JPH09189601A - Vibration analyzing method - Google Patents
Vibration analyzing methodInfo
- Publication number
- JPH09189601A JPH09189601A JP8000386A JP38696A JPH09189601A JP H09189601 A JPH09189601 A JP H09189601A JP 8000386 A JP8000386 A JP 8000386A JP 38696 A JP38696 A JP 38696A JP H09189601 A JPH09189601 A JP H09189601A
- Authority
- JP
- Japan
- Prior art keywords
- bearing
- degrees
- speed reducer
- freedom
- spring
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Landscapes
- Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
Abstract
Description
【０００１】[0001]
【発明の属する技術分野】本発明は、振動解析法に関
し、より詳細には、有限要素法を用いて、特に、結合部
に軸受および減速機が用いられている機械構造物の振動
解析を行う振動解析法に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a vibration analysis method, and more particularly, to a vibration analysis of a mechanical structure using a finite element method, in particular, a bearing and a speed reducer in a joint. Vibration analysis method.
【０００２】[0002]
【従来の技術】今日、ＣＡＥ（Ｃomputer Ａided Ｅngi
neering）の普及に伴い、有限要素解析による機械構造
物の振動解析が、実験による振動解析と併用して行われ
ている。従来、例えば、ロボットアームのように、アー
ムを回転支持する結合部を持つ機械構造物に対して有限
要素法により振動解析して固有振動数を求めると、求め
られた結果は、実験によって得られた固有振動数と一致
しないことが知られている。これは、有限要素法による
振動解析では、機械構造物の減衰が考慮できないこと
や、結合部をモデル化できないためである。このよう
に、機械構造物の有限要素解析による振動解析結果が、
実験で求められた結果と異なるという課題を解決するた
めに、従来は、実験で得られた固有振動数などを有限要
素解析により得られた固有振動数に代入して、逆問題と
して機械構造物の減衰や結合部の剛性を推定する方法を
とっている。2. Description of the Related Art Today, CAE (Computer Aided Engi)
With the widespread use of neering), vibration analysis of mechanical structures by finite element analysis is being performed in combination with experimental vibration analysis. Conventionally, for example, when a natural structure is obtained by performing a vibration analysis by a finite element method on a mechanical structure having a coupling portion that rotationally supports the arm, such as a robot arm, the obtained result is obtained by an experiment. It is known that it does not match the natural frequency. This is because the vibration analysis by the finite element method cannot consider the damping of the mechanical structure and the joint part cannot be modeled. In this way, the vibration analysis result of the finite element analysis of the mechanical structure is
In order to solve the problem that the result is different from the result obtained in the experiment, conventionally, the natural frequency obtained in the experiment is substituted into the natural frequency obtained by the finite element analysis, and the mechanical structure is used as an inverse problem. The method is to estimate the damping of and the stiffness of the joint.
【０００３】[0003]
【発明が解決しようとする課題】上述のように、実験か
ら得られた固有振動数などを用いた逆問題として機械構
造物の減衰や結合部の剛性を推定する手法をとると、試
作以前において、有限要素解析によって、結合部を持つ
機械構造物の固有振動数を、比較的高い精度で求めるこ
とはできなかった。また、結合部に変更があった場合に
は、実験をやり直し、あらためて、機械構造物の減衰や
結合部の剛性を推定し直さなければならないので、これ
らの対策を短時間で行うことができなかった。As described above, the method of estimating the damping of the mechanical structure and the rigidity of the joint as an inverse problem using the natural frequency obtained from the experiment, etc. It was not possible to obtain the natural frequency of a mechanical structure having a joint with relatively high accuracy by finite element analysis. In addition, if there is a change in the joint, it is necessary to repeat the experiment and re-estimate the damping of the mechanical structure and the rigidity of the joint, so these measures cannot be taken in a short time. It was
【０００４】本発明は、特に、結合部に軸受および減速
機を用いた機械構造物に対して行われる有限要素法を用
いた振動解析において、軸受および減速機を６自由度の
ばねを用いてモデル化し、このモデル化に際しては、既
知の物性値をもったばねで、最低限のばね本数を用いた
結合部をもつ機械構造物とし、該機械構造物を試作する
以前に比較的精度の良い固有振動数を求め、更に、結合
部を変更する場合でも変更する軸受や、減速機に従って
定められるばねの取り付け位置や、ばね定数の数値を変
更するだけで短時間に対応できるようにすることを目的
とする。In particular, the present invention uses a 6-degree-of-freedom spring for a bearing and a speed reducer in a vibration analysis using a finite element method performed on a mechanical structure using a bearing and a speed reducer for a joint. Modeling is performed using a spring having a known physical property value as a mechanical structure having a connecting portion using the minimum number of springs, and with a relatively accurate characteristic before the mechanical structure is prototyped. The purpose is to obtain the frequency and to make it possible to respond in a short time by simply changing the bearings that are changed even when changing the coupling part, the mounting position of the spring determined according to the reducer, and the numerical value of the spring constant. And
【０００５】[0005]
【課題を解決するための手段】請求項１の発明は、結合
部に軸受および減速機を用いた機械構造物の振動解析を
有限要素法を用いて行う振動解析法において、前記結合
部に用いる前記軸受および減速機を各々６自由度をもつ
ばねでモデル化することにより、結合部をもつ機械構造
物試作前に該機械構造物の固有振動を比較的高い精度で
求められるようにし、かつ、結合部を変更する場合でも
単時間で処理できるようにしたものである。According to a first aspect of the present invention, a vibration analysis method for performing mechanical vibration analysis of a mechanical structure using a bearing and a speed reducer for the joint is used for the joint. By modeling the bearing and the speed reducer with springs each having 6 degrees of freedom, it is possible to obtain the natural vibration of the mechanical structure with relatively high accuracy before the prototype of the mechanical structure having the coupling portion is produced, and Even if the connecting part is changed, it can be processed in a single time.
【０００６】請求項２の発明は、請求項１の発明におい
て、前記軸受をモデル化した前記６自由度を持つばねの
取り付け位置を、該軸受内径の円周上に角度９０度ごと
に定めた４点とし、前記減速機をモデル化した前記６自
由度を持つばねの取り付け位置を、該減速機の軸径の円
周上に角度９０度ごとに定めた４点、さらに、該減速機
のカップラー外径の円周上に角度９０度ごとに定めた４
点にすることにより、最小のモデル化されたばね本数で
請求項１と同じ効果が、より簡易に得られるようにした
ものである。According to a second aspect of the present invention, in the first aspect of the invention, the mounting position of the spring having the six degrees of freedom that models the bearing is determined on the circumference of the bearing inner diameter at every 90 degrees. There are four points, and the mounting positions of the springs having the six degrees of freedom that model the speed reducer are set at four points every 90 degrees on the circumference of the shaft diameter of the speed reducer. 4 on the circumference of the outside diameter of the coupler for every 90 degrees
By making the point, the same effect as in claim 1 can be more easily obtained with the minimum number of modeled springs.
【０００７】請求項３の発明は、請求項１の発明におい
て、前記軸受をモデル化した６自由度を持つばねは、縦
方向の並進と横方向周りの回転の自由度を２つ持ち、前
記減速機をモデル化した６自由度を持つばねは、横方向
の２つの並進と縦方向周りの回転の自由度を持たせるこ
とにより、請求項１と同じ効果が、より簡易に得られる
ようにしたものである。According to a third aspect of the present invention, in the first aspect of the invention, the spring having six degrees of freedom modeling the bearing has two degrees of freedom of translation in a longitudinal direction and rotation in a lateral direction. A spring having 6 degrees of freedom modeling a reduction gear has two degrees of freedom of translation in the lateral direction and rotation in the longitudinal direction so that the same effect as that of claim 1 can be obtained more easily. It was done.
【０００８】請求項４の発明は、請求項２又は３の発明
において、前記軸受および減速機をモデル化した６自由
度を持つばねの縦、横方向の並進のばね定数には剛結合
とする値を、３方向の回転のばね定数には、該軸受の曲
げ剛性、および該減速機のねじり剛性の値をもたせるこ
とにより、請求項１と同じ効果が、より簡易に得られる
ようにしたものである。According to a fourth aspect of the present invention, in the second or third aspect of the invention, a rigid coupling is used for the longitudinal and lateral translational spring constants of the spring having 6 degrees of freedom that models the bearing and the speed reducer. The spring constant of rotation in three directions is made to have the bending rigidity of the bearing and the torsional rigidity of the speed reducer so that the same effect as that of claim 1 can be obtained more easily. Is.
【０００９】請求項５の発明は、請求項２又は４の発明
において、前記軸受および減速機をモデル化した前記６
自由度を持つばねの取り付け位置や、前記軸受の曲げ剛
性および減速機のねじり剛性の値として該軸受および減
速機の寸法および使用される材料に定められた物性値を
用いることにより、請求項１と同じ効果が、より簡易に
得られるようにしたものである。According to a fifth aspect of the present invention, in the second or fourth aspect of the present invention, the bearing and the speed reducer are modeled.
The spring mounting position having a degree of freedom, the bending rigidity of the bearing, and the torsional rigidity of the speed reducer, using the physical property values determined by the dimensions of the bearing and the speed reducer and the material used. The same effect as that can be obtained more easily.
【００１０】[0010]
【発明の実施の形態】図１は、本発明による振動解析法
の実施の形態を説明するための機械構造物の一例を示す
図で、図中、１は構造物１（以後、構造物１と記す）、
２は構造物２（以後、構造物２と記す）、３は結合部
（軸受、減速機）、４は支持部である。1 is a diagram showing an example of a mechanical structure for explaining an embodiment of a vibration analysis method according to the present invention, in which 1 is a structure 1 (hereinafter structure 1) ),
Reference numeral 2 is a structure 2 (hereinafter referred to as structure 2), 3 is a coupling portion (bearing, speed reducer), and 4 is a support portion.
【００１１】図１に示す機械構造物は、支持部４に一端
側が固定された長尺な構造物１と、該構造物１の他端下
方側に一端が支持され斜線で図示した結合部３と、該結
合部３の他端に構造物１と平行に一端が支持された長尺
の構造物２とからなっている。The mechanical structure shown in FIG. 1 has a long structure 1 whose one end is fixed to a supporting portion 4, and a connecting portion 3 whose one end is supported below the other end of the structure 1 and which is shown by hatching. And a long structure 2 having one end supported in parallel with the structure 1 at the other end of the coupling portion 3.
【００１２】結合部３は、構造物１と結合部３とを回転
自在に結合するボールベアリング等の軸受と結合部３と
構造物２を回転自在に結合する軸受と、これら軸受同志
を連結する減速機とから構成されているものと想像す
る。The coupling portion 3 couples a bearing such as a ball bearing that rotatably couples the structure 1 and the coupling portion 3 and a bearing that rotatably couples the coupling portion 3 and the structure 2 to each other. Imagine that it consists of a speed reducer.
【００１３】従って、図１に示した機械構造物におい
て、結合部３には軸方向の引張り力、軸まわりの捩れ
力、曲げ力が作用しており、結合部３を構成する軸受お
よび減速機にも上記の力による力が作用している。結合
部３の設計においては、回転軸、軸受および減速機に
は、設計仕様上最大の力が作用したときの内部応力が、
構成する材料の弾性限界内において充分なマージンをも
った値に定められている。このため、有限要素法を用い
た振動解析においては、結合部３を軸受、および減速機
で構成したと仮定し、軸受および減速機をそれぞれ６自
由度をもつばねでモデル化することができる（請求項
１）。Therefore, in the mechanical structure shown in FIG. 1, a tensile force in the axial direction, a twisting force around the axis, and a bending force act on the joint portion 3, so that the bearing and the speed reducer constituting the joint portion 3 are acted upon. Also, the force due to the above force acts. In designing the coupling portion 3, the internal stress when the maximum force in the design specifications acts on the rotary shaft, the bearing, and the speed reducer is
It is set to a value with a sufficient margin within the elastic limit of the constituent materials. Therefore, in the vibration analysis using the finite element method, it is assumed that the coupling portion 3 is composed of the bearing and the speed reducer, and the bearing and the speed reducer can be modeled by springs each having 6 degrees of freedom ( Claim 1).
【００１４】なお、ばねによりモデル化する場合、軸受
および減速機を６自由度をもつ一つのばねでモデル化す
るのではなく、軸受および減速機の回転軸と直角な面を
等分に区分し、各々の面に作用する応力分布に従って定
められたばね定数のばねを各々の面に取り付けられた複
数のばねによりモデル化し、振動解析精度をあげること
ができる。When modeling with a spring, the bearing and the speed reducer are not modeled with one spring having six degrees of freedom, but the surface orthogonal to the rotation axis of the bearing and the speed reducer is divided into equal parts. , A spring having a spring constant determined according to a stress distribution acting on each surface can be modeled by a plurality of springs attached to each surface to improve vibration analysis accuracy.
【００１５】図２は、本発明による振動解析法の実施の
形態に係る軸受のモデル例を説明するための図で、図２
（Ａ）は軸受斜視図、図２（Ｂ）は、図２（Ａ）に示し
た軸受を６自由度をもつ４本のばねでモデル化した図で
あり、図中、５は軸受、６，７，８，９は６自由度をも
つばねである。FIG. 2 is a diagram for explaining an example of a bearing model according to the embodiment of the vibration analysis method according to the present invention.
2A is a perspective view of the bearing, and FIG. 2B is a diagram in which the bearing shown in FIG. 2A is modeled by four springs having 6 degrees of freedom. , 7, 8 and 9 are springs having 6 degrees of freedom.
【００１６】図２（Ａ）に示した軸受５は、例えば、ボ
ール軸受で、内径Ｄ1のインナーレースと、ボールと、
アウターレースで構成され、アウターレースの外周は剛
性部材（図示せず）に固定されている。軸受５のインナ
ーレースの内周５ａには、回転軸（図示せず）が嵌め込
まれ、Ｘ−Ｙ面と直角な軸Ｚまわりに回転する。このた
め、軸受５は外周が固定された円環状のばね板の作用を
もっており、回転軸を介して回転する回転、および構造
物２を片持支持することによる曲げ力により、軸Ｘ，
Ｙ，Ｚ方向の力および軸Ｘまわりの回転力ＲX、軸Ｙま
わりの回転力ＲY、軸Ｚまわりの回転力ＲZからなる６自
由度の向きの力を受けている。これらの力の入力点を、
回転軸が固定された軸受５の内径Ｄ1のインナーレース
内周５ａを９０°毎に分割した位置、すなわち内周５ａ
と直角軸Ｘ，Ｙが各々交わる点Ｐ1，Ｐ2，Ｐ3，Ｐ4の位
置の力として代表できる。図２（Ｂ）のばね６，７，
８，９は、各々点Ｐ1，Ｐ2，Ｐ3，Ｐ4に対応して設けら
れた６自由度をもつばねである。The bearing 5 shown in FIG. 2A is, for example, a ball bearing, which has an inner race having an inner diameter D 1 and a ball.
It is composed of an outer race, and the outer circumference of the outer race is fixed to a rigid member (not shown). A rotating shaft (not shown) is fitted on the inner circumference 5a of the inner race of the bearing 5 and rotates about an axis Z perpendicular to the XY plane. Therefore, the bearing 5 has the action of an annular spring plate whose outer periphery is fixed, and is rotated by the rotating shaft, and the bending force by cantilever supporting the structure 2 causes the shaft X,
It receives a force in the directions of 6 degrees of freedom consisting of a force in the Y and Z directions and a rotational force R X about the axis X , a rotational force R Y about the axis Y , and a rotational force R Z about the axis Z. The input points of these forces are
Position where the inner circumference 5a of the inner race having the inner diameter D 1 of the bearing 5 to which the rotating shaft is fixed is divided every 90 °, that is, the inner circumference 5a
Can be represented as the force at the position of points P 1 , P 2 , P 3 , P 4 where the orthogonal axes X and Y intersect. The springs 6 and 7 of FIG.
Reference numerals 8 and 9 are springs having 6 degrees of freedom provided corresponding to the points P 1 , P 2 , P 3 , and P 4 , respectively.
【００１７】図３は、本発明による振動解析法の実施の
形態に係る減速機のモデル例を説明するための図で、図
３（Ａ）は減速機斜視図、図２（Ｂ）は、図３（Ａ）に
示した減速機を６自由度をもつ８本のばねでモデル化し
た図であり、図中、１０は減速機、１１は入力軸部、１
２はカップラー部、１３，１４，１５，１６，１７，１
８，１９，２０は６自由度をもつばねである。FIG. 3 is a diagram for explaining an example of a model of a speed reducer according to an embodiment of a vibration analysis method according to the present invention. FIG. 3 (A) is a perspective view of the speed reducer, and FIG. 2 (B) is It is the figure which modeled the speed reducer shown in Drawing 3 (A) by eight springs which have 6 degrees of freedom. In the figure, 10 is a speed reducer, 11 is an input shaft part, 1
2 is a coupler part, 13, 14, 15, 16, 17, 1
8, 19, and 20 are springs having 6 degrees of freedom.
【００１８】図３（Ａ）に示した減速機１０は、Ｚ軸ま
わりに回転される外径Ｄ2の入力軸１１と、入力軸部１
１の回転を所定の低回転に減速し回転出力する内径Ｄ3
のカップラー部１２とからなり、減速機１０は入力軸部
１１、カップラー部１２は、共に、軸Ｘ，Ｙ，Ｚ方向の
力および軸Ｘまわりの回転力ＲX、軸Ｙまわりの力ＲY、
軸Ｚまわりの力ＲZからなる６自由度の向きの力を受け
る。これらの力の作用点を、入力軸部１１側では直交軸
Ｘ，Ｙ上に外径Ｄ2の外周１１ａを９０°毎に四分割し
た位置Ｑ1，Ｑ2，Ｑ3，Ｑ4で代表し、カップラー部１２
側では、内径Ｄ3の内周１２ａを９０°毎に分割した位
置、すなわち、内周１２ａと直交軸Ｘ，Ｙが各々交わる
内周１２ａを四分割した位置Ｓ1，Ｓ2，Ｓ3，Ｓ4で代表
される。The speed reducer 10 shown in FIG. 3A has an input shaft 11 having an outer diameter D 2 rotated about the Z axis and an input shaft portion 1.
Inner diameter D 3 that decelerates the rotation of 1 to a predetermined low rotation and outputs the rotation
The input shaft portion 11 of the speed reducer 10 and the coupler portion 12 both of the forces in the X, Y, and Z directions and the rotational force R X about the axis X and the force R Y about the axis Y. ,
It receives a force in the direction of 6 degrees of freedom consisting of the force R Z about the axis Z. The point of action of these forces, represented by orthogonal axes X, position was quartered the outer periphery 11a of the outer diameter D 2 for each 90 ° on Y Q 1, Q 2, Q 3, Q 4 denotes an input shaft portion 11 side And coupler section 12
On the side, a position obtained by dividing the inner periphery 12a for each 90 ° of the inner diameter D 3, i.e., the position S 1 where the orthogonal axes X and the inner periphery 12a, Y is divided into four inner peripheral 12a each intersect, S 2, S 3, It is represented by S 4 .
【００１９】図３（Ｂ）に示すばね１３，１４，１５，
１６は、各々外径Ｄ2の入力軸１１側の外周１１ａを四
分割した位置Ｑ1，Ｑ2，Ｑ3，Ｑ4に対応して定められた
６自由度をもつばねでモデル化したもので、ばね１７，
１８，１９，２０は各々内径Ｄ3のカップラー側１２の
内周１２ａを四分割した位置Ｓ1，Ｓ2，Ｓ3，Ｓ4に対応
して定められた６自由度をもつばねでモデル化したもの
である。The springs 13, 14, 15, shown in FIG.
Reference numeral 16 is a model of a spring having 6 degrees of freedom defined corresponding to positions Q 1 , Q 2 , Q 3 , Q 4 in which the outer circumference 11a of the outer diameter D 2 on the input shaft 11 side is divided into four. And the spring 17,
18, 19 and 20 are modeled by springs having 6 degrees of freedom defined corresponding to positions S 1 , S 2 , S 3 and S 4 which are obtained by dividing the inner circumference 12a of the coupler side 12 of the inner diameter D 3 into four. It was done.
【００２０】図２，図３に示すように、軸受５および減
速機１０において、該軸受５、減速機１０に作用する力
を、最小な数で代表する四分割した位置に取り付けられ
た６自由度をもつ４本のばねでモデル化したもので、振
動解析の精度が向上し、しかも、モデル化されたばねの
本数も最小であるから有限要素解析も簡単に行うことが
できる（請求項２に対応）。As shown in FIG. 2 and FIG. 3, in the bearing 5 and the speed reducer 10, the forces acting on the bearing 5 and the speed reducer 10 are mounted in the four divided positions represented by the minimum number. Modeling with four springs with a certain degree improves the accuracy of vibration analysis, and since the number of modeled springs is the minimum, the finite element analysis can be easily performed. Correspondence).
【００２１】このように、軸受５および減速機１０を６
自由度をもつばねでモデル化し、更に、ばねの本数を最
小にして振動解析の精度を高め、且つ簡易化することを
可能としたが、更にまた、軸受５および減速機１０のモ
デル化されたばねに対し、各々に作用する力の面から自
由度を定めることにより振動解析をより簡易化すること
ができる。In this way, the bearing 5 and the speed reducer 10 are
Although it is possible to improve the accuracy of vibration analysis by simplifying the modeling with a spring having a degree of freedom and minimizing the number of springs, the modeled springs of the bearing 5 and the speed reducer 10 are also provided. On the other hand, the vibration analysis can be further simplified by determining the degree of freedom in terms of the force acting on each.
【００２２】図４は、図２（Ｂ）に示した６自由度をも
つモデル化されたばねがもつ軸受の自由度を説明するた
めの図であり、煩雑を避けるため図２（Ｂ）を再図示し
たものである。FIG. 4 is a diagram for explaining the degree of freedom of the bearing of the modeled spring having the six degrees of freedom shown in FIG. 2B. To avoid complication, FIG. 2B is reproduced. It is the one illustrated.
【００２３】図２に示した軸受５は、前述のように、結
合部３の構成要素として構造物１に支持され、構造物２
の一端を回転可能に片持ち支持するので、軸受５には、
外周が固定されて生ずる軸方向の引張り力による曲げ力
と、構造物２を回転しながら片持ち支持することによる
軸Ｚと直角方向の曲げ力が作用し、しかも、曲げ力の方
向は軸Ｚまわりの回転に従って変化するので、６自由度
をもつばね６，７，８，９の自由度であるＺ方向に作用
する曲げ力による並進と、軸受の曲げ力によるＸ軸まわ
りの回転力ＲXおよびＹ軸まわりの回転力ＲYの２つの自
由度、すなわち横方向まわりの２つの自由度であらわす
ことができる。As described above, the bearing 5 shown in FIG. 2 is supported by the structure 1 as a component of the coupling portion 3, and the structure 2 is supported.
Since one end of is rotatably supported by a cantilever,
A bending force due to an axial pulling force generated when the outer periphery is fixed and a bending force perpendicular to the axis Z due to cantilever support of the structure 2 while rotating act, and the direction of the bending force is the axis Z. Since it changes in accordance with the rotation around, the translation by the bending force acting in the Z direction, which is the freedom of the springs 6, 7, 8, 9 having 6 degrees of freedom, and the rotational force R X about the X axis by the bending force of the bearing. and Y 2 degrees of freedom of rotational force R Y about axis, i.e. can be expressed in two degrees of freedom around the lateral.
【００２４】図５は、図３（Ｂ）に示した６自由度をも
つモデル化されたばねをもつ減速機の自由度を説明する
ための図であり、煩雑を避けるため、図３（Ｂ）を再図
示したものである。FIG. 5 is a diagram for explaining the degrees of freedom of the speed reducer having the modeled spring having the six degrees of freedom shown in FIG. 3B, and in order to avoid complication, FIG. Is re-illustrated.
【００２５】図３に示した減速機１０は、入力軸１１と
該入力軸１１から回転力が伝達されるカップラー１２と
からなっており、減速機１０を６自由度をもつばねでモ
デル化するためには、入力軸部１１とカップラー部１２
との機能を分離して定める必要がある。入力軸部１１
は、カップラー部１２と位置関係が定められ、入力軸部
１１とカップラー部１２との間の偏心によりＸ，Ｙ方向
に移動するので、入力軸部１１側の６自由度をもつモデ
ル化されたばねの自由度は横方向の２つの並進で代表さ
れ、カップラー部１２には軸Ｚまわりの負荷トルクが作
用するので、軸Ｚまわりの回転の自由度をもたせること
ができる（請求項３に対応）。The speed reducer 10 shown in FIG. 3 comprises an input shaft 11 and a coupler 12 to which a rotational force is transmitted from the input shaft 11, and the speed reducer 10 is modeled by a spring having 6 degrees of freedom. In order to do so, the input shaft portion 11 and the coupler portion 12
It is necessary to specify the functions of and separately. Input shaft 11
Has a positional relationship with the coupler portion 12 and moves in the X and Y directions due to the eccentricity between the input shaft portion 11 and the coupler portion 12, so a modeled spring having 6 degrees of freedom on the input shaft portion 11 side. Is represented by two translations in the lateral direction, and the load torque about the axis Z acts on the coupler portion 12, so that the coupler section 12 can have the degree of freedom of rotation about the axis Z (corresponding to claim 3). .
【００２６】なお、図２乃至図５に示した軸受５および
減速機１０をモデル化した６自由度をもつばねにおい
て、縦方向の並進は、軸受５に作用する縦方向の重力に
よるもので、横方向の並進は、入力軸部１１の曲げ応力
によるものであるから、並進によるモデル化した６自由
度をもつばねのばね定数は剛結合とする値を、Ｘ，Ｙ，
Ｚ軸まわりの３方向ＲX，ＲY，ＲZの回転のばね定数と
して、軸受５では軸受５の曲げ剛性を、減速機１０では
ねじり剛性の値を持たせることができる（請求項４に対
応）。In the spring having 6 degrees of freedom that models the bearing 5 and the speed reducer 10 shown in FIGS. 2 to 5, the vertical translation is due to the vertical gravity acting on the bearing 5. Since the translation in the lateral direction is due to the bending stress of the input shaft portion 11, the spring constant of the spring having 6 degrees of freedom modeled by the translation is X, Y,
As the spring constants of rotations in three directions R X , R Y , and R Z around the Z axis, the bearing 5 can have the bending rigidity of the bearing 5 and the reduction gear 10 can have the value of the torsional rigidity (claim 4). Correspondence).
【００２７】以上、軸受５および減速機１０のモデル化
した６自由度をもつ各々ばねの取り付け位置や適用され
るばね定数およびねじり剛性等の物性値は、適用される
軸受５および減速機１０のカタログ等に仕様として記載
された内外径等の寸法値や物性値または材質から定めら
れる値とする（請求項５に対応）。このことにより、結
合部３が変更した場合でも、モデル化されたばねのばね
定数を変更するだけで、試作することなく、有限要素法
による解析により簡易に機械構造物の固有振動数を定め
ることができる。As described above, the physical properties such as the mounting position of each spring having the modeled 6 degrees of freedom of the bearing 5 and the speed reducer 10 and the applied spring constant and torsional rigidity are the same as those of the applied bearing 5 and the speed reducer 10. The value is determined from the dimensional value such as the inner and outer diameters, the physical property value, or the material described in the catalog, etc. (corresponding to claim 5). As a result, even if the coupling portion 3 is changed, the natural frequency of the mechanical structure can be easily determined by analysis by the finite element method without changing the spring constant of the modeled spring and making a prototype. it can.
【００２８】図６は、請求項１乃至５の何れかに記載の
振動解析法による機械構造物としてのロボットアームの
実施例を説明するための図で、図中、３０はロボットア
ーム、３１は支柱、３２は第１アーム、３３は第２アー
ム、３４はタレット取付フレーム、３５はハンド、３
６，３７，３８は結合部である。FIG. 6 is a view for explaining an embodiment of a robot arm as a mechanical structure by the vibration analysis method according to any one of claims 1 to 5, wherein 30 is a robot arm and 31 is a robot arm. A column, 32 is a first arm, 33 is a second arm, 34 is a turret mounting frame, 35 is a hand, 3
Reference numerals 6, 37 and 38 are connecting portions.
【００２９】図６に示したロボットアーム３０は、一端
が固定された鉛直な支柱３１の上端面に結合部３６が取
り付けられ、該結合部３６に一端が片持支持された第１
アーム３２が回転自在に取り付けられ、該第１アーム３
２の他端側に結合部３７が取り付けられ、該結合部３７
により前記第１アーム３２と平行な第２アーム３３の一
端側が回転自在に支持され、更に、該第２アーム３３の
他端側には該第２アーム３３と直角なハンド３５を有す
るタレット取付フレーム３４が結合部３８により支持さ
れている、つまり、３個の結合部３６，３７，３８を有
する３関節のロボットアームで、各々の結合部３６，３
７，３８に本発明による振動解析法が適用される。In the robot arm 30 shown in FIG. 6, a connecting portion 36 is attached to an upper end surface of a vertical support column 31 having one end fixed, and the connecting portion 36 is cantilevered at one end.
The arm 32 is rotatably attached to the first arm 3
The coupling part 37 is attached to the other end side of the
The one end side of the second arm 33 parallel to the first arm 32 is rotatably supported by the turret mounting frame, and the other end side of the second arm 33 has a hand 35 perpendicular to the second arm 33. 34 is supported by a joint 38, that is, a three-joint robot arm having three joints 36, 37, 38, each of which has a joint 36, 3
The vibration analysis method according to the present invention is applied to 7, 38.
【００３０】[0030]
【発明の効果】請求項１の発明は、結合部に軸受および
減速機を用いた機械構造物の振動解析を有限要素法を用
いて行う振動解析法において、前記結合部に用いる前記
軸受および減速機を各々６自由度をもつばねでモデル化
したので、結合部をもつ機械構造物試作前に該機械構造
物の固有振動を比較的高い精度で求められ、かつ、結合
部を変更する場合でも、変更した軸受や減速機の６自由
度をもつばねを変更するだけで単時間で処理できる。According to a first aspect of the present invention, in a vibration analysis method for performing vibration analysis of a mechanical structure using a bearing and a speed reducer in a coupling portion by using a finite element method, the bearing and the reduction gear used in the coupling portion are used. Since the machine is modeled with springs each having 6 degrees of freedom, the natural vibration of the mechanical structure can be obtained with comparatively high precision before the prototype of the mechanical structure having the coupling portion, and even when the coupling portion is changed. The processing can be done in a single time simply by changing the changed bearing or the spring having 6 degrees of freedom of the speed reducer.
【００３１】請求項２の発明は、請求項１の発明におい
て、前記軸受をモデル化した前記６自由度を持つばねの
取り付け位置を、該軸受内径の円周上に角度９０度ごと
に定めた４点とし、前記減速機をモデル化した前記６自
由度を持つばねの取り付け位置を、該減速機の軸径の円
周上に角度９０度ごとに定めた４点、さらに、該減速機
のカップラー外径の円周上に角度９０度ごとに定めた４
点にしたので、請求項１と同じ効果が簡易に得られる。According to a second aspect of the present invention, in the first aspect of the present invention, the mounting position of the spring having the six degrees of freedom that models the bearing is determined on the circumference of the inner diameter of the bearing at every 90 degrees. There are four points, and the mounting positions of the springs having the six degrees of freedom that model the speed reducer are set at four points every 90 degrees on the circumference of the shaft diameter of the speed reducer. 4 on the circumference of the outside diameter of the coupler for every 90 degrees
Since this is the point, the same effect as that of claim 1 can be easily obtained.
【００３２】請求項３の発明は、請求項１の発明におい
て、前記軸受をモデル化した６自由度を持つばねは、縦
方向の並進と横方向周りの回転の自由度を２つ持ち、前
記減速機をモデル化した６自由度を持つばねは、横方向
の２つの並進と縦方向周りの回転の自由度を持たせるよ
うにしたので、請求項１と同じ効果がより簡単に得られ
る。According to a third aspect of the invention, in the first aspect of the invention, the spring having six degrees of freedom modeling the bearing has two degrees of freedom of longitudinal translation and two degrees of rotation around the lateral direction. Since the spring having 6 degrees of freedom modeling the reduction gear has two degrees of freedom of translation in the lateral direction and rotation about the longitudinal direction, the same effect as in claim 1 can be more easily obtained.
【００３３】請求項４の発明は、請求項２又は３の発明
において、前記軸受および減速機をモデル化した６自由
度を持つばねの縦、横方向の並進のばね定数には剛結合
とする値を、３方向の回転のばね定数には、該軸受の曲
げ剛性、および該減速機のねじり剛性の値をもたせるよ
うにしたので、請求項１と同じ効果が得られる。According to a fourth aspect of the present invention, in the second or third aspect of the invention, a rigid coupling is used for the longitudinal and lateral translational spring constants of the spring having 6 degrees of freedom that models the bearing and the speed reducer. Since the spring constant of rotation in three directions has the values of the bending rigidity of the bearing and the torsional rigidity of the speed reducer, the same effect as in claim 1 can be obtained.
【００３４】請求項５の発明は、請求項２又は４の発明
において、前記軸受および減速機をモデル化した前記６
自由度を持つばねの取り付け位置や、前記軸受の曲げ剛
性および減速機のねじり剛性の値として該軸受および減
速機の寸法および使用される材料に定められた物性値を
用いたので、請求項１と同じ効果がより簡易に得られ
る。According to a fifth aspect of the present invention, in the second or fourth aspect of the present invention, the bearing and the speed reducer are modeled as the sixth aspect.
The physical property value determined by the size of the bearing and the speed reducer and the material used as the bending rigidity of the bearing and the torsional rigidity of the speed reducer are used. The same effect as can be obtained more easily.
【図１】 本発明による振動解析法の実施の形態を説明
するための機械構造物の一例を示す図である。FIG. 1 is a diagram showing an example of a mechanical structure for explaining an embodiment of a vibration analysis method according to the present invention.
【図２】 本発明による振動解析法の実施の形態に係る
軸受のモデル例を説明するための図である。FIG. 2 is a diagram for explaining an example of a bearing model according to an embodiment of a vibration analysis method according to the present invention.
【図３】 本発明による振動解析法の実施の形態に係る
減速機のモデル例を説明するための図である。FIG. 3 is a diagram for explaining a model example of a speed reducer according to an embodiment of a vibration analysis method according to the present invention.
【図４】 図２（Ｂ）に示した６自由度をもつモデル化
されたばねをもつ軸受の自由度を説明するための図であ
る。FIG. 4 is a diagram for explaining the degrees of freedom of a bearing having a modeled spring having six degrees of freedom shown in FIG. 2 (B).
【図５】 図３（Ｂ）に示した６自由度をもつモデル化
されたばねをもつ減速機の自由度を説明するための図で
ある。FIG. 5 is a diagram for explaining the degrees of freedom of the speed reducer having a modeled spring having six degrees of freedom shown in FIG. 3 (B).
【図６】 請求項１乃至５の何れかに記載の振動解析法
による機械構造物としてのロボットアームの実施例を説
明するための図である。FIG. 6 is a diagram for explaining an embodiment of a robot arm as a mechanical structure by the vibration analysis method according to any one of claims 1 to 5.
１…構造物１、２…構造物２、３…結合部（軸受、減速
機）、４…支持部、５…軸受、６，７，８，９…６自由
度をもつばね、１０…減速機、１１…入力軸部、１２…
カップラー部、１３，１４，１５，１６，１７，１８，
１９，２０…６自由度をもつばね。DESCRIPTION OF SYMBOLS 1 ... Structure 1, 2 ... Structure 2, 3 ... Coupling part (bearing, speed reducer), 4 ... Support part, 5 ... Bearing, 6,7,8,9 ... Spring with 6 degrees of freedom, 10 ... Deceleration Machine, 11 ... Input shaft, 12 ...
Coupler part, 13, 14, 15, 16, 17, 18,
19, 20 ... Spring with 6 degrees of freedom.
Claims (5)
構造物の振動解析を有限要素法を用いて行う振動解析法
において、前記結合部に用いる前記軸受および減速機を
各々６自由度をもつばねでモデル化することを特徴とす
る振動解析法。1. A vibration analysis method for performing vibration analysis of a mechanical structure using a bearing and a speed reducer in a joint using a finite element method, wherein each of the bearing and the speed reducer used in the joint has 6 degrees of freedom. A vibration analysis method characterized by modeling with a spring.
持つばねの取り付け位置を、該軸受内径の円周上に角度
９０度ごとに定めた４点とし、前記減速機をモデル化し
た前記６自由度を持つばねの取り付け位置を、該減速機
の軸径の円周上に角度９０度ごとに定めた４点、及び、
該減速機のカップラー外径の円周上に角度９０度ごとに
定めた４点の計８点にすることを特徴とする請求項１に
記載の振動解析法。2. A modeled model of the speed reducer is provided with four mounting positions of a spring having the six degrees of freedom modeling the bearing, which are defined at every 90 degrees on the circumference of the bearing inner diameter. Four mounting positions of springs having six degrees of freedom are defined on the circumference of the shaft diameter of the speed reducer at every 90 degrees, and
The vibration analysis method according to claim 1, wherein a total of 8 points, that is, 4 points determined at every 90 ° angle, are provided on the circumference of the coupler outer diameter of the speed reducer.
ばねは、縦方向の並進と横方向周りの回転の自由度を２
つ持ち、前記減速機をモデル化した６自由度を持つばね
は、横方向の２つの並進と縦方向周りの回転の自由度を
持つことを特徴とする請求項１に記載の振動解析法。3. A spring having 6 degrees of freedom that models the bearing has two degrees of freedom of longitudinal translation and lateral rotation.
2. The vibration analysis method according to claim 1, wherein the spring having 6 degrees of freedom, which has a model of the speed reducer and has two degrees of freedom of translation in a lateral direction and rotation in a longitudinal direction.
自由度を持つばねの縦、横方向の並進のばね定数には剛
結合とする値を、３方向の回転のばね定数には、該軸受
の曲げ剛性、および、前記減速機のねじり剛性の値をも
つことを特徴とする請求項２又は３に記載の振動解析
法。4. The bearing and reduction gear modeled 6
The longitudinal and lateral translational spring constants of the spring having a degree of freedom are rigidly coupled, the three-directional rotation spring constants are the flexural rigidity of the bearing, and the torsional rigidity of the speed reducer. The vibration analysis method according to claim 2 or 3, wherein
記６自由度を持つばねの取り付け位置や、前記軸受の曲
げ剛性および減速機のねじり剛性の値として該軸受およ
び減速機の寸法および使用される材料に定められた物性
値を用いることを特徴とする請求項２又は４に記載の振
動解析法。5. The dimensions of the bearing and the speed reducer are used as the mounting position of the spring having the 6 degrees of freedom that models the bearing and the speed reducer, and the bending rigidity of the bearing and the torsional rigidity of the speed reducer. The vibration analysis method according to claim 2 or 4, wherein the physical property values defined for the material are used.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP8000386A JPH09189601A (en) | 1996-01-08 | 1996-01-08 | Vibration analyzing method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP8000386A JPH09189601A (en) | 1996-01-08 | 1996-01-08 | Vibration analyzing method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPH09189601A true JPH09189601A (en) | 1997-07-22 |
Family
ID=11472374
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP8000386A Pending JPH09189601A (en) | 1996-01-08 | 1996-01-08 | Vibration analyzing method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH09189601A (en) |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2008128742A (en) * | 2006-11-17 | 2008-06-05 | Toyota Central R&D Labs Inc | Apparatus and method for analyzing vibration in rotating structure |
| JP2008250410A (en) * | 2007-03-29 | 2008-10-16 | Toyota Motor Corp | Method for analyzing strength of fastened structure |
| JP2010217110A (en) * | 2009-03-18 | 2010-09-30 | Toyota Motor Corp | Method for creating drive shaft assy model |
| JP2011198073A (en) * | 2010-03-19 | 2011-10-06 | Nsk Ltd | Modelling method, analysis method, modelling system, and analysis system for rolling bearing |
| JP2015052823A (en) * | 2013-09-05 | 2015-03-19 | Ntn株式会社 | Calculation service method/device of bearing characteristic and user terminal |
| CN110795876A (en) * | 2019-10-23 | 2020-02-14 | 珠海格力智能装备有限公司 | Method for establishing finite element equivalent model of speed reducer |
-
1996
- 1996-01-08 JP JP8000386A patent/JPH09189601A/en active Pending
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2008128742A (en) * | 2006-11-17 | 2008-06-05 | Toyota Central R&D Labs Inc | Apparatus and method for analyzing vibration in rotating structure |
| JP2008250410A (en) * | 2007-03-29 | 2008-10-16 | Toyota Motor Corp | Method for analyzing strength of fastened structure |
| JP2010217110A (en) * | 2009-03-18 | 2010-09-30 | Toyota Motor Corp | Method for creating drive shaft assy model |
| JP2011198073A (en) * | 2010-03-19 | 2011-10-06 | Nsk Ltd | Modelling method, analysis method, modelling system, and analysis system for rolling bearing |
| JP2015052823A (en) * | 2013-09-05 | 2015-03-19 | Ntn株式会社 | Calculation service method/device of bearing characteristic and user terminal |
| CN110795876A (en) * | 2019-10-23 | 2020-02-14 | 珠海格力智能装备有限公司 | Method for establishing finite element equivalent model of speed reducer |
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