be seen from FIG. This is because the relative curvature is infinite, the sign is not changed, and the contact point locus line is not interrupted. In order to avoid this contact point, it is possible to optimize the starting point Qic of the tooth profile correction curve, the center of curvature Oc, etc., as in the method of avoiding corner contact.

  As described above, when the tooth profile according to the present invention is used, no corners or apex angle occurs. The relative curvature is infinite, and the stress at the contact point of the tooth profile does not become infinite. Accordingly, noise and wear caused by these can be avoided, and the tooth surface is not damaged by causing scratches, wear, shavings, oil shortage, and the like.

  Although the tooth profile correction by the specific curve of the tooth profile 1 has been described above, the tooth profile correction by the specific curve is similarly performed for the tooth profile 2 meshing with the tooth profile. The tooth profile correction by the specific curve of the tooth profile 1 is effective for the above pitch error, and the tooth profile correction by the specific curve of the tooth profile 2 is effective for the above error of the pitch error and the sign reverse. Further, although the case of the right tooth surface with right twist has been described mainly, the same applies to the left twist and left tooth surface. The curved tooth profile has been described centering on the case of an arc. However, the curve is not limited to an arc, and the same applies to an ellipse, a hyperboloid, and other cases.

  In the first embodiment, straight tooth profile correction and curved tooth profile correction are considered. However, tooth profile correction in which both tooth shapes are combined can be considered. FIG. 27 is an explanatory diagram of a tooth profile when a large curve tooth profile correction is taken. As shown in FIG. 27, when the curved tooth profile correction is made large, avoidance per corner becomes easy, but the bending on the tooth tip side becomes large. The compound tooth profile can prevent excessive bending of the tooth tip side.

  FIG. 28 is an explanatory diagram of a tooth profile in the case of complex tooth profile correction, and 2801 represents a straight line. In the complex tooth profile, the tip of the curved tooth profile is corrected with a straight line in contact with the arc. This may be considered as a case where the straight correction tooth profile is cut by a curve in contact with both curves between the involute and the straight line.

  According to the present invention, a spur gear excellent in noise reduction and wear resistance can be realized. Therefore, it can be widely used in machines that require a spur gear as a machine element having a quiet and strong strength.

101 Gear 1
102 Gear 2
103 Gear 1 shaft 104 Gear 2 shaft 105 Design reference surface 106 Design reference point 201 Tooth profile 1 m
202 Tooth profile 2m
203 Tooth profile 1n
204 Tooth profile 2n
205 Tooth profile m pair 206 Tooth profile n pair 207 Pitch error 208 Tooth root circle 1
209 Tip circle 1
210 root circle 2
211 Tip circle 2
212 Rotation 213 Original tooth profile 1m
301 Tooth profile normal 302 Tooth profile normal 2
303 Intersection P2
304 Contact point Q
305 Contact point Q2
306 distance r1
307 distance r2
308 radius rg1
309 radius rg2
310 Angular velocity ω1
311 Angular velocity ω2
312 Gear center line 401 Tooth surface 501 Tooth profile 1
502 Tooth profile 2
503 (order 1)
504 (order 2)
505 (order 3)
506 Pitch 507 Contact point locus line 508 Rotation 801 Per corner 901 Twice contact 1301 Correction part 1302 Cut area 1303 Tooth profile correction start point 1304 Correction angle 1401 (order 4)
1501 (order 5)
1601 Per apex angle 2001 Involute 2002 Arc 2003 Base circle 2004 Contact Qb
2005 center of curvature 2006 arc radius 2007 circle passing through tooth center 2201 reference involute 1
2202 Modified Involute 1
2203 Reference Involute 2
2204 Modified Involute 2
2205 Counter-correction involute error 2206 Contact point locus line before correction 2207 Reference involute 1
2208 Modified Involute 1
2209 Reference Involute 2
2210 Modified Involute 2
2211 Error correction 2212 Tooth profile center line 2801 Straight line

Claims (1)

  The tooth tip is a pair of involute tooth profiles that have been modified with a curved tooth profile. For each tooth profile, the starting point of the modified tooth profile on the involute tooth profile is Qic, the tooth profile normal at the start point is Nic, and the intersection of the normal and the basic circle When Qb is set, the curvature center Oc of the curvature at the starting point Qic of the correction curve is determined on the tooth profile normal Nic, the center of curvature Oc is determined between the starting point Qic and the intersection point Qb, and the correction tooth profile is a correction tooth profile toward the tooth tip. The involute tooth profile before the correction is a curved curve, the correction tooth profile start point Qic is set on the tooth tip side of the circle centering on the gear axis through the center of the tooth, and the specifications of the curved correction tooth profile are in contact with each other. A spur gear characterized by determining a contact point on a tooth profile at a moment when contact is transferred from a pair to a tooth profile pair to be contacted next, on a tooth profile excluding a tooth tip.

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