JP2008250410A - Method for analyzing strength of fastened structure - Google Patents
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本発明は、締結構造体の強度解析方法に関し、さらに詳しくは、おねじ部材とめねじ部材とを締結してなる締結構造体の強度を解析する方法に関するものである。 The present invention relates to a fastening structure strength analysis method, and more particularly to a method of analyzing the strength of a fastening structure formed by fastening a male screw member and a female screw member.
例えばボルトなどのおねじ部材をナットなどのめねじ部材と締結してなる締結構造体において、その応力、ひずみ、変形などから強度を解析するために、従来から有限要素法(FEM)に基づいてプログラムされたFEM解析ソフトウエアを一般に使用している(たとえば特許文献1を参照)。有限要素法による解析では、締結構造体をモデル化して節点によって複数の要素に分割したメッシュを仮想し、各メッシュ毎に方程式を作ってこれをもとに全体としての方程式を組み立てて計算を行っている。 For example, in a fastening structure in which a male screw member such as a bolt is fastened to a female screw member such as a nut, in order to analyze the strength from the stress, strain, deformation, etc., based on the conventional finite element method (FEM) Programmed FEM analysis software is generally used (see, for example, Patent Document 1). In the analysis by the finite element method, a fastening structure is modeled and a mesh divided into multiple elements by nodes is hypothesized, an equation is created for each mesh, and the equation as a whole is assembled and calculated. ing.
このような有限要素法を用いて締結構造体の強度を解析するに際しては、図16に示すように、応力が集中するおねじ部材1とめねじ部材2の互いに接触するねじ山付近を特に詳細なメッシュに分割している。そして、従来では一般に、FEM解析ソフトウエアを用いて締結構造体の強度を解析するに際して、メッシュの節点毎におねじ部材1とめねじ部材2との互いのねじ山の接触を定義して、接触部位に生じる応力などを各節点毎に計算する必要があった。また、有限要素法による締結構造体の強度解析においては、図17に示すように、締結する際に発生する応力が時間の経過と比例して増加せず、応力の変化を線形として計算することができないことから非線形として扱い、線形として扱える区間に区切って、線形として近似させて計算を区切られた区間毎に反復して行って解析していた。 When analyzing the strength of the fastening structure using such a finite element method, as shown in FIG. 16, the vicinity of the thread where the stress-concentrated male screw member 1 and female screw member 2 contact each other is particularly detailed. It is divided into meshes. Conventionally, generally, when analyzing the strength of the fastening structure using FEM analysis software, the contact of the thread members of the screw member 1 and the female screw member 2 is defined for each node of the mesh. It was necessary to calculate the stress generated in the part for each node. Further, in the strength analysis of the fastening structure by the finite element method, as shown in FIG. 17, the stress generated during fastening does not increase in proportion to the passage of time, and the change in stress is calculated as linear. Therefore, it was treated as non-linear, divided into sections that could be treated as linear, approximated as linear, and the calculation was repeated for each section that was divided and analyzed.
上述したように、従来の技術では、FEM解析ソフトウエアを用いて締結構造体の強度を解析するに際して、メッシュの節点毎におねじ部材とめねじ部材との互いのねじ山の接触を繰返し定義し、さらに、各節点毎に接触部位に生じる応力を計算する必要があるため、解析のための処理が煩雑で手間がかかり、解析に時間がかかるという問題があった。 As described above, in the conventional technology, when analyzing the strength of the fastening structure using the FEM analysis software, the contact between the thread members of the screw member and the female screw member is repeatedly defined for each node of the mesh. Furthermore, since it is necessary to calculate the stress generated at the contact portion for each node, there is a problem that the processing for analysis is complicated and time-consuming, and the analysis takes time.
また、従来の有限要素法による締結構造体の強度解析においては、図17に示したように、非線形として扱うために反復して計算を行う必要があることから、解析に時間がかかるという問題があった。 Further, in the strength analysis of the fastening structure by the conventional finite element method, as shown in FIG. 17, since it is necessary to repeatedly perform the calculation in order to treat it as non-linear, there is a problem that the analysis takes time. there were.
本発明は、上述した問題に鑑みてなされたもので、簡単な構成で、短時間で容易に締結構造体の強度解析を行うことができる方法を提供することを目的とする。 The present invention has been made in view of the above-described problems, and an object of the present invention is to provide a method capable of easily analyzing the strength of a fastening structure in a short time with a simple configuration.
上記の課題を解決するために、本発明は、おねじ部材とめねじ部材とを締結してなる締結構造体の強度を解析する方法であって、おねじ部材とめねじ部材の接触部位が受ける応力と等価なバネに置き換えて、強度の解析に必要な計算を行うことを特徴とするものである。 In order to solve the above-described problem, the present invention is a method for analyzing the strength of a fastening structure formed by fastening a male screw member and a female screw member, and a stress that is applied to a contact portion between the male screw member and the female screw member. It is characterized in that the calculation necessary for the strength analysis is performed instead of a spring equivalent to.
本発明によれば、おねじ部材とめねじ部材の接触部位が受ける応力と等価なバネに置き換えることにより、従来の技術のように非線形として扱うために計算を反復して行う必要がなく、線形として扱うことができるため、強度の解析に必要な計算にかかる時間を短縮することができ、しかも容易に解析を行うことができる。 According to the present invention, by replacing with a spring equivalent to the stress received by the contact portion of the male screw member and the female screw member, it is not necessary to repeat the calculation to treat it as non-linear as in the prior art, and as a linear Since it can be handled, the time required for the calculation required for the strength analysis can be shortened, and the analysis can be easily performed.
(発明の態様)
以下に、本願において特許請求が可能と認識されている発明(以下、「請求可能発明」という場合がある。請求可能発明は、少なくとも、請求の範囲に記載された発明である「本発明」ないし「本願発明」を含むが、本願発明の下位概念発明や、本願発明の上位概念あるいは別概念の発明を含むこともある。)の態様をいくつか例示し、それらについて説明する。各態様は請求項と同様に、項に区分し、各項に番号を付し、必要に応じて他の項の番号を引用する形式で記載する。これは、あくまでも請求可能発明の理解を容易にするためであり、請求可能発明を構成する構成要素の組み合わせを、以下の各項に記載されたものに限定する趣旨ではない。つまり、請求可能発明は、各項に付随する記載,実施例の記載等を参酌して解釈されるべきであり、その解釈に従う限りにおいて、各項の態様にさらに他の構成要素を付加した態様も、また、各項の態様から構成要素を削除した態様も、請求可能発明の一態様となり得るのである。なお、以下の各項において、(1)項が請求項1に相当し、(2)項が請求項2に相当する。
(Aspect of the Invention)
In the following, the invention that is claimed to be claimable in the present application (hereinafter referred to as “claimable invention”. The claimable invention is at least the “present invention” to the invention described in the claims. Some aspects of the present invention, including subordinate concept inventions of the present invention, superordinate concepts of the present invention, or inventions of different concepts) will be illustrated and described. As with the claims, each aspect is divided into sections, each section is numbered, and is described in a form that cites the numbers of other sections as necessary. This is for the purpose of facilitating the understanding of the claimable invention, and is not intended to limit the combinations of the constituent elements constituting the claimable invention to those described in the following sections. In other words, the claimable invention should be construed in consideration of the description accompanying each section, the description of the embodiments, etc., and as long as the interpretation is followed, another aspect is added to the form of each section. In addition, an aspect in which constituent elements are deleted from the aspect of each item can be an aspect of the claimable invention. In each of the following items, item (1) corresponds to claim 1 and item (2) corresponds to claim 2.
(1) おねじ部材とめねじ部材とを締結してなる締結構造体の強度を解析する方法であって、
おねじ部材とめねじ部材の接触部位が受ける応力と等価なバネに置き換えて、強度の解析に必要な計算を行うことを特徴とする締結構造体の強度解析方法。
(1) A method for analyzing the strength of a fastening structure formed by fastening a male screw member and a female screw member,
A strength analysis method for a fastening structure, wherein a calculation necessary for strength analysis is performed by replacing a spring equivalent to a stress received by a contact portion of a male screw member and a female screw member.
(1)項に記載の発明では、おねじ部材とめねじ部材の接触部位が受ける応力と等価なバネに置き換える。バネの解析は、線形として扱うことができるため、従来の技術のように非線形として扱うために計算を反復して行う必要がなく、強度の解析に必要な計算を短時間で容易に行うことができる。 In the invention described in item (1), the spring is replaced with a spring equivalent to the stress received by the contact portion between the male screw member and the female screw member. Since spring analysis can be handled as linear, there is no need to repeat calculations to handle them as non-linear as in the prior art, and calculations required for strength analysis can be easily performed in a short time. it can.
(2) おねじ部材とめねじ部材の接触部位における節点の径方向、周方向、および垂直方向に作用するバネを定義して、各バネのバネ定数に基づいて強度の解析に必要な計算を行うことを特徴とする(1)項に記載の締結構造体の強度解析方法。 (2) Define springs that act in the radial, circumferential, and vertical directions of the nodes at the contact portion of the male screw member and female screw member, and perform calculations necessary for strength analysis based on the spring constant of each spring The strength analysis method for a fastening structure according to item (1), wherein:
(2)項に記載の発明では、(1)に記載の発明において、おねじ部材とめねじ部材の接触部位における節点の径方向、周方向、および垂直方向に作用するバネを仮想して、各仮想されたバネの接触部位が受ける応力と等価なバネ定数を求める。おねじ部材とめねじ部材の接触部位が受ける応力と等価なバネ定数のバネを定義するため、おねじ部材とめねじ部材の接触部位が受ける応力を容易に把握して、おねじ部材とめねじ部材とを締結してなる締結構造体の強度を解析することができる。 In the invention described in item (2), in the invention described in item (1), each of the springs acting in the radial direction, circumferential direction, and vertical direction of the node at the contact portion between the male screw member and the female screw member is virtually assumed. A spring constant equivalent to the stress experienced by the virtual contacted part of the spring is obtained. In order to define a spring with a spring constant equivalent to the stress received by the contact part of the male screw member and the female screw member, the stress received by the contact part of the male screw member and the female screw member can be easily grasped, It is possible to analyze the strength of a fastening structure formed by fastening the.
本発明の実施の一形態を図1〜図15に基づいて詳細に説明する。図において同じ符号は、同様または相当する部分を示すものとする。
本発明は、概略、おねじ部材1とめねじ部材2とを締結してなる締結構造体の強度を解析する方法であって、おねじ部材1とめねじ部材2のねじ山の接触部位における節点の径方向、周方向、および垂直方向に作用するバネを仮想し、各仮想されたバネの、接触部位が受ける応力と等価なバネ定数kr、kθ、knを求めて定義し、接触部位が受ける応力を前記バネに置き換えて、強度の解析に必要な計算を行うものである。
An embodiment of the present invention will be described in detail with reference to FIGS. In the drawings, the same reference numerals denote the same or corresponding parts.
The present invention is generally a method for analyzing the strength of a fastening structure formed by fastening a male screw member 1 and a female screw member 2, and is a method of analyzing the nodes at the contact points of the threads of the male screw member 1 and the female screw member 2. The stress acting on the contact part is defined by obtaining spring constants kr, kθ, kn equivalent to the stresses of the contact parts of the hypothetical springs acting in the radial, circumferential and vertical directions. Is replaced with the spring to perform calculations necessary for strength analysis.
図1は、本発明の方法による手順の実施の一形態全体を示したブロック図である。おねじ部材1とめねじ部材2とを締結してなる締結構造体の強度を解析するにあたり、準備として、図3および図8に示すようにおねじ部材であるボルト1のメッシュ(計算モデル)を作成するとともに、図2に示すようにボルト1を締結するめねじが形成された治具2のメッシュ(計算モデル)を作成して、ボルト1と治具2のメッシュにおいて互いのねじ山の接触を定義する(図1のS1)。なお、ボルト1と治具2のねじ山は、実際には螺旋状に形成されているが、図8などに示された実施の形態におけるメッシュでは複数の環状に形成された形状のメッシュに簡略化されている。このように簡略化することは、有限要素法による解析では一般的に行われている事項である。 FIG. 1 is a block diagram showing an overall embodiment of a procedure according to the method of the present invention. In analyzing the strength of a fastening structure formed by fastening the male screw member 1 and the female screw member 2, as a preparation, as shown in FIGS. 3 and 8, a mesh (calculation model) of the bolt 1 which is a screw member is used. As shown in FIG. 2, a mesh (calculation model) of the jig 2 on which the female screw for fastening the bolt 1 is formed as shown in FIG. 2 is created, and the threads of the bolt 1 and the jig 2 are brought into contact with each other. Define (S1 in FIG. 1). In addition, although the thread of the bolt 1 and the jig 2 is actually formed in a spiral shape, the mesh in the embodiment shown in FIG. 8 and the like is simplified to a mesh having a plurality of annular shapes. It has become. Such simplification is a common practice in analysis by the finite element method.
次いで、図4に示すようにボルト1のメッシュに軸力Fを与える計算を実施して(図1のS2)、図5に示すようにねじ山の接触面に沿った径方向の摩擦力Frと滑り量(変位量)δrを求め(図1のS3)、また、図6に示すようにボルト1のメッシュにトルクTを与える計算を実施して(図1のS2)、図7に示すようにボルト1と治具2とのねじ山の接触面に沿った周方向の摩擦力Fθと滑り量(変位量)δθを求める(図1のS3)。これらの径方向の摩擦力Frと滑り量δr、および、周方向の摩擦力Fθと滑り量δθは、FEM解析ソフトウエアの数値解析を用いて、仮想仕事の原理に基づいた計算により求めることができる。 Next, a calculation for applying an axial force F to the mesh of the bolt 1 as shown in FIG. 4 (S2 in FIG. 1) is performed, and a radial frictional force Fr along the contact surface of the thread as shown in FIG. And a slip amount (displacement amount) δr are obtained (S3 in FIG. 1), and calculation is performed to give torque T to the mesh of the bolt 1 as shown in FIG. 6 (S2 in FIG. 1), as shown in FIG. Thus, the circumferential frictional force Fθ and the slip amount (displacement amount) δθ along the contact surface of the screw thread between the bolt 1 and the jig 2 are obtained (S3 in FIG. 1). These radial friction force Fr and slip amount δr, and circumferential friction force Fθ and slip amount δθ can be obtained by calculation based on the principle of virtual work using numerical analysis of FEM analysis software. it can.
続いて、径方向の摩擦力Frと滑り量δrの比から径方向の定数krを求めるとともに(kr=Fr/δr)、周方向の摩擦力Fθと滑り量δθの比から周方向の定数kθを求め(kθ=Fθ/δθ)、また、ねじ山に垂直な方向の定数knを後述するように求める(図1のS4)。なお、図1におけるS1〜S4の工程は、従来の技術における有限要素法によるFEM解析ソフトウエアを用いた解析の工程と同様ではあるが、従来の技術では接触の定義や接触部位に生じる応力の計算を節点毎に繰返し行う必要があったのに対して、本発明を実施するための準備として一度行うだけにすぎない点で異なる。 Subsequently, a radial constant kr is obtained from the ratio of the radial friction force Fr and the slip amount δr (kr = Fr / δr), and the circumferential constant kθ is calculated from the ratio of the circumferential friction force Fθ and the slip amount δθ. (Kθ = Fθ / δθ) and a constant kn in a direction perpendicular to the thread is obtained as described later (S4 in FIG. 1). In addition, although the process of S1-S4 in FIG. 1 is the same as the process of the analysis using the FEM analysis software by the finite element method in the prior art, in the prior art, the definition of contact and the stress generated in the contact site While the calculation had to be repeated at every node, it differs in that it was only performed once in preparation for carrying out the present invention.
次に、図9〜図12に示すように、ボルト1のおねじと治具2のめねじとの接触部位の間における節点の、接触面の径方向と周方向と垂直方向との3方向にそれぞれ作用するものと仮想されるバネを定義する(図1のS5)。径方向のバネにはその定数として先に計算されたkrを適用し、周方向のバネにはその定数として先に計算されたkθを適用する。また、接触面に対して垂直方向に仮想されたバネの定数knは、おねじとめねじのねじ山の互いの接触面は離れることがないものと考えられるので、充分に大きい値、たとえば1010[N/m]などを設定する(図1のS6)。そして、これらの節点毎にそれぞれ定義された3方向のバネは、例えば図13に示すように、バネ定義の宣言、定義するバネの名前、定義するバネの座標系、バネ力が作用する方向、およびバネ定数が、汎用のFEM解析ソフトウエア(たとえば、商品名ABAQUS)におけるバネの解析プログラムに自動または手動でそれぞれ入力される。 Next, as shown in FIGS. 9 to 12, the three nodes in the radial direction of the contact surface, the circumferential direction, and the vertical direction at the nodes between the contact portions of the male screw 1 of the bolt 1 and the female screw of the jig 2. A spring that is supposed to act on each of these is defined (S5 in FIG. 1). The previously calculated kr as the constant is applied to the radial spring, and the previously calculated kθ is applied to the circumferential spring as the constant. Further, the constant kn of the spring imaginary in the direction perpendicular to the contact surface is considered to be a sufficiently large value, for example, 10 10 , because the contact surfaces of the threads of the male screw and the female screw are not separated from each other. [N / m] and the like are set (S6 in FIG. 1). The three-direction springs defined for each of these nodes are, for example, as shown in FIG. 13, a declaration of the spring definition, the name of the spring to be defined, the coordinate system of the spring to be defined, the direction in which the spring force acts, And the spring constant are automatically or manually input into a spring analysis program in general-purpose FEM analysis software (for example, trade name ABAQUS).
次に、FEM解析ソフトウエアのプログラムが実際に従来と同様に有限要素法による解析を誤って行うことがないように、先の工程(図1のS1)で定義されたボルト1と治具2のメッシュにおける互いのねじ山の接触定義を削除する(図1のS7)。 Next, the bolt 1 and jig 2 defined in the previous step (S1 in FIG. 1) are used so that the FEM analysis software program does not actually perform the analysis by the finite element method in the same manner as in the past. 1 is deleted (S7 in FIG. 1).
その後、実際に応力を評価したい各種条件(たとえば図14に示した引張の他に、締結、捩り、曲げ等)での計算を実施して強度の解析を行う(図1のS8)。この強度の解析には、上述した各種条件をシミュレートして求められた応力、ひずみ、変形などに基づいて評価することができる。 After that, the strength is analyzed by performing calculation under various conditions (for example, fastening, twisting, bending, etc. in addition to the tension shown in FIG. 14) for which stress is actually evaluated (S8 in FIG. 1). This strength analysis can be evaluated based on stress, strain, deformation, and the like obtained by simulating the various conditions described above.
本発明では、図1のS4で求められた節点における径方向および周方向の定数を仮想定義したバネの定数として使用するため、おねじ部材1とめねじ部材2のねじ山の接触部位が受ける応力と等価なバネに置き換えて線形計算することができる。そのため、従来の非線形計算のような反復計算を行う必要がないことから、計算回数を削減することができ、よって、図15に比較して示すように、線形計算を行うことができる本発明によれば、従来の非線形計算と比べて、解析に要する時間を例えば3分の2程度にまで短縮することができる。 In the present invention, since the radial and circumferential constants obtained at S4 in FIG. 1 are used as spring constants that are virtually defined, the stress experienced by the contact portion of the thread of the male screw member 1 and female screw member 2 It is possible to perform a linear calculation by replacing with a spring equivalent to. Therefore, since it is not necessary to perform iterative calculation as in the conventional non-linear calculation, the number of calculations can be reduced. Therefore, as shown in comparison with FIG. 15, the present invention is capable of performing linear calculation. Therefore, compared with the conventional nonlinear calculation, the time required for the analysis can be shortened to, for example, about two thirds.
1:ボルト(おねじ部材)、 2:治具(めねじ部材)、 kr:径方向のバネ定数、 kθ:周方向のバネ定数、 kn:ねじ山に垂直な方向のバネ定数
1: Bolt (male thread member) 2: Jig (female thread member), kr: Spring constant in the radial direction, kθ: Spring constant in the circumferential direction, kn: Spring constant in the direction perpendicular to the thread
Claims (2)
おねじ部材とめねじ部材の接触部位が受ける応力と等価なバネに置き換えて、強度の解析に必要な計算を行うことを特徴とする締結構造体の強度解析方法。 A method of analyzing the strength of a fastening structure formed by fastening a male screw member and a female screw member,
A strength analysis method for a fastening structure, wherein a calculation necessary for strength analysis is performed by replacing a spring equivalent to a stress received by a contact portion of a male screw member and a female screw member.
The springs acting in the radial direction, the circumferential direction, and the vertical direction at the contact portion between the male screw member and the female screw member are defined, and calculations necessary for strength analysis are performed based on the spring constant of each spring. The strength analysis method of the fastening structure according to claim 1.
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CN114357818A (en) * | 2021-11-22 | 2022-04-15 | 西安热工研究院有限公司 | Method for checking strength of T-shaped nut at blade root of wind generating set |
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