WO2010122955A1 - 円すいころ軸受およびその設計方法 - Google Patents
円すいころ軸受およびその設計方法 Download PDFInfo
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- WO2010122955A1 WO2010122955A1 PCT/JP2010/056828 JP2010056828W WO2010122955A1 WO 2010122955 A1 WO2010122955 A1 WO 2010122955A1 JP 2010056828 W JP2010056828 W JP 2010056828W WO 2010122955 A1 WO2010122955 A1 WO 2010122955A1
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- crowning
- contact
- inner ring
- contact portion
- tapered roller
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C33/00—Parts of bearings; Special methods for making bearings or parts thereof
- F16C33/30—Parts of ball or roller bearings
- F16C33/34—Rollers; Needles
- F16C33/36—Rollers; Needles with bearing-surfaces other than cylindrical, e.g. tapered; with grooves in the bearing surfaces
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C19/00—Bearings with rolling contact, for exclusively rotary movement
- F16C19/22—Bearings with rolling contact, for exclusively rotary movement with bearing rollers essentially of the same size in one or more circular rows, e.g. needle bearings
- F16C19/34—Bearings with rolling contact, for exclusively rotary movement with bearing rollers essentially of the same size in one or more circular rows, e.g. needle bearings for both radial and axial load
- F16C19/36—Bearings with rolling contact, for exclusively rotary movement with bearing rollers essentially of the same size in one or more circular rows, e.g. needle bearings for both radial and axial load with a single row of rollers
- F16C19/364—Bearings with rolling contact, for exclusively rotary movement with bearing rollers essentially of the same size in one or more circular rows, e.g. needle bearings for both radial and axial load with a single row of rollers with tapered rollers, i.e. rollers having essentially the shape of a truncated cone
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C2240/00—Specified values or numerical ranges of parameters; Relations between them
- F16C2240/40—Linear dimensions, e.g. length, radius, thickness, gap
- F16C2240/50—Crowning, e.g. crowning height or crowning radius
Definitions
- the surface pressure of the contact portion is larger between the rollers and the inner ring than between the rollers and the outer ring, so it is desirable to provide a main crowning on the inner ring. If the inner ring is provided with a crowning represented by a logarithmic function (hereinafter referred to as “logarithmic crowning”), there will be wrinkles at both ends of the inner ring raceway surface. There is a possibility that the grinding wheel for finishing does not work sufficiently in the vicinity, resulting in processing failure.
- the connecting portion with the portion formed by the logarithmic curve of the logarithmic crowning among the bus bars of the non-contact portion crowning portion may be made to coincide with the slope of the logarithmic curve.
- the bus bar of the contact portion crowning portion and the bus bar of the non-contact portion crowning portion can be continued more smoothly at the connection point.
- the bus line of the contact portion crowning portion may be formed by a logarithmic curve of logarithmic crowning represented by the following equation.
- K 1 and z m may be optimally designed using a mathematical optimization method.
- the inner ring raceway surface may be crowned, and the sum of the crowning drop amount on the inner ring raceway surface and the crowning drop amount on the outer periphery of the roller may be a predetermined value.
- the tapered roller bearing design method of the present invention is a tapered roller bearing design method including inner and outer rings and rollers, wherein at least a roller rolling surface on the outer periphery of the roller is formed with a crowning, and a crowning forming portion of the roller rolling surface is provided.
- a contact portion crowning portion that is in the axial range of the inner ring raceway surface and is in contact with the inner ring raceway surface, and a non-contact portion crowning portion that is out of the axial range of the inner ring raceway surface and is not in contact with the inner ring raceway surface.
- the contact portion crowning portion and the non-contact portion crowning portion are configured such that the bus bars extending in the roller axis direction are expressed by different functions and are smoothly connected to each other at the connection points. Formed by a logarithmic curve of logarithmic crowning represented by the formula, the curvature of the bus of the non-contact portion crowning portion in the vicinity of the connection point, Smaller design than the generatrix curvature of the contact portion crowning portion.
- (A) is a figure showing the relationship between the bus
- (B) is a figure showing the relationship between the maximum value of Mises equivalent stress, and a logarithmic crowning parameter. It is a figure which shows the crowning shape of the roller of the tapered roller bearing which concerns on 2nd Embodiment of this invention. It is a figure which shows the crowning shape of the roller of the tapered roller bearing which concerns on 3rd Embodiment of this invention. It is a figure which shows crowning shapes, such as an inner ring
- the inner ring raceway surface 1a has a straight line extending in the inner ring axial direction.
- An outer ring raceway surface 2a facing the inner ring raceway surface 1a is formed on the inner periphery of the outer ring 2, and there is no wrinkle.
- the outer ring raceway surface 2a has a straight line extending in the outer ring axial direction.
- crowning is formed on the roller rolling surface on the outer periphery of the roller 3, and chamfers 6 and 6 are applied to both ends of the roller 3.
- the crowning forming portion of the roller rolling surface is formed into a contact portion crowning portion 7 and a non-contact portion crowning portion 8.
- the contact portion crowning portion 7 is in the axial range of the inner ring raceway surface 1a and contacts the inner ring raceway surface 1a.
- the non-contact portion crowning portion 8 is out of the axial range of the inner ring raceway surface 1a and is not in contact with the inner ring raceway surface 1a.
- the contact pressure on the inner ring 1 side and the contact part on the outer ring 2 side have higher surface pressure because the inner ring 1 side has a smaller equivalent radius in the circumferential direction. Therefore, in designing the crowning, the contact on the inner ring 1 side may be considered.
- a radial load of 35% of the basic dynamic load rating acts on a tapered roller bearing, nominal number 30316, and the misalignment is 1/600. At this time, it is assumed that the misalignment is inclined in the direction in which the surface pressure increases on the large diameter side rather than the small diameter side of the roller 3.
- the basic dynamic load rating means that the direction and size are such that when the same bearing group is individually operated under the condition that the inner ring 1 is rotated and the outer ring 2 is stationary, the low rated life is 1 million revolutions. A load that does not fluctuate.
- the misalignment is a misalignment between a housing (not shown) fitted with the outer ring 2 and a shaft fitted with the inner ring 1 and is expressed as a fraction as described above as an inclination amount.
- the bus of the contact portion crowning portion 7 is formed by a logarithmic curve of logarithmic crowning represented by the following equation.
- the maximum drop amount of the crowning of the roller 3 is 69 ⁇ m.
- the area G in FIG. 3A is an area E facing the grinding relief portions 1b and 1c of the inner ring 2 in FIG.
- the area G of the roller 3 does not have to be logarithmic crowning, and may be a straight line, a circular arc, or another function. Even if the G region of the roller 3 is a straight line, a circular arc, or other functions, the entire roller has the same surface pressure distribution as in the case of logarithmic crowning, and there is no functional difference.
- the optimal logarithmic crowning can be designed by appropriately selecting K 1 and z m in the functional expression representing the logarithmic crowning. Crowning is generally designed to reduce the maximum surface pressure or stress at the contact. Here, it is assumed that the rolling fatigue life occurs according to the yield condition of Mises, and K 1 and z m are selected so as to minimize the maximum value of the equivalent stress of Mises.
- K 1 and z m can be selected using an appropriate mathematical optimization method.
- Various algorithms for mathematical optimization methods have been proposed.
- One of the direct search methods is that optimization can be performed without using the derivative of the function. Useful when functions and variables cannot be directly represented by mathematical expressions.
- the optimal values of K 1 and z m are obtained using the Rosenbrock method, which is one of the direct search methods.
- the crowning in the region G in FIG. 3 (A) may have any shape, but the contact with the outer ring 2 and the formability of the grindstone during processing are considered.
- the slope is smaller than the slope of the logarithmic crowning portion at the connection point P1 with the logarithmic crowning portion.
- Giving a gradient larger than the gradient of the logarithmic crowning portion for the crowning in the region G is not desirable because the drop amount increases. That is, it is desirable that the crowning and logarithmic crowning in the region G are designed so that the gradients coincide at the connection point P1 and are smoothly connected.
- the case where the crowning of the G region of the roller 3 is a straight line is illustrated by a dotted line, and the case of an arc is illustrated by a thick solid line.
- the drop amount Dp of the crowning of the roller 3 is, for example, 36 ⁇ m.
- the crowning drop amount Dp of the roller 3 is, for example, 40 ⁇ m.
- the crowning is formed on the roller rolling surface on the outer periphery of the roller 3, a grinding stone is applied to the roller rolling surface more and more than necessary when the crowning is formed only on the inner ring raceway surface 1a. obtain. Therefore, the processing defect with respect to a rolling surface can be prevented beforehand.
- the crowning formed on the roller rolling surface can reduce the surface pressure and the stress at the contact portion, thereby extending the life of the tapered roller bearing.
- the curvature R8 of the bus of the non-contact portion crowning portion 8 in the vicinity of the connection point P1 between the contact portion crowning portion 7 and the non-contact portion crowning portion 8 is larger than the curvature R7 of the bus line of the contact portion crowning portion 7.
- the drop amount Dp at both ends of the roller 3 can be reduced. Therefore, for example, the amount of grinding can be suppressed from that of the conventional single arc crowning, the processing efficiency of the rollers 3 can be improved, and the manufacturing cost can be reduced.
- the bus of the non-contact portion crowning portion 8 may have either a large-diameter portion or a small-diameter side portion or a circular arc.
- the drop amount Dp can be reduced more than that in which the generatrix of the entire roller rolling surface is represented by a logarithmic curve, for example. Therefore, the amount of grinding can be reduced.
- the generatrix of the non-contact portion crowning portion 8 may have either a large diameter side portion or a small diameter side portion or both straight lines (see FIG. 4). In the second embodiment, only the portion on the large diameter side is a straight line). In this case, the drop amount Dp can be further reduced as compared with the case where the bus of the non-contact portion crowning portion 8 is an arc.
- a part or all of the bus of the contact portion crowning portion 7 may be represented by logarithmic crowning.
- the contact portion crowning portion 7 represented by the logarithmic crowning can reduce the surface pressure and the stress at the contact portion, thereby extending the life of the tapered roller bearing.
- the bus line of the contact portion crowning portion 7 is formed by a straight portion 7 a formed flat along the roller axis direction and a portion 7 b formed by a logarithmic curve of logarithmic crowning. May be represented.
- the crowning may be provided not only on the roller 3 but also on the inner ring 1.
- the crowning portion 9 of the inner ring 1 is shown.
- the sum of the drop amount of the roller 3 and the drop amount of the inner ring 1 is made equal to the optimized drop amount.
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- Engineering & Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Rolling Contact Bearings (AREA)
Abstract
Description
上記「滑らかに連続する」とは、角を生じずに連続することであり、理想的には、接触部クラウニング部分の母線と、非接触部クラウニング部分の母線とが、互いの連続点において、共通の接線を持つように続くことで、すなわち上記母線が上記連続点で連続的微分可能な関数であることである。
上記非接触部クラウニング部分の母線は、大径側の部分および小径側の部分のいずれか一方または両方が直線であっても良い。この場合、非接触部クラウニング部分の母線を円弧とする場合よりもさらにドロップ量の低減を図ることができる。
上記接触部クラウニング部分の母線が、ころ軸方向に沿って平坦に形成されたストレート部分と、対数クラウニングの対数曲線で形成された部分とによって表されても良い。
上記ストレート部分の長さが、ころ全長の1/2以上であることが、クラウニングの加工精度を確保するうえで望ましい。
内輪軌道面にクラウニングが施されており、この内輪軌道面のクラウニングのドロップ量と、ころの外周のクラウニングのドロップ量との和が所定の値となるものであっても良い。
この実施形態に係る円すいころ軸受は、図1に示すように、内輪1と、外輪2と、これら内外輪1,2間に介在する複数個の円すいころ3とを備えている。内輪1の外周には内輪軌道面1aが形成され、この内輪軌道面1aの大径側および小径側に大鍔4および小鍔5をそれぞれ有する。内輪軌道面1aと大鍔4とが交わる隅部には、研削逃げ部1bが形成され、内輪軌道面1aと小鍔5との隅部には、研削逃げ部1cが形成されている。上記内輪軌道面1aは、内輪軸方向に延びる母線が直線となっている。外輪2の内周には、内輪軌道面1aに対向する外輪軌道面2aが形成され、鍔無しとされ、外輪軌道面2aは外輪軸方向に延びる母線が直線となっている。
これら接触部クラウニング部分7と非接触部クラウニング部分8は、ころ軸方向に延びる母線が、互いに異なる関数で表されかつ互いに接続点P1で滑らかに連続する線である。上記接続点P1の近傍における前記非接触部クラウニング部分8の母線の曲率R8を、前記接触部クラウニング部分7の母線の曲率R7よりも小さく設定している。
円すいころ軸受、呼び番号30316に基本動定格荷重の35%のラジアル荷重が作用し、ミスアライメントが1/600である場合について検討する。このとき、ミスアライメントは、ころ3の小径側でなく大径側で面圧が高くなる方向に傾くとする。上記基本動定格荷重とは、内輪1を回転させ外輪2を静止させた条件で、一群の同じ軸受を個々に運転したとき、低格寿命が100万回転になるような、方向と大きさが変動しない荷重をいう。上記ミスアライメントは、外輪2を嵌合した図示外のハウジングと、内輪1を嵌合した軸との心ずれであり、傾き量として上記のような分数にて表記する。
対数クラウニングを表す関数式中のK1,zmを適切に選択することによって,最適な対数クラウニングを設計することができる。
クラウニングは一般的に接触部の面圧もしくは応力の最大値を低下させるように設計する。ここでは,転動疲労寿命はMisesの降伏条件にしたがって発生すると考え,Misesの相当応力の最大値を最小にするようにK1,zmを選択する。
図5に示す第3実施形態のように、接触部クラウニング部分7の母線が、ころ軸方向に沿って平坦に形成されたストレート部分7aと、対数クラウニングの対数曲線で形成された部分7bとによって表されても良い。
1a…内輪軌道面
2…外輪
3…ころ
7…接触部クラウニング部分
8…非接触部クラウニング部分
L1…ころ全長
P1…接続点
R7,R8…曲率
Claims (11)
- 内外輪およびころを含む円すいころ軸受であって、少なくともころの外周のころ転動面にクラウニングを形成し、ころ転動面のクラウニング形成部分を、内輪軌道面の軸方向範囲にあって内輪軌道面に接する接触部クラウニング部分と、内輪軌道面の軸方向範囲から外れて内輪軌道面に非接触となる非接触部クラウニング部分とに形成し、これら接触部クラウニング部分と非接触部クラウニング部分は、ころ軸方向に延びる母線が、互いに異なる関数で表されかつ互いに接続点で滑らかに連続する線であり、上記接続点の近傍における前記非接触部クラウニング部分の母線の曲率が、前記接触部クラウニング部分の母線の曲率よりも小さい円すいころ軸受。
- 請求項1において、上記非接触部クラウニング部分の母線は、大径側の部分および小径側の部分のいずれか一方または両方が円弧である円すいころ軸受。
- 請求項1において、上記非接触部クラウニング部分の母線は、大径側の部分および小径側の部分のいずれか一方または両方が直線である円すいころ軸受。
- 請求項1において、上記接触部クラウニング部分の母線の一部または全部が対数クラウニングで表される円すいころ軸受。
- 請求項4において、上記接触部クラウニング部分の母線が、ころ軸方向に沿って平坦に形成されたストレート部分と、対数クラウニングの対数曲線で形成された部分とによって表される円すいころ軸受。
- 請求項5において、上記ストレート部分の長さが、ころ全長の1/2以上である円すいころ軸受。
- 請求項4において、上記非接触部クラウニング部分の母線のうち、対数クラウニングの対数曲線で形成された部分との接続部を、同対数曲線の勾配と一致させる円すいころ軸受。
- 請求項8において、上記式のうち、少なくともK1,zmについて数理的最適化手法を利用して最適設計した円すいころ軸受。
- 請求項8において、内輪軌道面にクラウニングが施されており、この内輪軌道面のクラウニングのドロップ量と、ころの外周のクラウニングのドロップ量との和が所定の値となる円すいころ軸受。
- 内外輪およびころを含む円すいころ軸受の設計方法であって、少なくともころの外周のころ転動面にクラウニングを形成し、ころ転動面のクラウニング形成部分を、内輪軌道面の軸方向範囲にあって内輪軌道面に接する接触部クラウニング部分と、内輪軌道面の軸方向範囲から外れて内輪軌道面に非接触となる非接触部クラウニング部分とに形成し、
これら接触部クラウニング部分と非接触部クラウニング部分は、ころ軸方向に延びる母線が、互いに異なる関数で表されかつ互いに接続点で滑らかに連続する線とし、上記接触部クラウニング部分の母線を、次式で表される対数クラウニングの対数曲線により形成し、上記接続点の近傍における前記非接触部クラウニング部分の母線の曲率を、前記接触部クラウニング部分の母線の曲率よりも小さく設計する円すいころ軸受の設計方法。
Priority Applications (3)
Application Number | Priority Date | Filing Date | Title |
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US13/138,873 US8858088B2 (en) | 2009-04-24 | 2010-04-16 | Tapered roller bearing and method of designing the same |
EP10767012.7A EP2423523B1 (en) | 2009-04-24 | 2010-04-16 | Tapered roller bearing and method of designing same |
CN201080017858.9A CN102414465B (zh) | 2009-04-24 | 2010-04-16 | 圆锥滚子轴承及其设计方法 |
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JP2009-105854 | 2009-04-24 | ||
JP2009105854A JP5334665B2 (ja) | 2009-04-24 | 2009-04-24 | 円すいころ軸受およびその設計方法 |
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EP (1) | EP2423523B1 (ja) |
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Also Published As
Publication number | Publication date |
---|---|
EP2423523A1 (en) | 2012-02-29 |
JP2010255730A (ja) | 2010-11-11 |
JP5334665B2 (ja) | 2013-11-06 |
CN102414465B (zh) | 2014-08-20 |
EP2423523A4 (en) | 2012-10-31 |
CN102414465A (zh) | 2012-04-11 |
EP2423523B1 (en) | 2017-03-08 |
US8858088B2 (en) | 2014-10-14 |
US20120033909A1 (en) | 2012-02-09 |
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