JP2014098438A - Double helical gear - Google Patents

Double helical gear Download PDF

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JP2014098438A
JP2014098438A JP2012250447A JP2012250447A JP2014098438A JP 2014098438 A JP2014098438 A JP 2014098438A JP 2012250447 A JP2012250447 A JP 2012250447A JP 2012250447 A JP2012250447 A JP 2012250447A JP 2014098438 A JP2014098438 A JP 2014098438A
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gear
tooth
helical teeth
yamaba
pair
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JP6067338B2 (en
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Mitsushige Ooka
三茂 大岡
Tetsuya Hoguchi
徹也 穂口
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O Oka Corp
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Abstract

PROBLEM TO BE SOLVED: To provide a double helical gear in which a pair of helical teeth having right and left twisting directions opposite to each other are integrally formed by a cold forging from an annular coarse material, a mold structure is properly modified to eliminate a phase shift in a tooth facing direction and improve a dedendum strength with high accuracy.SOLUTION: This invention relates to a double helical gear in which a pair of helical teeth having opposite right and left twisting directions are formed on the same axis of an outer peripheral surface of a cylindrical coarse material and an interface area is arranged between the pair of helical teeth, the interface area is constituted by a groove or a rib.

Description

ヤマバ歯車は捩じれ方向が左右逆向きの一対のヘリカル歯を同一軸上で隣り合わせに組み合わせた歯車であり、平行軸の間に動力伝達を行ない主として各種産業機械等の歯車装置に使用される比較的大型の歯車である。ヤマバ歯車はヘリボーン歯車とかダブルヘリカル歯車とも呼ばれる。産業機械等に通常のヘリカル歯車を使用した場合、スラスト力を止めるためにストッパーを設けるので機械の広いスペースを必要とする。一方、ヤマバ歯車を使用するとスラスト力が相殺されるので、ストッパーが不要となり産業機械等は小さいスペースで済む。主に、ヤマバ歯車は鉄道車両駆動系の平行カルダン歯車装置、歯車ポンプ式のゴム、合成ゴムまたは天然ゴム等のエラストマーを混練しながら可塑化して押し出す歯車ポンプ式押出機、遊星歯車のプラネット歯車に適用される。ヤマバ歯車は左右捩じれ方向が逆向きの一対のヘリカル歯車が同一周面に隣り合わせに組み合わされ、軸方向のスラスト力が打ち消される歯車である。スラスト荷重が生じないので、原理的には静粛性が得られる理想的な歯車であるが、現実には機械加工によって左右捩じれ方向が逆向きの一対のヘリカル歯を歯切りすることは困難である。そこで、本発明のヤマバ歯車は、左右捩じれ方向が逆向きの一対のヘリカル歯を同一軸上で隣り合わせに組み合わせた一体方式の歯車に関し、鍛造によって左右捩じれ方向が逆向きの一対のヘリカル歯を形成し、どちらかといえば小型の歯車である。   A YAMABA gear is a gear that combines a pair of helical teeth whose torsional directions are opposite to each other on the same axis, and transmits power between parallel axes, which is relatively used mainly in gear devices of various industrial machines. It is a large gear. Yamaba gear is also called a helibone gear or double helical gear. When a normal helical gear is used for an industrial machine or the like, a stopper is provided to stop the thrust force, so that a large space of the machine is required. On the other hand, if the YAMABA gear is used, the thrust force is canceled out, so that a stopper is not required and the industrial machine or the like can be a small space. Mainly, YAMABA gears are used in parallel cardan gears for railway vehicle drive systems, gear pump type extruders that are plasticized and extruded while mixing elastomers such as gear pump type rubber, synthetic rubber or natural rubber, and planetary gears for planetary gears. Applied. A YAMABA gear is a gear in which a pair of helical gears whose left and right twist directions are opposite to each other are combined on the same peripheral surface side by side to cancel the axial thrust force. No thrust load is generated, so in principle it is an ideal gear that can achieve quietness, but in reality it is difficult to cut a pair of helical teeth with opposite left and right twist directions by machining . Therefore, the Yamaba gear of the present invention relates to an integrated gear in which a pair of helical teeth whose left and right twist directions are opposite to each other are combined on the same axis, and a pair of helical teeth whose left and right twist directions are opposite is formed by forging. If anything, it is a small gear.

従来のヤマバ歯車は一体方式或いは組み立て方式により製造されている。一体式ヤマバ歯車の使用例を図9に示す。ここでは上下の平行軸S1、S2の間にヤマバ歯車W10、W10が噛み合う。一体方式は、ギヤシェーパ加工によって歯切りをするために中央部に工具刃の逃げ溝を設ける。同図上段のヤマバ歯車W10は、左右の捩じれ方向が逆向きの一対のヘリカル歯1、2およびその間の溝4から構成される。即ち、ヤマバ歯車W10は一体の円筒粗材の軸方向左右に、捩じれ方向が左右逆向きの一対のヘリカル歯1、2を機械歯切りによって形成し、これらの間にギヤシェーパ刃の逃げ又は干渉防止の溝4を設けたものである。
一方、組み立て方式は、其々の円筒素材に捩じれ方向が逆向きのヘリカル歯をホブ加工によって別個に形成し、同一軸上で左右の捩じれ方向が逆向きの一対のヘリカル歯を結合したものである。即ち、其々の円筒素材に捩じれ方向が逆向きの一対のヘリカル歯を個々に作り、これらを焼嵌め等によって同一軸上で合体させたものである。
Conventional Yamaba gears are manufactured by an integral method or an assembly method. FIG. 9 shows an example of use of the integrated yamaba gear. Here, the Yamaba gears W10 and W10 mesh between the upper and lower parallel axes S1 and S2. In the integral system, a clearance groove for a tool blade is provided in the center portion for gear cutting by gear shaper processing. The YAMABA gear W10 in the upper part of the figure is composed of a pair of helical teeth 1 and 2 whose left and right twist directions are opposite to each other and a groove 4 therebetween. In other words, the Yamaba gear W10 is formed by mechanically cutting a pair of helical teeth 1 and 2 having a twisted direction opposite to the left and right in the axial direction of the integral cylindrical coarse material, and preventing the gear shaper blade from escaping or interfering therebetween. The groove 4 is provided.
On the other hand, the assembly method is a method in which helical teeth with opposite twist directions are separately formed on each cylindrical material by hobbing, and a pair of helical teeth with opposite twist directions on the same axis are combined. is there. That is, a pair of helical teeth whose directions of twisting are opposite to each other are individually formed in each cylindrical material, and these are combined on the same axis by shrink fitting or the like.

ヤマバ歯車に関しては、以下のような提案がなされている。ヤマバ歯車は自動車のトランスミッションに使用されることは無くその応用例は多くないが、例えば鉄道車両の原動機からの伝達経路に使用される。吊掛式の鉄道車両用駆動装置に使用される組み立式の大型ヤマバ歯車の例を以下に示す。左右に捩じれ方向の異なる一対のハスバ歯車輪を組合わせた内径部に一個の歯車ボスを微小な径差摺動可能により嵌合してヤマバ歯車とし、歯車輪と歯車ボスの側面方向となる両面に円板状の板バネを付設させ、この板バネの外径部辺を歯車輪に、内径部辺を歯車ボスにボルトによって螺着した構造である(特許文献1参照)。
同様に、ヤマバ歯車の応用例を示したもので、ハウジング内部のヤマバ歯車に対してハウジング外部から挿入したヤマバ歯車のヤマバ歯車同士の噛み合わせを容易にした例がある。詳細には、ハウジングの外側に配置されて駆動軸に取り付けられた駆動側の第1のヤマバ歯車と、上記ハウジングの内部に配置された従動側の第2のヤマバ歯車と、上記ハウジングの側壁に形成され第1のヤマバ歯車の駆動軸を保持するための組込み用穴と、上記組込み用穴に略すき間なく嵌合されて上記第1のヤマバ歯車の駆動軸を保持する軸受部材とを備え、上記ハウジング内部の第2のヤマバ歯車に対してハウジング外側から挿入した第1のヤマバ歯車を噛み合わせて歯車結合するヤマバ歯車の組立構造において、上記ハウジング内部の第2のヤマバ歯車をその回転軸方向に移動可能とし、第1のヤマバ歯車を上移動させて上記組込み用穴に差し込み、該第1のヤマバ歯車を下移動させて第2のヤマバ歯車に噛み合わせ、第1及び第2のヤマバ歯車が噛み合った状態でそれらをハウジングの内側方向に移動させて、上記ハウジング側壁の組込み用穴内に上記軸受部材を嵌合して組み立てるようにしたものである(特許文献2参照)。
また、本件出願人(以下出願人)は一体方式のヤマバ歯車に関し次のような提案をしている。即ち、ヤマバ歯車を鍛造手段により一体形成可能としたもので、ダイとパンチの夫々対向面へ向かい合わせに同径の凹部が設けられ、それら凹部の内周面に、互いに傾斜方向を逆とするヘリカル歯形形成用歯型を有するダイとパンチとから成る鍛造型内へ素材を据込んで、前記素材の周囲から各ヘリカル歯形形成用歯型内へ歯形を張り出し形成する成形方法である。他に、ダイとパンチの夫々対向面へ向かい合わせに同径の凹部を設け、両凹部の内周面へ、互いに傾斜方向を逆とするヘリカル歯形形成用歯型を形成し、少なくとも前記ダイとパンチの各ヘリカル歯形形成用歯部を夫々回動自在に支持して成る成形装置、及び鍛造型で素材を拘束し、前記上型と下型とから軸穴に相当する素材の中心へポンチを押し込むことにより、素材の周囲に各ヘリカル歯形形成用歯型内へ歯形を張り出し形成する方法である(特許文献3参照)。
The following proposals have been made for Yamaba gears. The YAMABA gear is not used for automobile transmissions and its applications are not many. For example, it is used for a transmission path from a prime mover of a railway vehicle. An example of an assembly-type large YAMABA gear used in a hanging railway vehicle drive device is shown below. A single gear boss is fitted to the inner diameter of a pair of helical gears with different twisting directions to the left and right to allow a small diameter difference to be slidable to form a yamaba gear. This is a structure in which a disc-shaped plate spring is attached, and the outer diameter side of this plate spring is screwed to a toothed wheel and the inner diameter side is screwed to a gear boss with a bolt (see Patent Document 1).
Similarly, an application example of the YAMABA gear is shown, and there is an example in which the YAMABA gears of the YAMABA gear inserted from the outside of the housing are easily meshed with each other. Specifically, a first YAMABA gear on the drive side that is disposed outside the housing and attached to the drive shaft, a second YAMABA gear on the driven side that is disposed inside the housing, and a side wall of the housing A built-in hole for holding the drive shaft of the first yamaba gear formed, and a bearing member that is fitted in the built-in hole without any gap and holds the drive shaft of the first yamaba gear; In the assembly structure of a YAMABA gear in which the first YAMABA gear inserted from the outside of the housing is engaged with the second YAMABA gear inside the housing, and the gears are coupled, the second YAMABA gear inside the housing is rotated in the direction of its rotation axis. The first yamaba gear is moved upward and inserted into the mounting hole, the first yamaba gear is moved downward and meshed with the second yamaba gear, and the first and second They are moved inwardly of the housing in a double-helical state in which gears are engaged, in which as assembled fitted the bearing member embedded within the bore of the housing side wall (see Patent Document 2).
In addition, the present applicant (hereinafter referred to as the applicant) has made the following proposals regarding the integrated Yamaba gear. That is, the YAMABA gear can be integrally formed by forging means, and recessed portions of the same diameter are provided facing the opposing surfaces of the die and the punch, and the inclined directions are opposite to each other on the inner peripheral surface of the recessed portions. In this molding method, a material is placed in a forging die composed of a die having a helical tooth profile forming die and a punch, and a tooth profile is formed by projecting from the periphery of the material into each helical tooth profile forming die. In addition, a concave portion having the same diameter is provided facing the opposing surfaces of the die and the punch, respectively, and a helical tooth profile forming tooth mold having opposite inclination directions is formed on the inner peripheral surface of both concave portions, and at least the die The forming device configured to rotatably support each helical tooth profile forming tooth portion of the punch, and the material is restrained by the forging die, and the punch is moved from the upper die and the lower die to the center of the material corresponding to the shaft hole. This is a method in which a tooth profile is formed by being pushed into each helical tooth profile forming tooth mold around the material (see Patent Document 3).

実公昭61−10039号公報Japanese Utility Model Publication No. 61-10039 特開2007−132436号公報JP 2007-132436 A 特開平5−277618号公報JP-A-5-277618

以上の通りであって、特許文献に代表されるように、従来のヤマバ歯車には以下のような問題点がある。   As described above, as represented by patent documents, the conventional YAMABA gear has the following problems.

組立て方式のヤマバ歯車は左右の捩じれ方向が逆向きの一対のヘリカル歯を夫々別個に形成した後、合体するので歯筋位相のズレや歯厚のばらつき等が生じて高精度のものが得られない。また、左右の捩じれ方向が逆向きの一対のヘリカル歯を合体させて一体方式のヤマバ歯車を製造する場合は、工程が増え大幅なコスト高をまねく。一方、特許文献1の組み立て方式も同様に、高精度のものを得るのは困難である。また、特許文献3の、鍛造手段によってヤマバ歯車を一体成形する方法によると、左右方向に捩じれた一対のヘリカル歯の歯筋位相が一致したヤマバ歯車を得るには金型に多くの工夫を必要とし、実用化は困難である。   The assembly-type YAMABA gear is formed with a pair of helical teeth whose left and right twist directions are opposite to each other, and then combined, so that the tooth phase shifts and tooth thickness variations occur, resulting in high accuracy gears. Absent. In addition, when a pair of helical teeth whose left and right twist directions are opposite to each other are combined to manufacture an integral type YAMABA gear, the number of processes increases and the cost increases significantly. On the other hand, it is difficult to obtain a highly accurate assembly method of Patent Document 1 as well. In addition, according to the method of integrally forming a yamaba gear by forging means in Patent Document 3, a lot of ingenuity is required in the mold to obtain a yamaba gear in which the tooth trace phases of a pair of helical teeth twisted in the left-right direction coincide And practical application is difficult.

そこで、本出願発明は以上のような課題に着目してなされたもので、捩じれ方向が逆向きの一対のヘリカル歯を冷間鍛造によって一体化成形することを基本とする。本出願発明は、円環状の粗材から左右捩じれ方向が逆向きの一対のヘリカル歯を冷間鍛造によって一体化成形し、金型構造に工夫を加えることによって歯筋方向で位相ずれが無く高精度で、かつ歯元強度を向上させたヤマバ歯車を提供することを目的としている。   Accordingly, the present invention has been made paying attention to the above problems, and is based on integrally forming a pair of helical teeth having opposite twist directions by cold forging. In the present invention, a pair of helical teeth with opposite left and right twist directions are integrally formed by cold forging from an annular rough material, and the die structure is devised to increase the phase without causing a phase shift in the tooth trace direction. An object of the present invention is to provide a YAMABA gear with high accuracy and improved tooth root strength.

近年では鍛造技術の進歩によって様々な形状の歯車を鍛造によって成形し、機械加工を省くことが可能となってきた。そこで、本出願発明者等は、冷間鍛造により歯形の精度のよい歯形が得られることに着目し、また、金型に工夫を凝らすことによってヘリカル歯の歯筋方向で位相ずれが無く、かつ、冷間鍛造よって形成されたファイバフロー(以下ファイバフロー)をそのまま生かすことによって歯車の強度に優れるという知見を得た。本出願発明のヤマバ歯車はかかる知見を基に具現化したもので、請求項1の発明は、円筒粗材の外周面に、左右に捩じれ方向が逆向きの一対のヘリカル歯を同一軸上に形成し、前記一対のヘリカル歯の間に境界域を設けたヤマバ歯車であって、前記境界域は溝或いはリブから構成されることを特徴とするヤマバ歯車である。
請求項2の発明は、前記請求項1の特徴に加えて、前記リブは、一対のヘリカル歯の境界域側における端面の全周に亘って連接することを特徴とするヤマバ歯車である。
請求項3の発明は、前記請求項1の特徴に加えて、前記溝の幅は、3mm未満であることを特徴とするヤマバ歯車である。
請求項4の発明は、前記請求項1の特徴に加えて、前記ヘリカル歯は、歯筋に沿ってクラウニング又はエンドレリーフの歯形にすることを特徴とするヤマバ歯車である。
なお、本願発明では、歯筋方向の歯形において膨らみの有る無しに係わらずヘリカル歯と称し、特に歯筋方向の歯形において膨らみを設ける場合は、クラウニング又はエンドレリーフを施したヘリカル歯と称する。
In recent years, with the advance of forging technology, it has become possible to form variously shaped gears by forging and omit machining. Therefore, the inventors of the present application pay attention to the fact that a tooth profile with a good tooth profile can be obtained by cold forging, and there is no phase shift in the tooth trace direction of the helical tooth by devising a mold, and The present inventors have found that the strength of the gear is excellent by utilizing the fiber flow (hereinafter referred to as fiber flow) formed by cold forging as it is. The YAMABA gear of the invention of the present application is embodied based on such knowledge, and the invention of claim 1 is characterized in that a pair of helical teeth whose directions of twisting are reversed to the left and right are arranged on the same axis on the outer peripheral surface of the cylindrical coarse material. A yamaba gear formed and provided with a boundary region between the pair of helical teeth, wherein the boundary region is constituted by a groove or a rib.
The invention according to claim 2 is the YAMABA gear which is characterized in that, in addition to the feature of claim 1, the rib is connected over the entire circumference of the end face on the boundary region side of the pair of helical teeth.
According to a third aspect of the present invention, in addition to the feature of the first aspect, the width of the groove is less than 3 mm.
The invention according to claim 4 is the yamaba gear characterized in that, in addition to the feature of claim 1, the helical teeth have a crowning or end relief tooth profile along the tooth trace.
In the present invention, the tooth profile in the tooth trace direction is referred to as a helical tooth regardless of whether or not the tooth profile is bulged. In particular, when a bulge is provided in the tooth profile in the tooth trace direction, it is referred to as a crowned or end-relieved helical tooth.

本願発明によれば、冷間鍛造によって捩じれ方向が左右逆向きの一対のヘリカル歯を同一軸上で一体化形成させたので左右歯筋の位相が一致した一体方式のヤマバ歯車を得ることができた。本願発明のヤマバ歯車は二形体があり、左右捩じれ方向が逆向きの一対のヘリカル歯の間にリブを設ける方式或いは、左右一対のヘリカル歯の間に溝を設ける方式である。従来の一体方式のヤマバ歯車では、左右の捩じれ方向が逆向きの一対のヘリカル歯の間にギヤシェーパ刃による歯切り加工のために工具刃逃げ用の溝を設けた。この溝はギヤシェーパ加工によるストロークの関係上溝幅寸法4mm以上を必要とした。本願発明の溝を設ける方式では、溝幅寸法を3mm未満或いは2mm程度まで減少させることが可能である。その結果、ヤマバ歯車の全体軸長寸法を短縮できるので、軽量コンパクト化が可能である。一方、歯列の全周に亘ってリブが形成されるので、このリブによって強度が補強され上下ヘリカル歯の分割部において耐曲げ疲労強度が向上する。また、本願発明のヘリカル歯は、鍛造によって歯形が形成されるので歯形内部に歯形に沿ったファイバフローが密に形成され、その結果ヘリカル歯の耐面圧疲労強度が改善されるとともに、歯元における耐曲げ疲労強度が向上する。   According to the present invention, a pair of helical teeth whose twist directions are opposite to each other by cold forging are integrally formed on the same axis, so that an integrated Yamaba gear in which the phases of the left and right tooth traces coincide can be obtained. It was. The Yamaba gear of the present invention has two forms, and is a method of providing a rib between a pair of helical teeth whose left and right twist directions are opposite, or a method of providing a groove between a pair of left and right helical teeth. In the conventional integrated type YAMABA gear, a tool blade escape groove is provided between a pair of helical teeth whose left and right twist directions are opposite to each other for gear cutting with a gear shaper blade. This groove required a groove width dimension of 4 mm or more due to a stroke due to gear shaper processing. In the method of providing the groove of the present invention, the groove width dimension can be reduced to less than 3 mm or about 2 mm. As a result, the overall axial length of the YAMABA gear can be shortened, so that it is possible to reduce the weight and size. On the other hand, since ribs are formed over the entire circumference of the dentition, the strength is reinforced by the ribs, and the bending fatigue resistance is improved at the divided portions of the upper and lower helical teeth. In addition, since the helical tooth of the present invention has a tooth profile formed by forging, the fiber flow along the tooth profile is densely formed inside the tooth profile, and as a result, the surface pressure fatigue strength of the helical tooth is improved and the tooth root is also formed. The bending fatigue strength at is improved.

実施例1のヤマバ歯車を冷間鍛造によって成形する円環状粗材の図である。It is a figure of the annular | circular shaped rough material which shape | molds the Yamaba gear of Example 1 by cold forging. 同上、円環状粗材を成形開始する前の金型が開いた状態を示す図である。It is a figure which shows the state which the metal mold | die before starting shaping | molding of an annular | circular crude material same as the above. 同上、上下の金型が閉じて成形を開始する状態を示す図である。It is a figure which shows the state which an upper and lower metal mold | die closes and starts shaping | molding same as the above. 同上、成形、歯切りが完了した状態を示す図である。It is a figure which shows the state which shaping | molding and gear cutting completed as above. 同上、円環状粗材から冷間鍛造により歯切りが完了した実施形体を示す図である。It is a figure which shows the implementation form which gear cutting was completed from the annular | circular shaped rough material by cold forging same as the above. 同上、リブを有するヤマバ歯車の断面図である。It is sectional drawing of the YAMABA gear which has a rib same as the above. 同上、冷間鍛造の際に生じるファイバフローの状態を示す図である。It is a figure which shows the state of the fiber flow produced in the case of cold forging same as the above. 実施例2の溝を有するヤマバ歯車の断面図である。It is sectional drawing of the yamaba gear which has a groove | channel of Example 2. FIG. 従来例によるヤマバ歯車を示す図である。It is a figure which shows the yamaba gear by a prior art example.

本出願発明の実施の形態を、添付図面に例示した本出願発明の実施例に基づいて以下に具体的に説明する。   Embodiments of the present invention will be specifically described below based on examples of the present invention illustrated in the accompanying drawings.

本実施例について、図1〜図6を参照しながら説明する。図1は、本実施例1のヤマバ歯車を冷間鍛造によって成形する円環状粗材の図である。図2は、円環状粗材を成形する前の金型が開いた状態を示す図である。図3は、上下の金型が閉じて成形を開始する状態を示す図である。図4は、成形、歯切りが完了した状態を示す図である。図5は、円環状粗材から冷間鍛造により歯切りが完了した実施形体を示す図である。図6は、リブを有するヤマバ歯車の断面図である。図7は、冷間鍛造の際に生じるファイバフローの状態を示す図である。   The present embodiment will be described with reference to FIGS. FIG. 1 is a diagram of an annular coarse material formed by cold forging the Yamaba gear of the first embodiment. FIG. 2 is a view showing a state in which the mold before the annular coarse material is molded is opened. FIG. 3 is a diagram showing a state in which the upper and lower molds are closed and molding is started. FIG. 4 is a diagram illustrating a state in which molding and gear cutting have been completed. FIG. 5 is a diagram showing an embodiment in which gear cutting is completed by cold forging from an annular coarse material. FIG. 6 is a cross-sectional view of a yamaba gear having ribs. FIG. 7 is a diagram showing a state of fiber flow that occurs during cold forging.

本実施例のヤマバ歯車の製造プロセスについて主な工程を説明する。先ず、ヤマバ歯車に適した円柱素材を所定の軸長に切断、例えばビレットシャーによって切断した粗材を得る。この場合、粗材の材質としてヤマバ歯車に適した鋼材、例えば、SC鋼、SCR鋼、SCM鋼、SNC鋼、SNCM鋼等を使用することができる。次に、切断した粗材を例えば1200℃に加熱して熱間鍛造を施して中心部を穴が貫通した円環状にし、次いで内外周に機械加工を施した円環状の粗材W1を得、これを図1に示す。或いは、切断した粗材を冷間鍛造により穴を打ち抜く方法によって中心部を穴が貫通した円環状の粗材W1を得る。次に、この粗材W1の外周に捩じれ方向が左右逆向きの一対のヘリカル歯を形成するために、図2に示す金型装置に粗材W1をセットする。なお、粗材の材質としては樹脂を使用した小型歯車の用途もある。   The main steps of the manufacturing process of the YAMABA gear of this embodiment will be described. First, a cylindrical material suitable for a Yamaba gear is cut into a predetermined axial length, for example, a rough material cut by a billet shear is obtained. In this case, a steel material suitable for the Yamaba gear, such as SC steel, SCR steel, SCM steel, SNC steel, SNCM steel, etc., can be used as the material of the rough material. Next, the cut coarse material is heated to 1200 ° C., for example, and subjected to hot forging to form an annular shape with a hole passing through the center, and then an annular coarse material W1 that is machined on the inner and outer periphery is obtained. This is shown in FIG. Alternatively, an annular coarse material W1 in which a hole penetrates the center is obtained by a method of punching a hole in the cut coarse material by cold forging. Next, in order to form a pair of helical teeth whose directions of twisting are opposite to each other on the outer periphery of the coarse material W1, the coarse material W1 is set in the mold apparatus shown in FIG. In addition, there is a use of the small gear which uses resin as a material of a coarse material.

ここで、冷間鍛造による左右逆向きの一対のヘリカル歯を形成するための詳細について図2を参照しながら金型の構成について説明する。金型は上ラム側と下ベッド側に分離して構成される。上ラム側は外側の上パンチP1と内側中心部のマンドレルP2及び、上パンチP1を外から囲むダイ型Q1から構成される。下ラム側は外側のダイ型Q2とこの内周側の下パンチP3及び、この内側中心部の下パンチP4及びこの下方の突き上げ用のエジェクタP5から構成される。上ラム側のダイ型Q1の内周に歯筋が捩じれたヘリカル歯の歯型T1を設け、一方、下ベッド側のダイ型Q2の内周に歯型T1とは歯筋が左右逆向きに捩じれたヘリカル歯の歯型T2を設けた。成形完了した粗材を取り出すために上ラム側のダイQ1は回転自在の構造とする(図示省略)。下ベッド側は、ダイQ2、下パンチP3とも固定構造とする。   Here, the configuration of the mold will be described with reference to FIG. 2 for details of forming a pair of helical teeth in opposite directions by cold forging. The mold is configured separately on the upper ram side and the lower bed side. The upper ram side includes an outer upper punch P1, an inner center mandrel P2, and a die mold Q1 surrounding the upper punch P1 from the outside. The lower ram side includes an outer die mold Q2, a lower punch P3 on the inner peripheral side, a lower punch P4 on the inner central portion, and a push-up ejector P5 on the lower side. On the inner circumference of the upper ram side die mold Q1, a helical tooth tooth mold T1 is provided. On the other hand, on the inner circumference of the lower bed side die mold Q2, the tooth trace is opposite to the tooth mold T1. A twisted helical tooth type T2 was provided. The die Q1 on the upper ram side is configured to be rotatable (not shown) in order to take out the formed coarse material. The lower bed side has a fixed structure for both the die Q2 and the lower punch P3.

本実施例のヤマバ歯車は、左右逆向きの一対のヘリカル歯を形成するためには、上下のヘリカル歯が歯筋方向で位相ずれを防ぐことが重要である。そのためには、位相のズレを防止する何らかの機構を必要とするが、省略する。   In order for the Yamaba gear of the present embodiment to form a pair of helical teeth in opposite directions, it is important that the upper and lower helical teeth prevent a phase shift in the tooth trace direction. For this purpose, some mechanism for preventing phase shift is necessary, but is omitted.

次に、冷間鍛造によるヘリカル歯形成の手順を図3に基づいて説明する。上ラムが下降すると同時にダイQ2の上面に接触するまで、油圧他によってピンP2を下降させダイQ1を押し下げ加圧する。このようにして、ダイQ1とダイQ2との間に接触圧が生じて上下が閉じる。この状態で、上パンチP1を下降させることによって下パンチP3の上に載った円環状の粗材W1を加圧し、粗材W2へと塑性変形させる(図4)。この間に、ダイ型Q1の内周に設けた歯型T1によって上方のヘリカル歯1が形成される。同時に、ダイ型Q2の内周に設けた歯型T2によって下方のヘリカル歯2が逆方向に捩じれた状態に形成される。次に、外側のダイQ1とダイQ2とは閉じたまま、上ラムが後退し内側の上パンチP1が先に後退する。成形が完了すると、エジェクタP5を上昇させることによって粗材W2を取り出す。   Next, a procedure for forming helical teeth by cold forging will be described with reference to FIG. The pin P2 is lowered by hydraulic pressure or the like to press down and pressurize the die Q1 until the upper ram is lowered and contacts the upper surface of the die Q2. In this way, a contact pressure is generated between the die Q1 and the die Q2, and the upper and lower sides are closed. In this state, by lowering the upper punch P1, the annular coarse material W1 placed on the lower punch P3 is pressurized and plastically deformed into the coarse material W2 (FIG. 4). During this time, the upper helical tooth 1 is formed by the tooth mold T1 provided on the inner periphery of the die mold Q1. At the same time, the lower helical teeth 2 are twisted in the opposite direction by the tooth mold T2 provided on the inner periphery of the die mold Q2. Next, with the outer dies Q1 and Q2 closed, the upper ram moves backward and the inner upper punch P1 moves backward first. When the molding is completed, the coarse material W2 is taken out by raising the ejector P5.

図2に示した金型を使用して左右逆方向に捩じれた一対のヘリカル歯の歯切りが完了し、その粗材W2の詳細形状を断面図として図5に示す。外周に歯筋が左右逆方向に捩じれた一対のヘリカル歯1、2が上下に構成され、中心部に荒軸穴30が貫通する。そして、上下のヘリカル歯1、2の境界に粗リブ50がヘリカル歯の歯先面から外側径方向へ突出して形成され、このリブの形成が本実施例の特徴である。本粗材W2では、低い荷重によって加圧による肉流の流れるまま粗リブ50の他に余肉を形成させることが特徴である。即ち、荒軸穴30の外周側において、上下方向に余肉60、60を充満させ形成させる。また、上下ヘリカル歯1、2の歯底背面において、上下方向に充満させ余肉70、70を形成させる。後で、これらの余肉部は削り取る。   The pair of helical teeth twisted in the left and right directions using the mold shown in FIG. 2 is completed, and the detailed shape of the coarse material W2 is shown in FIG. 5 as a cross-sectional view. A pair of helical teeth 1 and 2 having tooth traces twisted in the opposite directions on the outer periphery are formed vertically, and the rough shaft hole 30 penetrates through the center. A coarse rib 50 is formed at the boundary between the upper and lower helical teeth 1 and 2 so as to protrude from the tip surface of the helical tooth in the outer radial direction, and the formation of this rib is a feature of this embodiment. The present rough material W2 is characterized in that a surplus wall is formed in addition to the rough ribs 50 while a meat flow caused by pressurization flows with a low load. That is, on the outer peripheral side of the rough shaft hole 30, the surpluses 60 and 60 are filled in the vertical direction and formed. Further, the back surfaces of the upper and lower helical teeth 1 and 2 are filled in the vertical direction to form the surplus thickness 70 and 70. Later, these surplus parts are scraped off.

次に、図5に示した粗材W2に機械加工を施してヤマバ歯車W100を得、図6に示す。即ち、内径に研削処理或いは上下端部の内周面取りを施すことにより上下に貫通する軸孔3を設ける。そして、上下のヘリカル歯1、2の境界において、歯先面から径方向外側へ突出した粗リブ50の外周先端面を面一に削り落としてリブ5を設ける。上下方向外側へはみ出た余肉60、60、70、70も削り落とす。同図(a)では、ヤマバ歯車W100を断面図で示す。同図(b)では記号O―A矢視図を示し、リブとヘリカル歯との関係が解る。ヘリカル歯周列の一部を示したが、ヘリカル歯1の周列の間にリブ5が配設される。本図では、ヘリカル歯2の歯先径とリブ5の外径を面一としたが、他にリブ5の先端部はヘリカル歯1、2の歯先面から凹むことでもよく、その詳細形状を同図(a)に部分的に拡大した図Eとして示す。リブ5の先端部はヘリカル歯1、2の歯先面から内側へ窪んだ凹みDを有する。或いは、リブ5の先端部はヘリカル歯1、2の歯先面から出っ張ることでもよい。   Next, the rough material W2 shown in FIG. 5 is machined to obtain a yamaba gear W100, which is shown in FIG. That is, the shaft hole 3 penetrating vertically is provided by grinding the inner diameter or chamfering the inner periphery of the upper and lower ends. Then, at the boundary between the upper and lower helical teeth 1 and 2, the rib 5 is provided by scraping the outer peripheral front end surface of the coarse rib 50 projecting radially outward from the tooth tip surface. The excess meat 60, 60, 70, 70 that protrudes outward in the vertical direction is also scraped off. In the figure (a), the yamaba gear W100 is shown with sectional drawing. In FIG. 5B, a symbol OA arrow view is shown, and the relationship between the rib and the helical tooth is understood. Although a part of the helical tooth circumferential row is shown, the rib 5 is disposed between the circumferential rows of the helical teeth 1. In this figure, the tooth tip diameter of the helical tooth 2 and the outer diameter of the rib 5 are flush with each other, but the tip of the rib 5 may be recessed from the tooth tip surfaces of the helical teeth 1 and 2, and its detailed shape Is shown as a partially enlarged view E in FIG. The tip of the rib 5 has a recess D that is recessed inward from the tooth tip surfaces of the helical teeth 1 and 2. Or the front-end | tip part of the rib 5 may protrude from the tooth tip surface of the helical teeth 1 and 2. FIG.

本実施例によるヤマバ歯車は以上のように構成され、以下に作用について説明する。   The YAMABA gear according to this embodiment is configured as described above, and its operation will be described below.

本実施例では、上述したように冷間鍛造によって左右逆に捩じれた一対のヘリカル歯の間にリブを設ける。鍛造の際上方からパンチP1によって粗材W2を押し潰し、一方下方からはパンチP3によって粗材W2を押し潰す(図3、4参照)。この時、ヘリカル歯の内部に鍛造流が形成されその状態を模式的に図7に示す。同図(a)では、上下パンチによって粗材W2が上下方向から押し潰されることによって、上下方向から肉流F1、F2の流れが生じる状態を示す。金型の構造からは、上下のヘリカル歯1、2の境界に間隙を設け、このスペースの外側先端は閉鎖部を設けない。上下パンチによって粗材W2が加圧されるまま肉流F1、Fとして流れ、合流して外側へ流れてそのまま上下ヘリカル歯の間隙を埋めることによって粗リブ50が形成される。同図(b)では、同図(a)の記号B―B’矢視図として、歯形内部におけるファイバフローの形成状態を模式的に示す。本実施例では間隙の外側先端は閉じられていないので、上下パンチによって加圧されるまま肉流F1、F2となって合流し、上下のヘリカル歯の境界を埋め粗リブ50が形成する。また、本実施例では、意識的に余肉を間隙の外周側へ押し出すので、肉流が充満して先端部位まで張る。通常、鍛造においては肉流の逃げ路は設けないが、本実施例の冷間鍛造では敢えて逃げ道を設けることによって肉流を先端部位まで充満させて欠肉を防ぐことができた。仮に、リブ間隙の外側先端に閉鎖部を設けると先端に空気だまりができて肉流が充満せず、欠肉を生じる。このような要領によって粗リブ50に欠肉を発生させることなく、先端角部位まで張らせることができた。ここで、本実施例におけるファイバフローの形成についてその濃密度の状態を模式的に示した同図(b)を参照しながら説明する。歯形の中心線Cに沿って上下方向及び歯形の中心線Cの左右で歯先にかけて歯面の表層部においてファイバフローが密に均等に形成されるとともに、歯形の内部までファイバフローの間隔が密に繊維状に形成されるので、歯形全体として内部組織が均等化され、ヘリカル歯の耐面圧疲労強度が改善されるとともに、歯元における耐曲げ疲労強度が向上する。このことに加えて、本実施例では歯列の全周に亘ってリブが形成されるので、このリブによって強度が補強され上下ヘリカル歯の分割部において更に耐曲げ疲労強度が向上する。   In the present embodiment, as described above, a rib is provided between a pair of helical teeth twisted in the left and right direction by cold forging. During forging, the coarse material W2 is crushed by the punch P1 from above, while the coarse material W2 is crushed by the punch P3 from below (see FIGS. 3 and 4). At this time, a forging flow is formed inside the helical tooth, and the state thereof is schematically shown in FIG. FIG. 6A shows a state in which the flow of meat flows F1 and F2 is generated from the vertical direction when the rough material W2 is crushed from the vertical direction by the vertical punch. From the mold structure, a gap is provided at the boundary between the upper and lower helical teeth 1 and 2, and the outer end of this space is not provided with a closing portion. The coarse ribs 50 are formed by filling the gaps between the upper and lower helical teeth as they flow as the meat flows F1 and F while being pressed by the upper and lower punches as the meat flows F1 and F. FIG. 6B schematically shows a fiber flow formation state in the tooth profile as a view taken along arrow B-B ′ in FIG. In the present embodiment, since the outer tip of the gap is not closed, the meat flows F1 and F2 are joined while being pressurized by the upper and lower punches, and the rough ribs 50 are formed by filling the boundaries of the upper and lower helical teeth. Further, in this embodiment, since the surplus is consciously pushed out to the outer peripheral side of the gap, the meat flow is filled and stretched to the tip portion. Normally, the fork of the meat flow is not provided in the forging, but the cold forging of the present embodiment was able to prevent the lack of thickness by filling the meat flow to the tip portion by intentionally providing the escape path. If a closed portion is provided at the outer tip of the rib gap, an air pool is formed at the tip, the meat flow does not fill, and a lack of thickness occurs. By such a procedure, the rough rib 50 could be stretched to the tip corner portion without causing a lack of thickness. Here, the formation of the fiber flow in the present embodiment will be described with reference to FIG. The fiber flow is densely and evenly formed in the surface layer portion of the tooth surface along the tooth profile center line C in the vertical direction and on the left and right sides of the tooth profile center line C, and the fiber flow is closely spaced to the inside of the tooth profile. Therefore, the internal structure of the tooth profile is equalized as a whole, the surface pressure fatigue strength of the helical tooth is improved, and the bending fatigue strength at the tooth base is improved. In addition to this, in this embodiment, a rib is formed over the entire circumference of the dentition, so that the strength is strengthened by this rib, and the bending fatigue strength is further improved in the divided portion of the upper and lower helical teeth.

本出願発明の実施例2について、図8を参照しながら説明する。同図(a)には、図5に示した粗材W2を加工して得られたヤマバ歯車W200を示す。同図(b)には歯筋方向の修正をしたクラウニングの歯形を示し、同図(c)では歯筋方向で二重に修正をしたダブルクラウニングを示す。同図8(a)のヤマバ歯車W200は、軸穴、両端面を旋削及び浸炭後の研削加工を施し、或いは軸穴の内周面取りを施して上下に貫通する軸孔3を設けることによって得られる。そして、上下のヘリカル歯1、2の境界において、図5に示す粗リブ50を削り落として溝4を設ける。粗リブ50の太さが大きい程、鍛造の際肉流を充満させ易い。従って、溝4の幅寸法を大きくする方が製作し易いが、試行錯誤の結果溝4の幅は3mm未満或いは2mmまで狭めることが可能であることを確認した。   A second embodiment of the present invention will be described with reference to FIG. The same figure (a) shows the Yamaba gear W200 obtained by processing the rough material W2 shown in FIG. FIG. 4B shows the crowning tooth profile corrected in the direction of the tooth trace, and FIG. 5C shows double crowning corrected in the direction of the tooth trace. The YAMABA gear W200 shown in FIG. 8A is obtained by providing a shaft hole 3 penetrating up and down by grinding the shaft hole and both ends thereof after turning and carburizing, or by chamfering the inner periphery of the shaft hole. It is done. Then, at the boundary between the upper and lower helical teeth 1 and 2, the coarse rib 50 shown in FIG. The greater the thickness of the coarse rib 50, the easier it is to fill the meat flow during forging. Therefore, although it is easier to manufacture if the width dimension of the groove 4 is increased, it has been confirmed through trial and error that the width of the groove 4 can be reduced to less than 3 mm or 2 mm.

本実施例によるヤマバ歯車は以上のように構成され、以下に作用について説明する。   The YAMABA gear according to this embodiment is configured as described above, and its operation will be described below.

従来のヤマバ歯車では、一対のヘリカル歯を歯切りするために工具刃の干渉を防止するために一対のヘリカル歯の境界に溝を設ける。通常の歯切り加工はホブ切り又はギヤシェーパによって行うが、特にギヤシェーパの場合刃の干渉を防ぐために工具刃のストロークの余裕代が必要となる。通常、工具刃の逃がし代となる溝の幅寸法は4mm以上が必要とされる。本実施例では、鍛造時に発生するボスを削り除くことによって溝を形成するが、溝の幅寸法は大小如何なる寸法でも可能であり、最大は3mm未満から最小は2mmまで減少させることができる。本実施例の場合、従来の機械加工による歯切りの場合の溝幅寸法の4mmに比べて小さいので、ヤマバ歯車の軸方向の全体長さを短小にし、軽量化できる効果がある。次に、歯筋方向の修正をした歯形を本実施例2のヘリカル歯1、2に適用することができる。図8(b)のクラウニングを施したヘリカル歯は、歯筋方向に沿って中央部において膨らみ量Lが5μ程度あり、歯幅両端部が逃げて薄くなる。或いは、図8(c)のダブルクラウニングは、歯筋に沿って二か所で膨らみ量L1、量L2がそれぞれ5μ程度であり、それぞれの歯幅両端部が逃げて薄くなる。また、図8(b)、(c)では、歯筋方向の歯形をエンドレリーフにして歯幅両端部を適度に逃がしたヘリカル歯にすることも考えられる。図8(c)の場合、歯幅両端部を逃がすときの歯筋方向の長さの比率は、例えば端部から中央へG1、G2、G3の長さの比率は1対3対2が考えられる。図8(b)、図8(c)の歯形を選ぶことによって、ヘリカル歯の加工精度のばらつき或いは噛み合う歯車同士の組み付け精度のばらつきが吸収されるので、噛み合う歯車同士の片当たりを防ぐことができる。その結果、振動が減少するとともにノイズ発生が抑えられる。なお、実施例1のリブを設けたヤマバ歯車でも同様に、歯筋方向の歯形をクラウニング又はエンドレリーフを施したヘリカル歯にすることは勿論可能である。   In the conventional YAMABA gear, a groove is provided at the boundary between the pair of helical teeth in order to cut the pair of helical teeth and prevent interference between the tool blades. Normal gear cutting is performed by hobbing or gear shaper, but especially in the case of a gear shaper, a margin for the stroke of the tool blade is required to prevent blade interference. Usually, the width dimension of the groove that becomes the allowance for the tool blade is required to be 4 mm or more. In this embodiment, the groove is formed by removing the boss generated during forging, but the width of the groove can be any size, and the maximum can be reduced from less than 3 mm to the minimum of 2 mm. In the case of the present embodiment, since the groove width dimension in the case of gear cutting by conventional machining is smaller than 4 mm, there is an effect that the entire length of the YAMABA gear in the axial direction can be reduced and the weight can be reduced. Next, the tooth profile corrected in the tooth trace direction can be applied to the helical teeth 1 and 2 of the second embodiment. The helical tooth subjected to crowning in FIG. 8B has a bulge amount L of about 5 μm in the center along the tooth trace direction, and both end portions of the tooth width escape and become thin. Alternatively, in the double crowning of FIG. 8C, the bulge amounts L1 and L2 are about 5 μ at two locations along the tooth trace, and both end portions of each tooth width escape and become thin. Further, in FIGS. 8B and 8C, it is also conceivable that the tooth profile in the tooth trace direction is an end relief and the helical tooth is formed by appropriately releasing both ends of the tooth width. In the case of FIG. 8C, the ratio of the length in the tooth trace direction when the both ends of the tooth width are released is, for example, the ratio of the lengths G1, G2, and G3 from the end to the center is considered as 1 to 3 to 2. It is done. By selecting the tooth profile shown in FIGS. 8B and 8C, the variation in the processing accuracy of the helical teeth or the variation in the assembling accuracy between the meshing gears can be absorbed, so that the contact between the meshing gears can be prevented. it can. As a result, vibration is reduced and noise generation is suppressed. In the same way, it is of course possible to make the tooth profile in the tooth trace direction into a helical tooth with crowning or end relief as well in the Yamaba gear provided with the ribs of Example 1.

本出願発明のヤマバ歯車は冷間鍛造によって歯形が完成するので、ホブ、シェービング等の機械加工によって鍛造面が削り取られるようなことがなく、内部のファイバフローをそのまま保持して歯車の耐久性を向上させることができる。機械加工によって生じたバリを除去するための機械加工を施す必要もないため、加工コストを低減することができる。従って、本出願発明のヤマバ歯車は樹脂の混練機のような特殊用途に限らず工作機械、荷役建設機械、ロボット等各種の機械装置の用途に適用できる。   Since the tooth shape of the Yamaba gear of the present invention is completed by cold forging, the forged surface is not scraped off by machining such as hobbing, shaving, etc., and the internal fiber flow is maintained as it is to improve the durability of the gear. Can be improved. Since it is not necessary to perform machining for removing burrs generated by machining, machining costs can be reduced. Therefore, the YAMABA gear of the present invention is not limited to special applications such as a resin kneader, but can be applied to various machine devices such as machine tools, cargo handling construction machines, and robots.

S1、S2 平行軸
W1 円環状粗材
W2 ヘリカル歯粗材
W10、W100、W200 ヤマバ歯車
P1 上パンチ、P2 ピン
P3 下パンチ、P4 エジェクタ、P5 ノックアウトピン
Q1 ダイ型、Q2 下ダイ型
T1、T2 歯型
C コッターピン
D 凹み
F ファイバフロー
F1、F2 肉流
L、L1、L2 膨らみ量
1、 2 ヘリカル歯
3 軸穴、30粗軸穴
4 溝
5 リブ、50 粗リブ
60、70 余肉部
11 歯先面、12 歯面、16 歯元
S1, S2 Parallel axis W1 Circular coarse material W2 Helical tooth coarse material W10, W100, W200 Yamaba gear P1 Upper punch, P2 Pin P3 Lower punch, P4 Ejector, P5 Knockout pin Q1 Die type, Q2 Lower die type T1, T2 Teeth Type C Cotter pin D Recess F Fiber flow F1, F2 Meat flow
L, L1, L2 Swelling amount 1, 2 Helical tooth 3 Shaft hole, 30 Coarse shaft hole 4 Groove 5 Rib, 50 Coarse rib 60, 70 Extra portion 11 Tooth surface, 12 Tooth surface, 16 Tooth base

Claims (4)

円筒粗材の外周面に、捩じれ方向が左右逆向きの一対のヘリカル歯を同一軸上に形成し、前記一対のヘリカル歯の間に境界域を設けたヤマバ歯車であって、
前記境界域は溝或いはリブから構成されることを特徴とするヤマバ歯車。
On the outer peripheral surface of the cylindrical coarse material, a pair of helical teeth whose torsional directions are opposite to each other are formed on the same axis, and a YAMABA gear provided with a boundary region between the pair of helical teeth,
The boundary area is formed of a groove or a rib.
前記リブは、一対のヘリカル歯の境界域側における端面の全周に亘って連接することを特徴とする請求項1記載のヤマバ歯車。   2. The YAMABA gear according to claim 1, wherein the rib is connected over the entire circumference of the end surface on the boundary region side of the pair of helical teeth. 前記溝の幅は、3mm未満であることを特徴とする請求項1記載のヤマバ歯車。   2. The YAMABA gear according to claim 1, wherein the width of the groove is less than 3 mm. 前記ヘリカル歯は、歯筋方向に沿ってクラウニング又はエンドレリーフを施したことを特徴とする請求項1記載のヤマバ歯車。   The YAMABA gear according to claim 1, wherein the helical teeth are crowned or end-relieved along a tooth trace direction.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111488682A (en) * 2020-04-09 2020-08-04 北京理工大学 Involute helical gear pair tooth width modification dynamic model establishing method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH05277618A (en) * 1991-12-20 1993-10-26 Oooka Giken Kk Method and device for forming double-helical gear
JP2008101699A (en) * 2006-10-19 2008-05-01 Enplas Corp Pair of resin double helical gears
JP2011202676A (en) * 2010-03-24 2011-10-13 O-Oka Corp Gear including wave-like groove near dedendum

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH05277618A (en) * 1991-12-20 1993-10-26 Oooka Giken Kk Method and device for forming double-helical gear
JP2008101699A (en) * 2006-10-19 2008-05-01 Enplas Corp Pair of resin double helical gears
JP2011202676A (en) * 2010-03-24 2011-10-13 O-Oka Corp Gear including wave-like groove near dedendum

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111488682A (en) * 2020-04-09 2020-08-04 北京理工大学 Involute helical gear pair tooth width modification dynamic model establishing method
CN111488682B (en) * 2020-04-09 2022-11-08 北京理工大学 Involute helical gear pair tooth width modification dynamic model establishing method

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