JP4172972B2

JP4172972B2 - Swing bearing

Info

Publication number: JP4172972B2
Application number: JP2002262726A
Authority: JP
Inventors: 誠二高橋
Original assignee: NTN Corp
Current assignee: NTN Corp
Priority date: 2002-09-09
Filing date: 2002-09-09
Publication date: 2008-10-29
Anticipated expiration: 2022-09-09
Also published as: JP2004100805A

Description

【０００１】
【発明の属する技術分野】
この発明は、油圧ポンプ、油圧モータ、ＨＳＴ（ハイドロスタティックトランスミッション）に組み込まれた斜板等の可動部材を揺動自在に支持する揺動軸受に関する。
【０００２】
【従来の技術】
建設機械や農機等に使用される油圧ポンプ、油圧モータ、ＨＳＴでは、装置内に組み込まれた斜板の角度を調整することにより、機械の運転速度を調整することができる。この斜板には数トンの大きな荷重がかかるため、斜板の角度調整時のトルクを軽減する目的で、ころを転動体として用いた揺動軸受が組み込まれている。
【０００３】
図５は、このような揺動軸受の使用状態の一例を示す（特許文献１参照。）。この揺動軸受は、固定部材５１に固定され、凹円弧状の転走面５２ａを有する軌道輪５２と、この転走面５２ａに沿って配列された複数のころ５３と、各ころ５３を転動自在に保持する保持器５４とから成り、凸円弧状面５５ａを有する斜板５５を、各ころ５３に当接させて揺動自在に支持するようにしたものである。各ころ５３は、一般的なラジアル軸受と同様に、保持器５４の両側部５６と、両側部５６に差し渡された複数の柱部５７とで形成される各ポケットに収容されて転動自在に保持されている。
【０００４】
【特許文献１】
特開昭６１−２１５８１２号公報（第３図）
【０００５】
上述したような揺動軸受は、一般的なラジアル軸受よりも静荷重に対する強度が求められることが多いので、静定格荷重を重視して設計することが望ましく、そのためには、できるだけころを多く配列することが有効である。しかし、配列できるころの本数は、隣り合うころの間に保持器の柱部が介在しているために制限されており、静定格荷重を一定の限度以上に大きくすることは困難である。
【０００６】
また、この種の揺動軸受のうち、軌道輪の転走面から固定部材側へ貫通するようにあけた孔を用いて軸受を固定部材に固定するタイプのものでは、ころが転動中に固定用の孔にかかることが不安視される場合があるが、孔にかかる位置を避けてころを配列しようとすると、従来よりもころの本数が少なくなって静定格荷重が小さくなってしまう。
【０００７】
これに対して、本出願人は、本発明に先立って、保持器の柱部をなくすことによって従来よりも多くのころを配列できるようにした揺動軸受を提案した（特願２００１−１２９４４８号）。この揺動軸受は、図６（ａ）、（ｂ）に示すように、軌道輪６１の転走面６１ａに沿って配列される各ころ６２の軸方向両端に突起部６２ａを設け、この突起部６２ａを保持器６３の周方向両端で連結された一対の側部６４の溝６４ａに嵌め込んでころ６２を保持するもので、保持器６３には柱部が形成されていない。従って、配列できるころ６２の本数は従来よりも多くすることができるが、ころ６２の端面を加工して突起６２ａを形成する必要があるため、ころ６２の製作費が高く、軸受が全体として高価なものになってしまう。また、ころ径寸法に設計上の制約ができるため、軸受全体としての設計の自由度が小さくなる問題もある。
【０００８】
【発明が解決しようとする課題】
そこで、この発明の課題は、配列できるころの本数が多く、かつ安価に製作することができる揺動軸受を提供することである。
【０００９】
【課題を解決するための手段】
上記の課題を解決するため、この発明は、固定部材に固定され、凹円弧状の転走面を有する軌道輪と、この凹円弧状の転走面に沿って配列された複数のころと、前記転走面に沿って円弧状に延びる一対の側部とこの両側部に差し渡された複数の柱部とで前記各ころを転動自在に保持する保持器とから成り、凸円弧状面を有する可動部材を前記各ころに当接させて揺動自在に支持する揺動軸受において、前記保持器を前記軌道輪に揺動可能に係合させる手段と、前記保持器の軌道輪周方向端からの抜け止め手段とを設けて、前記軌道輪と保持器とを一体化し、前記保持器の各柱部を前記各ころの中心軸を通る円弧状面と前記可動部材の凸円弧状面との間に形成した構成を採用した。
【００１０】
すなわち、軌道輪と保持器とを一体化して保持器の柱部で保持器外周側からのころの脱落を防止する必要をなくし、保持器の各柱部を各ころの中心軸を通る円弧状面と可動部材の凸円弧状面との間に形成して、各ころが保持器内周側から脱落しないように保持することにより、隣り合うころどうしの間に保持器の柱部が介在しないようにして、ころに特別な加工を施すことなく、配列できるころの本数を増やしたのである。
【００１１】
前記ころの配列を総ころ配列とすることにより、総ころ軸受相当の静定格荷重を確保することができる。
【００１２】
また、前記軌道輪がその転走面に前記固定部材に固定されるための孔を有するものである場合は、前記各ころを前記軌道輪の固定用孔の位置を除いた転走面上を転動するように配列することができる。
【００１３】
すなわち、軌道輪に固定用孔がある場合に、各ころが転動中に軌道輪の固定用孔にかからないように設計しても、ころの本数が従来よりも減ることがなく、従来と同等以上の静定格荷重が得られる。
【００１４】
【発明の実施の形態】
以下、図１乃至図４に基づき、この発明の実施形態を説明する。図１乃至図３は第１の実施形態を示す。この揺動軸受は、図１（ａ）、（ｂ）に示すように、凹円弧状の転走面１ａを有する軌道輪１と、この凹円弧状の転走面１ａに沿って配列された複数のころ２と、各ころ２を転動自在に保持する保持器３とから成り、軌道輪１を固定部材（図示省略）に固定し、凸円弧状面４ａを有する可動部材４を各ころ２に当接させて揺動自在に支持するようにしたものである。なお、軌道輪１は、鋼材からの削り出しにより成形されているが、鋼板をプレス加工して成形してもよい。また、保持器３は、ころ２の組み込みを容易にするため、樹脂材料で形成されている。
【００１５】
前記軌道輪１は、両側端に各ころ２の端面に沿って張り出す鍔部５が周方向全長にわたって設けられ、後述するように一方の鍔部５で保持器３と係合するようになっている。また、その周方向長さは保持器３よりも長く形成され、周方向両端部に保持器３の周方向端面と間隔をおいて対向するストッパ６が設けられており、このストッパ６で保持器３の軌道輪１周方向端からの抜け落ちを防止するようになっている。
【００１６】
一方、前記保持器３は、軌道輪１の転走面１ａに沿って円弧状に延びる一対の側部７に複数の柱部８が差し渡されており、一方の側部７の周方向中央位置に、断面が鉤状で、その先端部が軌道輪１の鍔部５の外側面の湾曲部に沿うように形成された係合部９が設けられ、これにより軌道輪１と一体化されている。そして、この係合部９で係合部９と対向する位置に配されたころ２とともに鍔部５を把持しながら、鍔部５に案内されて揺動するようになっている。
【００１７】
また、図１（ｃ）にも示すように、保持器３の各柱部８は、各ころ２の中心軸を通る円弧状面１０と可動部材４の凸円弧状面４ａとの間に形成されており、各ころ２を保持器３内周側から脱落しないように保持している。これは、上述したように一体化された軌道輪１と保持器３にころ２を組み込むため、柱部８は保持器３外周側からのころ２の脱落を防止する必要がないからである。
【００１８】
従って、この揺動軸受は、隣り合うころ２どうしの間に保持器３の柱部８が介在しておらず、従来よりも多数のころ２を配列して静定格荷重を大きくすることができる。ころ２どうしの間隔は自由に設定できるが、図１の例では、各ころ２が隙間なく総ころ状態で組み込まれており、総ころ軸受相当の静定格荷重が確保されている。しかも、ころ２には特別な加工を施す必要がないので、安価に製作することができ、軸受全体としての設計上の制約も少ない。
【００１９】
なお、図１では軌道輪１の両側に鍔部５を設けた例を示したが、図２に示すように、鍔部５は軌道輪１１の片側にのみ設けてもよい。
【００２０】
また、軌道輪と保持器とを一体化する方法は、上述したものに限らず、保持器を軌道輪に揺動可能に係合させるとともに、保持器の軌道輪周方向端からの抜け止めをすることができれば、どのような手段を用いてもよい。
【００２１】
例えば、保持器の周方向抜け止め手段の変形例としては、図３に示すように、保持器１２を軌道輪１３よりも長く形成して、その周方向両端部に軌道輪１３の周方向端面と間隔をおいて対向するストッパ１４を設けたものを採用することもできる。
【００２２】
また、軌道輪と保持器とを係合させる位置については、種々の選択が可能であり、周方向の複数の位置で係合させるようにしてもよい。
【００２３】
図４（ａ）、（ｂ）は、第２の実施形態を示す。この揺動軸受は、軌道輪１５が図２の例と同様に片鍔タイプで、その転走面１５ａの周方向中央位置に、図示省略した固定部材に軸受を固定するための貫通孔１５ｂが設けられている。そして、保持器１６の周方向中央位置には、他の位置に設けられている柱部１７と同様に、両側部１８に台形断面のダミー部１９が差し渡されており、各ころ２が転動しながら保持器１６とともに所定の角度で揺動しても、軌道輪１５の固定用孔１５ｂにはかからないようになっている。なお、保持器１６は周方向中央より若干図面左側へずれた位置で軌道輪１５に係合している。その他の部分の構成は、保持器１６の周方向の抜け止めが図３の例と同様に保持器１６の周方向端部のストッパ１４で行われる点を含めて、第１の実施形態と同じである。
【００２４】
すなわち、この実施形態では、各ころ２が軌道輪１５の固定用孔１５ｂの位置を除いた転走面１５ａ上を転動するように配列されているが、保持器１６のダミー部１９の位置を除いて各ころ２が隙間なく配列されているので、従来と同等以上のころ本数および静定格荷重が得られる。
【００２５】
【発明の効果】
以上のように、この発明の揺動軸受は、軌道輪と保持器とを一体化し、保持器の各柱部を各ころの中心軸を通る円弧状面と可動部材の凸円弧状面との間に形成して、隣り合うころどうしの間に保持器の柱部が介在しないようにしたものであるから、従来よりも配列できるころの本数が多く、静定格荷重を大きくすることができる。しかも、ころには特別な加工を施す必要がないので、安価に製作することができ、軸受全体としての設計上の制約も少ない。
【００２６】
また、軌道輪の転走面に固定用の孔がある場合に、各ころを固定用孔の位置を除いた転走面上を転動するように配列しても、ころの本数が従来よりも減ることがなく、従来と同等以上の静定格荷重が得られる。
【図面の簡単な説明】
【図１】ａは第１の実施形態の揺動軸受の一部切欠き正面図、ｂはａのＩ−Ｉ線に沿った断面図、ｃはａの要部拡大正面図
【図２】図１（ｂ）に対応した軌道輪形状の変形例を示す断面図
【図３】図１の保持器の周方向抜け止め手段の変形例を示す一部切欠き正面図
【図４】ａは第２の実施形態の揺動軸受の一部切欠き正面図、ｂはａのIV−IV線に沿った断面図
【図５】従来の揺動軸受の使用状態の一例を示す縦断正面図
【図６】ａは従来の揺動軸受の別の例の縦断正面図、ｂはａのVI−VI線に沿った断面図
【符号の説明】
１軌道輪
１ａ転走面
２ころ
３保持器
４可動部材
４ａ凸円弧状面
５鍔部
６ストッパ
７側部
８柱部
９係合部
１０円弧状面
１１軌道輪
１２保持器
１３軌道輪
１４ストッパ
１５軌道輪
１５ａ転走面
１５ｂ孔
１６保持器
１７柱部
１８側部
１９ダミー部[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a rocking bearing for swingably supporting a movable member such as a swash plate incorporated in a hydraulic pump, a hydraulic motor, or an HST (hydrostatic transmission).
[0002]
[Prior art]
In hydraulic pumps, hydraulic motors, and HSTs used in construction machines and agricultural machines, the operating speed of the machine can be adjusted by adjusting the angle of the swash plate incorporated in the apparatus. Since a large load of several tons is applied to the swash plate, a rocking bearing using a roller as a rolling element is incorporated for the purpose of reducing torque when adjusting the angle of the swash plate.
[0003]
FIG. 5 shows an example of the usage state of such a rocking bearing (see Patent Document 1). The oscillating bearing is fixed to a fixed member 51 and has a raceway ring 52 having a concave arcuate rolling surface 52a, a plurality of rollers 53 arranged along the rolling surface 52a, and the rollers 53. A swash plate 55 having a convex arcuate surface 55a is supported by each roller 53 so as to be swingable. Each roller 53 is housed in each pocket formed by both side portions 56 of the retainer 54 and a plurality of pillar portions 57 inserted between the both side portions 56, like a general radial bearing, and can freely roll. Is held in.
[0004]
[Patent Document 1]
JP 61-215812 (Fig. 3)
[0005]
Oscillating bearings as described above often require strength against static loads compared to general radial bearings. Therefore, it is desirable to design with an emphasis on static load rating. For this purpose, arrange as many rollers as possible. It is effective to do. However, the number of rollers that can be arranged is limited because the retainer column portion is interposed between adjacent rollers, and it is difficult to increase the static load rating beyond a certain limit.
[0006]
Of these types of oscillating bearings, the type in which the bearing is fixed to the fixed member using a hole penetrating from the rolling surface of the raceway to the fixed member side, There is a case where it is feared that the fixing hole is applied. However, if the rollers are arranged so as to avoid the position applied to the hole, the number of the rollers is reduced as compared with the conventional case, and the static load rating is reduced.
[0007]
On the other hand, prior to the present invention, the present applicant has proposed a rocking bearing in which a larger number of rollers can be arranged than before by eliminating the column portion of the cage (Japanese Patent Application No. 2001-129448). ). As shown in FIGS. 6A and 6B, this rocking bearing is provided with projections 62a at both ends in the axial direction of the rollers 62 arranged along the rolling surface 61a of the bearing ring 61. The roller 62 is held by fitting the portion 62 a into the groove 64 a of the pair of side portions 64 connected at both ends in the circumferential direction of the cage 63, and the cage 63 has no column portion. Therefore, the number of rollers 62 that can be arranged can be increased as compared with the conventional case. However, since it is necessary to process the end face of the rollers 62 to form the protrusions 62a, the manufacturing cost of the rollers 62 is high, and the entire bearing is expensive. It will become something. In addition, since the design of the roller diameter can be restricted, there is a problem that the degree of freedom of design of the entire bearing is reduced.
[0008]
[Problems to be solved by the invention]
Accordingly, an object of the present invention is to provide a rocking bearing that has a large number of rollers that can be arranged and can be manufactured at low cost.
[0009]
[Means for Solving the Problems]
In order to solve the above-mentioned problem, the present invention is a fixed ring, a race ring having a concave arc-shaped rolling surface, and a plurality of rollers arranged along the concave arc-shaped rolling surface, Convex arcuate surface comprising a pair of side portions extending in an arc shape along the rolling surface and a cage for holding the rollers in a freely rolling manner by a plurality of column portions extending across the both side portions. A swinging bearing that swingably supports a movable member having a contact with each of the rollers, and means for swingably engaging the cage with the raceway, and a raceway circumferential direction of the cage A retaining means from the end is provided, the raceway and the cage are integrated, and each column portion of the cage passes through a central axis of each roller and a convex arcuate surface of the movable member The structure formed between the two was adopted.
[0010]
That is, it is unnecessary to prevent the roller from falling from the outer peripheral side of the cage by integrating the bearing ring and the cage, and each column portion of the cage passes through the central axis of each roller. Formed between the surface and the convex arcuate surface of the movable member so that each roller does not fall off from the inner circumferential side of the cage, so that the pillar portion of the cage does not intervene between adjacent rollers In this way, the number of rollers that can be arranged was increased without applying special processing to the rollers.
[0011]
By making the arrangement of the rollers into a full-roller arrangement, a static load rating equivalent to a full-roller bearing can be ensured.
[0012]
Further, when the raceway has a hole for fixing to the fixing member on the rolling surface, the rollers are placed on the rolling surface excluding the position of the fixing hole of the raceway. Can be arranged to roll.
[0013]
In other words, when the bearing ring has a fixing hole, even if it is designed so that each roller does not hit the fixing hole of the bearing ring during rolling, the number of rollers will not decrease compared to the conventional one, and it will be the same as before. The above static load rating is obtained.
[0014]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, an embodiment of the present invention will be described with reference to FIGS. 1 to 3 show a first embodiment. As shown in FIGS. 1 (a) and 1 (b), the oscillating bearing is arranged along a raceway ring 1 having a concave arc-shaped rolling surface 1a and the concave arc-shaped rolling surface 1a. It comprises a plurality of rollers 2 and a cage 3 that holds each roller 2 in a freely rollable manner. The bearing ring 1 is fixed to a fixed member (not shown), and the movable member 4 having a convex arcuate surface 4a is fixed to each roller. 2 is supported so that it can swing freely. In addition, although the bearing ring 1 is shape | molded by cutting out from steel materials, you may shape | mold by pressing a steel plate. The cage 3 is formed of a resin material in order to facilitate the assembly of the rollers 2.
[0015]
The bearing ring 1 is provided with flanges 5 extending along the end faces of the rollers 2 on both side ends over the entire length in the circumferential direction, and is engaged with the cage 3 at one flange part 5 as will be described later. ing. Moreover, the circumferential direction length is formed longer than the holder | retainer 3, and the stopper 6 which opposes the circumferential direction end surface of the holder | retainer 3 at intervals is provided in the circumferential direction both ends, and this holder | retainer 6 holds 3 is prevented from falling off from one end in the circumferential direction.
[0016]
On the other hand, the retainer 3 has a plurality of column portions 8 extending between a pair of side portions 7 extending in an arc shape along the rolling surface 1 a of the raceway ring 1. At the position, there is provided an engagement portion 9 having a cross-section in cross section and a tip portion of which is formed along the curved portion of the outer surface of the flange portion 5 of the bearing ring 1. ing. The engaging portion 9 swings while being guided by the flange portion 5 while gripping the flange portion 5 together with the roller 2 disposed at a position facing the engaging portion 9.
[0017]
As shown in FIG. 1C, each column portion 8 of the cage 3 is formed between an arcuate surface 10 passing through the central axis of each roller 2 and a convex arcuate surface 4 a of the movable member 4. Each roller 2 is held so as not to drop from the inner peripheral side of the cage 3. This is because the roller 2 is incorporated into the raceway 1 and the cage 3 that are integrated as described above, and therefore the column portion 8 does not need to prevent the roller 2 from falling off from the outer peripheral side of the cage 3.
[0018]
Therefore, in this oscillating bearing, the column portion 8 of the cage 3 is not interposed between the adjacent rollers 2, and a larger number of rollers 2 can be arranged than in the prior art to increase the static load rating. . Although the interval between the rollers 2 can be set freely, in the example of FIG. 1, each roller 2 is assembled in a full roller state without a gap, and a static load rating equivalent to a full roller bearing is secured. In addition, since it is not necessary to apply special processing to the roller 2, it can be manufactured at low cost, and there are few design restrictions as the entire bearing.
[0019]
In addition, although the example which provided the collar part 5 in the both sides of the track ring 1 was shown in FIG. 1, the collar part 5 may be provided only in the one side of the track ring 11, as shown in FIG.
[0020]
Further, the method of integrating the raceway and the cage is not limited to the above-described method, and the cage is engaged with the raceway so as to be swingable, and the cage is prevented from coming off from the circumferential end of the raceway. Any means may be used as long as it can be done.
[0021]
For example, as a modification of the circumferential retaining means of the cage, as shown in FIG. 3, the cage 12 is formed longer than the race ring 13, and the circumferential end face of the race ring 13 is formed at both circumferential ends. It is also possible to employ one provided with a stopper 14 that is opposed to each other at an interval.
[0022]
Various positions can be selected for the position where the race ring and the cage are engaged, and they may be engaged at a plurality of positions in the circumferential direction.
[0023]
4 (a) and 4 (b) show a second embodiment. In this oscillating bearing, the bearing ring 15 is a single-sided type as in the example of FIG. 2, and a through hole 15b for fixing the bearing to a fixing member (not shown) is provided at the circumferential center position of the rolling surface 15a. Is provided. A dummy portion 19 having a trapezoidal cross section is provided on both side portions 18 at the center position in the circumferential direction of the cage 16 in the same manner as the column portions 17 provided at other positions. Even if the cage 16 is swung at a predetermined angle while moving, it does not reach the fixing hole 15b of the race 15. Note that the cage 16 is engaged with the race 15 at a position slightly shifted to the left side of the drawing from the center in the circumferential direction. The configuration of the other parts is the same as that of the first embodiment, including that the retainer 16 is prevented from coming off in the circumferential direction by the stopper 14 at the circumferential end of the retainer 16 as in the example of FIG. It is.
[0024]
That is, in this embodiment, each roller 2 is arranged so as to roll on the rolling surface 15a excluding the position of the fixing hole 15b of the bearing ring 15, but the position of the dummy portion 19 of the cage 16 Since the rollers 2 are arranged without any gaps, the number of rollers and the static load rating equal to or greater than those of the prior art can be obtained.
[0025]
【The invention's effect】
As described above, the oscillating bearing according to the present invention integrates the bearing ring and the cage, and each column portion of the cage is formed by the arc-shaped surface passing through the center axis of each roller and the convex arc-shaped surface of the movable member. Since it is formed between the adjacent rollers so that the pillar portion of the cage does not intervene between them, the number of rollers that can be arranged is larger than in the prior art, and the static load rating can be increased. Moreover, since it is not necessary to apply special processing to the rollers, the rollers can be manufactured at a low cost, and there are few design restrictions for the entire bearing.
[0026]
Also, when there are fixing holes on the raceway surface of the race, even if each roller is arranged so as to roll on the rolling surface excluding the position of the fixing hole, the number of rollers is larger than before. The static load rating equal to or higher than the conventional one can be obtained.
[Brief description of the drawings]
FIG. 1a is a partially cutaway front view of a rocking bearing of a first embodiment, b is a sectional view taken along line II of a, and c is an enlarged front view of a main part of a. FIG. FIG. 3 is a sectional view showing a modification of the raceway shape corresponding to FIG. 1 (b). FIG. 3 is a partially cutaway front view showing a modification of the circumferential retaining means of the cage in FIG. FIG. 5 is a partially cutaway front view of a rocking bearing according to a second embodiment, and b is a cross-sectional view taken along line IV-IV in FIG. 6a is a longitudinal front view of another example of a conventional rocking bearing, and b is a cross-sectional view taken along line VI-VI in FIG.
DESCRIPTION OF SYMBOLS 1 Track ring 1a Rolling surface 2 Roller 3 Cage 4 Movable member 4a Convex arcuate surface 5 ridge part 6 Stopper 7 Side part 8 Column part 9 Engagement part 10 Arcuate surface 11 Track ring 12 Holder 13 Track ring 14 Stopper 15 Raceway 15a Rolling surface 15b Hole 16 Cage 17 Pillar part 18 Side part 19 Dummy part

Claims

A bearing ring fixed to the fixing member and having a concave arc-shaped rolling surface, a plurality of rollers arranged along the concave arc-shaped rolling surface, and a pair extending in an arc shape along the rolling surface And a plurality of pillars extending between the two sides, and a holder for holding the rollers in a rollable manner, and a movable member having a convex arcuate surface is brought into contact with the rollers. In the swing bearing that is swingably supported , at least one side end of the race is provided with a flange portion that extends along an end surface of the roller, and an engagement portion that engages with the flange portion is provided on the cage. The retainer is guided by the flange while swinging while holding the flange together with the rollers disposed at positions where the retainer faces the engagement portion. It provided retaining hands stage from HanawaAmane direction end, by integrating the cage and the bearing ring, each pillar of the cage Rocking bearing, characterized in that formed between the convex arcuate surface of the arcuate surface and the movable member passing through the central axis of each roller a.

The rocking bearing according to claim 1, wherein the roller arrangement is a full roller arrangement.

The bearing ring has a hole for fixing to the fixing member on the rolling surface, and the rollers roll on the rolling surface excluding the position of the fixing hole of the bearing ring. The rocking bearing according to claim 1, which is arranged in a row.

The means for arranging the rollers so as to roll on a rolling surface excluding the position of the fixing hole of the track ring passes a dummy part that is close to and faces the fixing hole on both sides of the cage. The rocking bearing according to claim 3, wherein the roller is not applied to the fixing hole even if the rollers roll with a cage at a predetermined angle while rolling.