JP2018112206A - Skewed shaft gear and intersecting shaft gear - Google Patents
Skewed shaft gear and intersecting shaft gear Download PDFInfo
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Abstract
Description
本発明は、摩耗に強くかつ騒音の少ない食い違い軸歯車および交叉軸歯車に関するものである。 The present invention relates to a staggered shaft gear and a cross shaft gear which are resistant to wear and have low noise.
食い違い軸歯車および交叉軸歯車は機械要素として用いられている。これまで、これら歯車のピッチ誤差による騒音の低減に関する研究や技術は見られない。本特許では一対の歯車の両者に、ピッチ誤差による騒音の低減の為に歯先側に特別な歯面修正をおこなう。 Staggered shaft gears and crossed shaft gears are used as machine elements. So far, there has been no research or technology related to noise reduction due to the pitch error of these gears. In this patent, both the pair of gears are subjected to special tooth surface correction on the tooth tip side in order to reduce noise due to pitch error.
特許文献１ではウォームをウォームホイールに押付けた時のギヤ同士の食込みを防ぐ為に、ウォームの歯底部にＲ形状の歯形修正が施してあるが、本特許と目的、歯形修正の方法が異なる。特許文献２では、歯幅方向中央部を中心にして荷重の集中を軽減させる為に歯形修正面を設けている。これもまた、本特許と目的、歯形修正の方法が異なる。 In Patent Document 1, an R-shaped tooth profile correction is applied to the tooth bottom of the worm in order to prevent the gears from biting when the worm is pressed against the worm wheel. However, the purpose and the method of tooth profile correction differ from this patent. In Patent Document 2, a tooth profile correction surface is provided in order to reduce the concentration of load around the central portion in the tooth width direction. Again, this patent differs from the purpose and method of tooth profile correction.
発明が解決しようとする課題は、食い違い軸歯車および交叉軸歯車のピッチ誤差による騒音を低減させることである。 The problem to be solved by the invention is to reduce the noise caused by the pitch error of the staggered shaft gear and the cross shaft gear.
課題を解決するための手段は、歯面の歯先側をピッチ誤差を吸収し、かつ広角あたりや歯先の角あたりが無い、特定の曲面状に歯面修正することである。 Means for solving the problem is to correct the tooth surface of the tooth surface to a specific curved surface that absorbs the pitch error and does not have a wide angle or a tooth angle.
本発明により、ピッチ誤差による騒音が低減され耐摩耗に優れた歯車を実現できる。 According to the present invention, it is possible to realize a gear with reduced noise due to pitch error and excellent wear resistance.
発明を実施するための形態は、歯面の歯先側をピッチ誤差を吸収し、かつ広角あたりや歯先の角あたりが無い特定の曲面状に歯面修正した一対の食い違い軸歯車および交叉軸歯車である。 A mode for carrying out the invention is a pair of staggered shaft gears and a cross shaft in which a tooth surface side of a tooth surface absorbs a pitch error and has a tooth surface modified to have a specific curved surface without a wide angle or a corner of the tooth tip. It is a gear.
まず、ピッチ誤差による騒音発生の原因を明らかにする。 First, the cause of noise generation due to pitch error will be clarified.
等角速度比の点接触歯車を基本に考える。不等角速度比の場合や線接触歯車の場合は，等角速度比の場合と同様に論じ，同様の結果を得ることができる。かみあっている歯車１、２の歯面対を歯面対nとし、歯面対nの次にかみあう歯面対を歯面対mとする。また、歯面対n上の歯形対を歯形対nとし、歯面対m上の歯形対を歯形対mとする。歯形対は接触点軌跡線上でお互いに接する一対の歯形である。歯形対は点接触歯車の場合１つ定まるが、線接触歯車の場合は無数に存在する。線接触歯車の場合はその中から、歯面１上の最後の接触点を歯先とする歯形を選択する。 Consider a point contact gear with a constant angular velocity ratio. In the case of the unequal angular velocity ratio or in the case of the line contact gear, the discussion can be made in the same manner as in the case of the equiangular velocity ratio, and the same result can be obtained. The tooth surface pair of the gears 1 and 2 that are engaged is a tooth surface pair n, and the tooth surface pair that meshes next to the tooth surface pair n is a tooth surface pair m. Further, a tooth profile pair on the tooth surface pair n is a tooth profile pair n, and a tooth profile pair on the tooth surface pair m is a tooth profile pair m. The tooth profile pair is a pair of tooth profiles that touch each other on the contact point locus line. One tooth shape pair is determined in the case of a point contact gear, but innumerable in the case of a line contact gear. In the case of a line contact gear, a tooth profile with the tip of the last contact point on the tooth surface 1 is selected.
図１は、ピッチ誤差により歯形対nが接触し、歯形対mに隙間ができている状態を示している。ここでは、ピッチ誤差を角ピッチの誤差で表す。図１は説明の為の概念図である．概念図は理解しやすいように平面的に示しているが、実際には立体的である。以下同様の図も同じである。 FIG. 1 shows a state where the tooth profile pair n is in contact with the pitch error and a gap is formed in the tooth profile pair m. Here, the pitch error is expressed as an angular pitch error. Figure 1 is a conceptual diagram for explanation. The conceptual diagram is shown two-dimensionally for easy understanding, but is actually three-dimensional. The same applies to the following drawings.
図１の１０１は歯車１、１０２は歯車２、１０３は歯形１、１０４は歯形２、１０５は歯形対ｍ、１０６は歯形１、１０７は歯形２、１０８は歯形対ｎ、１０９は歯底円１、１１０は歯先円１、１１１は歯底円２、１１２は歯先円２、１１３は角ピッチの誤差ΔψDを表す。
1, 101 is the gear 1, 102 is the gear 2, 103 is the tooth profile 1, 104 is the tooth profile 2, 105 is the tooth profile m, 106 is the
角ピッチの誤差ΔψDの符号は図１のように歯形対ｍの歯形１と歯形対ｎの歯形１が広がる場合を正（＋）とする。また、図２のように狭まる場合を負（−）とする。角ピッチ誤差は歯形１の角ピッチ誤差と歯形２の換算角ピッチ誤差を合わせたものである。換算角ピッチ誤差は歯形２の角ピッチ誤差を歯形１側の角ピッチ誤差に換算したものである。 The sign of the angular pitch error ΔψD is positive (+) when the tooth profile 1 of the tooth profile pair m and the tooth profile 1 of the tooth profile pair n spread as shown in FIG. Moreover, the case where it narrows like FIG. 2 is made into negative (-). The angular pitch error is a combination of the angular pitch error of the tooth profile 1 and the converted angular pitch error of the tooth profile 2. The converted angular pitch error is obtained by converting the angular pitch error of the tooth profile 2 into the angular pitch error on the tooth profile 1 side.
各歯面間のピッチ誤差の符号や大きさはまちまちである。例えば、ピッチ誤差が（＋）の場合、一般にとなりの符号は（−）となる。後述するが、図１に示す正の角ピッチ誤差の場合、歯車１の歯面修正によりピッチ誤差を吸収する。図３は符号が（−）の場合の図２を１８０度回転させて示したもので、図１と同様の形を示す。従って、負の角ピッチ誤差の場合は、正の角ピッチ誤差の場合と同様にして歯車２の歯面修正によりピッチ誤差を吸収する必要がある。すなわち、正負の角ピッチ誤差に対応するには、歯車１、２の両方に歯面修正を施す必要があることを意味する。これはここで明らかにした重要な知見である。以下では、図１に示す正の角ピッチ誤差の場合を主体として述べる。 The sign and size of the pitch error between each tooth surface varies. For example, when the pitch error is (+), the next sign is generally (-). As will be described later, in the case of the positive angular pitch error shown in FIG. 1, the pitch error is absorbed by correcting the tooth surface of the gear 1. FIG. 3 shows FIG. 2 rotated by 180 degrees when the sign is (−) and shows the same shape as FIG. Therefore, in the case of a negative angular pitch error, it is necessary to absorb the pitch error by correcting the tooth surface of the gear 2 in the same manner as in the case of the positive angular pitch error. That is, in order to cope with positive and negative angular pitch errors, it means that both the gears 1 and 2 need to be subjected to tooth surface correction. This is an important finding revealed here. Hereinafter, the case of the positive angular pitch error shown in FIG. 1 will be mainly described.
図４は図１に示す歯形対n１０８の歯形の回転と接触点軌跡線の様子を示す。 FIG. 4 shows the rotation of the tooth profile of the tooth profile pair n108 shown in FIG.
図４の４０１は接触点軌跡線Q、４０２は接触点軌跡線Qr、４０３は接触点Q1、４０４は接触点Q2、４０５は接触点Q3、４０６は接触点Q3rを表す。 4, 401 represents a contact point locus line Q, 402 represents a contact point locus line Qr, 403 represents a contact point Q1, 404 represents a contact point Q2, 405 represents a contact point Q3, and 406 represents a contact point Q3r.
G1は歯形１(符号１０６)、G2はG1とかみあう歯形２(符号１０７)であり、Ｑ４０１はG1とG2の接触点軌跡線である。歯形対n１０８の接触点は回転と共に、接触点軌跡線上および歯形１上を、歯形１の歯元側Ｑ1４０３から歯先Ｑ2４０４へ移動する。この間は角速度比が一定であるのでピッチ誤差は同じで縮まらない。角速度比が一定に近い場合もピッチ誤差はあまり縮まらない。 G1 is a tooth profile 1 (reference numeral 106), G2 is a tooth profile 2 (reference numeral 107) that meshes with G1, and Q401 is a contact point locus line between G1 and G2. The contact point of the tooth profile pair n108 moves along the contact point locus line and the tooth profile 1 from the tooth base side Q1403 of the tooth profile 1 to the tooth tip Q2404 with rotation. During this time, since the angular velocity ratio is constant, the pitch error is the same and does not shrink. Even when the angular velocity ratio is almost constant, the pitch error is not reduced so much.
接触点が歯先Ｑ2へ移動した後は、歯形１が回転しても歯形１上の接触点は歯先に留まる。歯形１を歯先から連続して伸びた仮想の歯形を考えた場合、回転と共に歯面は延伸部上の点Ｑ3４０５で外接するので、歯先と歯形2との間は隙間ができ、実際には歯形２が回転して角として突き出た歯先に接触する。または，歯形１が回転して歯先が歯形２に接触する。これにより、歯形上の接触点が留まった状態で接触点は歯車軸１の周りを回動しＱ3r４０６に移動する。その間、角あたりの状態で歯形対n１０８は角ピッチの誤差ΔψD１１３を吸収する。ΔψDの吸収が完了すると、歯形対m１０５が新たに接触し歯形対n１０８が離れる。これにより、歯形対nから次の歯形対mへの接触点の移行がおこなわれる。 After the contact point moves to the tooth tip Q2, even if the tooth profile 1 rotates, the contact point on the tooth profile 1 remains at the tooth tip. Considering a virtual tooth profile in which the tooth profile 1 is continuously extended from the tooth tip, the tooth surface circumscribes at the point Q3405 on the extension part with rotation, so there is a gap between the tooth tip and the tooth profile 2, Contacts the tooth tip protruding as a corner when the tooth profile 2 rotates. Alternatively, the tooth profile 1 rotates and the tooth tip contacts the tooth profile 2. As a result, the contact point rotates around the gear shaft 1 and moves to Q3r406 while the contact point on the tooth profile remains. Meanwhile, in the state around the corner, the tooth profile pair n108 absorbs the angular pitch error ΔψD113. When the absorption of ΔψD is completed, the tooth profile pair m105 comes into contact again and the tooth profile pair n108 is separated. Thereby, the transition of the contact point from the tooth profile pair n to the next tooth profile pair m is performed.
ここで重要なのは、角あたりを通してピッチ誤差の吸収がなされ、衝撃無く歯形から歯形への接触点の移行がおこなわれることである。しかしながら、角あたりはすべり率無限や相対曲率無限、応力無限状態を示し摩耗、騒音を発生させる。すべり率無限は歯車１速度方向と接触点軌跡線方向が一致するためである。相対曲率無限は、歯形１上の角点の曲率が無限大となるため、相対曲率も無限大となるためである。ここで、歯形対n１０８から歯形対m１０５への接触点の移行する瞬間を除き、歯形対nでの接触と歯形対mでの接触が同時に起こることはなく実質かみあい率１の状態となる。また、接触点軌跡線の領域は回転方向に偏位する。 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, the corners show infinite slip rate, relative curvature infinite, and stress infinite states, and generate wear and noise. The slip ratio is infinite because the gear 1 speed direction and the contact point locus line direction coincide. The relative curvature infinite is because the curvature of the corner point on the tooth profile 1 is infinite and the relative curvature is also infinite. Here, except for the moment when the contact point from the tooth profile pair n108 to the tooth profile pair m105 shifts, the contact at the tooth profile pair n and the contact at the tooth profile pair m do not occur at the same time, and the substantial meshing ratio is 1. Further, the region of the contact point locus line is deviated in the rotation direction.
図５は歯面の歯先側を曲面でカットした修正歯面を示す。図５の５０１は元歯面、５０２は修正歯面、５０３は歯面修正領域、５０４は歯元、５０５は歯先を表す。 FIG. 5 shows a modified tooth surface obtained by cutting the tooth tip side of the tooth surface with a curved surface. In FIG. 5, reference numeral 501 denotes an original tooth surface, 502 denotes a correction tooth surface, 503 denotes a tooth surface correction region, 504 denotes a tooth base, and 505 denotes a tooth tip.
図６は曲面でカットした歯面修正の場合の、歯形対nの歯形の回転と接触点軌跡線の様子を示す。図６の６０１は接触点軌跡線Qr、６０２は接触点Q2、６０３は接触点Q3、６０４は接触点Q4、６０５は接触点Q3r、６０６は接触点Q4rを表す。 FIG. 6 shows the rotation of the tooth profile of the tooth profile pair n and the state of the contact point locus line in the case of correction of the tooth surface cut with a curved surface. In FIG. 6, 601 represents a contact point locus line Qr, 602 represents a contact point Q2, 603 represents a contact point Q3, 604 represents a contact point Q4, 605 represents a contact point Q3r, and 606 represents a contact point Q4r.
G1は歯面１上の歯形１、G2はG1とかみあう歯面２上の歯形２、ＱはG1とG2の接触点軌跡線である。歯形対n１０８の接触点は歯面１の歯元側Ｑ1４０３から回転と共にカット開始点Ｑ2６０２へ移動する。この間は角速度比が一定であるのでピッチ誤差は同じで縮まらない。角速度比が一定に近い場合も同様である。 G1 is the tooth profile 1 on the tooth surface 1, G2 is the tooth profile 2 on the tooth surface 2 that meshes with G1, and Q is the contact point locus line between G1 and G2. The contact point of the tooth profile pair n108 moves from the root side Q1403 of the tooth surface 1 to the cutting start point Q2602 with rotation. During this time, since the angular velocity ratio is constant, the pitch error is the same and does not shrink. The same applies when the angular velocity ratio is nearly constant.
接触点がカット開始点Ｑ2６０２へ移動した後は、歯形１が回転しても歯形上の接触点はカット開始点に留まり、空間上の接触点は歯車軸１の周りを回動しＱ3r６０５に移動する。元歯形を考えた場合、回転と共に歯面は歯形上の点Ｑ3６０３で外接するので、カット開始点と歯形2との間は隙間ができ、歯形２が回転して角として突き出たカット開始点に接触する。または，歯形１が回転してカット開始点が歯形２に接触する。すなわち、接触点Ｑ2６０２から接触点Ｑ3r６０５の間では，角あたりの状態で歯形対n１０８はΔψD１１３を吸収する。この角あたりは歯先での角あたりに比べると広角での角あたりになるので、ここではこの角あたりを広角あたりと定義する。 After the contact point moves to the cut start point Q2602, even if the tooth profile 1 rotates, the contact point on the tooth profile remains at the cut start point, and the contact point on the space rotates around the gear shaft 1 and moves to Q3r605. To do. Considering the original tooth profile, the tooth surface circumscribes at the point Q3603 on the tooth profile as it rotates, so there is a gap between the cut start point and the tooth profile 2, and the tooth profile 2 rotates to the cut start point protruding as a corner. Contact. Alternatively, the tooth profile 1 rotates and the cutting start point contacts the tooth profile 2. That is, between the contact point Q2602 and the contact point Q3r605, the tooth profile pair n108 absorbs ΔψD113 in the state around the corner. Since this per corner is around a wide angle compared to that at the tip of the tooth, this per corner is defined as a wide angle.
ΔψDの吸収が不足の場合は、回転と共に接触点は修正歯形上を歯先に向かってΔψDを吸収しながら移動しＱ4rへ６０６向かう。接触点Ｑ4rに至ってもΔψDの吸収が不足の場合は、回転と共に接触点は歯先に留まって角あたりの状態でΔψDを吸収する。開始点Ｑ1以降ΔψDの吸収が完了した時点で歯形対m１０５が新たに接触し歯形対n１０８が離れる。これにより、歯形対nから次の歯形対mへの接触点の移行がおこなわれる。 If the absorption of ΔψD is insufficient, the contact point moves along the correction tooth profile toward the tooth tip while absorbing ΔψD along with the rotation and heads toward Q4r 606. If the absorption of ΔψD is insufficient even after reaching the contact point Q4r, the contact point stays at the tooth tip with rotation and absorbs ΔψD in the state around the corner. After the start point Q1, when the absorption of ΔψD is completed, the tooth profile pair m105 newly comes into contact with the tooth profile pair n108. Thereby, the transition of the contact point from the tooth profile pair n to the next tooth profile pair m is performed.
ここで重要なのは、カット開始点Ｑ2６０２からＱ3r６０５への間は広角あたりになり、広角あたりを通してピッチ誤差の吸収がなされ、衝撃無く歯形から歯形への接触点の移行がおこなわれることである。しかしながら、広角あたりも角あたり同様すべり率無限や相対曲率無限、応力無限状態を示し摩耗、騒音を発生させる。但し、歯先での角あたりに比べると広角での角あたりとなり曲面あたり側に近いので騒音は低減される。すべり率無限は歯車１速度方向と接触点軌跡線方向が一致するためである。相対曲率無限は、歯形１上の角点の曲率が無限大となるため、相対曲率も無限大となるためである。ここで、歯形対nから歯形対mへの接触点の移行する瞬間を除き、歯形対nでの接触と歯形対mでの接触が同時に起こることはなく実質かみあい率１の状態となる。また、接触点軌跡領域は偏位する。 What is important here is that the area between the cut start point Q2602 and Q3r605 is around a wide angle, the pitch error is absorbed through the wide angle, and the contact point is transferred from the tooth profile to the tooth profile without impact. However, wear and noise are generated around the wide angle as well, with the same infinite slip rate, infinite relative curvature, and infinite stress. However, noise is reduced because it is near the corner at the wide angle and closer to the curved surface side than at the corner at the tooth tip. The slip ratio is infinite because the gear 1 speed direction and the contact point locus line direction coincide. The relative curvature infinite is because the curvature of the corner point on the tooth profile 1 is infinite and the relative curvature is also infinite. Here, except for the moment of transition of the contact point from the tooth profile pair n to the tooth profile pair m, the contact at the tooth profile pair n and the contact at the tooth profile pair m do not occur at the same time, and the substantial meshing ratio is 1. Further, the contact point locus region is deviated.
次に、ピッチ誤差吸収式を誘導する。図７に示すように、歯車１、２を考える。 Next, a pitch error absorption formula is derived. Consider the gears 1 and 2 as shown in FIG.
図７の７０１は歯車１軸Ｓ1、７０２は歯車２軸Ｓ2、７０３は歯車１軸と２軸の共通垂線、７０４は角速度１ω1、７０５は角速度２ω2、７０６は原点Ｏ1、７０７は点Ｏ2、７０８は座標Ｘ、７０９は座標系Ｙ、７１０は座標Ｚ、７１１は単位ベクトルｉb、７１２は単位ベクトルｊb、７１３は単位ベクトルｋb、７１４は接触点Ｑ、７１５は接触点の位置ベクトルＱbを表す。(以下では，ベクトルを記号の後にbを加えて表す)。 7, reference numeral 701 denotes a gear 1 axis S1, 702 denotes a gear 2 axis S2, 703 denotes a common perpendicular to the gear 1 axis and the two axes, 704 denotes an angular velocity 1ω1, 705 denotes an angular velocity 2ω2, 706 denotes an origin O1, 707 denotes a point O2, and 708. Is a coordinate X, 709 is a coordinate system Y, 710 is a coordinate Z, 711 is a unit vector ib, 712 is a unit vector jb, 713 is a unit vector kb, 714 is a contact point Q, and 715 is a position vector Qb of the contact point. (In the following, the vector is expressed by adding b after the symbol).
図７に示すように、歯車１、２の軸の共通垂線７０３と歯車１、２軸の交点をＯ1７０６、Ｏ2７０７とし、Ｏ1を原点とし、共通垂線方向をＸ７０８、歯車１方向をＺ７１０、ＸとＺに垂直な方向をＹ７０９とする座標を考え、Ｘ、Ｙ、Ｚ座標の方向単位ベクトルをｉb７１１、ｊb７１２、ｋb７１３とする。Ｏ1７０６を始点とする接触点Ｑ７１４の位置ベクトルをＱb７１５、Ｏ1からＯ2へのベクトルをDb７１６、角速度１をω1７０４、角速度２をω2７０５、回転比をｉとする。 As shown in FIG. 7, the intersections of the common vertical axis 703 of the gears 1 and 2 and the gears 1 and 2 are O1706 and O2707, O1 is the origin, the common vertical direction is X708, and the gear 1 direction is Z710 and X. Consider a coordinate whose direction perpendicular to Z is Y709, and let ib711, jb712, and kb713 be direction unit vectors of the X, Y, and Z coordinates. The position vector of the contact point Q714 starting from O1706 is Qb715, the vector from O1 to O2 is Db716, the angular velocity 1 is ω1704, the angular velocity 2 is ω2705, and the rotation ratio is i.
前述のように、ピッチ誤差は広角あたり、修正歯面での接触、角あたりにより吸収される。まず、無修正かつ歯先が伸びた元歯面上の接触点Ｑ７１４を考える。接触点を求める式は知られている。接触点が定まれば、共通歯面法線方向が定まる。接触点での相対速度ベクトルをＶb、歯面の共通歯面法線の単位ベクトルをＮbとすれば、接触点でのかみあい条件は次式(数１)、(数２)となる。 As described above, the pitch error is absorbed by the wide angle, the contact with the corrected tooth surface, and the corner. First, consider the contact point Q714 on the original tooth surface where the tooth tip is uncorrected and the tooth tip is extended. The formula for determining the contact point is known. If the contact point is determined, the common tooth surface normal direction is determined. If the relative velocity vector at the contact point is Vb and the unit vector of the common tooth surface normal of the tooth surface is Nb, the contact condition at the contact point is expressed by the following equations (Equation 1) and (Equation 2).
（数１）
Ｎb・Ｖb＝0
（数２）
Ｖb＝ω2ｊb×(Ｑb−Db)−ω1ｋb×Ｑb
(Equation 1)
Nb ・ Vb = 0
(Equation 2)
Vb = ω2jb × (Qb−Db) −ω1 kb × Qb
回転比ｉは式(数１)、(数２)より次式(数３)となる。
（数３）
ｉ＝ω1 / ω2＝｛Ｎb・(ｊb×(Ｑb−Db))｝/｛Ｎb・(ｋb×Ｑb)｝
The rotation ratio i is expressed by the following expression (Expression 3) from Expressions (Expression 1) and (Expression 2).
(Equation 3)
i = ω1 / ω2 = {Nb · (jb × (Qb−Db))} / {Nb · (kb × Qb)}
接触点での歯面１の回転角ψ1は、時間ｔとして次式(数４)となる。ここで、歯面修正面の始点を接触点とするときの歯面１、２の回転角を零とする。ψ1の積分の範囲は０からｔであり、ｔが０のときψ1も０である。ω2は一定とする。不等角速度比の場合は、角速度比が時間と共に変化するのでｉは時間tの関数となる。等角速度比の場合は、角速度比が一定なのでｉは一定となる。そしてψ1は次式(数５)となる。ψ2は歯面２の回転角である。 The rotation angle ψ 1 of the tooth surface 1 at the contact point is expressed by the following equation (Equation 4) as time t. Here, the rotation angle of the tooth surfaces 1 and 2 when the starting point of the tooth surface correction surface is the contact point is set to zero. The integration range of ψ1 is from 0 to t, and when t is 0, ψ1 is also 0. ω2 is assumed to be constant. In the case of an unequal angular velocity ratio, since the angular velocity ratio changes with time, i is a function of time t. In the case of a constant angular velocity ratio, i is constant because the angular velocity ratio is constant. Ψ1 is expressed by the following equation (Equation 5). ψ2 is the rotation angle of the tooth surface 2.
（数４）
ψ1＝∫ｉω2 dt
（数５）
ψ1＝ω1ｔ＝ｉω2ｔ＝ｉψ2
(Equation 4)
ψ1 ＝ ∫iω2 dt
(Equation 5)
ψ 1 = ω 1 t = iω 2 t = iψ 2
次に修正後の歯面を考える。この場合の修正前後で値が異なる記号は添え字ｒを付す。接触点ＱはＱr、接触点の位置ベクトルＱbはＱbr、角速度ω1はω1r、回転比ｉはｉr、接触点での相対速度ベクトルＶbはＶbr、歯面の共通歯面法線の単位ベクトルＮbはＮbrである。角速度ω2はω2で同じである。歯面１の回転角ｉrの式は、修正前の歯面の場合と同様にして、次式(数６)、(数７)となる。ψ1rの積分の範囲は０からｔであり、ｔが０のときψ1rも０である。角速度比は時間と共に変化するのでｉrは時間tの関数となる。 Next, consider the modified tooth surface. In this case, a symbol having a different value before and after correction is given a subscript r. The contact point Q is Qr, the contact point position vector Qb is Qbr, the angular velocity ω1 is ω1r, the rotation ratio i is ir, the relative velocity vector Vb at the contact point is Vbr, and the unit vector Nb of the tooth surface common tooth surface normal is Nbr. The angular velocity ω2 is the same as ω2. The expression of the rotation angle ir of the tooth surface 1 is expressed by the following expressions (Expression 6) and (Expression 7), similarly to the case of the tooth surface before correction. The integration range of ψ1r is from 0 to t, and when t is 0, ψ1r is also 0. Since the angular velocity ratio changes with time, ir is a function of time t.
（数６）
ψ1r＝∫ｉrω2 dt
（数７）
ｉr＝ω1r / ω2＝｛Ｎbr・(ｊb×(Ｑbr−Db))｝/｛Ｎbr・(ｋb×Ｑbr)｝
(Equation 6)
ψ1r ＝ ∫irω2 dt
(Equation 7)
ir = ω1r / ω2 = {Nbr · (jb × (Qbr−Db))} / {Nbr · (kb × Qbr)}
歯面修正後の歯形上の点を接触点とするときの歯車１、２の回転角をψ1r、ψ2とする。また、歯車２の回転角が同じψ2の場合の、歯面修正前の歯車１の回転角をψ1とする。ここで、歯車１の修正後の回転角ψ1rと修正前の回転角ψ1の差をΔψ1とすれば、角ピッチ誤差を吸収する条件は次式(数８)となる。これは、歯車２の同一回転角に対する、歯車１の修正後の回転角ψ1rが修正前の回転角ψ1に比べ大きいことである。ここで、このΔψ1を角ピッチ誤差吸収角とよぶ。 The rotation angle of the gear 1 and 2 when the contact point a point on the tooth profile after the tooth surface modify Pusai1r, and [psi 2. In addition, when the rotation angle of the gear 2 is the same φ 2 , the rotation angle of the gear 1 before the tooth surface correction is φ 1. Here, if the difference between the corrected rotation angle ψ1r of the gear 1 and the uncorrected rotation angle ψ1 is Δψ1, the condition for absorbing the angular pitch error is expressed by the following equation (Equation 8). This is because the rotation angle ψ1r after correction of the gear 1 with respect to the same rotation angle of the gear 2 is larger than the rotation angle ψ1 before correction. Here, this Δψ1 is referred to as an angular pitch error absorption angle.
（数８）
Δψ1＝ψ1r−ψ1 > 0
(Equation 8)
Δψ1 ＝ ψ1r−ψ1> 0
以上のことより、ピッチ誤差による騒音を防止する為の必要条件を整理すれば、 From the above, if we organize the necessary conditions to prevent noise due to pitch error,
条件１(ピッチ誤差吸収) ：修正歯面を歯面の歯先側かつ内側に設けること。これにより、早い段階でピッチ誤差を連続的に吸収することができ、角あたりを防ぐことが可能となる。 Condition 1 (Pitch error absorption): A modified tooth surface is provided on the tooth tip side and inside of the tooth surface. As a result, pitch errors can be absorbed continuously at an early stage, and corners can be prevented.
条件２(広角あたりの防止) ：修正歯面は歯面に内接する曲面とすること。これにより、歯面上に不連続線が現れることがなく広角あたりを防ぐことができる。 Condition 2 (Prevention per wide angle): The modified tooth surface should be a curved surface inscribed in the tooth surface. As a result, discontinuous lines do not appear on the tooth surface, and a wide-angle area can be prevented.
条件３(角あたりの防止) ：修正歯面の修正面の構成要素を、修正歯面の歯先から一定量内側の接触点で、ピッチ誤差をすべて吸収する条件式を満たすように定めること。これにより、角あたりを防ぐことができる。 Condition 3 (Prevention per corner): The components of the correction surface of the correction tooth surface should be determined so as to satisfy the conditional expression that absorbs all pitch errors at the contact point inside the correction tooth surface by a certain amount. Thereby, the corner hit can be prevented.
修正歯面１の歯先から一定量内側の点が接触点である場合の角ピッチ誤差吸収角をΔψ1Lとし、角ピッチ誤差の設計上の公差の最大値をΔψDとする。ここで、歯先から一定量内側の歯面上の接触点でピッチ誤差を吸収する条件は、ピッチ誤差吸収角が公差の最大値より大きいことで有り次式(数９)で表される。ここで、ピッチ誤差ΔψDは歯車１の角ピッチ誤差と、歯車２の角ピッチ誤差を歯車１の角ピッチ誤差に換算したものを合わせたものである。実際のΔψ1Lは誤差や安全率等を考慮し元のΔψ1Lより大きくとることになる。 The angle pitch error absorption angle when the point inside the tooth tip of the corrected tooth surface 1 is a contact point is Δψ1L, and the maximum design tolerance of the angle pitch error is ΔψD. Here, the condition for absorbing the pitch error at the contact point on the tooth surface a certain amount inside from the tooth tip is that the pitch error absorption angle is larger than the maximum tolerance, and is expressed by the following equation (Equation 9). Here, the pitch error ΔψD is a combination of the angular pitch error of the gear 1 and the angular pitch error of the gear 2 converted into the angular pitch error of the gear 1. The actual Δψ1L is larger than the original Δψ1L in consideration of errors and safety factors.
（数９）
Δψ1L > ΔψD
(Equation 9)
Δψ1L> ΔψD
この条件式(数９)を満たす修正面を決定する修正面構成要素を与える方法としては次の解法がある。修正面構成要素は、例えば、円で補正する場合は円の中心位置や円の半径である。 There is the following solution as a method for providing a correction surface component for determining a correction surface that satisfies this conditional expression (Equation 9). The correction surface component is, for example, the center position of the circle or the radius of the circle when correcting with a circle.
解法１ ：条件式を修正面構成要素を求める式に変形して解を求める方法
解法２ ：条件式に修正面構成要素を代入し，数値解法により解を求める方法
解法３ ：修正面構成要素を変数として種々の値を与え，歯面と接触点の軌跡をシ ミュレーションして、解を求める方法
Solution 1: A method for obtaining a solution by transforming a conditional expression into a formula for obtaining a corrected surface component. Solution 2: A method for obtaining a solution by a numerical solution by substituting the modified surface component into a conditional equation. Solution 3: A modified surface component. A method to obtain solutions by simulating the tooth surface and contact point trajectories by giving various values as variables
生産上は、生産ラインで実際のあるいは基準の相手歯車とかみ合わせ、歯面対nから歯面対mへの移行時の歯面対nの接触点が歯先を除く歯形上に位置しているか、画像処理を用いて評価判定することもできる。 In production, meshing with the actual or reference mating gear on the production line, is the contact point of tooth surface pair n at the transition from tooth surface pair n to tooth surface pair m positioned on the tooth profile excluding the tooth tip? Evaluation can also be made using image processing.
歯形工具により歯面を加工する場合は、平歯車のように工具歯形の歯底側に歯形修正を加えることにより、歯形の歯先側が修正された修正歯面を得ることができる。これは、成形歯切り、創成歯切りによらず可能である。例えば、ホブの歯形修正、ハイポイドギヤにおける環状カッターの歯形修正、ウォームギヤにおけるバイトの歯形修正等が考えられる。歯形により理論的に歯面を構成し数値加工する歯面の場合も同様である。歯形修正曲線としては、円、楕円、インボリュート曲線、直線と円弧の合成曲線等が考えられる。 When a tooth surface is machined with a tooth profile tool, a modified tooth surface in which the tooth tip side of the tooth profile is corrected can be obtained by applying a tooth profile correction to the tooth bottom side of the tool tooth profile like a spur gear. This is possible regardless of molding gear cutting or generating gear cutting. For example, the tooth profile correction of the hob, the tooth profile correction of the annular cutter in the hypoid gear, the tooth profile correction of the bite in the worm gear, etc. can be considered. The same applies to a tooth surface that theoretically forms a tooth surface based on the tooth profile and is numerically processed. As the tooth profile correction curve, a circle, an ellipse, an involute curve, a combined curve of a straight line and an arc, and the like can be considered.
条件４(先細り防止) ：修正歯面の曲率の大きさは必要最低限とすること。これにより、歯の先細りによる強度やかみあいに関する問題を防げる．歯面修正が小さ過ぎるとピッチ誤差の吸収が不満足となり、大きいと歯先の先細りや角速度比の変化が大きくなる。ピッチ誤差が大きい場合、歯面修正が大きくなり歯先の先細りや角速度比の変化が大きくなる。従って、ピッチ誤差は極力小さく抑える必要がある。 Condition 4 (Preventing taper): The curvature of the modified tooth surface should be the minimum necessary. This prevents problems related to strength and contact caused by tooth taper. If the tooth surface correction is too small, the absorption of the pitch error is unsatisfactory, and if it is large, the tip of the tooth tip and the change in the angular velocity ratio become large. When the pitch error is large, the tooth surface correction becomes large, and the taper of the tooth tip and the change in the angular velocity ratio become large. Therefore, it is necessary to keep the pitch error as small as possible.
条件５(符号対応) ：歯車１、２の両方に上記の歯面修正を施すこと。これは重要なことで、歯車１、２の片方のみに上記の歯面修正を施した場合は符号の＋−のいずれかのピッチ誤差に対応できない。 Condition 5 (corresponding to the code): Apply the above tooth surface correction to both gears 1 and 2. This is important, and if the tooth surface correction is applied to only one of the gears 1 and 2, it cannot cope with any of the + and-sign pitch errors.
図８は上記の条件を満たす歯面修正の場合の、歯形対nの歯形の回転と接触点軌跡線の様子を示す。 FIG. 8 shows the rotation of the tooth profile of the tooth profile pair n and the state of the contact point locus line in the case of the tooth surface correction satisfying the above conditions.
図８の８０１は歯形１Ｇ1、８０２は接触点軌跡線Ｑr、８０３は接触点Ｑ2、８０４は接触点Ｑ3、８０５は接触点Ｑ4、８０６は接触点Ｑ3rを表す。 In FIG. 8, 801 represents the tooth profile 1G1, 802 represents the contact point locus line Qr, 803 represents the contact point Q2, 804 represents the contact point Q3, 805 represents the contact point Q4, and 806 represents the contact point Q3r.
Ｇ1は歯面１上の歯形１、Ｇ2はＧ1とかみあう歯面２上の歯形２、Ｑ４０４はＧ1とＧ2の接触点軌跡線である。 G1 is a tooth profile 1 on the tooth surface 1, G2 is a tooth profile 2 on the tooth surface 2 that meshes with G1, and Q404 is a contact point locus line between G1 and G2.
歯形対n１０８の接触点は歯面１の歯元側Ｑ1４０３から回転と共に歯形修正開始点Ｑ2８０３へ移動する。この間は角速度比が一定であるのでピッチ誤差は同じで縮まらない。角速度比が一定に近い場合も同様である。 The contact point of the tooth profile pair n108 moves from the tooth root side Q1403 of the tooth surface 1 to the tooth profile correction start point Q2803 with rotation. During this time, since the angular velocity ratio is constant, the pitch error is the same and does not shrink. The same applies when the angular velocity ratio is nearly constant.
接触点が歯形修正開始点Ｑ2へ移動した後は、回転と共に接触点は修正歯形上を歯先に向かってΔψD１１３を吸収しながら移動しＱ3r８０６へ向かう。修正前の元歯形を考えた場合、回転と共に歯面は歯形上の点Ｑ3８０４で外接するので、Ｑ3rを通る歯形１と歯形2との間は隙間ができ、歯形２が回転して歯形１と接触する。または、歯形１が回転して歯形２に接触する。これにより、歯形対nはΔψDを吸収する。 After the contact point moves to the tooth profile correction start point Q2, the contact point moves on the correction tooth profile toward the tooth tip while absorbing ΔψD113 and moves toward Q3r806. Considering the original tooth profile before correction, the tooth surface circumscribes at the point Q3804 on the tooth profile as it rotates, so that there is a gap between the tooth profile 1 and the tooth profile 2 passing through Q3r. Contact. Alternatively, the tooth profile 1 rotates and contacts the tooth profile 2. As a result, the tooth profile pair n absorbs ΔψD.
さらに、回転と共に接触点は修正歯形上を歯先に向かってΔψDを吸収しながら移動しＱ4r８０７へ向かう。元歯形を考えた場合、回転と共に歯面は歯形上の点Ｑ4８０５で外接するので、Ｑ4rを通る歯形１と歯形2との間は隙間ができ、歯形２が回転して歯形１と接触する。または，歯形１が回転して歯形２に接触する。これにより、歯形対nはΔψDを吸収する。この時点で、ΔψD１１３の吸収が完了し、歯形対n１０８から次の歯形対m１０５への接触点の移行がおこなわれる。 Further, the contact point moves along the correction tooth profile toward the tooth tip while absorbing ΔψD along with the rotation, and moves toward Q4r807. Considering the original tooth profile, the tooth surface circumscribes at the point Q4805 on the tooth profile as it rotates, so that there is a gap between the tooth profile 1 and the tooth profile 2 passing through Q4r, and the tooth profile 2 rotates and contacts the tooth profile 1. Alternatively, the tooth profile 1 rotates and contacts the tooth profile 2. As a result, the tooth profile pair n absorbs ΔψD. At this time, the absorption of ΔψD113 is completed, and the transition of the contact point from the tooth profile pair n108 to the next tooth profile pair m105 is performed.
ここで重要なのは、衝撃そして広角あたりや角あたりがなく歯形から歯形への接触点の移行がおこなわれることである。すなわち、すべり率無限や相対曲率無限、応力無限状態となって摩耗、騒音を発生させることはない。なお、歯面対nから歯面対mへの接触点の移行する瞬間を除き、歯面対nでの接触と歯面対mでの接触が同時に起こることはなく実質かみあい率１の状態となる。また、接触点軌跡領域の偏位は縮小する。 What is important here is that the contact point shifts from the tooth profile to the tooth profile without impact and around a wide angle or corner. In other words, the slip rate is infinite, the relative curvature is infinite, the stress is infinite, and no wear or noise is generated. Except for the moment of transition of the contact point from the tooth surface pair n to the tooth surface pair m, the contact at the tooth surface pair n and the contact at the tooth surface pair m do not occur at the same time, and the state of the substantial meshing rate is 1. Become. Further, the deviation of the contact point locus region is reduced.
ねじれは右ねじれでも左ねじれでも同様である。左右の歯面は右歯面でも左歯面でも同様である。回転方向は正方向でも逆方向でも同様である。 The twist is the same for both right and left twists. The same applies to the right and left tooth surfaces. The rotation direction is the same in both the forward and reverse directions.
以上は，幾何学的な考察であるが，力による変形がある場合でも同様である。歯圧による歯の変形がある場合は、歯車対ｎから歯車対ｍへの接触点および力の移行が、瞬間的ではあるが微小時間をかけておこなわれる。
歯圧による歯の変形がある場合は、歯車対ｎから歯車対ｍへの接触点および力の移行が、瞬間的ではあるが微小時間をかけておこなわれる。
The above is a geometrical consideration, but it is the same even when there is deformation due to force. When there is a deformation of the tooth due to the tooth pressure, the transition of the contact point and the force from the gear pair n to the gear pair m is instantaneously performed over a very short time.
When there is a deformation of the tooth due to the tooth pressure, the transition of the contact point and the force from the gear pair n to the gear pair m is instantaneously performed over a very short time.
本発明により、騒音や耐摩耗に優れた歯車を実現できる。その為、静粛かつ強い強度を備えた機械要素としての歯車が要求される機械において広く利用可能である。 According to the present invention, a gear excellent in noise and wear resistance can be realized. Therefore, the present invention can be widely used in machines that require a gear as a machine element having a quiet and strong strength.
１０１ 歯車１
１０２ 歯車２
１０３ 歯形１
１０４ 歯形２
１０５ 歯形対ｍ
１０６ 歯形１
１０７ 歯形２
１０８ 歯形対ｎ
１０９ 歯底円１
１１０ 歯先円１
１１１ 歯底円２
１１２ 歯先円２
１１３ 角ピッチ誤差ΔψD
４０１ 接触点軌跡線Ｑ
４０２ 接触点軌跡線Ｑr
４０３ 接触点Ｑ1
４０４ 接触点Ｑ2
４０５ 接触点Ｑ3
４０６ 接触点Ｑ3r
５０１ 元歯面
５０２ 修正歯面
５０３ 歯面修正領域
５０４ 歯元
５０５ 歯先
６０１ 接触点軌跡線Ｑr
６０２ 接触点Ｑ2
６０３ 接触点Ｑ3
６０４ 接触点Ｑ4
６０５ 接触点Ｑ3r
６０６ 接触点Ｑ4r
７０１ 歯車１軸Ｓ1
７０２ 歯車２軸Ｓ2
７０３ 歯車１軸と２軸の共通垂線
７０４ 角速度１
７０５ 角速度２
７０６ 原点Ｏ1
７０７ 点Ｏ2
７０８ 座標Ｘ
７０９ 座標Ｙ
７１０ 座標Ｚ
７１１ 単位ベクトルｉb
７１２ 単位ベクトルｊb
７１３ 単位ベクトルｋb
７１４ 接触点Ｑ
７１５ 接触点位置ベクトルＱb
７１６ ベクトルＤb
８０１ 歯形１Ｇ1
８０２ 接触点軌跡線Ｑr
８０３ 接触点Ｑ2
８０４ 接触点Ｑ3
８０５ 接触点Ｑ4
８０６ 接触点Ｑ3r
８０７ 接触点Ｑ4r
101 Gear 1
102 Gear 2
103 Tooth profile 1
104 Tooth profile 2
105 Tooth profile vs. m
106 Tooth profile 1
107 Tooth profile 2
108 Tooth profile vs. n
109 root circle 1
110 Tooth circle 1
111 root circle 2
112 Tooth circle 2
113 Angular pitch error ΔψD
401 Contact point locus line Q
402 Contact point locus line Qr
403 Contact point Q1
404 Contact point Q2
405 Contact point Q3
406 Contact point Q3r
501 Original tooth surface 502 Correction tooth surface 503 Tooth surface correction region 504 Tooth base 505 Tooth tip 601 Contact point locus line Qr
602 Contact point Q2
603 Contact point Q3
604 Contact point Q4
605 Contact point Q3r
606 Contact point Q4r
701 Gear 1 axis S1
702 Gear 2 shaft S2
703 Gear 1 axis and 2 axis common perpendicular 704 Angular velocity 1
705 Angular velocity 2
706 Origin O1
707 points O2
708 coordinate X
709 coordinate Y
710 coordinate Z
711 Unit vector ib
712 Unit vector jb
713 unit vector kb
714 Contact point Q
715 Contact point position vector Qb
716 Vector Db
801 Tooth profile 1G1
802 Contact point locus line Qr
803 Contact point Q2
804 Contact point Q3
805 Contact point Q4
806 Contact point Q3r
807 Contact point Q4r
Claims (1)
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2017001489A JP2018112206A (en) | 2017-01-07 | 2017-01-07 | Skewed shaft gear and intersecting shaft gear |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2017001489A JP2018112206A (en) | 2017-01-07 | 2017-01-07 | Skewed shaft gear and intersecting shaft gear |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JP2018112206A true JP2018112206A (en) | 2018-07-19 |
Family
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Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP2017001489A Pending JP2018112206A (en) | 2017-01-07 | 2017-01-07 | Skewed shaft gear and intersecting shaft gear |
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| Country | Link |
|---|---|
| JP (1) | JP2018112206A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108953550A (en) * | 2018-08-01 | 2018-12-07 | 中南大学 | The point tooth surface design method of spur gear |
| CN111120624A (en) * | 2019-12-04 | 2020-05-08 | 武汉市精华减速机制造有限公司 | Contact stress homogenization-based cycloidal gear tooth profile modification method |
| CN112541235A (en) * | 2020-12-04 | 2021-03-23 | 重庆大学 | Universal design method for hypoid gear pair |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0796441A (en) * | 1993-09-24 | 1995-04-11 | Eisuke Yokoyama | Backlash eliminating structure in worm-worm wheel mechanism |
| JP2005075274A (en) * | 2003-09-03 | 2005-03-24 | Honda Motor Co Ltd | Electric power steering device |
| JP2010221855A (en) * | 2009-03-24 | 2010-10-07 | Hitachi Automotive Systems Ltd | Electric power steering device |
| JP2016008682A (en) * | 2014-06-25 | 2016-01-18 | 大竹技研株式会社 | Hypoid gear |
-
2017
- 2017-01-07 JP JP2017001489A patent/JP2018112206A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0796441A (en) * | 1993-09-24 | 1995-04-11 | Eisuke Yokoyama | Backlash eliminating structure in worm-worm wheel mechanism |
| JP2005075274A (en) * | 2003-09-03 | 2005-03-24 | Honda Motor Co Ltd | Electric power steering device |
| JP2010221855A (en) * | 2009-03-24 | 2010-10-07 | Hitachi Automotive Systems Ltd | Electric power steering device |
| JP2016008682A (en) * | 2014-06-25 | 2016-01-18 | 大竹技研株式会社 | Hypoid gear |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108953550A (en) * | 2018-08-01 | 2018-12-07 | 中南大学 | The point tooth surface design method of spur gear |
| CN111120624A (en) * | 2019-12-04 | 2020-05-08 | 武汉市精华减速机制造有限公司 | Contact stress homogenization-based cycloidal gear tooth profile modification method |
| CN112541235A (en) * | 2020-12-04 | 2021-03-23 | 重庆大学 | Universal design method for hypoid gear pair |
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