JP2010052019A - Simulation method for sand mold casting - Google Patents

Simulation method for sand mold casting Download PDF

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JP2010052019A
JP2010052019A JP2008220321A JP2008220321A JP2010052019A JP 2010052019 A JP2010052019 A JP 2010052019A JP 2008220321 A JP2008220321 A JP 2008220321A JP 2008220321 A JP2008220321 A JP 2008220321A JP 2010052019 A JP2010052019 A JP 2010052019A
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casting
mold
temperature
analysis
sand
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Akira Yoshizawa
亮 吉沢
Rin O
麟 王
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Proterial Ltd
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Hitachi Metals Ltd
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Abstract

<P>PROBLEM TO BE SOLVED: To obtain a simulation method for sand mold casting where, when a casting composed of a cast steel or a cast iron is obtained by sand mold casting, at least one selected from strain, displacement and stress can be analyzed at high precision. <P>SOLUTION: The simulation method for sand mold casting includes: a factor-creation step where an analysis model at least composed of a casting factor and a mold factor is created; a thermal conduction analyzing step (S3) where the thermal conduction of the casting factor and the mold factor is analyzed with the lapse of time to obtain the temperature of the casting element and the mold element; and a thermal deformation analyzing step (S4) including a constriction condition set step (S41) where, based on the temperature of the mold factor obtained by the thermal conduction analysis step (S3), the constriction conditions of the casting by the mold are set and an elastoplasticity analyzing step (S42) where, based on the set constriction conditions, the temperature variation and thermal expansion coefficient of the casting factor, the deformation of the casting factor is analyzed with the lapse of time, and at least one selected from the strain, displacement and stress of the casting factor is obtained. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

本発明は、砂型鋳物のシミュレーション方法に関し、詳しくは、例えば、鋳鉄や鋳鋼からなる鋳物を砂型鋳造で得る際に、鋳物に生じる歪み、変位又は応力の少なくとも１つを求める砂型鋳物のシミュレーション方法に関する。   The present invention relates to a sand mold casting simulation method, and more particularly, to a sand mold casting simulation method for obtaining at least one of distortion, displacement or stress generated in a casting when a casting made of cast iron or cast steel is obtained by sand casting. .

鋳物の製造にあたっては、引け巣や湯境等の湯流れや凝固に起因する鋳造欠陥はもとより、鋳造時に発生する変形、寸法不良、きれ、割れ等の鋳造欠陥を抑制することが課題となる。変形、寸法不良、きれ、割れ等は、鋳造時に鋳物各部に生じる歪み（内部歪み、永久歪み、塑性歪みなど）、変位又は応力に起因して発生する。歪み、変位又は応力は、鋳造時に鋳物各部の冷却速度の違いにより生じる不均一な温度分布と、これによる不均一な熱膨脹及び熱収縮によって生じる。また、歪み、変位又は応力は、鋳型による鋳物の拘束の状態によって、その発生の程度に影響を受ける。なお、鋳型による鋳物の拘束とは、鋳物に生じる歪みや変位によって、鋳物が鋳型のキャビティの内壁面を越えて移動することを規制することを意味する。   In the production of castings, it is a challenge to suppress casting defects such as deformation, dimensional defects, cracks, and cracks that occur during casting, as well as casting defects caused by flow and solidification of shrinkage cavities and hot water boundaries. Deformation, dimensional defects, cracks, cracks, etc. occur due to strain (internal strain, permanent strain, plastic strain, etc.), displacement or stress generated in each part of the casting during casting. Strain, displacement or stress is caused by non-uniform temperature distribution caused by differences in cooling rate of each part of the casting at the time of casting, and non-uniform thermal expansion and contraction caused thereby. Further, strain, displacement, or stress is affected by the degree of generation depending on the state of restraint of the casting by the mold. The restriction of the casting by the mold means that the casting is restricted from moving beyond the inner wall surface of the cavity of the mold due to distortion or displacement generated in the casting.

従来は、鋳物に鋳造欠陥として変形、寸法不良、きれ、割れ等が発生すると、これを対策するために、例えば、鋳造用模型や鋳造方案の修正、発生した変形や寸法不良の矯正などの施策を経験や実験に基づいて試行錯誤を繰り返して実施するとういう方法が採られていた。したがって変形、寸法不良、きれ、割れ等の鋳造欠陥を対策するには、再鋳造や再検査に労力を要し、工数とコストが費やされるという問題があった。   Conventionally, when deformation, dimensional defects, cracks, cracks, etc. occur as casting defects in castings, measures such as correction of casting models and casting plans, correction of generated deformations and dimensional defects, etc. are taken as countermeasures. The method of repeating trial and error based on experience and experiment was adopted. Therefore, in order to deal with casting defects such as deformation, dimensional defects, cracks, and cracks, there is a problem that labor is required for re-casting and re-inspection, and man-hours and costs are consumed.

近年では、鋳造の設計段階において、ＣＡＥ（Ｃｏｍｐｕｔｅｒ Ａｉｄｅｄ Ｅｎｇｉｎｅｅｒｉｎｇ）により、湯流れ解析や凝固解析を行って、事前に、鋳造に最適な鋳造方案を得て、引け巣や湯境の発生を予知、防止することが行われてきている。一方、鋳造時に発生する変形、寸法不良、きれ、割れ等は、引け巣や湯境と同様に鋳造時に留意すべき課題であるにも関わらず、これらの現象を設計段階で事前に解析する手法はほとんど存在せず、一部存在する解析手法も実際の鋳物に生じる歪み、変位又は応力の予測として一層の解析精度の向上が求められている。   In recent years, at the casting design stage, CAE (Computer Aided Engineering) is used to perform molten metal flow analysis and solidification analysis to obtain an optimal casting method for casting in advance and predict the occurrence of shrinkage nests and molten metal boundaries. Prevention has been done. On the other hand, although deformation, dimensional defects, cracks, cracks, etc. that occur during casting are issues that should be noted during casting, as with shrinkage cavities and hot water boundaries, these phenomena are analyzed in advance at the design stage. However, there is a need for further improvement in analysis accuracy as a prediction of strain, displacement or stress generated in actual castings.

例えば、特許文献１には、ダイカスト鋳造により得られた鋳物に存在する残留歪及び残留応力を予測するダイカストシミュレーション方法として、鋳型要素、鋳物要素、および加圧要素としての微小要素に分割する要素作成ステップと、熱的特性値に基づいて鋳物要素の温度と固相率を求める凝固解析ステップと、鋳物要素の機械的特性値を求めると共に、加圧要素によって鋳物要素に加圧力を付加し、加圧力と機械的特性値とを基にして、鋳物要素の歪み、変位及び応力を求める途中応力解析ステップと、鋳物要素の全てが固相になった後に熱的特性値に基づいて鋳物要素の温度を求める冷却解析ステップと、途中応力解析ステップにおいて得られた鋳物要素の歪み、変位および応力を初期値として用い、鋳物要素の歪み、変位及び応力を求める熱応力解析ステップとを有する、解析技術を開示している。   For example, in Patent Document 1, as a die casting simulation method for predicting residual strain and residual stress existing in a casting obtained by die casting, an element creation that is divided into a mold element, a casting element, and a minute element as a pressure element A solidification analysis step for determining the temperature and solid phase ratio of the casting element based on the step, the thermal characteristic value, the mechanical characteristic value of the casting element, and applying pressure to the casting element by the pressurizing element. An intermediate stress analysis step for determining the distortion, displacement and stress of the casting element based on the pressure and the mechanical characteristic value, and the temperature of the casting element based on the thermal characteristic value after all of the casting element is in solid phase. The distortion, displacement and stress of the casting element obtained in the cooling analysis step and the stress analysis step in the middle are used as initial values to determine the distortion, displacement and stress of the casting element. And a Mel thermal stress analysis step, discloses an analysis technique.

この特許文献１のシミュレーション方法によれば、凝固途中における各鋳物要素の歪み、変位及び応力を得て、これに積み重ねるように凝固後における各鋳物要素の歪み、変位及び応力を求めることで、残留歪みおよび残留応力の小さい鋳物を設計することができるとしている。   According to the simulation method of Patent Document 1, the distortion, displacement, and stress of each casting element during solidification are obtained, and the distortion, displacement, and stress of each casting element after solidification are obtained so as to be stacked on this, It is said that castings with low strain and residual stress can be designed.

また、非特許文献１には、「砂型鋳鉄鋳物に発生する残量応力のＦＥＭ解析」と題して、汎用の有限要素法（ＦＥＭ）解析による温度分布解析と残留応力解析により複雑形状の鋳鉄鋳物の残留応力分布を予測する解析手法を開示している。非特許文献１では、温度分布解析において、熱応力・熱変形解析に必要な温度分布は、鋳物−鋳型間を含めた熱解析（湯流れ時の溶湯温度変化を考虜した凝固解析）により求めるのではなく、熱電対により実測した鋳物の温度より推定して求めた温度分布を与えることにより考慮したとしている。また、残留応力解析においては、解析開始の初期条件として鋳物全体が弾性化する時期として、鋳物の最も冷却の遅い部位が弾性状態へ遷移する温度である共析変態温度以下の温度となった時期以降の温度変化について弾塑性応力解析を行ったとしている。また、鋳型の拘束については、通常解枠が共析変態温度付近で行われること、砂型のため拘束の影響が小さいと考えられるため解析の対象からはずしたとしている。   Also, Non-Patent Document 1, entitled “FEM Analysis of Residual Stress Generated in Sand Cast Iron Castings”, has a complex shape cast iron casting by temperature distribution analysis and residual stress analysis by general-purpose finite element method (FEM) analysis. An analysis method for predicting the residual stress distribution is disclosed. In Non-Patent Document 1, in the temperature distribution analysis, the temperature distribution required for thermal stress / deformation analysis is obtained by thermal analysis including between casting and mold (solidification analysis taking into account the change in molten metal temperature during molten metal flow). Instead, it is considered by giving a temperature distribution estimated and calculated from the temperature of a casting actually measured by a thermocouple. In the residual stress analysis, as the initial condition for starting the analysis, the time when the entire casting becomes elastic is the time when the slowest cooling part of the casting becomes a temperature below the eutectoid transformation temperature, which is the temperature at which the casting transitions to the elastic state. It is assumed that elasto-plastic stress analysis was performed for subsequent temperature changes. In addition, regarding the constraint of the mold, it is assumed that the solution is usually removed near the eutectoid transformation temperature.

非特許文献１によれば、開示した解析手法を実部品である砂型鋳造の鋳鉄製シリンダブロックに適用して解析値と実測値とを比較すると、絶対値的には残留応力の解析精度は低いものの、残留応力分布および鋳物形状や鋳造時の冷却条件など鋳造条件を変更した場合の残留応力の変化割合は解析と実測とで良く一致したとしている。   According to Non-Patent Document 1, when the disclosed analysis method is applied to a sand-cast cast iron cylinder block which is an actual part and the analysis value is compared with the actual measurement value, the analysis accuracy of the residual stress is low in absolute value. However, the residual stress distribution and the rate of change in residual stress when the casting conditions such as the casting shape and cooling conditions during casting are changed agree well between the analysis and the actual measurement.

特開２００６−２６７２３号公報JP 2006-26723 A 牧野浩、外３名、「鋳物」、社団法人日本鋳物協会、１９９１年１２月２５日、第６３巻、第１２号、ｐ．９５９−９６４Hiroshi Makino, 3 others, “Casting”, Japan Foundry Association, December 25, 1991, 63, 12, p. 959-964

しかしながら、従来提案されてきた鋳造時に発生する歪み、変位又は応力の解析方法では充分な解析精度が得られない場合があった。特に鋳造で用いる鋳型が金型の場合と砂型の場合とでは、鋳型による鋳物の拘束の状態が相違するため、実際の鋳物と解析とで発生する歪みや変位が乖離することがあった。   However, there has been a case where sufficient analysis accuracy cannot be obtained by the analysis method of strain, displacement, or stress generated during casting that has been conventionally proposed. In particular, when the mold used for casting is a mold and a sand mold, since the state of restraint of the casting by the mold is different, distortion and displacement generated between the actual casting and the analysis may be different.

例えば、アルミニウム合金などの鋳物を金型で鋳造する場合、金型では鋳物が室温に冷却されるまで、鋳型（金型）による鋳物の拘束の状態は変化しないと考えられる。したがって金型鋳造での歪み、変位又は応力を解析する場合には、拘束状態の変化を考慮することなく、例えば解析の開始から終了までの終始、鋳物が鋳型による拘束を受けた条件を設定して解析しても、解析と実際の鋳物とで得られた結果の乖離は小さく、解析精度への影響は少ない。   For example, when casting a casting such as an aluminum alloy with a mold, it is considered that the state of restraint of the casting by the mold (mold) does not change until the casting is cooled to room temperature. Therefore, when analyzing distortion, displacement, or stress in mold casting, the conditions under which the casting is constrained by the mold are set, for example, from the start to the end of the analysis without considering the change in the restraint state. Even if the analysis is performed, the difference between the result obtained by the analysis and the actual casting is small, and the influence on the analysis accuracy is small.

一方、砂型鋳造の場合、砂型が鋳物となる高温の溶湯に曝されると、砂粒同士を固着する粘結材が融解又は分解して鋳型強度が低下する。例えば、鋳鉄や鋳鋼の鋳造などで１３００℃以上の高温の溶湯を砂型からなる鋳型に注湯する場合には、鋳型に対する入熱量が多く鋳型強度の低下が大きいため、鋳物への拘束の状態が変化する。また、入熱により硬化する鋳型や、逆に入熱により崩壊し易い鋳型など、鋳型（砂型）の種類によって、鋳造時の鋳物への拘束の状態も変化する。例えば、崩壊性の良いシェル鋳型や、鋳造時に水分凝縮層を生成する生砂からなる鋳型（生型）は、注湯後、短時間で鋳型強度が低下して拘束が解放される。一方、フラン鋳型やＣＯ2鋳型は比較的高い強度と硬度を有し、注湯後、比較的長時間に亘って鋳型強度を保持して拘束を維持する。 On the other hand, in the case of sand mold casting, when the sand mold is exposed to a high-temperature molten metal that becomes a casting, the caking material that fixes the sand particles melts or decomposes, and the mold strength decreases. For example, when pouring a molten metal having a high temperature of 1300 ° C. or higher into a mold made of sand mold, such as in cast iron or cast steel, the amount of heat input to the mold is large and the mold strength is greatly reduced. Change. Further, the state of restraint on the casting at the time of casting also varies depending on the type of mold (sand mold) such as a mold that hardens by heat input and a mold that easily collapses by heat input. For example, a shell mold with good disintegration and a mold (green mold) made of green sand that forms a moisture condensed layer during casting, the mold strength decreases in a short time after pouring, and the constraint is released. On the other hand, furan molds and CO 2 molds have relatively high strength and hardness, and after casting, the mold strength is maintained for a relatively long time to maintain the restraint.

また、例えば、アルミニウム合金やマグネシウム合金など比重が小さく低融点の鋳物を、砂型からなる鋳型で鋳造する場合、鋳物から鋳型への入熱量が少なく鋳型の強度低下が小さいため、鋳物が室温に冷却されるまで鋳型はその強度を保持する。したがって、このような鋳物と鋳型の組み合せの場合には、例え鋳型が砂型であっても、金型と同様に、鋳物が鋳型による拘束を受けた状態が変化しない。   For example, when casting a low melting point casting such as an aluminum alloy or a magnesium alloy with a sand mold, the amount of heat input from the casting to the mold is small and the strength of the mold is small, so the casting is cooled to room temperature. The mold retains its strength until done. Therefore, in the case of such a combination of a casting and a mold, even if the mold is a sand mold, the state in which the casting is restrained by the mold does not change as in the case of the mold.

このように鋳造時の鋳型による鋳物の拘束の状態は、鋳型が金型と砂型とで相違し、また鋳型が砂型でもその種類によって、さらには鋳物と砂型との組み合せによっても相違する。従来、鋳型、特に砂型による鋳物の拘束条件まで考慮して鋳物の歪み、変位又は応力を解析する方法についての提案は見当たらない。   As described above, the state of restraint of the casting by the casting mold differs depending on whether the casting mold is a mold or a sand mold, and whether the casting mold is a sand mold or a combination of the casting and the sand mold. Conventionally, there has been no proposal for a method for analyzing distortion, displacement or stress of a casting in consideration of a constraint condition of a casting, particularly a casting by a sand mold.

特許文献１のダイカストシミュレーション方法は、鋳物に生じる歪み、変位及び応力を求める解析技術を開示しているが、鋳型はダイカスト、即ち金型であって、砂型鋳造の場合の鋳型による鋳物の拘束状態の変化について考慮されていないため、砂型鋳物に生じる歪み、変位又は応力の予測として十分な解析精度を得られない虞がある。   The die casting simulation method of Patent Document 1 discloses an analysis technique for obtaining distortion, displacement and stress generated in a casting, but the mold is a die casting, that is, a mold, and the restraint state of the casting by the mold in the case of sand casting. Therefore, there is a possibility that sufficient analysis accuracy cannot be obtained as a prediction of strain, displacement or stress generated in the sand casting.

非特許文献１の砂型鋳鉄鋳物に発生する残留応力のＦＥＭ解析では、熱応力・熱変形解析で必要な温度分布は、実測した数十点の鋳物の温度から推定して求めた温度分布を与えており、注湯から室温まで冷却する過程での温度分布と時間変化を湯流れ解析や凝固解析で計算していない。さらに非特許文献１では、鋳型の拘束については、砂型のため拘束の影響が小さいと考えられるため解析の対象からはずした、として鋳型が無い状態で弾塑性応力解析を行っており、鋳型による鋳物の拘束は解析に考慮されていない。   In the FEM analysis of residual stress generated in sand cast iron castings of Non-Patent Document 1, the temperature distribution required for thermal stress / thermal deformation analysis is the temperature distribution obtained by estimating from the temperature of several tens of castings actually measured. The temperature distribution and the time change during the process of cooling from the pouring to room temperature are not calculated by the hot water flow analysis or solidification analysis. Further, in Non-Patent Document 1, elasto-plastic stress analysis is performed in a state where there is no mold because the restriction of the mold is excluded from the analysis target because it is considered that the influence of the restriction is small due to the sand mold. This constraint is not considered in the analysis.

本発明の課題は、上記した実情に鑑みてなされたもので、例えば、鋳鉄や鋳鋼からなる鋳物を、砂型鋳造で得る際に、鋳物に生じる歪み、変位又は応力の少なくとも１つを、高精度に解析できる、砂型鋳物のシミュレーション方法を得ることにある。   An object of the present invention has been made in view of the above-described circumstances. For example, when a casting made of cast iron or cast steel is obtained by sand casting, at least one of distortion, displacement, or stress generated in the casting is highly accurate. It is to obtain a sand casting simulation method that can be analyzed easily.

本発明者らは、上記課題について鋭意研究した。その結果、実際の砂型鋳造では、一般に鋳型が溶湯と接触、加熱されて鋳型の形状を保持できなくなる点に着目して、砂型鋳物のシミュレーションにおいて、鋳型要素の温度に基づいて鋳型による鋳物の拘束条件を設定して熱変形解析することで、上記課題が解決できるとの知見を得て本発明に想到した。   The present inventors diligently studied on the above problems. As a result, in actual sand mold casting, focusing on the fact that the mold cannot keep its shape due to contact and heating with the molten metal, in the sand mold casting simulation, the mold is restrained by the mold based on the temperature of the mold element. The inventors have obtained the knowledge that the above problems can be solved by setting conditions and performing thermal deformation analysis, and have arrived at the present invention.

すなわち、本発明の砂型鋳物のシミュレーション方法は、少なくとも一部が砂型からなる鋳型内に溶湯を注入して凝固させることにより所望形状の鋳物を得る際に、鋳物に生じる歪み、変位又は応力の少なくとも１つを求める砂型鋳物のシミュレーション方法であって、少なくとも鋳物要素及び鋳型要素からなる解析モデルを作成する要素作成工程（Ｓ１）と、前記鋳物要素及び前記鋳型要素の伝熱を経時的に解析して、前記鋳物要素及び前記鋳型要素の温度を求める熱伝導解析工程（Ｓ３）と、前記熱伝導解析工程（Ｓ３）により得られた前記鋳型要素の温度に基づいて、鋳型による鋳物の拘束条件を設定する拘束条件設定ステップ（Ｓ４１）と、設定された拘束条件、前記鋳物要素の温度変化量及び熱膨張係数に基づいて、前記鋳物要素の変形を経時的に解析して、前記鋳物要素の歪み、変位又は応力の少なくとも１つを求める弾塑性解析ステップ（Ｓ４２）と、をもつ熱変形解析工程（Ｓ４）と、を有することを特徴とする。   That is, the sand mold casting simulation method of the present invention provides at least distortion, displacement, or stress generated in a casting when a casting having a desired shape is obtained by injecting molten metal into a mold made of at least a sand mold and solidifying. A method of simulating a sand mold casting for obtaining one, an element creation step (S1) for creating an analysis model comprising at least a casting element and a mold element, and analyzing heat transfer of the casting element and the mold element over time. Then, based on the temperature of the mold element obtained by the heat conduction analysis step (S3) for obtaining the temperature of the casting element and the mold element and the temperature of the mold element obtained by the heat conduction analysis step (S3), the constraint condition of the casting by the mold is determined. Based on the set constraint condition setting step (S41), the set constraint condition, the temperature change amount of the cast element, and the thermal expansion coefficient, the cast element A thermal deformation analysis step (S4) having an elastic-plastic analysis step (S42) for analyzing deformation over time to obtain at least one of distortion, displacement or stress of the casting element. To do.

本発明の砂型鋳物のシミュレーション方法においては、前記拘束条件設定ステップ（Ｓ４１）は、前記鋳型要素の温度変化に基づいて鋳型による鋳物の拘束条件判定の要否を決定する拘束条件判定要否設定ステップ（Ｓ４１１）と、拘束条件判定を要する場合に、前記鋳型要素の温度と鋳型の拘束判定温度とを比較して拘束の有無を判定する拘束条件判定ステップ（Ｓ４１２）と、前記鋳物要素に拘束条件を設定するステップと、を有することが好ましい。前記鋳型の拘束判定温度は、鋳型温度と鋳型強度との関係から、鋳型の形状を保持できないものと見なせる温度とすることが望ましい。   In the sand casting casting simulation method of the present invention, the constraint condition setting step (S41) is a constraint condition determination necessity setting step for determining whether or not the constraint condition determination of the casting by the mold is necessary based on the temperature change of the mold element. (S411) and a constraint condition determination step (S412) for determining whether there is a constraint by comparing the temperature of the mold element and the constraint determination temperature of the mold when a constraint condition determination is required, and a constraint condition on the casting element Preferably, the step of setting The mold restraint determination temperature is preferably set to a temperature at which it is considered that the shape of the mold cannot be maintained from the relationship between the mold temperature and the mold strength.

本発明の砂型鋳物のシミュレーション方法においては、前記熱伝導解析工程（Ｓ３）の前に、溶湯が前記鋳物要素を流動して充填される挙動を経時的に解析して、前記鋳物要素の温度を求める流動解析工程（Ｓ２）を行い、前記流動解析工程（Ｓ２）で得られた溶湯の充填完了時の前記鋳物要素の温度を前記熱伝導解析工程（Ｓ３）の初期温度として付与することが好ましい。   In the sand casting casting simulation method of the present invention, prior to the heat conduction analysis step (S3), the behavior of the molten metal flowing and filling the casting element over time is analyzed to determine the temperature of the casting element. It is preferable that the flow analysis step (S2) to be obtained is performed, and the temperature of the casting element at the completion of filling of the molten metal obtained in the flow analysis step (S2) is given as the initial temperature of the heat conduction analysis step (S3). .

本発明の砂型鋳物のシミュレーション方法は、前記鋳型に金属製部材を含み、前記熱変形解析工程（Ｓ４）の解析の開始から終了まで終始、前記金属製部材に拘束有りの拘束条件を設定してもよい。   The sand casting casting simulation method of the present invention includes a metal member in the mold, and sets a restraint condition with restraint on the metal member from the start to the end of the analysis in the thermal deformation analysis step (S4). Also good.

本発明の砂型鋳物のシミュレーション方法によれば、例えば、鋳鉄や鋳鋼からなる鋳物を砂型鋳造で得る際に、鋳物各部の不均一な熱膨脹及び熱収縮によって生じる歪み、変位又は応力の少なくとも１つを、鋳型の拘束状態の変化も考慮して高精度に求めることができる。これにより、鋳造の設計段階で、鋳造時に生じる歪み、変位又は応力を正確に求められるので、これらに起因する変形、寸法不良、きれ、割れ等の鋳造欠陥の予知、防止に寄与する。   According to the sand casting simulation method of the present invention, for example, when a casting made of cast iron or cast steel is obtained by sand casting, at least one of distortion, displacement or stress caused by uneven thermal expansion and thermal contraction of each part of the casting is obtained. In addition, it can be obtained with high accuracy in consideration of changes in the constraint state of the mold. Accordingly, distortion, displacement, or stress generated during casting can be accurately obtained at the casting design stage, which contributes to the prediction and prevention of casting defects such as deformation, dimensional defects, cracks, and cracks.

以下、図面を参照して、本発明の好適な実施の形態を例示的に詳しく説明する。図１は、本発明の実施の形態における砂型鋳物のシミュレーション方法の全体の流れを示すフローチャートである。図２は、図１における熱変形解析工程において実施する拘束条件設定の手順を示すフローチャートである。なお、本発明のシミュレーション方法は、以下に説明する実施の形態に従って作成されたプログラムをコンピュータにより実行することで実現される。   Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the drawings. FIG. 1 is a flowchart showing the overall flow of a sand casting casting simulation method according to an embodiment of the present invention. FIG. 2 is a flowchart showing a procedure for setting a constraint condition performed in the thermal deformation analysis step in FIG. The simulation method of the present invention is realized by executing a program created according to the embodiment described below by a computer.

（１）要素作成工程（Ｓ１）
要素作成工程Ｓ１では、少なくとも製品となる鋳物の形状データを３次元ＣＡＤデータとして作成し又は予め作成された該形状データを取り込んで、また、鋳造に必要な湯口、湯道、押湯、堰などの鋳造方案部の形状データ、さらに鋳物の周囲に鋳型の形状データを作成し、これらの各形状データを多面体からなる複数の微小要素に分割した後、該微小要素を鋳物又は鋳型と定義し、少なくとも鋳物要素及び鋳型要素からなる解析モデルを作成する工程である。なお、解析モデルは、鋳物要素及び鋳型要素のほかに、必要に応じて空気要素を作成する。 (1) Element creation process (S1)
In the element creation step S1, at least shape data of a casting that is a product is created as three-dimensional CAD data, or the shape data that has been created in advance is taken in, and a gate, runner, feeder, weir, etc. necessary for casting After creating the shape data of the casting plan part of the casting mold and the shape data of the mold around the casting, and dividing each of these shape data into a plurality of microelements composed of polyhedrons, the microelements are defined as castings or molds, This is a step of creating an analysis model comprising at least casting elements and mold elements. The analysis model creates an air element as necessary in addition to the casting element and the mold element.

本発明においては、鋳物の外側を形成する外型である主型や、鋳物の中空部を形成する中子など、鋳型のうち少なくとも一部が砂型から構成される鋳造方法を解析の対象とし、砂型からなる鋳型を砂型要素と定義する。また、砂型のみから構成されるものの他に、砂型以外の部材として金属製部材が含まれてもよい。金属製部材としては、例えば、引け巣の発生を抑制するためのチルと呼ばれる冷却部材や、主型としての金型が挙げられる。チルや金型などの金属製部材が鋳型に含まれる場合は、鋳型要素のうち、金属製部材の位置する微小要素を金属製部材要素として、砂型要素とは別に定義する。鋳型要素のうち、主型を金型として金属製部材要素として、中子を砂型要素として定義すれば、例えば、アルミニウム合金の低圧鋳造法やグラビティ（重力）鋳造法を対象とした解析モデルを作成できる。   In the present invention, the main mold that is the outer mold that forms the outside of the casting, the core that forms the hollow portion of the casting, etc. A sand mold is defined as a sand mold element. Moreover, in addition to what is comprised only of a sand mold | type, metal members may be contained as members other than a sand mold | type. Examples of the metal member include a cooling member called a chill for suppressing the occurrence of shrinkage and a mold as a main mold. When a metal member such as a chill or a mold is included in the mold, a minute element on which the metal member is located is defined as a metal member element among the mold elements separately from the sand mold element. Of the mold elements, if you define the main mold as a metal member element and the core as a sand mold element, for example, you can create an analysis model for low pressure casting and gravity (gravity) casting of aluminum alloys it can.

なお、複数の微小分割要素の作成には、部位毎に微小要素に分割する位置を座標として与える方法や、所望の微小要素の大きさを与えれば自動で微小要素を生成する要素作成プログラムなどを用いてもよい。また、鋳型要素を作成する場合には、鋳物の形状データのみから、鋳型の厚さを定義して、鋳物要素の周囲に鋳型要素を簡易に作成してもよい。   To create a plurality of micro-divided elements, there are a method of giving the position to be divided into micro-elements for each part as coordinates, an element creating program for automatically generating micro-elements if a desired micro-element size is given, etc. It may be used. Further, when creating a mold element, the mold element may be easily created around the casting element by defining the thickness of the casting mold only from the shape data of the casting.

予め作成された鋳物の形状を取り込むための３次元ＣＡＤデータの形式は、様々な形式のデータを用いることができる。例えば、国際規格ＩＧＥＳ（Ｉｎｉｔｉａｌ Ｇｒａｐｈｉｃｓ Ｅｘｃｈａｎｇｅ Ｓｐｅｃｉｆｉｃａｔｉｏｎ）形式やＳＴＬ（Ｓｔｅｒｅｏ Ｌｉｔｈｏｇｒａｐｈｙ）形式などが利用できる。   Various types of data can be used as the format of the three-dimensional CAD data for taking in the shape of the casting created in advance. For example, an international standard IGES (Initial Graphics Exchange Specification) format, STL (Stereo Lithography) format, or the like can be used.

（２）流動解析工程（Ｓ２）
流動解析工程Ｓ２は必ずしも実施しなくてもよいが、実施すれば、後述する熱伝導解析工程Ｓ３における、各要素の初期温度などをより実際の鋳造に近づけて設定できるので解析精度の向上に寄与して好ましい。流動解析工程Ｓ２は、溶湯が鋳物要素に充填される挙動を流動解析で計算する。本工程Ｓ２は、上記要素作成工程Ｓ１で作成した、鋳物要素の一部である湯口要素に溶湯の流入量又は流入圧力を、各要素に密度、比熱、熱伝導率及び粘性係数などの物性値、初期温度及び初期圧力を、鋳物要素と鋳型要素など異種要素間の伝熱条件として熱伝達係数を、付与した後、例えば、ナビエ−ストークスの式などを利用して、鋳物要素における溶湯の位置、温度、圧力などを求める。鋳物要素が充填完了した時の各要素の温度を、次の熱伝導解析工程Ｓ３の初期温度として利用する。 (2) Flow analysis process (S2)
The flow analysis step S2 is not necessarily performed, but if it is performed, the initial temperature of each element in the heat conduction analysis step S3 described later can be set closer to the actual casting, which contributes to the improvement of the analysis accuracy. It is preferable. In the flow analysis step S2, the behavior of the molten metal filling the casting element is calculated by flow analysis. In this step S2, the inflow amount or the inflow pressure of the molten metal is created in the element creation step S1, and the physical property values such as density, specific heat, thermal conductivity and viscosity coefficient are given to each element. After applying a heat transfer coefficient as a heat transfer condition between different elements such as a casting element and a mold element, using an initial temperature and an initial pressure, for example, using the Navier-Stokes formula, the position of the molten metal in the casting element Find the temperature, pressure, etc. The temperature of each element when the casting element is completely filled is used as the initial temperature of the next heat conduction analysis step S3.

なお、湯境など湯流れ（溶湯の流動）に起因する鋳造欠陥を注視しなくともよい場合や、鋳物の歪み、変位又は応力の解析として必要な精度が確保できる場合や、歪み、変位又は応力の解析結果の絶対値には拘らず相対的、定性的な結果のみ得ようとする場合などは、流動解析工程Ｓ２を省略してもよい。これにより解析工数（手間）や計算時間を短縮できる。   In addition, when it is not necessary to pay attention to casting defects caused by hot water flow (flow of molten metal) such as a hot water boundary, when it is possible to ensure the accuracy necessary for analysis of casting distortion, displacement or stress, or when distortion, displacement or stress is The flow analysis step S2 may be omitted when only relative and qualitative results are to be obtained regardless of the absolute value of the analysis result. As a result, it is possible to shorten the analysis man-hours (labor) and calculation time.

（３）熱伝導解析工程（Ｓ３）
熱伝導解析工程Ｓ３は、熱移動や潜熱を考慮した非定常熱伝導解析によって各要素についての熱の伝導を計算する工程である。本工程Ｓ３は、少なくとも鋳物要素及び鋳型要素に密度、比熱、熱伝導率及び凝固潜熱などの物性値及び初期温度を付与し、また鋳物要素と鋳型要素など異種要素間の伝熱条件として熱伝達係数などを付与した後、全ての鋳物要素に溶湯が充填した初期状態から、微小時間間隔毎に鋳物要素と鋳型要素の経時的な温度を求める。 (3) Thermal conduction analysis process (S3)
The heat conduction analysis step S3 is a step of calculating heat conduction for each element by unsteady heat conduction analysis in consideration of heat transfer and latent heat. In this step S3, physical property values such as density, specific heat, thermal conductivity and latent heat of solidification and initial temperature are given to at least the casting element and the mold element, and heat transfer is performed as a heat transfer condition between different elements such as the casting element and the mold element. After giving a coefficient etc., the temperature with time of a casting element and a casting_mold | template element is calculated | required for every micro time interval from the initial state in which all the casting elements were filled with the molten metal.

熱伝導解析工程Ｓ３で付与する各要素の初期温度は、流動解析工程Ｓ２を実施した場合は、鋳物要素が充填完了した時の各要素の温度を利用することができる。一方、流動解析工程Ｓ２を省略した場合は、鋳物要素、鋳型要素の所定の初期温度を直接付与する。   As the initial temperature of each element applied in the heat conduction analysis step S3, when the flow analysis step S2 is performed, the temperature of each element when the casting element is completely filled can be used. On the other hand, when the flow analysis step S2 is omitted, predetermined initial temperatures of the casting element and the mold element are directly applied.

熱伝導解析工程Ｓ３は、鋳物の引け巣予測を目的に実施されるので、通常は、鋳物の凝固が終了した時点で解析を終了する。しかし、本発明においては、鋳物の歪、変位又は応力を求めるため、鋳物の凝固が終了した後も継続して鋳物が所定の温度に低下するまで解析を継続する必要がある。熱伝導解析工程Ｓ３は、全ての鋳物要素が所定の温度として室温、例えば２５℃に達した後に解析を終了すれば、高い解析精度が得られるので好ましい。なお、鋳物の歪み、変位又は応力の解析として必要な精度が確保できる場合は、鋳物要素の最も高い温度が所定の温度として、例えば２００℃に達した時点で解析を終了してもよい。これにより、解析時間の短縮を図れる。   Since the heat conduction analysis step S3 is performed for the purpose of predicting the shrinkage cavity of the casting, the analysis is usually finished when the solidification of the casting is finished. However, in the present invention, in order to obtain the distortion, displacement or stress of the casting, it is necessary to continue the analysis until the casting is lowered to a predetermined temperature even after the solidification of the casting is finished. The heat conduction analysis step S3 is preferable because high analysis accuracy can be obtained if the analysis is finished after all casting elements reach room temperature, for example, 25 ° C., as a predetermined temperature. In addition, when the accuracy required for the analysis of the distortion, displacement or stress of the casting can be ensured, the analysis may be terminated when the highest temperature of the casting element reaches, for example, 200 ° C. Thereby, the analysis time can be shortened.

（４）熱変形解析工程（Ｓ４）
熱変形解析工程Ｓ４は、上記の熱伝導解析工程Ｓ３で得られた鋳物要素及び鋳型要素の温度と、後述する鋳型による鋳物の拘束条件とに基づいて、弾塑性解析によって鋳物要素の熱膨脹及び熱収縮にともなう歪み、変位又は応力を計算する工程である。本工程Ｓ４は、鋳物要素に耐力、ヤング率、歪み硬化指数、ポアソン比などの機械的性質、熱膨張係数及び拘束条件を付与した後、上記の熱伝導解析工程Ｓ３において経時的に求めた鋳物要素の温度から、微少時間間隔毎の鋳物要素の温度変化量を求め、求めた温度変化量に付与した熱膨張係数を乗じて、弾塑性解析によって鋳物要素の変形を経時的に求める。次いで求めた変形の解析結果と機械的性質に基づいて、歪み、変位又は応力を求める。 (4) Thermal deformation analysis step (S4)
In the thermal deformation analysis step S4, the thermal expansion and heat of the casting element are analyzed by elastoplastic analysis based on the temperature of the casting element and the mold element obtained in the heat conduction analysis step S3 and the constraint condition of the casting by the mold described later. This is a process of calculating strain, displacement or stress accompanying shrinkage. In this step S4, the casting obtained in the above heat conduction analysis step S3 over time after mechanical properties such as yield strength, Young's modulus, strain hardening index, Poisson's ratio, thermal expansion coefficient and constraint conditions were given to the casting element. From the temperature of the element, the amount of change in the temperature of the casting element is obtained at every minute time interval, and the deformation of the casting element is obtained over time by elastic-plastic analysis by multiplying the obtained amount of temperature change by the thermal expansion coefficient. Next, strain, displacement, or stress is obtained based on the obtained analysis result and mechanical properties of the deformation.

本工程Ｓ４で付与する拘束条件は、初期条件としては鋳型による鋳物の拘束有りとして計算を開始し、計算開始後は、本工程Ｓ４に含まれる後述する拘束条件設定ステップＳ４１において、鋳型による鋳物の拘束の有無を判定して与える。なお、機械的性質は、温度によってその値が変化する場合は温度毎に値を与えるが、その値の変化量が少ない場合には一定値を用いてもよい。   The constraint condition to be applied in this step S4 starts the calculation as the initial condition is that the casting is restricted by the mold. After the calculation is started, in the constraint condition setting step S41 described later included in this step S4, the casting condition of the casting by the mold is started. Judgment is made on the presence or absence of restraint. The mechanical property is given for each temperature when the value changes with temperature, but a constant value may be used when the amount of change in the value is small.

熱変形解析工程Ｓ４と熱伝導解析工程Ｓ３は微小時間間隔毎に夫々の解析工程を順次行ってもよいし、熱伝導解析工程Ｓ３の終了後に、熱変形解析工程Ｓ４を行ってもよい。熱伝導解析工程Ｓ３終了後に熱変形解析工程Ｓ４を行う場合には、熱伝導解析工程Ｓ３で求めた鋳物要素と鋳型要素の経時的な温度を、微小時間間隔毎又はこれより長い時間間隔毎に保存しておき、熱変形解析工程Ｓ４ではこの保存した温度を読み込んで解析を行ってもよい。また、熱変形解析工程Ｓ４と熱伝導解析工程Ｓ３の微小時間間隔は同一であってもよいし、異なってもよい。例えば、熱変形解析工程Ｓ４の微小時間間隔を、熱伝導解析工程Ｓ３のそれよりも長い時間間隔とすればシミュレーション全体に要する計算時間を短縮できる。   The thermal deformation analysis step S4 and the heat conduction analysis step S3 may be performed sequentially for each minute time interval, or after the heat conduction analysis step S3 is completed, the heat deformation analysis step S4 may be performed. When the thermal deformation analysis step S4 is performed after the heat conduction analysis step S3, the temperature with time of the casting element and the mold element obtained in the heat conduction analysis step S3 is set at every minute time interval or every longer time interval. The temperature may be stored, and in the thermal deformation analysis step S4, the stored temperature may be read and analyzed. Further, the minute time intervals of the thermal deformation analysis step S4 and the heat conduction analysis step S3 may be the same or different. For example, if the minute time interval in the thermal deformation analysis step S4 is set to a longer time interval than that in the heat conduction analysis step S3, the calculation time required for the entire simulation can be shortened.

熱変形解析工程Ｓ４は、熱伝導解析工程Ｓ３の開始、即ち全ての鋳物要素に溶湯が充填した初期状態から、鋳物要素の温度が凝固終了温度以下の所定の温度に到達するまで解析を実施する（Ｓ５）。本工程Ｓ４の解析の開始は、要求される解析精度を確保できれば、熱伝導解析工程Ｓ３で全ての鋳物要素が凝固終了温度に到達した温度から開始してもよい。また、本工程Ｓ４の解析の終了は、全ての鋳物要素が所定の温度として室温、例えば２５℃に達した後に解析を終了すれば、高い解析精度が得られるので好ましい。なお、鋳物の歪み、変位又は応力の解析として必要な精度が確保できる場合は、鋳物要素の最も高い温度が所定の温度として、例えば２００℃に達した時点で解析を終了してもよい。これにより、解析時間の短縮を図れる。   The thermal deformation analysis step S4 performs the analysis from the start of the heat conduction analysis step S3, that is, from the initial state where all the casting elements are filled with the molten metal until the temperature of the casting elements reaches a predetermined temperature equal to or lower than the solidification end temperature. (S5). The analysis in this step S4 may be started from the temperature at which all casting elements have reached the solidification end temperature in the heat conduction analysis step S3 as long as the required analysis accuracy can be ensured. In addition, the analysis in this step S4 is preferably completed if the analysis is completed after all casting elements have reached a room temperature, for example, 25 ° C., as a predetermined temperature because high analysis accuracy can be obtained. In addition, when the accuracy required for the analysis of the distortion, displacement or stress of the casting can be ensured, the analysis may be terminated when the highest temperature of the casting element reaches, for example, 200 ° C. Thereby, the analysis time can be shortened.

要素作成工程Ｓ１、流動解析工程Ｓ２、熱伝導解析工程Ｓ３及び熱変形解析工程Ｓ４の弾塑性解析Ｓ４２で使用する解析用のプログラムは特に限定されるものではなく、有限要素法、直交差分法を用いた市販の解析プログラムを使用できる。   The analysis program used in the elastic-plastic analysis S42 of the element creation step S1, the flow analysis step S2, the heat conduction analysis step S3, and the thermal deformation analysis step S4 is not particularly limited, and the finite element method and the orthogonal difference method are used. The commercially available analysis program used can be used.

（５）拘束条件設定ステップ（Ｓ４１）
次に熱変形解析工程Ｓ４で鋳物要素に付与する拘束条件の設定手順について図２に示す拘束条件設定ステップＳ４１に沿って説明する。本ステップＳ４１は本発明を特徴づける主要なステップである。実際の砂型鋳造では、注湯前の鋳型はその温度が室温で強度を発現して形状を保持して鋳物を拘束しているが、注湯後の鋳型は溶湯と接触して温度上昇して強度が低下して、特定の温度以上ではその形状を保持できなくなり、鋳物を拘束しなくなる。拘束条件設定ステップＳ４１は、この実際の鋳造で生じる現象を解析で再現するため、鋳型要素の温度に応じて、鋳型による鋳物の拘束の有無を判定して、鋳物要素に拘束条件を設定する。 (5) Restriction condition setting step (S41)
Next, the setting procedure of the constraint condition given to the casting element in the thermal deformation analysis step S4 will be described along the constraint condition setting step S41 shown in FIG. This step S41 is a main step characterizing the present invention. In actual sand mold casting, the mold before pouring shows strength at room temperature and retains the shape to constrain the casting. However, the mold after pouring rises in temperature due to contact with the molten metal and strength. Decreases, the shape cannot be maintained above a specific temperature, and the casting is not restrained. In the constraint condition setting step S41, in order to reproduce the phenomenon that occurs in the actual casting by analysis, whether or not the casting is restrained by the mold is determined according to the temperature of the mold element, and the constraint condition is set for the casting element.

本発明で「拘束する」又は「拘束有りに設定する」とは、熱変形解析工程Ｓ４で実施する弾塑性解析の際に、鋳物要素の節点（頂点）が、後述する拘束判定温度未満の温度の鋳型要素の領域には移動できないように設定することをいう。「拘束しない」又は「拘束無しに設定する」とは、熱変形解析工程Ｓ４で実施する弾塑性解析の際に、鋳物要素の節点（頂点）が、後述する拘束判定温度以上の温度の鋳型要素の領域に移動できるように設定することをいう。   In the present invention, “restraint” or “set to be constrained” means a temperature at which a node (vertex) of a casting element is lower than a constraint determination temperature described later in the elastic-plastic analysis performed in the thermal deformation analysis step S4. It is set so that it cannot move to the area of the template element. “Do not constrain” or “set without constrain” refers to a mold element in which a node (vertex) of a casting element has a temperature equal to or higher than a restraint determination temperature described later in the elastic-plastic analysis performed in the thermal deformation analysis step S4. It is set to be able to move to the area.

なお、鋳型にチルや金型などの金属製部材を配設する場合は、金属製部材は温度が上昇しても砂型のように崩壊せず、鋳型としての形状を保持するので、鋳物の温度が、注湯から所定の温度に至る全温度範囲で鋳物を拘束する。従って、熱変形解析工程Ｓ４では、解析の開始から終了までの終始、鋳物要素の節点が、金属製部材の領域には変位できない条件（拘束有り）を設定する。なお、金属製部材の材質としては、鋳鋼、鋳鉄、鋼、銅合金など各種の金属材料を使用できる。   When a metal member such as a chill or a mold is disposed in the mold, the metal member does not collapse like a sand mold even if the temperature rises, and retains the shape as the mold. However, the casting is restrained in the entire temperature range from the pouring to a predetermined temperature. Accordingly, in the thermal deformation analysis step S4, a condition (with constraint) is set so that the node of the casting element cannot be displaced in the region of the metal member from the start to the end of the analysis. In addition, as a material of a metal member, various metal materials such as cast steel, cast iron, steel, and copper alloy can be used.

拘束条件設定ステップＳ４１は、図２に示すように拘束条件を判定するか否かを決定する拘束条件判定要否設定ステップＳ４１１と、拘束条件の判定が必要な場合に、鋳型要素の温度と予め求めた鋳型が鋳物を拘束できなくなる温度（以下、拘束判定温度という）とを比較して拘束条件を判定する拘束条件判定ステップＳ４１２とからなる。   In the constraint condition setting step S41, as shown in FIG. 2, the constraint condition determination necessity setting step S411 for determining whether or not the constraint condition is determined, and the temperature of the mold element in advance when the constraint condition needs to be determined. It comprises a constraint condition determination step S412 for determining a constraint condition by comparing with a temperature at which the obtained mold cannot restrain the casting (hereinafter referred to as a constraint determination temperature).

まず、拘束条件判定要否設定ステップＳ４１１では、鋳型の温度変化に基づいて拘束条件を判定するか否かを決定する。具体的には、鋳型要素の温度について１つ前の計算結果と最新の計算結果とを比較して、鋳型要素の温度が上昇していれば、拘束条件判定ステップＳ４１２に進み、鋳型要素の温度が等しければ又は下降していれば拘束条件の判定はしないと判断する。拘束条件の判定をしない場合は、１つ前の計算で用いた拘束条件の設定のまま弾塑性解析ステップＳ４２を行う。鋳型の温度変化に基づいて拘束条件を判定することとしたのは、温度が上昇する場合は拘束条件が変化する可能性があり、温度が等しい又は下降する場合は拘束条件が変化しないと判断されるためである。   First, in the constraint condition determination necessity setting step S411, it is determined whether or not the constraint condition is determined based on the temperature change of the mold. Specifically, the previous calculation result is compared with the latest calculation result for the temperature of the mold element, and if the temperature of the mold element is increased, the process proceeds to constraint condition determination step S412 and the temperature of the mold element is determined. If they are equal or descending, it is determined that the constraint condition is not determined. When the constraint condition is not determined, the elasto-plastic analysis step S42 is performed with the constraint condition used in the previous calculation being set. The reason for determining the constraint condition based on the temperature change of the mold is that the constraint condition may change when the temperature rises, and it is determined that the constraint condition does not change when the temperature is equal or decreases. Because.

拘束条件判定ステップＳ４１２では、予め実験等により求めた鋳型の拘束判定温度により拘束の有無を判定して拘束条件を設定する。具体的には、最新の計算で求めた鋳型要素の温度と、拘束判定温度とを比較して、鋳型要素の温度が、拘束判定温度未満なら拘束有り、拘束判定温度以上なら拘束無しと判断する。   In the restraint condition determination step S412, the restraint condition is set by determining the presence or absence of restraint based on the restraint judgment temperature of the mold obtained in advance through experiments or the like. Specifically, the temperature of the mold element obtained by the latest calculation is compared with the restraint determination temperature, and if the mold element temperature is less than the restraint judgment temperature, it is determined that there is restraint, and if it is equal to or higher than the restraint judgment temperature, it is determined that there is no restraint. .

拘束有りと判断された場合は、鋳物要素の節点に対して、これが拘束判定温度未満の温度の鋳型要素の領域に移動できない設定を付与する。一方、拘束無しと判断された場合は、鋳物要素の節点に対して、これが拘束判定温度以上の温度の鋳型要素の領域に移動できる設定を付与する。   If it is determined that there is a constraint, a setting is given to the node of the casting element that cannot move to the mold element region having a temperature lower than the constraint determination temperature. On the other hand, when it is determined that there is no constraint, a setting is given to the node of the casting element so that it can move to the mold element region having a temperature equal to or higher than the constraint determination temperature.

次に、拘束条件判定ステップＳ４１２で設定された拘束条件を用いて弾塑性解析ステップＳ４２を行う。なお、弾塑性解析ステップＳ４２の初回の計算は、全ての鋳物要素に対して拘束有りの条件で開始する。   Next, the elastic-plastic analysis step S42 is performed using the constraint conditions set in the constraint condition determination step S412. Note that the first calculation in the elasto-plastic analysis step S42 starts under the condition that all casting elements are constrained.

（５−１）鋳型の拘束判定温度
鋳型による拘束の有無判定など拘束条件設定のためには、砂型からなる鋳型が温度上昇して強度が低下して鋳物を拘束しなくなる温度、即ち鋳型の拘束判定温度を予め求めて、拘束条件判定ステップＳ４１２で付与しておく必要がある。鋳型が鋳物を拘束しなくなる温度を厳密に求めることは困難なことから、本発明においては、鋳型がその形状を保持できないと見なせる温度をもって鋳型の拘束判定温度と定義した。 (5-1) Mold restraint judgment temperature In order to set restraint conditions such as judgment of presence / absence of restraint by mold, the temperature at which the mold made of sand mold rises in temperature and decreases in strength and does not restrain the casting, that is, mold restraint. The determination temperature needs to be obtained in advance and given in the constraint condition determination step S412. Since it is difficult to precisely determine the temperature at which the mold does not restrain the casting, in the present invention, the temperature at which the mold can be regarded as unable to retain its shape is defined as the mold restraint judgment temperature.

本実施の形態では、実験に基づく経験的方法として、鋳型温度と鋳型強度との関係を調査して拘束判定温度を設定する場合について例示的に以下説明する。ここでは鋳型の拘束判定温度は、加熱した鋳型の強度の測定から求めた鋳型温度−鋳型強度特性に基づく強度の変化と、加熱状態での鋳型の観察結果と、から鋳型の形状を保持できないと見なせる温度と定義した。   In the present embodiment, as an empirical method based on an experiment, the case where the constraint determination temperature is set by investigating the relationship between the mold temperature and the mold strength will be exemplarily described below. Here, the mold restraint judgment temperature is that the shape of the mold cannot be maintained from the change in strength based on the mold temperature-mold strength characteristic obtained from the measurement of the strength of the heated mold and the observation result of the mold in the heated state. It was defined as the temperature that can be considered.

図３は、砂型の１つであるシェル鋳型の鋳型温度−鋳型強度特性の一例を示す図である。シェル鋳型での鋳型温度−鋳型強度特性を得る方法として、寸法１０ｍｍ×１０ｍｍ×６０ｍｍのシェル鋳型の試験片を作製し、得られた試験片を恒温保持可能な加熱炉で大気雰囲気中１００〜１０００℃の所定の温度で３分間加熱し、試験片を加熱炉から取出し後速やかに鋳型強度を測定した。鋳型強度は代表値として曲げ強さで評価し、その測定方法は、ＪＩＳ Ｋ−６９１０規格「フェノール樹脂試験方法」に規定の曲げ強さ試験での操作、計算を適用した。なお、鋳型強度の代表値としては特に限定されず、曲げ強さ、圧縮強さ、抗圧力、抗折力などから鋳型温度−鋳型強度特性を得ることができる。また、鋳型強度の測定方法としては、ＪＩＳや（社）日本鋳造技術協会（現在、（社）日本鋳造協会に統合）で規定する各種試験方法を適用できる。   FIG. 3 is a diagram illustrating an example of a mold temperature-mold strength characteristic of a shell mold that is one of sand molds. As a method for obtaining the mold temperature-mold strength characteristics in the shell mold, a test piece of a shell mold having a size of 10 mm × 10 mm × 60 mm is prepared, and the obtained test piece is 100 to 1000 in an air atmosphere in a heating furnace capable of maintaining a constant temperature. The mold was heated at a predetermined temperature of 3 ° C. for 3 minutes, and the mold strength was measured immediately after the test piece was taken out of the heating furnace. The mold strength was evaluated by bending strength as a representative value, and the measurement method was the operation and calculation in the bending strength test defined in JIS K-6910 standard “phenol resin test method”. The representative value of the mold strength is not particularly limited, and the mold temperature-mold strength characteristic can be obtained from bending strength, compressive strength, coercive pressure, bending strength, and the like. In addition, as a method for measuring the mold strength, various test methods defined by JIS or the Japan Casting Technology Association (currently integrated with the Japan Casting Association) can be applied.

図３の鋳型温度−鋳型強度特性に示すように、例示したシェル鋳型の鋳型強度は、鋳型温度の上昇とともに、約４００℃までは暫減し、約４００〜５００℃の温度範囲では激減し、約５００℃以上では再び暫減する、という変化を示した。加熱炉内での加熱中又は取出し、運搬等の取り扱い中など、加熱状態での試験片（鋳型）の観察結果によれば、約４００℃までは鋳型の表面からの砂粒の脱落が認められるもののその量は僅かであり、約４００℃を超えると鋳型表面からの砂粒の脱落、剥離が顕著となり、約５００℃で表面から深さ方向で数ｍｍの表層部分が剥離して崩壊した。   As shown in the mold temperature-mold strength characteristic of FIG. 3, the mold strength of the illustrated shell mold gradually decreases to about 400 ° C. as the mold temperature increases, and drastically decreases in the temperature range of about 400 to 500 ° C. It showed a change that it decreased again for a while at about 500 ° C or higher. According to the observation results of the test pieces (molds) in the heated state, such as during heating in the heating furnace or during handling such as taking out, transporting, etc., the sand particles fall off from the mold surface up to about 400 ° C. The amount was very small, and when the temperature exceeded about 400 ° C., sand grains dropped off from the mold surface and exfoliated, and a surface layer portion of several mm in the depth direction from the surface exfoliated and collapsed at about 500 ° C.

このことから、例示したシェル鋳型は、約４００℃までは砂粒同士を固着する粘結材の軟化や一部融解によって鋳型強度が低下し、約４００℃以上では粘結材の融解又は分解が顕著となるために砂粒同士を固着する結合力が消失して鋳型表面から砂粒が脱落、剥離して鋳型が崩壊を開始し、更なる加熱にともなって鋳型の崩壊が表面から内部に及び、約５００℃付近で最も崩壊が顕著となり、５００℃以上では更に内部までは崩壊しない状態に達したものと推察される。   From this, the illustrated shell mold has a lower mold strength due to softening or partial melting of the binder that fixes sand particles up to about 400 ° C., and melting or decomposition of the binder is remarkable at about 400 ° C. or higher. Therefore, the bonding force for fixing the sand grains disappears, the sand grains fall off from the mold surface, peels off and the mold starts to collapse, and with further heating, the mold collapses from the surface to the inside. It is presumed that the collapse is most noticeable at around ℃, and that the state of not breaking down to the inside is reached at 500 ℃ or higher.

上記した鋳型温度−鋳型強度特性と加熱状態での鋳型の観察結果とから、例示したシェル鋳型では、加熱により鋳型強度が激減から再び暫減に転じる温度に達すると、表面から内部まで崩壊が進んでしまい鋳型の形状を保持できないものと見なし、当該温度を拘束判定温度とし、鋳型温度がそれ以上では鋳型が鋳物を拘束しなくなるものと定義した。具体的には、５００℃を拘束判定温度として設定し、拘束条件判定ステップＳ４１２において、熱伝導解析工程Ｓ３で求めた鋳型温度が５００℃未満では鋳型による鋳物の拘束有り、５００℃以上では拘束無しと判定する。   Based on the above-mentioned mold temperature-mold strength characteristics and the result of observation of the mold in the heated state, in the illustrated shell mold, when the temperature reaches a temperature at which the mold strength suddenly decreases again from heating, the collapse proceeds from the surface to the inside. Therefore, it was considered that the shape of the mold could not be maintained, and this temperature was defined as a restraint judgment temperature, and it was defined that the mold would not restrain the casting when the mold temperature was higher than that. Specifically, 500 ° C. is set as the restraint judgment temperature, and in the restraint condition judgment step S412, the casting is restrained by the mold when the mold temperature obtained in the heat conduction analysis step S3 is less than 500 ° C., and there is no restraint when the temperature is 500 ° C. or more. Is determined.

本発明では、上記例示のようにして求められる拘束判定温度を、解析の対象となる鋳型毎に設定しておき、上記拘束条件判定ステップＳ４１２で記載したように、求めた鋳型要素の温度と拘束判定温度とを比較して、拘束の有無を判定して拘束条件を設定する。   In the present invention, the constraint determination temperature obtained as described above is set for each mold to be analyzed, and as described in the constraint condition determination step S412, the determined template element temperature and constraint are determined. The restraint condition is set by comparing the judgment temperature and judging the presence or absence of restraint.

なお、一旦、鋳型温度が上昇して拘束判定温度以上となった場合、即ち、鋳型の形状を保持できないと見なされる場合には、既に砂粒同士を固着する結合力は消失しているので、その後、鋳物や鋳型の冷却により鋳型温度が再び低下しても砂粒同士を固着する結合力が回復することなく鋳型は崩壊したままである。このように砂型は不可逆的な性質を有するので、鋳物の冷却にともなって鋳型温度の低下により鋳型要素の温度が再び拘束判定温度以下の温度となって拘束有りの領域に入っても、一旦拘束無しに設定した拘束条件は変更しない。前述した拘束条件判定要否設定ステップＳ４１１で鋳型要素の温度変化を判定しているのは、上述の砂型の不可逆的な性質を考慮して、鋳型要素の温度変化が上昇局面であれば拘束条件が変化する可能性があるので拘束条件判定ステップＳ４１２に進み、一方、鋳型要素の温度変化が停滞又は下降の局面であれば拘束条件は変化しないので拘束条件判定ステップＳ４１２に進まないと判断させるためである。   In addition, once the mold temperature rises and exceeds the restraint determination temperature, that is, when it is considered that the shape of the mold cannot be maintained, the bonding force for fixing the sand particles has already disappeared. Even if the mold temperature is lowered again by cooling the casting or the mold, the mold remains broken without recovering the bonding force for fixing the sand grains. As described above, the sand mold has an irreversible property. Therefore, even if the temperature of the mold element becomes lower than the restraint judgment temperature due to a decrease in the mold temperature as the casting is cooled, the sand mold is once restrained. The constraint condition set to None is not changed. In the restriction condition determination necessity setting step S411 described above, the temperature change of the mold element is determined in consideration of the irreversible nature of the sand mold described above if the temperature change of the mold element is in the rising phase. In order to determine that the constraint condition does not change if the temperature change of the mold element is stagnant or descending, and therefore does not proceed to the constraint condition determination step S412. It is.

以上、本実施の形態では、鋳型の拘束判定温度の求め方として、鋳型温度と鋳型強度との関係を調査してこれを求める場合を例示して説明したが、拘束判定温度の求め方は、上記に限定されず、理論的方法や実験に基づいた経験的方法を用いて求めることができる。例えば、鋳型を加熱して温度毎に表面安定度を測定し、表面安定度を評価指標として鋳型がその形状を保持できないと見なせる温度を定義して拘束判定温度を決定してもよい。   As described above, in the present embodiment, as a method for obtaining the constraint determination temperature of the mold, the case where the relationship between the mold temperature and the mold strength is investigated and obtained is described as an example. It is not limited to the above, but can be obtained using a theoretical method or an empirical method based on experiments. For example, the restraint determination temperature may be determined by measuring the surface stability for each temperature by heating the mold and defining the temperature at which the mold cannot hold the shape using the surface stability as an evaluation index.

また、本実施の形態では、砂型としてシェル鋳型を例示して説明したが、本発明のシミュレーション方法は、対象とする鋳型の種類は特に限定されず、シェル鋳型以外に、有機ＣＯ2鋳型、水ガラスＣＯ2鋳型、コールドボックス鋳型、ウォームボックス鋳型、フラン鋳型、エステル硬化鋳型、フェノールウレタン鋳型、生型など各種の砂型に適用できる。 Further, in this embodiment, the shell mold is exemplified as the sand mold, but the simulation method of the present invention is not particularly limited in the type of the target mold. In addition to the shell mold, the organic CO 2 mold, water It can be applied to various sand molds such as glass CO 2 mold, cold box mold, warm box mold, furan mold, ester curing mold, phenol urethane mold, green mold and the like.

例えば、図４は、ＣＯ2ガス硬化型アルカリフェノール鋳型からなる有機ＣＯ2鋳型の鋳型温度−鋳型強度特性の一例を示す図である。図４の鋳型温度−鋳型強度特性に示すように、例示した有機ＣＯ2鋳型では、鋳型温度の上昇とともに鋳型強度が低下し、約４００〜６００℃の温度範囲で顕著な低下を示し、約６００℃以上では暫減する現象を示すとともに、約６００℃で鋳型表面から数ｍｍの表層部分が剥離、崩壊した。例示した有機ＣＯ2鋳型は、鋳型の形状を保持できないと見なせる拘束判定温度を６００℃として設定することができる。 For example, FIG. 4 is a diagram showing an example of mold temperature-template strength characteristics of an organic CO 2 mold made of a CO 2 gas curable alkali phenol mold. As shown in the mold temperature-mold strength characteristic of FIG. 4, in the exemplified organic CO 2 mold, the mold strength decreases with increasing mold temperature, and shows a remarkable decrease in a temperature range of about 400 to 600 ° C. At a temperature higher than or equal to 0 ° C., a phenomenon of decreasing for a while was shown, and at about 600 ° C., a surface layer portion of several mm from the mold surface peeled and collapsed. In the exemplified organic CO 2 mold, the constraint determination temperature at which the shape of the mold cannot be held can be set as 600 ° C.

以下、本発明の実施例として、砂型鋳物のシミュレーション方法について説明する。本実施例では、試験鋳物を砂型鋳造する際に発生する変位と応力について、本発明のシミュレーション方法による解析を実施するとともに、解析精度を検証するために実際の鋳造を実施し、得られた解析値と実測値とを比較評価した。なお本実施例では、何れも市販の有限要素法のソフトとして、要素作成工程Ｓ１での要素分割には自動要素分割ソフトを、流動解析工程Ｓ２の計算には湯流れ解析ソフトを、熱伝導解析工程Ｓ３の計算には熱伝導解析ソフトを、弾塑性解析ステップＳ４２の計算には熱変形解析ソフトを使用した。   Hereinafter, as an embodiment of the present invention, a sand casting casting simulation method will be described. In this example, the displacement and stress generated when sand casting a test casting is analyzed by the simulation method of the present invention, and actual casting is performed to verify the analysis accuracy, and the obtained analysis The value and the measured value were compared and evaluated. In this embodiment, all are commercially available finite element method software, automatic element division software for element division in the element creation step S1, hot water flow analysis software for calculation in the flow analysis step S2, and heat conduction analysis. For the calculation of step S3, heat conduction analysis software was used, and for the elastic-plastic analysis step S42, heat deformation analysis software was used.

図５は、実施例に供した試験鋳物１００を示し、本発明のシミュレーション方法で予測され、また実際の鋳造で発生した変位と応力の評価位置を示した図である。図６は、図５に示す試験鋳物１００を解析及び鋳造するための試験鋳型２００の概略形状を示し、（ａ）は平面図、（ｂ）は（ａ）での矢視Ｘ−Ｘ断面図である。この試験鋳型２００は、部位１〜６から構成される試験鋳物１００と堰５、６とを造型したキャビティ１０１、及び砂型２０１からなる。試験鋳型２００を用いて、図示しない注湯口と方案部を経由して、堰５、６から溶湯を注入、凝固させることを想定した本発明のシミュレーション方法を実施するとともに実際の試験鋳物１００を鋳造した。試験鋳物１００は、平行する２本の柱１、２と、該柱１、２の両端部を連結する三角形状の締結部３、４とを有し、柱１を幅２０ｍｍ、柱２を幅４０ｍｍとし、柱１、２及び締結部３、４の肉厚を５ｍｍとしている。   FIG. 5 shows a test casting 100 used in the example, and is a diagram showing an evaluation position of displacement and stress predicted by the simulation method of the present invention and generated in actual casting. 6 shows a schematic shape of a test mold 200 for analyzing and casting the test casting 100 shown in FIG. 5, (a) is a plan view, and (b) is a cross-sectional view taken along line XX in (a). It is. The test mold 200 includes a cavity 101 in which a test casting 100 composed of parts 1 to 6 and weirs 5 and 6 are formed, and a sand mold 201. Using the test mold 200, the simulation method according to the present invention, which assumes the injection and solidification of molten metal from the weirs 5 and 6 through a pouring port and a design part (not shown), is performed, and an actual test casting 100 is cast. did. The test casting 100 includes two parallel columns 1 and 2 and triangular fastening portions 3 and 4 that connect both ends of the columns 1 and 2. The column 1 has a width of 20 mm and the column 2 has a width. The thickness of the columns 1 and 2 and the fastening portions 3 and 4 is 5 mm.

次に本実施例での変位と応力の評価方法について説明する。変位は、解析終了及び実際の鋳造後に室温に達した試験鋳物１００について、図５に示す点２１を基準点（ゼロ（０）点）として、前記基準点２１に対する後述する各評価点のｚ座標方向（図５の紙面に対して垂直方向）の移動量（ｍｍ）をもって変位量（以下、ｚ方向変位量という）として評価した。評価点は、図５で符合２２〜２５で示す４点、及び各点（２１と２２、２２と２３、２１と２４、２４と２５）を結ぶ直線上の任意の複数点とした。なお、解析の変位量は、本発明の熱伝導解析工程を開始する前の評価点２１における鋳物要素の節点の位置をゼロとして基準点とし、基準点に対する熱伝導解析工程を終了後の各評価点に対応する鋳物要素の節点の相対的な位置データからｚ方向変位量を算出した。また、実際の鋳物の変位量は、鋳造後の試験鋳物１００の各評価点について、接触式の３次元測定器を用いてｚ方向変位量を実測した。なお、ｚ座標方向の移動量を評価したのは、試験鋳物１００のような、相対的に肉厚に対して広い平面を有する薄肉鋳物では、歪や変形がｚ座標方向に顕著に発生するためである。   Next, a displacement and stress evaluation method in this embodiment will be described. For the test casting 100 that has reached room temperature after the end of analysis and actual casting, the displacement is the z coordinate of each evaluation point described later with respect to the reference point 21 with the point 21 shown in FIG. 5 as the reference point (zero (0) point). The displacement (mm) in the direction (perpendicular to the paper surface of FIG. 5) was evaluated as the displacement (hereinafter referred to as z-direction displacement). The evaluation points were four points indicated by reference numerals 22 to 25 in FIG. 5 and arbitrary plural points on a straight line connecting the respective points (21 and 22, 22 and 23, 21 and 24, 24 and 25). Note that the displacement amount of the analysis is set as a reference point with the position of the node of the casting element at the evaluation point 21 before starting the heat conduction analysis process of the present invention as zero, and each evaluation after the heat conduction analysis process with respect to the reference point is finished. The amount of displacement in the z direction was calculated from the relative position data of the nodes of the casting element corresponding to the points. Further, the actual amount of displacement of the casting was actually measured by using a contact-type three-dimensional measuring device for each evaluation point of the test casting 100 after casting. The amount of movement in the z-coordinate direction was evaluated because distortion and deformation significantly occur in the z-coordinate direction in a thin-walled casting having a relatively wide plane with respect to the wall thickness, such as the test casting 100. It is.

応力は、解析終了及び実際の鋳造後に室温に達した試験鋳物１００に残留する応力（残留応力）をもって評価し、図５に示す鋳物側面の評価点３１〜３５の残留応力を求めた。解析値の残留応力は、熱伝導解析工程終了後の各評価点に対応する鋳物要素の節点の応力データを残留応力とした。また、実際の鋳物の残留応力は、試験鋳物１００の評価点３１〜３５に歪みゲージを貼り付け、その後、切断面Ｃ１、Ｃ２を機械的に切断して切断前後での歪み量の差を歪みゲージで検出し、実測した歪み量の差から残留応力を算出した。   The stress was evaluated by the residual stress (residual stress) in the test casting 100 that reached room temperature after the end of analysis and actual casting, and the residual stress at the evaluation points 31 to 35 on the casting side surface shown in FIG. 5 was obtained. For the residual stress of the analysis value, the stress data of the nodal point of the casting element corresponding to each evaluation point after the end of the heat conduction analysis process was used as the residual stress. Further, the residual stress of the actual casting is obtained by applying a strain gauge to the evaluation points 31 to 35 of the test casting 100, and then mechanically cutting the cut surfaces C1 and C2 to distort the difference in strain before and after cutting. The residual stress was calculated from the difference in the strain amount detected by the gauge and measured.

（実施例１）
実施例１は、図６に示す砂型２０１を有機ＣＯ2鋳型、試験鋳物１００をオーステナイト系鋳鋼からなる鋳物、と想定して本発明の方法による砂型鋳物のシミュレーションを行った。 Example 1
In Example 1, assuming that the sand mold 201 shown in FIG. 6 is an organic CO 2 mold and the test casting 100 is a casting made of austenitic cast steel, the sand casting was simulated by the method of the present invention.

（要素作成工程Ｓ１）
実施例１の要素作成工程Ｓ１では、鋳物要素、鋳型要素及び空気要素から構成される解析モデルを作成した。まず、図５、６に示す試験鋳物１００の形状を３次元ＣＡＤデータとして作成し、堰５、６及び図示しない湯口、湯道などの鋳造方案部及び鋳型として砂型２０１の形状データを作成した後、当該データを多面体からなる複数の微小要素に分割した。次に微小要素のうち、試験鋳物１００、及び堰５、６などの鋳造方案部に位置する微小要素を鋳物要素に、砂型２０１に位置する微小要素を砂型要素に、さらに砂型２０１の外周部に図示しない空気を空気要素として定義して解析モデルとした。実施例１における微小要素の大きさは、要素の一辺の長さとして、鋳物要素で１．５〜３ｍｍ、鋳型要素及び空気要素で３〜５ｍｍであった。 (Element creation process S1)
In the element creation step S1 of Example 1, an analysis model composed of a casting element, a mold element, and an air element was created. First, the shape of the test casting 100 shown in FIGS. 5 and 6 is created as three-dimensional CAD data, and the shape data of the sand mold 201 is created as a casting plan portion such as the weirs 5 and 6 and a not-shown gate and runner and a mold. The data was divided into a plurality of microelements made of a polyhedron. Next, among the microelements, the microelements located in the casting plan part such as the test casting 100 and the weirs 5 and 6 are used as the casting elements, the microelements located in the sand mold 201 are used as the sand mold elements, and the sand mold 201 is disposed on the outer peripheral part. An analysis model was defined by defining air (not shown) as an air element. The size of the microelement in Example 1 was 1.5 to 3 mm for the casting element and 3 to 5 mm for the casting element and the air element as the length of one side of the element.

（熱伝導解析工程Ｓ３）
実施例１は、流動解析工程Ｓ２を省略して熱伝導解析工程Ｓ３を実施した。まず、要素作成工程Ｓ１で作成した解析モデルの鋳物要素及び鋳型要素に物性値として密度、比熱、熱伝導率及び凝固潜熱などを付与し、鋳物要素と鋳型要素、鋳物要素と空気要素、鋳型要素と空気要素など、異種要素間の伝熱条件として熱伝達係数を付与した。また、各要素に所定の初期温度として、鋳物要素には注湯温度１６００℃を、鋳型要素及び空気要素には室温２５℃を付与した。なお、各要素の初期温度は、予め実験等で求めた実測の温度があれば、これを付与してもよい。次に、付与した初期温度、物性値及び熱伝達係数に基づいて、非定常熱伝導解析によって熱の伝導を計算し、全ての鋳物要素に溶湯が充填した状態から、全ての鋳物要素の温度が室温になるまで、微小時間間隔毎に鋳物要素と鋳型要素の経時的な温度を求めた。 (Heat conduction analysis step S3)
In Example 1, the flow analysis step S2 was omitted and the heat conduction analysis step S3 was performed. First, density, specific heat, thermal conductivity, latent heat of solidification, etc. are given as physical property values to the casting elements and mold elements of the analytical model created in the element creation step S1, and the casting elements and mold elements, casting elements and air elements, mold elements A heat transfer coefficient was given as a heat transfer condition between different elements such as air and air elements. Further, as a predetermined initial temperature for each element, a casting temperature of 1600 ° C. was given to the casting element, and a room temperature of 25 ° C. was given to the mold element and the air element. Note that the initial temperature of each element may be given if there is an actually measured temperature obtained beforehand through experiments or the like. Next, based on the applied initial temperature, physical properties, and heat transfer coefficient, heat conduction is calculated by unsteady heat conduction analysis, and from the state where all casting elements are filled with molten metal, the temperature of all casting elements is calculated. The temperature over time of the casting element and the mold element was determined every minute time interval until the temperature reached room temperature.

（熱変形解析工程Ｓ４）
熱変形解析工程Ｓ４では、鋳物要素に耐力、ヤング率、歪み硬化指数、ポアソン比などの機械的性質、熱膨張係数及び初期の拘束条件を付与した。本実施例では、鋳物要素の温度に依存して機械的性質及び熱膨張係数の値が変化するように設定した。また、初期の拘束条件として、鋳物要素に鋳型による鋳物の拘束有りを設定した。次に、付与した機械的性質、熱膨張係数及び初期の拘束条件と、上記の熱伝導解析工程Ｓ３で経時的に求めた鋳物要素と鋳型要素の温度データと、後述する拘束条件設定ステップＳ４１で設定した鋳型による鋳物の拘束条件とに基づいて、弾塑性解析ステップＳ４２を実施した。弾塑性解析ステップＳ４２では、微少時間間隔毎の鋳物要素の温度変化量と付与した熱膨張係数から、熱膨脹及び熱収縮にともなう鋳物要素の変形を求め、次いで求めた変形の解析結果と機械的性質に基づいて、変位又は応力を経時的に求めた。 (Thermal deformation analysis step S4)
In the thermal deformation analysis step S4, mechanical properties such as yield strength, Young's modulus, strain hardening index, Poisson's ratio, thermal expansion coefficient, and initial constraint conditions were given to the casting element. In this example, the mechanical properties and the coefficient of thermal expansion were set to change depending on the temperature of the casting element. In addition, as an initial restraint condition, the casting element was restrained from casting by a mold. Next, the given mechanical properties, thermal expansion coefficient and initial constraint conditions, the temperature data of the casting elements and mold elements obtained over time in the heat conduction analysis step S3, and the constraint condition setting step S41 described later The elasto-plastic analysis step S42 was performed based on the set casting constraint with the mold. In the elasto-plastic analysis step S42, the deformation of the casting element due to thermal expansion and contraction is obtained from the temperature change amount of the casting element at every minute time interval and the applied thermal expansion coefficient, and then the analysis result and mechanical properties of the obtained deformation are obtained. Based on the above, displacement or stress was obtained over time.

（拘束条件設定スッテプＳ４１）
熱変形解析工程Ｓ４の弾塑性解析ステップＳ４２を行う際に鋳物要素に付与する拘束条件としては、上述したとおり初期条件は拘束有りとして計算を開始し、計算開始後は、拘束条件設定ステップＳ４１で拘束の有無を判定して与えた。拘束条件設定ステップＳ４１では、まず鋳型の温度変化に基づいて拘束条件を判定するか否かを決定する拘束条件判定要否設定ステップＳ４１１を実施し、鋳型要素の温度が上昇していれば、拘束条件判定ステップＳ４１２に進み、前記温度が不変又は下降していれば拘束条件の判定をしないで、１つ前の計算で用いた拘束の設定を用いて弾塑性解析ステップＳ４２を行った。 (Restriction condition setting step S41)
As a constraint condition to be given to the casting element when performing the elasto-plastic analysis step S42 of the thermal deformation analysis step S4, the calculation is started with the initial condition being constrained as described above, and after the calculation is started, the constraint condition is set in step S41. The presence or absence of restraint was determined and given. In the constraint condition setting step S41, first, a constraint condition determination necessity setting step S411 for determining whether or not the constraint condition is determined based on the temperature change of the mold is performed. If the temperature of the mold element is increased, the constraint condition is determined. Proceeding to condition determination step S412, if the temperature is unchanged or decreasing, the constraint condition is not determined, and the elastic-plastic analysis step S42 is performed using the constraint setting used in the previous calculation.

拘束条件判定ステップＳ４１２では、予め実験により求めた鋳型の拘束判定温度により拘束の有無を判定して拘束条件を設定した。実施例１の拘束判定温度は、前述した実施の形態で図４に示した有機ＣＯ2鋳型の拘束判定温度を用いて６００℃に設定した。実施例１の拘束条件判定ステップＳ４１２では、熱伝導解析工程Ｓ３で経時的に求めた鋳型要素の温度データのうち鋳型要素の温度と拘束判定温度６００℃とを比較して、鋳型要素の温度が、６００℃未満なら鋳型による鋳物の拘束有り、６００℃以上なら拘束無しと判定して鋳物要素に拘束条件を設定した。 In the restraint condition determination step S412, the restraint condition is set by determining the presence or absence of restraint based on the restraint judgment temperature of the mold obtained in advance through experiments. The restraint judgment temperature of Example 1 was set to 600 ° C. using the restraint judgment temperature of the organic CO 2 mold shown in FIG. 4 in the embodiment described above. In the constraint condition determination step S412 of the first embodiment, the temperature of the mold element is compared with the temperature of the mold element in the temperature data of the mold element obtained with time in the heat conduction analysis step S3 and the constraint determination temperature of 600 ° C. When the temperature was lower than 600 ° C., the casting was restricted by the mold, and when the temperature was 600 ° C. or higher, it was determined that there was no restriction, and the restriction conditions were set for the casting elements.

拘束有りの設定では、弾塑性解析ステップＳ４２を実施する際に、鋳型による鋳物の拘束があるものとして、鋳物要素の節点が、拘束判定温度６００℃未満の温度の鋳型要素の領域には移動できないように設定し、一方、拘束無しの設定では、弾塑性解析ステップＳ４２を実施する際に、鋳型による鋳物の拘束がないものとして、鋳物要素の節点が、拘束判定温度６００℃以上の温度の鋳型要素の領域に移動できるように設定した。次に設定した拘束条件を用いて弾塑性解析ステップＳ４２を行った。   In the setting with constraint, when performing the elasto-plastic analysis step S42, it is assumed that the casting is constrained by the casting mold, and the node of the casting element cannot move to the region of the casting mold element having a temperature lower than the constraint determination temperature of 600 ° C. On the other hand, in the setting without constraint, when performing the elasto-plastic analysis step S42, it is assumed that the casting is not constrained by the mold, and the casting element has a node whose temperature is a constraint determination temperature of 600 ° C. or higher. Set to move to the element area. Next, the elastic-plastic analysis step S42 was performed using the set constraint conditions.

熱変形解析工程Ｓ４は、熱伝導解析工程Ｓ３の開始、即ち全ての鋳物要素に溶湯が充填した初期状態から、鋳物要素の変形の解析を開始し、全ての鋳物要素の温度が、所定の温度として２００℃に到達したところで解析を終了した。   The thermal deformation analysis step S4 starts the analysis of the deformation of the casting elements from the start of the heat conduction analysis step S3, that is, from the initial state in which all the casting elements are filled with molten metal, and the temperature of all the casting elements is a predetermined temperature. The analysis was terminated when the temperature reached 200 ° C.

実施例１の解析方法によって得られた変位と応力について、その解析値と鋳造での実測値とを比較評価した。図７は、実施例１の試験鋳物１００のｚ方向変位量を、解析値と実測値とで比較した図である。図７は横軸に各評価点をとり、縦軸にｚ方向変位量をとったものである。図７から、解析値と実測値とのｚ方向変位量の差は小さく、解析値は実測値によく一致して高い解析精度を示すことがわかる。なお、解析値と実測値のｚ方向変位量の誤差（［解析値と実測値のｚ方向変位量の差／実測値のｚ方向変位量］×１００）は、最大で２８％であった。   About the displacement and the stress obtained by the analysis method of Example 1, the analysis value and the actual measurement value in casting were compared and evaluated. FIG. 7 is a diagram comparing the z-direction displacement amount of the test casting 100 of Example 1 between the analysis value and the actual measurement value. In FIG. 7, the horizontal axis represents each evaluation point, and the vertical axis represents the amount of displacement in the z direction. From FIG. 7, it can be seen that the difference between the analysis value and the actual measurement value in the z-direction displacement is small, and the analysis value closely matches the actual measurement value and exhibits high analysis accuracy. The error in the z-direction displacement amount between the analysis value and the actual measurement value ([difference between the z-direction displacement amount between the analysis value and the actual measurement value / z-direction displacement amount of the actual measurement value) × 100] was 28% at the maximum.

図８は、実施例１の試験鋳物１００の残留応力を、解析値と実測値とで比較した図である。図８は横軸に各評価点をとり、縦軸には残留応力を引張又は圧縮に区別して表したものである。図８から、解析値と実測値との残留応力の差は、残留応力の絶対値が小さい評価点３４、３５でやや大きいものの、実際の鋳造で問題視される、残留応力の絶対値が大きく、かつ引張の残留応力を示した評価点３４、３５では、解析値と実測値との残留応力の差は小さく、解析値は実測値によく一致して高い解析精度を示すことがわかる。なお、解析値と実測値の残留応力の誤差（［解析値と実測値の残留応力の絶対値の差／実測値の残留応力の絶対値］×１００）は、最大で１０％であった。   FIG. 8 is a diagram comparing the residual stress of the test casting 100 of Example 1 between the analysis value and the actual measurement value. In FIG. 8, the horizontal axis represents each evaluation point, and the vertical axis represents the residual stress as distinguished from tension or compression. From FIG. 8, the difference in the residual stress between the analysis value and the actual measurement value is slightly large at the evaluation points 34 and 35 where the absolute value of the residual stress is small, but the absolute value of the residual stress which is regarded as a problem in actual casting is large. In addition, at the evaluation points 34 and 35 showing the tensile residual stress, it can be seen that the difference in the residual stress between the analysis value and the actual measurement value is small, and the analysis value closely matches the actual measurement value and shows high analysis accuracy. The error of the residual stress between the analysis value and the actual measurement value ([difference between absolute value of residual stress between analysis value and actual measurement value / absolute value of residual stress of actual measurement value] × 100) was 10% at maximum.

（実施例２）
実施例２では、実施例１で省略した流動解析工程Ｓ２も含めて本発明の砂型鋳物のシミュレーションを行った。実施例２は、実施例１と同様に、図６に示す砂型２０１を有機ＣＯ2鋳型、試験鋳物１００をオーステナイト系鋳鋼からなる鋳物、と想定して本発明の解析方法により砂型鋳物のシミュレーションを行った。以下、流動解析工程Ｓ２の実施にともない実施例１と相違する点についてのみ説明する。 (Example 2)
In Example 2, the sand casting of the present invention was simulated including the flow analysis step S2 omitted in Example 1. As in Example 1, Example 2 assumes that the sand mold 201 shown in FIG. 6 is an organic CO 2 mold and the test casting 100 is a casting made of austenitic cast steel, and simulates the sand casting by the analysis method of the present invention. went. Hereinafter, only differences from the first embodiment as the flow analysis step S2 is performed will be described.

（流動解析工程Ｓ２）
実施例１と同様に要素作成工程Ｓ１で解析モデルを作成した後、熱伝導解析工程Ｓ３を実施する前に、溶湯が鋳物要素に流入して充填される挙動を計算する流動解析工程Ｓ２を実施した。まず、要素作成工程Ｓ１で作成した解析モデルの鋳物要素及び鋳型要素に物性値として密度、比熱、熱伝導率、凝固潜熱、粘性係数及び初期圧力などを付与し、鋳物要素の一部である図示しない湯口要素に物性値及び初期圧力にくわえて更に鋳物要素に流入する溶湯の流量を付与し、実施例１と同様に、異種要素間の伝熱条件として熱伝達係数を付与した。また、各要素に所定の初期温度として、湯口要素には溶湯の注湯温度１６００℃を、鋳型要素及び空気要素には室温２５℃を付与した。 (Flow analysis step S2)
After the analysis model is created in the element creation step S1 as in the first embodiment, before the heat conduction analysis step S3, the flow analysis step S2 for calculating the behavior of the molten metal flowing into the casting element and filling is performed. did. First, a density, specific heat, thermal conductivity, latent heat of solidification, viscosity coefficient, initial pressure, and the like are given as physical property values to the casting element and the mold element of the analysis model created in the element creation step S1, and are shown as a part of the casting element. In addition to the physical property values and the initial pressure, the flow rate of the molten metal flowing into the casting element was further given to the gate element that did not, and the heat transfer coefficient was given as the heat transfer condition between the different elements as in Example 1. Moreover, as a predetermined initial temperature for each element, a molten metal pouring temperature of 1600 ° C. was given to the gate element, and a room temperature of 25 ° C. was given to the mold element and the air element.

流動解析工程Ｓ２では、鋳物となる溶湯が湯口要素から注入され鋳物要素に流入して充填される過程で、溶湯が砂型と接する部分で冷却される条件も加味して、鋳物要素が溶湯で充填されるまで、鋳物要素における溶湯の位置、温度、圧力などを求めた。流動解析工程Ｓ２の解析結果のうち、鋳物要素が充填完了した時の各要素の温度を、次の熱伝導解析工程Ｓ３の初期温度として用いた。   In the flow analysis step S2, the casting element is filled with the molten metal in consideration of the condition in which the molten metal to be cast is poured from the gate element, flows into the casting element and is filled and is cooled at the portion in contact with the sand mold. Until then, the position, temperature, pressure, etc. of the molten metal in the casting element were determined. Among the analysis results of the flow analysis step S2, the temperature of each element when the casting element was completely filled was used as the initial temperature of the next heat conduction analysis step S3.

次に、上記の流動解析工程Ｓ２により算出された鋳物及び鋳型の温度を、熱伝導解析工程Ｓ３の初期温度として付与した以外は実施例１と同様の方法で熱伝導解析工程Ｓ３及び熱変形解析工程Ｓ４を実施した。鋳型の拘束判定温度は、実施例１と同じく、前述した実施の形態で図４に示した有機ＣＯ2鋳型の拘束判定温度６００℃を使用した。 Next, the heat conduction analysis step S3 and the thermal deformation analysis are performed in the same manner as in Example 1 except that the casting and mold temperatures calculated in the flow analysis step S2 are given as the initial temperatures of the heat conduction analysis step S3. Step S4 was performed. As with the mold restraint determination temperature, the organic CO 2 mold restraint judgment temperature of 600 ° C. shown in FIG.

実施例２の解析方法によって得られた変位と応力について、その解析値と鋳造での実測値とを比較評価した。なお、変位と応力を評価した評価点は、図５に示す実施例１と同一の部位とした。また、変位と応力の実測値は実施例１と同一のデータを用いた。   About the displacement and stress obtained by the analysis method of Example 2, the analysis value and the actual measurement value in casting were compared and evaluated. The evaluation points for evaluating the displacement and stress were the same as those in Example 1 shown in FIG. Moreover, the same data as Example 1 were used for the actual measurement values of displacement and stress.

図９は、実施例２の試験鋳物１００のｚ方向変位量を、解析値と実測値とで比較した図である。図９は、実施例１の図７と同様、横軸に各評価点を、縦軸にｚ方向変位量をとったものである。図９から、解析値と実測値とのｚ方向変位量の差は小さく、解析値は実測値によく一致して高い解析精度を示すことがわかる。なお、実施例２での解析値と実測値のｚ方向変位量の誤差は、最大１８％であり、流動解析工程Ｓ２を省略した実施例１の最大誤差２８％に対して、誤差は凡そ半減しており、より高精度に変位を予測できることがわかる。これは、熱変形解析工程Ｓ４に先立って実施した流動解析工程Ｓ２で得られた鋳物及び鋳型の温度を、熱変形解析工程Ｓ４の初期温度として用いることで、より実際の鋳造に近い状態を解析できたためと考えられる。   FIG. 9 is a diagram comparing the z-direction displacement amount of the test casting 100 of Example 2 between the analysis value and the actual measurement value. FIG. 9 shows the evaluation points on the horizontal axis and the amount of displacement in the z direction on the vertical axis, as in FIG. 7 of Example 1. From FIG. 9, it can be seen that the difference in the z-direction displacement amount between the analysis value and the actual measurement value is small, and the analysis value closely matches the actual measurement value and exhibits high analysis accuracy. The error in the z-direction displacement between the analysis value and the actual measurement value in Example 2 is 18% at the maximum, and the error is about half of the maximum error of 28% in Example 1 in which the flow analysis step S2 is omitted. It can be seen that the displacement can be predicted with higher accuracy. This is because the temperature of the casting and mold obtained in the flow analysis step S2 performed prior to the thermal deformation analysis step S4 is used as the initial temperature of the thermal deformation analysis step S4, thereby analyzing a state closer to actual casting. It is thought that it was made.

図１０は、実施例２の試験鋳物１００の残留応力を、解析値と実測値とで比較した図である。図１０は横軸に各評価点をとり、縦軸に引張又は圧縮に区別した残留応力を表したものである。図１０から、解析値と実測値との残留応力の差は小さく、解析値が実測値によく一致して高い解析精度を示すことがわかる。なお、解析値と実測値の残留応力の誤差は、最大で５％であり、流動解析工程Ｓ２を省略した実施例１の最大誤差１０％に対して、誤差は半減しており、より高精度に応力を予測できることがわかる。   FIG. 10 is a diagram comparing the residual stress of the test casting 100 of Example 2 between the analysis value and the actual measurement value. In FIG. 10, the horizontal axis represents each evaluation point, and the vertical axis represents the residual stress distinguished between tension and compression. FIG. 10 shows that the difference in residual stress between the analysis value and the actual measurement value is small, and the analysis value closely matches the actual measurement value, indicating high analysis accuracy. The error of the residual stress between the analysis value and the actual measurement value is 5% at the maximum, and the error is halved with respect to the maximum error of 10% in Example 1 in which the flow analysis step S2 is omitted. It can be seen that the stress can be predicted.

（実施例３）
実施例３では、鋳型として、砂型をシェル鋳型とし、鋳型の一部に冷却部材（チル）として金属製部材を配設し、鋳物をオーステナイト系鋳鋼とした場合を想定して本発明の解析方法により砂型鋳物のシミュレーションを行った。 (Example 3)
In Example 3, assuming that the sand mold is a shell mold, a metal member is disposed as a cooling member (chill) in a part of the mold, and the casting is an austenitic cast steel, the analysis method of the present invention is used. The sand casting was simulated.

図１１は、実施例３の試験鋳物１００を解析及び鋳造するための金属製部材３００を配設した試験鋳型２００の概略形状を示し、（ａ）は平面図、（ｂ）は（ａ）での矢視Ｙ−Ｙ断面図である。図１１の試験鋳型２００は、砂型２０１をシェル鋳型とし、砂型２０１中に金属製部材３００を配設した以外は図６に示す試験鋳型２００と同様な構成とし、試験鋳物１００の形状、寸法等も図５及び図６と同様な構成としている。図１１で、試験鋳型２００には、試験鋳物１００の柱１のキャビティを構成する上下の鋳型の一部に砂型２０１に替えて冷却部材として金属製部材３００を配設している。なお、金属製部材３００の材質は、試験鋳物１００と同一材質のオーステナイト系鋳鋼とした。   FIG. 11 shows a schematic shape of a test mold 200 provided with a metal member 300 for analyzing and casting the test casting 100 of Example 3, (a) is a plan view, and (b) is (a). It is an arrow YY sectional drawing. The test mold 200 of FIG. 11 has the same configuration as the test mold 200 shown in FIG. 6 except that the sand mold 201 is a shell mold and the metal member 300 is disposed in the sand mold 201. The configuration is the same as that shown in FIGS. In FIG. 11, in the test mold 200, a metal member 300 is disposed as a cooling member in place of the sand mold 201 in part of the upper and lower molds constituting the cavity of the column 1 of the test casting 100. In addition, the material of the metal member 300 was an austenitic cast steel made of the same material as the test casting 100.

実施例３は、上記した鋳型の構成部材を変更した以外は実施例２と同様に解析を実施した。以下、鋳型の構成の変更にともない実施例２と相違する点についてのみ説明する。   In Example 3, the analysis was performed in the same manner as in Example 2 except that the above-described mold components were changed. Only the differences from the second embodiment due to the change in the mold configuration will be described below.

（要素作成工程Ｓ１）
鋳型要素のうち、金属製部材３００の位置する座標にある微小要素を金属製部材要素として定義した以外は実施例２と同様に解析モデルを作成した。 (Element creation process S1)
An analysis model was created in the same manner as in Example 2 except that, among the mold elements, a minute element at the coordinates where the metal member 300 is located was defined as a metal member element.

（流動解析工程Ｓ２）
鋳型要素として、砂型の要素にシェル鋳型の物性値を、金属製部材要素にオーステナイト系鋳鋼の物性値を付与し、砂型要素及び金属製部材要素とそれ以外の要素との異種要素間の熱伝達係数を付与し、金属製部材要素の初期温度を室温として２５℃を付与した。上記した以外は実施例２の流動解析工程Ｓ２と同様に、必要な条件を付与した後、鋳物要素が溶湯で充填するまで流動解析を実施して、充填完了時の各要素の温度を求めた。 (Flow analysis step S2)
As the mold element, the physical property value of the shell mold is given to the sand mold element, the physical property value of the austenitic cast steel is given to the metal member element, and the heat transfer between the dissimilar elements of the sand mold element and the metal member element and other elements A coefficient was given, and 25 ° C. was given with the initial temperature of the metallic member element being room temperature. Except as described above, in the same manner as in the flow analysis step S2 of Example 2, after providing the necessary conditions, flow analysis was performed until the casting element was filled with the molten metal, and the temperature of each element when filling was completed was obtained. .

（熱伝導解析工程Ｓ３）
鋳型要素である砂型要素及び金属製部材要素について、上記の流動解析工程Ｓ２と同様に、シェル鋳型及びオーステナイト系鋳鋼の夫々の物性値と異種要素間の熱伝達係数を付与するとともに、流動解析工程Ｓ２で算出された溶湯の充填完了時の鋳物及び鋳型の各要素の温度を初期温度として付与した。上記以外は、実施例２と同様として、全ての鋳物要素の温度が室温になるまで熱伝導解析工程Ｓ３を実施して、微小時間間隔毎に鋳物要素と鋳型要素の経時的な温度を求めた。 (Heat conduction analysis step S3)
For the sand mold element and the metal member element which are the mold elements, similarly to the flow analysis step S2, the physical properties of the shell mold and the austenitic cast steel and the heat transfer coefficient between different elements are given, and the flow analysis step The temperature of each element of the casting and mold at the completion of filling with the molten metal calculated in S2 was applied as the initial temperature. Except for the above, as in Example 2, the heat conduction analysis step S3 was performed until the temperature of all casting elements reached room temperature, and the time-dependent temperature of the casting element and the mold element was obtained at every minute time interval. .

（熱変形解析工程Ｓ４）
初期の拘束条件として、砂型要素及び金属製部材要素何れの鋳型からも鋳物が拘束される条件を鋳物要素に設定した。熱変形解析工程Ｓ４の開始後の拘束条件は、砂型要素については、実施例２と同様に後述する拘束条件設定ステップＳ４１を実施して鋳型による鋳物の拘束条件を設定した。一方、金属製部材は、温度が上昇しても砂型のように崩壊せず、鋳型としての形状を保持するので、後述する拘束条件設定ステップＳ４１は実施することなく、解析の開始から終了までの終始、鋳型による鋳物の拘束有りとして設定した。上記以外は、実施例２と同様の方法で熱変形解析工程Ｓ４を実施した。 (Thermal deformation analysis step S4)
As an initial constraint condition, a condition in which the casting is constrained from the mold of either the sand mold element or the metal member element was set as the casting element. As for the restraint conditions after the start of the thermal deformation analysis step S4, for sand mold elements, the restraint condition setting step S41 described later was performed in the same manner as in Example 2 to set the restraint conditions for the casting by the mold. On the other hand, the metal member does not collapse like a sand mold even if the temperature rises, and retains the shape as a mold. Therefore, from the start to the end of the analysis without performing the constraint condition setting step S41 described later. From the beginning, it was set that there was a restriction of the casting by the mold. Except for the above, the thermal deformation analysis step S4 was performed in the same manner as in Example 2.

（拘束条件設定ステップＳ４１）
拘束条件設定ステップＳ４１では、使用した拘束判定温度が異なる以外は実施例１で説明したと同様の方法で、拘束条件判定要否設定ステップＳ４１１、拘束条件判定ステップＳ４１２及び弾塑性解析ステップＳ４２を実施した。実施例３の拘束判定温度は、前述した実施の形態で図３に示したシェル鋳型の拘束判定温度を用いて５００℃に設定した。実施例３の拘束条件判定ステップＳ４１２では、熱伝導解析工程Ｓ３で経時的に求めた鋳型要素の温度データのうち鋳型要素の温度と拘束判定温度５００℃とを比較して、鋳型要素の温度が、５００℃未満なら鋳型による鋳物の拘束有り、５００℃以上なら拘束無しと判定して拘束条件を設定した。 (Restriction condition setting step S41)
In the constraint condition setting step S41, the constraint condition determination necessity setting step S411, the constraint condition determination step S412 and the elastoplastic analysis step S42 are performed in the same manner as described in the first embodiment except that the used constraint determination temperature is different. did. The restraint judgment temperature of Example 3 was set to 500 ° C. using the restraint judgment temperature of the shell mold shown in FIG. 3 in the embodiment described above. In the constraint condition determination step S412 of the third embodiment, the temperature of the mold element is compared with the temperature of the mold element in the temperature data of the mold element obtained with time in the heat conduction analysis step S3 and the constraint determination temperature of 500 ° C. When the temperature was lower than 500 ° C., the casting was restricted by the mold, and when the temperature was 500 ° C. or higher, it was determined that there was no restriction.

実施例３の解析方法によって得られた変位と応力について、その解析値と鋳造での実測値とを比較評価した。なお、変位と応力を評価した評価点は、図５に示す実施例１と同一の部位とした。また、変位と応力の実測値は、砂型をシェル鋳型として一部に金属製部材３００を配設した試験鋳型２００を用いて、オーステナイト系鋳鋼からなる試験鋳物１００を実際に鋳造して得られたデータを用いた。   About the displacement and stress obtained by the analysis method of Example 3, the analysis value and the actual measurement value in casting were compared and evaluated. The evaluation points for evaluating the displacement and stress were the same as those in Example 1 shown in FIG. In addition, the measured values of displacement and stress were obtained by actually casting a test casting 100 made of austenitic cast steel using a test mold 200 having a sand mold as a shell mold and a metal member 300 partially disposed therein. Data was used.

図１２は、実施例３の試験鋳物１００のｚ方向変位量を、解析値と実測値とで比較した図である。図１２は、横軸に各評価点を、縦軸にｚ方向変位量をとったものである。図１２から、解析値と実測値とのｚ方向変位量の差は小さく、高い解析精度を示すことがわかる。図１２から、評価点２１を略中央としてその近傍となる、金属製部材３００と接触する鋳物部位Ｄのｚ方向変位量は、ほぼゼロに近い値を示すとともに、解析値は実測値に極めてよく一致し、金属製部材が鋳物を終始拘束するために鋳物に変形が生じない現象を正確に予測していることがわかる。なお、実施例３の金属製部材３００と接触する部位Ｄ以外の解析値と実測値のｚ方向変位量の誤差は、最大１２％であり、解析値が実測値によく一致して高精度に変位を予測できることがわかる。   FIG. 12 is a diagram comparing the z-direction displacement amount of the test casting 100 of Example 3 between the analysis value and the actual measurement value. In FIG. 12, the horizontal axis represents each evaluation point, and the vertical axis represents the amount of displacement in the z direction. FIG. 12 shows that the difference in the amount of displacement in the z direction between the analysis value and the actual measurement value is small, indicating high analysis accuracy. From FIG. 12, the z-direction displacement amount of the casting part D, which is in the vicinity of the evaluation point 21 and in contact with the metal member 300, shows a value close to zero, and the analysis value is very good for the actual measurement value. It can be seen that the metal member accurately predicts the phenomenon that the casting does not deform because the metal member restrains the casting from start to finish. The error in the z-direction displacement amount between the analytical value and the actual measurement value other than the portion D that contacts the metal member 300 of Example 3 is 12% at the maximum, and the analytical value closely matches the actual measurement value with high accuracy. It can be seen that the displacement can be predicted.

図１３は、実施例３の試験鋳物１００の残留応力を、解析値と実測値とで比較した図である。図１３は横軸に各評価点をとり、縦軸に引張又は圧縮に区別した残留応力を表したものである。図１３から、解析値と実測値との残留応力の差は小さく、解析値が実測値によく一致して高い解析精度を示すことがわかる。なお、解析値と実測値の残留応力の誤差は、最大７％であり、高精度に応力を予測できることがわかる。   FIG. 13 is a diagram comparing the residual stress of the test casting 100 of Example 3 between the analysis value and the actual measurement value. In FIG. 13, the horizontal axis represents each evaluation point, and the vertical axis represents the residual stress differentiated between tension and compression. From FIG. 13, it can be seen that the difference in residual stress between the analysis value and the actual measurement value is small, and the analysis value closely matches the actual measurement value, indicating high analysis accuracy. Note that the error of the residual stress between the analysis value and the actual measurement value is 7% at the maximum, and it can be seen that the stress can be predicted with high accuracy.

（比較例）
本発明の比較例として、熱変形解析工程Ｓ４での鋳物要素に付与する拘束条件を、初期条件から解析終了に至るまで、鋳型による鋳物の拘束が無く、鋳物が自由に変形できるものとして、実施例２と同様、有機ＣＯ2鋳型を用いたオーステナイト系鋳鋼の鋳造を想定して砂型鋳物のシミュレーションを実施した。比較例では、要素作成工程Ｓ１、流動解析工程Ｓ２及び熱伝導解析工程Ｓ３は、本発明の解析方法を実施したが、熱変形解析工程Ｓ４では、拘束条件設定ステップＳ４１を実施せず、鋳型による鋳物の拘束は無いものとして弾塑性解析ステップＳ４２のみ行って解析を終了した。 (Comparative example)
As a comparative example of the present invention, the constraint condition to be applied to the casting element in the thermal deformation analysis step S4 is carried out on the assumption that the casting is not restricted by the mold from the initial condition to the end of the analysis, and the casting can be freely deformed. Similar to Example 2, a sand casting was simulated assuming the casting of austenitic cast steel using an organic CO 2 mold. In the comparative example, the element creation step S1, the flow analysis step S2, and the heat conduction analysis step S3 performed the analysis method of the present invention. However, in the thermal deformation analysis step S4, the constraint condition setting step S41 is not performed, and the mold is used. Only the elastic-plastic analysis step S42 was performed assuming that there was no constraint on the casting, and the analysis was completed.

比較例の解析方法によって得られた変位と応力について、その解析値と鋳造での実測値とを比較評価した。なお、変位と応力を評価した評価点は、実施例１と同一の部位とした。また、変位と応力の実測値は実施例１と同一のデータを用いた。   About the displacement and stress obtained by the analysis method of the comparative example, the analysis value and the actual measurement value in casting were compared and evaluated. The evaluation points for evaluating displacement and stress were the same as those in Example 1. Moreover, the same data as Example 1 were used for the actual measurement values of displacement and stress.

図１４は、比較例の試験鋳物のｚ方向変位量を、解析値と実測値とで比較した図である。図１４は横軸に各評価点を、縦軸にｚ方向変位量をとったものである。図１４から、比較例では、解析値と実測値とのｚ方向変位量の差が大きく、基準点とした評価点２１から遠ざかるにしたがって、解析値が実測値から乖離していることがわかる。比較例での解析値と実測値のｚ方向変位量の誤差は、最大で５７％であり、上記した実施例１、２と比較してｚ方向変位量の予測精度が低く、変位を定量的に予測するに充分な解析精度が得られない。   FIG. 14 is a diagram comparing the z-direction displacement of the test casting of the comparative example between the analysis value and the actual measurement value. In FIG. 14, the horizontal axis represents each evaluation point, and the vertical axis represents the amount of displacement in the z direction. FIG. 14 shows that in the comparative example, the difference in the z-direction displacement amount between the analysis value and the actual measurement value is large, and the analysis value deviates from the actual measurement value as the distance from the evaluation point 21 as the reference point increases. The error in the z-direction displacement amount between the analysis value and the actual measurement value in the comparative example is 57% at the maximum, and the prediction accuracy of the z-direction displacement amount is lower than in the first and second embodiments, and the displacement is quantitative However, sufficient analysis accuracy cannot be obtained.

図１５は、比較例の試験鋳物の残留応力を、解析値と実測値とで比較した図である。図１５は横軸に各評価点をとり、縦軸に残留応力を引張又は圧縮に区別して表したものである。図１５から、比較例では、解析値と実測値との残留応力の差が大きいことがわかる。比較例での解析値と実測値の残留応力の誤差は、最大で７２％であり、上記した実施例１、２と比較して残留応力の予測精度が低く、鋳造時の応力を予測するに充分な解析精度が得られない。   FIG. 15 is a diagram comparing the residual stress of the test casting of the comparative example between the analysis value and the actual measurement value. In FIG. 15, the horizontal axis represents each evaluation point, and the vertical axis represents residual stress classified into tension or compression. FIG. 15 shows that the difference in residual stress between the analysis value and the actual measurement value is large in the comparative example. The error of the residual stress between the analysis value and the actual measurement value in the comparative example is 72% at the maximum, and the prediction accuracy of the residual stress is low compared with the above-described Examples 1 and 2, and the stress at the time of casting is predicted. Sufficient analysis accuracy cannot be obtained.

以上、実施例で説明したとおり、本発明の砂型鋳物のシミュレーション方法は、鋳型の拘束判定温度に基づいて、鋳型の形状を保持するか否かの拘束条件を付与して熱変形解析することで、ｚ方向変位量と残留応力で評価した場合の解析値が実測値によく一致して誤差が小さく、高い解析精度を示し、砂型鋳物に生じる歪み、変位又は応力を高精度に予測できることがわかった。   As described above, as described in the embodiments, the sand casting casting simulation method of the present invention is based on the mold restraint determination temperature, and gives a restraint condition as to whether or not to retain the shape of the mold and performs thermal deformation analysis. The analysis value when evaluated by the amount of displacement in the z direction and the residual stress agrees well with the actual measurement value, and the error is small, showing high analysis accuracy, and it is understood that the distortion, displacement or stress generated in the sand casting can be predicted with high accuracy. It was.

本発明の実施の形態における砂型鋳物のシミュレーション方法の全体の流れを示すフローチャートである。It is a flowchart which shows the whole flow of the simulation method of the sand casting in embodiment of this invention. 図１における熱変形解析工程において実施する拘束条件設定の手順を示すフローチャートである。It is a flowchart which shows the procedure of the constraint condition setting implemented in the thermal deformation analysis process in FIG. シェル鋳型の鋳型温度−鋳型強度特性の一例を示す図である。It is a figure which shows an example of the mold temperature-mold intensity | strength characteristic of a shell mold. 有機ＣＯ2鋳型の鋳型温度−鋳型強度特性の一例を示す図である。Mold temperature of the organic CO 2 mold - is a diagram showing an example of mold strength characteristics. 実施例に供した試験鋳物と変位と応力の評価位置を示す図である。It is a figure which shows the test casting used for the Example, and the evaluation position of a displacement and stress. 試験鋳物を解析及び鋳造するための試験鋳型の概略形状を示す図である。It is a figure which shows the schematic shape of the test casting_mold | template for analyzing and casting a test casting. 実施例１の試験鋳物のｚ方向変位量を、解析値と実測値とで比較した図である。It is the figure which compared the z direction displacement amount of the test casting of Example 1 with the analysis value and the actual measurement value. 実施例１の試験鋳物の残留応力を、解析値と実測値とで比較した図である。It is the figure which compared the residual stress of the test casting of Example 1 with the analytical value and the measured value. 実施例２の試験鋳物のｚ方向変位量を、解析値と実測値とで比較した図である。It is the figure which compared the z direction displacement amount of the test casting of Example 2 with the analysis value and the actual measurement value. 実施例２の試験鋳物の残留応力を、解析値と実測値とで比較した図である。It is the figure which compared the residual stress of the test casting of Example 2 with the analysis value and the actual measurement value. 実施例３の試験鋳物を解析及び鋳造するための金属製部材を配設した試験鋳型の概略形状を示す図である。It is a figure which shows schematic shape of the test casting_mold | template which arrange | positioned the metal member for analyzing and casting the test casting of Example 3. FIG. 実施例３の試験鋳物のｚ方向変位量を、解析値と実測値とで比較した図である。It is the figure which compared the z direction displacement amount of the test casting of Example 3 with the analytical value and the measured value. 実施例３の試験鋳物の残留応力を、解析値と実測値とで比較した図である。It is the figure which compared the residual stress of the test casting of Example 3 with the analysis value and the actual measurement value. 比較例の試験鋳物のｚ方向変位量を、解析値と実測値とで比較した図である。It is the figure which compared the z direction displacement amount of the test casting of the comparative example with the analysis value and the actual measurement value. 比較例の試験鋳物の残留応力を、解析値と実測値とで比較した図である。It is the figure which compared the residual stress of the test casting of the comparative example with the analysis value and the actual measurement value.

符号の説明Explanation of symbols

１００：試験鋳物
１０１：キャビティ
２００：試験鋳型
２０１：砂型
３００：金属製部材
１、２：柱
３、４：締結部
５、６：堰
２１：基準点
２２〜２５：ｚ方向変位量の評価点
３１〜３５：残留応力の評価点
Ｃ１、Ｃ２：切断面
Ｄ：金属製部材と接触する鋳物部位 DESCRIPTION OF SYMBOLS 100: Test casting 101: Cavity 200: Test mold 201: Sand mold 300: Metal member 1, 2: Column 3, 4: Fastening part 5, 6: Weir 21: Reference point 22-25: Evaluation point of z direction displacement 31-35: Evaluation points of residual stress C1, C2: Cut surface D: Casting part in contact with metal member

Claims (5)

少なくとも一部が砂型からなる鋳型内に溶湯を注入して凝固させることにより所望形状の鋳物を得る際に、鋳物に生じる歪み、変位又は応力の少なくとも１つを求める砂型鋳物のシミュレーション方法であって、少なくとも鋳物要素及び鋳型要素からなる解析モデルを作成する要素作成工程（Ｓ１）と、前記鋳物要素及び前記鋳型要素の伝熱を経時的に解析して、前記鋳物要素及び前記鋳型要素の温度を求める熱伝導解析工程（Ｓ３）と、前記熱伝導解析工程（Ｓ３）により得られた前記鋳型要素の温度に基づいて、鋳型による鋳物の拘束条件を設定する拘束条件設定ステップ（Ｓ４１）と、設定された拘束条件、前記鋳物要素の温度変化量及び熱膨張係数に基づいて、前記鋳物要素の変形を経時的に解析して、前記鋳物要素の歪み、変位又は応力の少なくとも１つを求める弾塑性解析ステップ（Ｓ４２）と、をもつ熱変形解析工程（Ｓ４）と、を有することを特徴とする砂型鋳物のシミュレーション方法。   A sand casting simulation method for obtaining at least one of distortion, displacement or stress generated in a casting when a casting having a desired shape is obtained by injecting and solidifying a molten metal into a mold made of at least a sand mold. An element creation step (S1) for creating an analysis model consisting of at least a casting element and a mold element, and analyzing the heat transfer of the casting element and the mold element over time to determine the temperature of the casting element and the mold element. A heat conduction analysis step (S3) to be obtained; a restriction condition setting step (S41) for setting a restriction condition of the casting by the mold based on the temperature of the mold element obtained by the heat conduction analysis step (S3); The deformation of the casting element is analyzed over time based on the restricted conditions, the temperature change amount of the casting element, and the thermal expansion coefficient, so that the distortion, displacement, or displacement of the casting element is analyzed. Simulation method of sand casting, characterized in that it comprises a elastic-plastic analysis step (S42) determining at least one, and thermal deformation analysis step (S4) with the stress. 前記拘束条件設定ステップ（Ｓ４１）は、前記鋳型要素の温度変化に基づいて鋳型による鋳物の拘束条件判定の要否を決定する拘束条件判定要否設定ステップ（Ｓ４１１）と、拘束条件判定を要する場合に、前記鋳型要素の温度と鋳型の拘束判定温度とを比較して拘束の有無を判定する拘束条件判定ステップ（Ｓ４１２）と、前記鋳物要素に拘束条件を設定するステップと、を有する請求項１に記載の砂型鋳物のシミュレーション方法。   The constraint condition setting step (S41) includes a constraint condition determination necessity setting step (S411) for determining whether or not a constraint condition determination for a casting by a mold is necessary based on a temperature change of the mold element, and a constraint condition determination is required. And a constraint condition determining step (S412) for determining whether there is a constraint by comparing the temperature of the mold element and the constraint determination temperature of the mold, and a step of setting a constraint condition for the casting element. A method for simulating a sand casting as described in 1. 前記熱伝導解析工程（Ｓ３）の前に、溶湯が前記鋳物要素を流動して充填される挙動を経時的に解析して、前記鋳物要素の温度を求める流動解析工程（Ｓ２）を行い、前記流動解析工程（Ｓ２）で得られた溶湯の充填完了時の前記鋳物要素の温度を前記熱伝導解析工程（Ｓ３）の初期温度として付与することを特徴とする請求項１又は請求項２に記載の砂型鋳物のシミュレーション方法。   Before the heat conduction analysis step (S3), a flow analysis step (S2) for analyzing the behavior of the molten metal flowing and filling the casting element over time to obtain the temperature of the casting element is performed, The temperature of the said casting element at the time of completion of the filling of the molten metal obtained by the flow analysis process (S2) is provided as an initial temperature of the said heat conduction analysis process (S3). Simulation method for sand castings. 前記鋳型の拘束判定温度が、鋳型温度と鋳型強度との関係から、鋳型の形状を保持できないと見なせる温度である請求項１乃至請求項３のいずれかに記載の砂型鋳物のシミュレーション方法。   The sand mold casting simulation method according to any one of claims 1 to 3, wherein the mold restriction determination temperature is a temperature at which it is considered that the shape of the mold cannot be maintained from the relationship between the mold temperature and the mold strength. 前記鋳型に金属製部材を含み、前記熱変形解析工程（Ｓ４）の解析の開始から終了まで終始、前記金属製部材に拘束有りの拘束条件を設定することを特徴とする請求項１乃至請求項４のいずれかに記載の砂型鋳物のシミュレーション方法。   The metal mold is included in the mold, and from the start to the end of the analysis in the thermal deformation analysis step (S4), a restraint condition with restraint is set on the metal member. 4. The method for simulating a sand casting according to any one of 4 above.
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