JP2020163729A - Simulation device, simulation method, program and storage medium - Google Patents

Abstract

To provide a simulation device capable of simulating a shape of a parison in a pushout process in a relatively short time.SOLUTION: In this simulation device 100, a first physical model of a parison 1 in a pushout process is a physical model based on a motion equation of a mass point 21 assuming that the parison 1 is a viscoelastic body that expands and deforms along an expansion and contraction direction of a viscoelastic model 22 by connecting a plurality of connected mass points 21 and among the mass points 21 by the viscoelastic model 22. Further, a force acting on the parison 1 includes at least: a force generated in the viscoelastic model 22 acting on the parison 1; a gravity acting on the parison 1; and a force received from an airflow generated by sucking an air between the parison 1 and a mold 2.SELECTED DRAWING: Figure 4

Description

The present invention relates to simulation devices, simulation methods, programs and storage media.

Conventionally, a simulation device for simulating the shape of a parison in suction blow molding is known (see, for example, Non-Patent Document 1).

Non-Patent Document 1 discloses a method for simulating the shape of a parison in a push-out step of suction blow molding (a step in which the parison is extruded into a mold by an extruder). In this simulation method, the shape of the parison extruded into the mold while sucking out the air in the mold is obtained by numerical calculation. Specifically, the flow of air flowing through the space between the mold and the parison is approximated as the flow of Hele-Shaw. The Hele-Shaw approximation is an approximation of the flow of liquid flowing between two parallel plates having a relatively small interval as a two-dimensional flow. In addition, the K-BKZ model is used as the physical model of the parison. The K-BKZ model strains some functions (unit tensors) of the Maxwell model (a model that expresses viscoelasticity by combining a virtual spring that represents elasticity and a virtual dashpot that represents viscosity). It is a model replaced with a function that depends on. Then, in this simulation method, the parison is discretized into finite elements, and the shape of the parison extruded into the mold is simulated by the finite element method.

Kalonji. Kabanemi, Jean-Philippe Marcotte, "Numerical Simulation of Suction Blow Modeling Process for Producing Curved Ducts", POLYMER ENGINEERING & ENGINEERING &

However, in the simulation method described in Non-Patent Document 1, since the shape of the parison extruded into the mold by the finite element method is simulated, it is considered that it takes a relatively long time to simulate the shape of the parison. .. Therefore, it is desired to simulate the shape of the parison in the pushout process in a relatively short time.

The present invention has been made to solve the above problems, and one object of the present invention is a simulation device capable of simulating the shape of a parison in a pushout process in a relatively short time. , Simulation methods, programs and storage media.

In order to achieve the above object, the simulation device in the resin according to the first aspect of the present invention pushes the parison, which is a substantially tubular molten resin, into the mold while sucking out the air in the mold, and also into the mold. A simulation device that simulates the shape of a parison in viscoelastic molding, which forms a resin molded product by blowing air into the extruded parison, and is the first parison in the push-out process in which the parison is extruded into a mold by an extruder. A first physical model is provided with a first physical model generation unit that generates one physical model and a first shape calculation unit that calculates the shape of the parison in the pushout process by time-integrating the first physical model of the parison. Is an equation of motion of the plaques, assuming that the parison is a viscoelastic body that stretches and deforms along the expansion and contraction direction of the viscoelastic model by connecting a plurality of connected plaques and the pouches with a viscoelastic model. It is a physical model based on, and the force acting on the parison is generated by at least the force generated by the viscoelastic model acting on the parison, the gravity acting on the parison, and the suction of air between the parison and the mold. Including the force received from the airflow.

In the simulation device according to the first aspect, as described above, the first physical model expands and contracts the viscoelastic model by connecting a plurality of connected mass points and the mass points between the mass points by a viscoelastic model. It is a physical model based on the kinetic equation of mass points, assuming a viscoelastic body that stretches and deforms along the direction. The force acting on the parison is at least the force generated by the viscoelastic model acting on the parison and the force acting on the parison. Includes the force of gravity and the force received from the airflow generated by sucking the air between the parison and the mold. As a result, the parison is represented by a relatively simple physical model that stretches and deforms along the stretching direction of the viscoelastic model. In addition, the first shape calculation unit calculates the shape of the parison in the push-out process by time-integrating the first physical model of the parison. As a result, the shape of the parison is calculated by time-integrating a relatively simple physical model.Therefore, when the parison is discretized into finite elements and the shape of the parison extruded into the mold by the finite element method is simulated. In comparison, the shape of the parison in the pushout process can be simulated in a relatively short time.

In the simulation apparatus according to the first aspect, preferably, the force acting on the parison further includes a repulsive force when the parison collides with the mold and a frictional force when the parison and the mold come into contact with each other. With this configuration, the shape of the parison can be simulated while considering the influence of the mold on the parison, so that the shape of the parison can be simulated more precisely.

In the simulation apparatus according to the first aspect, preferably, the force acting on the parison further includes a force that generates a bending moment between adjacent viscoelastic models. With this configuration, the shape of the parison can be simulated while considering the effect of bending the parison, so that the shape of the parison can be simulated more precisely.

The simulation apparatus according to the first aspect preferably further includes a radius calculation unit that calculates a change in the radius of the parison based on the degree of extension of the parison based on the shape of the parison calculated by the first shape calculation unit. .. With this configuration, the shape of the parison including the radius of the parison can be simulated, so that the shape of the parison can be simulated more precisely.

The simulation apparatus according to the first aspect preferably further includes a thickness calculation unit that calculates a change in the thickness of the parison based on the degree of elongation of the parison based on the shape of the parison calculated by the first shape calculation unit. .. With this configuration, the shape of the parison including the thickness of the parison can be simulated, so that the shape of the parison can be simulated more precisely. Moreover, since the thickness is calculated, the strength of the resin molded product after molding can be predicted.

In the simulation apparatus according to the first aspect, preferably, the curvature calculation unit that calculates the curvature of the parison based on the angle between the viscoelastic models adjacent to each other and the curvature of the parison calculated by the curvature calculation unit are used. Further, a buckling determination unit for determining whether or not the parison buckles is provided. With this configuration, it is determined whether or not the parison buckles, so it is possible to determine whether or not a desired resin molded product can be molded.

In the simulation apparatus according to the first aspect, preferably, a second physical model for generating a second physical model of the parison in a blow process in which air is blown into the parison after being extruded into a mold to expand the parison. The generation unit, the shape of the parison after the pushout process calculated by the first shape calculation unit, and the second shape calculation unit that calculates the shape of the parison in the blow process based on the second physical model of the parison. Further prepare. With this configuration, the shape of the parison in the blow process is calculated based on the shape of the parison after the push-out process calculated by the first shape calculation unit, so that the shape of the parison after the blow process is calculated more accurately. The shape can be calculated.

In this case, preferably, the second physical model is a physical model that assumes that the parison is a viscoelastic body or an elastic body, and the force acting on the parison is due to the gravity acting on the parison and the air blown into the parison. It includes pressure, repulsive force when the parison collides with the mold, and frictional force when the parison and the mold come into contact with each other. With this configuration, the shape of the parison after the blow process can be simulated in a relatively short time by using a relatively simple second physical model.

In the simulation apparatus according to the first aspect, preferably, the flow path in the mold from which the parison is extruded has a straight pipe shape or a meandering pipe shape, and the first shape calculation unit has a straight pipe shape or a straight pipe shape. It is configured to calculate the shape of the parison inside the flow path in the mold having a meandering tube shape. With this configuration, it is possible to simulate the shape of the parison in the flow path in the mold having a straight pipe shape or a meandering pipe shape. When the flow path in the mold has a meandering tube shape, it is relatively difficult to determine whether or not a desired resin molded product is molded by suction blow molding. Therefore, simulating the shape of the parison as described above is particularly effective in determining whether or not a desired resin molded product is molded.

In the simulation method according to the second aspect of the present invention, the resin is extruded into the mold while sucking out the air in the mold, and the parison, which is a substantially tubular melting resin, is blown into the parison extruded into the mold. A simulation method that simulates the shape of a parison in suction blow molding, which forms a molded product, in which the parison is extruded into a mold by an extruder, and the step of generating the first physical model of the parison and the parison The first physical model includes a step of calculating the shape of the parison in the pushout process by time-integrating the first physical model, and the first physical model is a viscoelastic model between a plurality of mass points connecting the parisons and the mass points. It is a physical model based on the kinetic equation of the mass point, assuming that it is a viscoelastic body that stretches and deforms along the expansion and contraction direction of the viscoelastic model by being connected by. It includes the force generated by the viscoelastic model, the gravity acting on the parison, and the force received from the airflow generated by sucking the air between the parison and the mold.

In the simulation method based on the second aspect, as described above, the first physical model expands and contracts the viscoelastic model by connecting a plurality of connected mass points and the mass points between the mass points by a viscoelastic model. It is a physical model based on the kinetic equation of mass points, assuming a viscoelastic body that stretches and deforms along the direction. The force acting on the mass points is at least the force generated by the viscoelastic model acting on the mass point and the force acting on the parison. Includes the force of gravity and the force received from the airflow generated by sucking the air between the parison and the mold. As a result, the shape of the parison is calculated by time-integrating a relatively simple physical model.Therefore, when the parison is separated into finite elements and the shape of the parison extruded into the mold by the finite element method is simulated. In comparison, it is possible to provide a simulation method capable of simulating the shape of the parison in the pushout process in a relatively short time.

The program according to the third aspect of the present invention involves the step of generating the first physical model of the parison and the time integration of the first physical model of the parison in the pushout process in which the parison is extruded into the mold by the extruder. The first physical model includes a step of calculating the shape of the parison in the push-out process, and the first physical model is a viscoelastic model by connecting a plurality of connected mass points and the mass points between the mass points by a viscoelastic model. It is a physical model based on the kinetic equation of the mass point, assuming that it is a viscoelastic body that stretches and deforms along the expansion and contraction direction, and the force acting on the mass point is at least the force generated by the viscoelastic model acting on the parison and the parison. It includes the acting gravity and the force received from the airflow generated by sucking the air between the parison and the mold.

In the program according to the third aspect, as described above, in the first physical model, the parison is connected to a plurality of connected mass points and the mass points are connected to each other by a viscoelastic model, so that the viscoelastic model expands and contracts. It is a physical model based on the kinetic equation of the mass point, assuming that it is a viscoelastic body that stretches and deforms along the mass point. The force acting on the mass point is at least the force generated by the viscoelastic model acting on the mass point and the force acting on the parison. It includes gravity and the force received from the airflow generated by sucking the air between the parison and the mold. As a result, the shape of the parison is calculated by time-integrating a relatively simple physical model.Therefore, when the parison is separated into finite elements and the shape of the parison extruded into the mold by the finite element method is simulated. In comparison, it is possible to provide a program capable of simulating the shape of the parison in the pushout process in a relatively short time.

The storage medium according to the fourth aspect of the present invention is a resin by sucking out the air in the mold, extruding the parison, which is a substantially tubular melting resin, into the mold, and blowing air into the parison extruded into the mold. A storage medium for storing a program for simulating the shape of a parison in suction blow molding for molding a molded product, and a step of generating a first physical model of the parison in a push-out process in which the parison is extruded into a mold by an extruder. The first physical model includes a step of calculating the shape of the parison in the pushout process by time-integrating the first physical model of the parison, and the first physical model is between a plurality of mass points connecting the parisons and between the mass points. Is a physical model based on the kinetic equation of a mass point, assuming that the viscoelastic body is stretched and deformed along the expansion and contraction direction of the viscoelastic model by connecting the mass points, and the force acting on the mass point is at least parison. Memorize the program, including the force generated by the viscoelastic model acting on the force, the gravity acting on the parison, and the force received from the airflow generated by sucking the air between the parison and the mold.

In the storage medium according to the fourth aspect, as described above, the first physical model expands and contracts the viscoelastic model by connecting a plurality of connected mass points and the mass points between the mass points by a viscoelastic model. It is a physical model based on the kinetic equation of mass points, assuming a viscoelastic body that stretches and deforms along the direction. The force acting on the mass points is at least the force generated by the viscoelastic model acting on the mass point and the force acting on the parison. Includes the force of gravity and the force received from the airflow generated by sucking the air between the parison and the mold. As a result, the shape of the parison is calculated by time-integrating a relatively simple physical model.Therefore, when the parison is separated into finite elements and the shape of the parison extruded into the mold by the finite element method is simulated. In comparison, it is possible to provide a storage medium capable of simulating the shape of the parison in the pushout process in a relatively short time.

According to the present invention, as described above, the shape of the parison in the pushout process can be simulated in a relatively short time.

It is a figure for demonstrating suction blow molding. It is a figure which shows the resin molded article. It is a figure which shows the structure of the simulation apparatus by this embodiment. It is a figure which shows the 1st physical model. It is a figure for demonstrating the force received from the air flow generated by sucking the air between a parison and a mold. It is a figure (1) for demonstrating the radius which changes with the extension of a parison. It is a figure (2) for demonstrating the radius which changes with the extension of a parison. It is a figure (3) for demonstrating the radius which changes with the extension of a parison. It is a figure which shows the parison in a bent state. It is a figure which shows the parison in a buckled state. It is a figure which shows the relationship between a curvature and a bending moment. It is a flow chart for demonstrating the simulation method by this Embodiment. It is a figure which shows the shape of the parison calculated by the simulation. It is a figure which shows the mold by the modification.

Hereinafter, embodiments embodying the present invention will be described with reference to the drawings.

[The present embodiment]
(Simulation device configuration)
The configuration of the simulation apparatus 100 according to the present embodiment will be described with reference to FIGS. 1 to 13. The simulation device 100 is configured to simulate the shape of the parison 1 in suction blow molding.

As shown in FIG. 1, suction blow molding is resin molding by extruding a parison 1 into a mold 2 while sucking out air in a mold 2 and blowing air into the parison 1 extruded into the mold 2. It is to mold the product 3. The parison 1 is a substantially tubular molten resin. Further, suction blow molding is suitable for molding a resin molded product 3 (see FIG. 2) such as a turbo duct of an automobile, which is relatively long and has a complicated shape. Also, general blow molding is suitable for molding tanks, PET bottles and ducts. Note that blow molding is to mold the resin molded product 3 by blowing air into the parison 1 extruded into the mold 2, and unlike suction blow molding, the air in the mold 2 is not sucked out. ..

Further, as shown in FIG. 1, the suction blow molding includes a push-out step (FIG. 1 (b)) and a blow step (FIG. 1 (c)). In the push-out step, the parison 1 is pushed out into the flow path 2a in the mold 2 by the extruder. Here, in the present embodiment, the flow path 2a in the mold 2 from which the parison 1 is extruded has a meandering tube shape. Then, the simulation device 100 (the first shape calculation unit 12 described later) is configured to calculate the shape of the parison 1 inside the flow path 2a in the mold 2 having a meandering tube shape.

The mold 2 is divided into two in a direction (horizontal direction) orthogonal to the direction in which the parison 1 is extruded (vertical direction). As shown in FIGS. 1 (a) and 1 (b), the parison 1 is extruded into the flow path 2a of the mold 2 in a state where the mold 2 divided into two is closed. At this time, the air in the flow path 2a in the mold 2 is sucked out by a blower (not shown). Specifically, the air between the flow path 2a (wall) of the mold 2 and the outer surface of the parison 1 is sucked out by the blower.

Then, as shown in FIG. 1C, after the parison 1 penetrates the flow path 2a of the mold 2, the two-divided members 4 arranged on the upper side and the lower side of the mold 2 are formed. Moved closer to each other. As a result, the upper side and the lower side of the parison 1 are closed by being sandwiched between the members 4.

Then, as shown in FIG. 1C, in the blow step, the needle 5 is inserted into the parison 1 in which the upper side and the lower side are closed, and air is injected from the needle 5 into the parison 1. As a result, the parison 1 expands, and the resin molded product 3 having a desired shape (shape corresponding to the flow path 2a of the mold 2) is molded. After that, as shown in FIG. 1D, the two-divided mold 2 and the member 4 are moved so as to move away from each other. Then, the molded resin molded product 3 is taken out from the mold 2.

Here, in order to properly mold the resin molded product 3, it is necessary to grasp the state (shape, etc.) of the parison 1 in the flow path 2a of the mold 2 in the push-out step. Further, it is necessary to determine whether or not the resin molded product 3 having a desired shape can be molded. Further, in the blowing step, it is necessary to determine whether or not the resin molded product 3 having an appropriate thickness (thickness) can be molded. Then, in order to make the above determination, it takes a huge amount of time and cost to repeat the trial production of the resin molded product 3 based on the know-how of the user and the like. Therefore, the simulation device 100 of the present embodiment is configured to simulate the shape of the parison 1 in suction blow molding.

(Pushout process)
First, the configuration of the simulation device 100 for simulating the pushout process will be described.

As shown in FIG. 3, the simulation device 100 includes a first physical model generation unit 11. The first physical model generation unit 11 is configured to generate the first physical model of the parison 1 in the push-out process in which the parison 1 is pushed out to the mold 2 by the extruder 6. As shown in FIG. 4, the first physical model is a viscoelastic model 22 by connecting a plurality of mass points 21 to which the parison 1 is connected and the viscoelastic model (viscoelastic spring) 22 between the mass points 21. This is a physical model based on the kinetic equation of mass point 21, assuming a viscoelastic body that stretches and deforms along the stretching direction of the mass point 21.

なお、ｍは、質点２１の質量であり、ａは、質点２１の加速度である。以下、各々の力を具体的に説明する。 Then, in the present embodiment, the force acting on the parison 1 (hereinafter referred to as F) is at least the force generated by the viscoelastic model 22 acting on the parison 1 (hereinafter referred to as F1) and the force acting on the parison 1. Gravity (hereinafter referred to as F2) and the force received from the airflow generated by sucking the air between the parison 1 and the mold 2 (hereinafter referred to as F3) are included. The force (F) acting on the parison 1 is the repulsive force when the parison 1 collides with the mold 2 (hereinafter referred to as F4) and the frictional force when the parison 1 and the mold 2 come into contact with each other (hereinafter referred to as F4). Hereinafter referred to as F5) and. Further, the force acting on the parison 1 further includes a force for generating a bending moment between the viscoelastic models 22 adjacent to each other (force based on an angle, hereinafter referred to as F6). As a result, the equation of motion of the mass point 21 is expressed by the following mathematical formula 1.

Note that m is the mass of the mass point 21, and a is the acceleration of the mass point 21. Hereinafter, each force will be specifically described.

(Force F1 generated by viscoelastic model)
Specifically, as shown in FIG. 4, as the viscoelastic model 22, for example, the Maxwell model is used. In the Maxwell model, the viscoelastic model 22 includes a spring portion 22a and a dashpot portion 22b. The spring portion 22a and the dashpot portion 22b are connected in series with each other. The spring portion 22a has elasticity. The dashpot portion 22b has viscosity (plasticity). Then, the viscoelastic model 22 reproduces elasticity and viscosity (plasticity). Further, the parison 1 expands and contracts along the expansion and contraction direction (uniaxial direction) of each viscoelastic model 22. The force F1 generated by the viscoelastic model 22 is simply expressed by F1 = kx (k: elastic modulus, x: elongation of the viscoelastic model 22), but will be described in detail below.

ここで、Ｅは、ヤング率である。また、ダッシュポット部分２２ｂのひずみをε_ｄとする。そして、ダッシュポット部分２２ｂの応力σ_ｄは、下記の数式３により表される。

ここで、ηは、粘度であり、ε’は、ひずみ速度である。また、バネ部分２２ａの応力σ_ｓとダッシュポット部分２２ｂの応力σ_ｄとは釣り合う（等しい）ので、下記の数式４が成立する。

つまり、質点２１には、応力σ_ｓが作用する。なお、ダッシュポット部分２２ｂのひずみ（塑性ひずみ）ε_ｄに関して、下記の数式５が成立する。

ここで、ｄｔは、時間刻みである。そして、ある時点での塑性ひずみε_ｄに、ｄｔ時間経過後の塑性ひずみε_ｄが加算される。また、下記の数式６が成立する。

最後に、上記の応力にパリソン１の断面積を積算して、粘弾性モデル２２により発生する力Ｆ１に変換する。 Specifically, the total strain of the viscoelastic model 22 is ε. Let the strain of the spring portion 22a be ε _s . The stress σ _s of the spring portion 22a is expressed by the following mathematical formula 2.

Here, E is Young's modulus. Further, _let the strain of the dashpot portion 22b be ε _d . Then, the stress σ _d of the dashpot portion 22b is expressed by the following mathematical formula 3.

Here, η is the viscosity and ε'is the strain rate. Further, since the stress σ _s of the spring portion 22a and the stress σ _d of the dashpot portion 22b are balanced (equal to), the following equation 4 holds.

That is, the stress σ _s acts on the mass point 21. The following mathematical formula 5 holds for the strain (plastic strain) ε _d of the dashpot portion 22b.

Here, dt is in time increments. Then, the plastic strain epsilon _d at a certain time, plastic strain epsilon _d after the elapse time dt is added. Further, the following mathematical formula 6 is established.

Finally, the cross-sectional area of the parison 1 is integrated with the above stress and converted into the force F1 generated by the viscoelastic model 22.

ここで、ｇは、重力加速度である。 (Gravity F2)
The gravity F2 acting on the mass point 21 is expressed by the following mathematical formula 7.

Here, g is the gravitational acceleration.

ここで、ｄｐ／ｄｘは、軸方向の圧力である。ｒ_１は、外側の円管の半径であり、ｒ_２は、内側の円管の半径である。なお、気流から受けるＦ３は、時間的、および、金型２の流路２ａ内において、略一定とみなす。 (F3 received from airflow)
As shown in FIG. 5, F3 received from the airflow acting on the mass point 21 is represented by the force acting on the inner circular tube by the fluid flowing through the double circular tube. The double circular tube is one in which the inner circular tube having a small radius is arranged inside the outer circular tube having a large radius. The force acting on the inner circular tube (F3 received from the airflow acting on the mass point 21) is expressed by the following mathematical formula 8.

Here, dp / dx is the pressure in the axial direction. r ₁ is the radius of the outer circular tube and r ₂ is the radius of the inner circular tube. The F3 received from the airflow is considered to be substantially constant in time and in the flow path 2a of the mold 2.

なお、シミュレーションにおいては、上記のような反発力Ｆ４を質点２１に加えると、質点２１は、比較的大きく移動して、壁にめり込んだ状態となってしまう。そこで、質点２１が金型２（壁）にめり込んだ状態を解消するために、めり込み量に応じて少しずつ質点２１を動かし、最終的に反発係数を考慮した速度で壁から離間する処理を行っている。また、質点２１が金型２（壁）に衝突（接触）したか否かの判定は、一般的な既知の方法によって行われる。 (Repulsive force F4)
The repulsive force F4 when the mass point 21 collides with the mold 2 (wall) is calculated by the following formula 9 assuming that the velocity v before the collision is multiplied by e as the direction is reversed due to the collision with the wall. It is expressed by (force = momentum / dt).

In the simulation, when the repulsive force F4 as described above is applied to the mass point 21, the mass point 21 moves relatively large and is in a state of being sunk into the wall. Therefore, in order to eliminate the state in which the mass point 21 is sunk into the mold 2 (wall), the mass point 21 is moved little by little according to the amount of sunk, and finally the mass point 21 is separated from the wall at a speed in consideration of the coefficient of restitution. ing. Further, it is determined by a generally known method whether or not the mass point 21 has collided (contacted) with the mold 2 (wall).

ここで、μは、摩擦係数であり、Ｎは、垂直抗力である。 (Friction force F5)
The frictional force F5 when the mass point 21 and the mold 2 (wall) come into contact with each other is expressed by the following mathematical formula 10.

Here, μ is the coefficient of friction and N is the normal force.

なお、各質点２１に作用する力Ｆ６によって、パリソン１（複数の質点２１）が回転しないように、パリソン１に作用するモーメントがゼロになるように、力Ｆ６は、調整される。 (Force F6 to generate bending moment between viscoelastic models)
The force (force based on the angle θ) F6 that generates a bending moment between the viscoelastic models 22 is a function f of the angle θ between the viscoelastic models 22, and is expressed by the following mathematical formula 11.

The force F6 is adjusted so that the force F6 acting on each mass point 21 does not rotate the parison 1 (plurality of mass points 21) and the moment acting on the parison 1 becomes zero.

Further, in the present embodiment, as shown in FIG. 3, the simulation device 100 includes a first shape calculation unit 12. The first shape calculation unit 12 is configured to calculate the shape of the parison 1 in the pushout process by time-integrating the first physical model of the parison 1. For example, the first shape calculation unit 12 calculates the shape of the parison 1 by time-integrating the first physical model (the above mathematical formula 1) using the explicit method.

(Parison radius and thickness)
Further, in the present embodiment, the simulation device 100 includes a radius calculation unit 13. The radius calculation unit 13 is configured to calculate a change in the radius R (see FIG. 6) of the parison 1 based on the degree of elongation of the parison 1 based on the shape of the parison 1 calculated by the first shape calculation unit 12. Has been done.

そして、単位ベクトルＩが３６０度回転するまで、単位ベクトルＩを３０度ずつ回転させる処理を繰り返す。つまり、３０度ごとの等間隔で、膜要素の節点が発生される。そして、発生された膜要素の節点の接続することにより、膜要素が生成される。 As described above, the parison 1 is represented by a plurality of mass points 21 connected to each other by the viscoelastic model 22. Therefore, by generating a film element in the radial direction, the change in radius R accompanying the elongation of the parison 1 is simulated. Specifically, first, a measure for generating a node is performed. The position vector P of the node of the membrane element uses the position vector P0 of the center of the parison 1 (mass point 21), the radius R of the parison 1 at this position, and the unit vector I in the radial direction. Represented by.

Then, the process of rotating the unit vector I by 30 degrees is repeated until the unit vector I is rotated by 360 degrees. That is, nodes of the film element are generated at equal intervals of 30 degrees. Then, the membrane element is generated by connecting the nodes of the generated membrane element.

Further, the simulation device 100 includes a thickness calculation unit 14. The thickness calculation unit 14 is configured to calculate a change in the thickness t of the parison 1 based on the degree of elongation of the parison 1 based on the shape of the parison 1 calculated by the first shape calculation unit 12. Hereinafter, a method for calculating the change in the radius R and the change in the thickness t of the parison 1 will be specifically described.

ここで、ｌ_０は、伸長前のパリソン１の長さであり、ｌは、伸長後のパリソン１の長さである。次に、図７の円筒状のパリソン１を、図８に示すように、直方体形状に展開する。円筒状のパリソン１の外径（半径）を、Ｒとすると、円筒状のパリソン１の外周の長さは、２πＲとなる。また、パリソン１の厚みをｔとする。これにより、直方体形状に展開したパリソン１の上面の面積Ｓは、２πＲ×ｔとなる。また、直方体形状に展開したパリソン１の体積Ｖは、Ｓ×ｌとなる。 The change in radius R and the change in thickness t of parison 1 are calculated based on Poisson's ratio ν. First, the strain ε _{l in} the axial direction of the parison 1 (the direction in which the parison 1 extends) is expressed by the following mathematical formula 13.

Here, l ₀ is the length of the parison 1 before extension, and l is the length of the parison 1 after extension. Next, the cylindrical parison 1 of FIG. 7 is developed into a rectangular parallelepiped shape as shown in FIG. Assuming that the outer diameter (radius) of the cylindrical parison 1 is R, the length of the outer circumference of the cylindrical parison 1 is 2πR. Further, the thickness of the parison 1 is t. As a result, the area S of the upper surface of the parison 1 developed into a rectangular parallelepiped shape becomes 2πR × t. Further, the volume V of the parison 1 developed into a rectangular parallelepiped shape is S × l.

そして、厚みｔの変化に伴って、パリソン１の半径Ｒは、下記の数式１５のように変化する。

ここで、Ｒ_０は、伸長前の外径である。 Then, the change ε _t of the thickness t after the extension of the parison 1 is expressed by the following mathematical formula 14.

Then, as the thickness t changes, the radius R of the parison 1 changes as shown in the following mathematical formula 15.

Here, R ₀ is the outer diameter before extension.

そして、半径Ｒの変化に伴って、パリソン１の厚みｔは、下記の数式１７のように変化する。

ここで、ｔ_０は、伸長前の厚みである。 Further, the change ε _R of the radius R after the extension of the parison 1 is expressed by the following mathematical formula 16.

Then, as the radius R changes, the thickness t of the parison 1 changes as shown in the following mathematical formula 17.

Here, t ₀ is the thickness before elongation.

Further, in the present embodiment, as shown in FIG. 3, the simulation device 100 includes a curvature calculation unit 15. The curvature calculation unit 15 is configured to calculate the curvature of the parison 1 based on the angle between the viscoelastic models 22 adjacent to each other. Specifically, as shown in FIG. 9, the curvature calculation unit 15 is a parison 1 represented by a plurality of mass points 21 (viscoelastic model 22) during the time integration by the first shape calculation unit 12. The shape of is approximated by the spline curve CL. Then, the curvature of the parison 1 is calculated based on the spline curve CL.

ここで、ｒは、パリソン１の半径であり、ｔは、厚みである。また、σは、ポアソン比である。 Further, in the present embodiment, as shown in FIG. 3, the simulation device 100 includes a buckling determination unit 16. The buckling determination unit 16 is configured to determine whether or not the parison 1 buckles based on the curvature of the parison 1 calculated by the curvature calculation unit 15. Specifically, as shown in FIG. 10, when a relatively thin circular tube such as Parison 1 is put into a state of pure bending (a state in which only a bending moment acts), the cross section of the circular tube becomes flat and bent. Rigidity decreases. This phenomenon is called the Brazier effect. FIG. 10A shows a side view of the buckled parison 1, and FIG. 10B shows a cross-sectional view of the buckled parison 1. As shown in FIG. 11, when the curvature is larger than the point A having a curvature, the bending moment becomes smaller (bending). Therefore, when the curvature of the parison 1 calculated by the curvature calculation unit 15 becomes larger than the point A, the parison 1 buckles, so that it is determined that the resin molded product 3 cannot be appropriately generated. The dotted line in FIG. 11 represents the bending moment when it is assumed that the circular tube is not crushed (the cross section is not flattened). The bending moment is expressed by, for example, the following mathematical formula 18.

Here, r is the radius of the parison 1 and t is the thickness. Also, σ is Poisson's ratio.

(Blow process)
Next, the configuration of the simulation device 100 for simulating the blow process will be described. The blow process takes place a few seconds after the pushout process. Therefore, the temperature of the parison 1 is lowered. Further, the viscous property of the parison 1 has a small effect on the shape of the parison 1 in the blowing process, while the elastic property has a large effect. Therefore, in the present embodiment, the parison 1 in the blowing process is approximated as an elastic body.

なお、パリソン１に作用する重力Ｆ１１は、上記の数式７の重力Ｆ２と同様である。また、反発力Ｆ１３は、上記の数式９の反発力Ｆ４と同様である。また、摩擦力Ｆ１４は、上記の数式１０の摩擦力Ｆ５と同様である。 In the present embodiment, as shown in FIG. 3, the simulation device 100 includes a second physical model generation unit 17. The second physical model generation unit 17 is configured to generate a second physical model of the parison 1 in a blow process in which air is blown into the parison 1 after being extruded into the mold 2 to expand the parison 1. ing. The second physical model is a physical model assuming that the parison 1 is an elastic body. Then, in the second physical model, the force F acting on the parison 1 is the gravity F11 acting on the parison 1, the pressure F12 due to the air blown into the parison 1, and the time when the parison 1 collides with the mold 2. The repulsive force F13 and the frictional force F14 when the parison 1 and the mold 2 come into contact with each other are included. As a result, the equation of motion of the mass point 21 is expressed by the following equation 19. In the second physical model, the mass points 21 are the nodes of the film element (shell element) obtained by the simulation of the pushout process.

The gravity F11 acting on the parison 1 is the same as the gravity F2 in the above equation 7. Further, the repulsive force F13 is the same as the repulsive force F4 of the above formula 9. Further, the frictional force F14 is the same as the frictional force F5 of the above equation 10.

Further, the pressure F12 by air is generated as follows. First. Divide parison 1 into shell elements. Then, the stress (stress due to air) generated in each of the divided shell elements is converted into the pressure F12. The shell element means an element having a rigidity corresponding to the plate thickness in calculation while being a surface having a thickness of zero in appearance.

Further, in the present embodiment, as shown in FIG. 3, the simulation device 100 includes a second shape calculation unit 18. The second shape calculation unit 18 calculates the shape of the parison 1 in the blow process based on the shape of the parison 1 after the pushout process calculated by the first shape calculation unit 12 and the second physical model of the parison 1. It is configured to do. For example, the second shape calculation unit 18 calculates the shape of the parison 1 by time-integrating the second physical model (the above mathematical formula 19) using the explicit method.

As shown in FIG. 3, the first physical model generation unit 11, the first shape calculation unit 12, the radius calculation unit 13, the thickness calculation unit 14, the curvature calculation unit 15, the buckling determination unit 16, and the second physical model generation. The unit 17 and the second shape calculation unit 18 are composed of a program 40 (software) stored in the storage medium 30 inside the simulation device 100.

(Simulation method)
Next, a simulation method according to the present embodiment will be described with reference to FIG.

First, in step S1, input conditions for simulation are set. The input conditions are, for example, the initial radius R (or diameter) of the parison 1, the initial thickness t, the initial velocity of the parison 1 to be extruded (or the flow rate of the extrusion from which the initial velocity can be calculated), and the mass point 21. , The constant of the viscoelastic model 22, the elastic modulus of the spring portion 22a, the viscosity of the dashpot portion 22b, and the force that the mass point 21 of the parison 1 receives from the airflow. The number of viscoelastic models 22 can be obtained from the number of mass points 21. The input conditions are the shape of the flow path 2a (shape of the shell element) in the mold 2 from which the parison 1 is extruded, the friction coefficient of the mold 2, and the coefficient of restitution between the mold 2 and the parison 1. Including. Further, the input condition includes a time step (dt) for time integration.

Next, in step S2, the first physical model of the parison 1 in the pushout step is generated. The first physical model is generated based on the above mathematical formula 1.

Next, in step S3, the shape of the parison 1 in the pushout step is calculated. The shape of the parison 1 is an extension of the parison 1, a radius R of the parison 1, a thickness t of the parison 1, and the like. In step S3, the shape of the parison 1 is calculated by time-integrating the first physical model (the above mathematical formula 1) using the explicit method.

It should be noted that the simulation also takes into consideration that the length of the parison 1 increases with the passage of time. The dashpot portion 22b of the viscoelastic model 22 represents the action of plastic strain. As a result, when the viscoelastic model 22 is momentarily stretched (strained), the dashpot portion 22b is stretched over time when a force for maintaining the stretch is further applied. On the other hand, the elongation of the spring portion 22a becomes small. Even when the force for maintaining the elongation is removed, the elongation of the dashpot portion 22b is maintained. In this way, it is simulated that the length of the parison 1 becomes longer with the passage of time.

Next, in step S4, the curvature of the parison 1 is calculated, and it is determined whether or not the parison 1 buckles based on the calculated curvature of the parison 1. In addition, step S3 and step S4 are repeated until a predetermined condition (such as parison 1 penetrating the flow path 2a) is satisfied.

Next, in step S5, a second physical model of the parison 1 in the blow process is generated. The second physical model is generated based on the above mathematical formula 19. Further, the node of the film element calculated by the simulation of the pushout process is set as the mass point 21 of the second physical model.

Next, in step S6, the shape of the parison 1 in the blowing step is calculated. In step S6, the shape of the parison 1 is calculated by time-integrating the second physical model (the above mathematical formula 19) using the explicit method.

Next, the result of the simulation using the simulation device 100 of the present embodiment will be described.

As shown in FIG. 13, the parison 1 extruded into the flow path 2a in the mold 2 by the relatively simple first physical model of the present embodiment extends toward the outlet side of the flow path 2a with the passage of time. It was confirmed that it can be calculated. It was also confirmed that the first physical model of the present embodiment reproduces that the parison 1 (membrane element) is in contact with the mold 2.

(Effect of this embodiment)
Next, the effect of this embodiment will be described.

In the present embodiment, as described above, in the first physical model, the viscoelastic model 22 expands and contracts by connecting the parison 1 to the plurality of connected mass points 21 and the mass points 21 by the viscoelastic model 22. It is a physical model based on the kinetic equation of mass point 21 assuming a viscoelastic body that stretches and deforms along the direction, and the force acting on parison 1 is at least the force generated by the viscoelastic model 22 acting on parison 1. , The gravity acting on the parison 1 and the force received from the airflow generated by sucking the air between the parison 1 and the mold 2. As a result, the parison 1 is represented by a relatively simple physical model that stretches and deforms along the stretching direction of the viscoelastic model 22. In addition, the first shape calculation unit 12 calculates the shape of the parison 1 in the push-out process by time-integrating the first physical model of the parison 1. As a result, the shape of the parison 1 is calculated by time-integrating a relatively simple physical model. Therefore, the shape of the parison 1 that is discretized into finite elements and extruded into the mold 2 by the finite element method is obtained. The shape of the parison 1 in the pushout process can be simulated in a relatively short time as compared with the case of simulating.

Further, in the present embodiment, as described above, the forces acting on the parison 1 are the repulsive force when the parison 1 collides with the mold 2 and the frictional force when the parison 1 and the mold 2 come into contact with each other. Including further. As a result, the shape of the parison 1 can be simulated while considering the influence of the mold 2 on the parison 1, so that the shape of the parison 1 can be simulated more precisely.

Further, in the present embodiment, as described above, the force acting on the parison 1 further includes a force for generating a bending moment between the viscoelastic models 22 adjacent to each other. As a result, the shape of the parison 1 can be simulated while considering the influence when the parison 1 is curved, so that the shape of the parison 1 can be simulated more precisely.

Further, in the present embodiment, as described above, the radius calculation for calculating the change in the radius R of the parison 1 based on the degree of extension of the parison 1 based on the shape of the parison 1 calculated by the first shape calculation unit 12. A portion 13 is provided. As a result, the shape of the parison 1 including the radius R of the parison 1 can be simulated, so that the shape of the parison 1 can be simulated more precisely.

Further, in the present embodiment, as described above, the thickness calculation for calculating the change in the thickness t of the parison 1 based on the degree of elongation of the parison 1 based on the shape of the parison 1 calculated by the first shape calculation unit 12. A portion 14 is provided. As a result, the shape of the parison 1 including the thickness t of the parison 1 can be simulated, so that the shape of the parison 1 can be simulated more precisely. Further, since the thickness t is calculated, the strength of the resin molded product 3 after molding can be predicted.

Further, in the present embodiment, as described above, the curvature calculation unit 15 that calculates the curvature of the parison 1 based on the angle between the viscoelastic models 22 adjacent to each other, and the parison 1 calculated by the curvature calculation unit 15. A buckling determination unit 16 for determining whether or not the parison 1 buckles is provided based on the curvature of. As a result, it is determined whether or not the parison 1 buckles, so it is possible to determine whether or not the desired resin molded product 3 can be molded.

Further, in the present embodiment, as described above, the parison 1 in the blow process is based on the shape of the parison 1 after the push-out process calculated by the first shape calculation unit 12 and the second physical model of the parison 1. A second shape calculation unit 18 for calculating the shape of the above is provided. As a result, the shape of the parison 1 in the blow process is calculated based on the shape of the parison 1 after the push-out process calculated by the first shape calculation unit 12, so that the parison 1 after the blow process can be calculated more accurately. The shape can be calculated.

Further, in the present embodiment, as described above, the second physical model is a physical model assuming that the parison 1 is an elastic body, and the force acting on the parison 1 is the gravity acting on the parison 1 and the force acting on the parison 1. It includes the pressure due to the air blown into the inside, the repulsive force when the parison 1 collides with the mold 2, and the frictional force when the parison 1 and the mold 2 come into contact with each other. As a result, the shape of the parison 1 after the blow process can be simulated in a relatively short time by using a relatively simple second physical model.

Further, in the present embodiment, as described above, the first shape calculation unit 12 is configured to calculate the shape of the parison 1 inside the flow path 2a in the mold 2 having the meandering tube shape. There is. Thereby, the shape of the parison 1 in the flow path 2a in the mold 2 having the meandering tube shape can be simulated. When the flow path 2a in the mold 2 has a meandering tube shape, it is relatively difficult to determine whether or not the desired resin molded product 3 is molded by suction blow molding. Therefore, simulating the shape of the parison 1 as described above is particularly effective in determining whether or not the desired resin molded product 3 is molded.

[Modification example]
It should be noted that the embodiments and examples disclosed this time are exemplary in all respects and are not considered to be restrictive. The scope of the present invention is shown by the scope of claims rather than the description of the above-described embodiments and examples, and further includes all modifications (modifications) within the meaning and scope equivalent to the scope of claims.

For example, in the above embodiment, the force acting on the parison is the force generated by the viscoelastic model, the force received from the gravity, the airflow, the repulsive force when colliding with the mold, and the friction when contacting the mold. An example including a force and a force for generating a bending moment between viscoelastic models has been shown, but the present invention is not limited to this. For example, if the force acting on the parison includes at least the force generated by the viscoelastic model, gravity, and the force received from the air flow, the shape of the parison can be calculated. Further, the force acting on the parison may include a force other than the above-mentioned force.

Further, in the above embodiment, an example is shown in which the radius and thickness of the parison are calculated based on the degree of elongation of the parison (Poisson's ratio), but the present invention is not limited to this. For example, the radius and thickness of the parison may be calculated by a method other than Poisson's ratio.

Further, in the above embodiment, an example in which a buckling determination unit for determining whether or not the parison buckles is provided is shown, but the present invention is not limited to this. For example, the user may determine whether or not the parison buckles based on the calculated curvature of the parison without providing the buckling determination unit.

Further, in the above embodiment, an example in which the push-out process and the blow process are simulated is shown, but the present invention is not limited to this. For example, the simulation device may be configured to simulate only the pushout process.

Further, in the above embodiment, in the second physical model, an example in which the parison is assumed to be an elastic body is shown, but the present invention is not limited to this. For example, in the second physical model, the parison may be assumed to be a viscoelastic body.

Further, in the above embodiment, an example is shown in which the flow path in the mold 2 from which the parison is extruded has a meandering tube shape, but the present invention is not limited to this. For example, the flow path 7a in the mold 7 may have a straight pipe shape as in the mold 7 of the modified example of FIG.

Further, in the above embodiment, an example in which the Maxwell model is used as the viscoelastic model is shown, but the present invention is not limited to this. For example, the Viscoelastic model may be used as the viscoelastic model.

1 Parison 2, 7 Die 2a, 7a Flow path 3 Resin molded product 6 Extruder 11 1st physical model generator 12 1st shape calculation unit 13 Radiation calculation unit 14 Thickness calculation unit 15 Curvature calculation unit 16 Buckling determination unit 17 2nd physical model generator 18 2nd shape calculation unit 21 mass point 22 viscoelastic model 30 storage medium 40 program 100 simulation device

Claims (12)

In suction blow molding, in which a parison, which is a substantially tubular molten resin, is extruded into the mold while sucking out air in the mold, and air is blown into the parison extruded into the mold to form a resin molded product. A simulation device that simulates the shape of the parison.
A first physical model generation unit that generates a first physical model of the parison in a push-out step in which the parison is pushed out to the mold by an extruder.
It is provided with a first shape calculation unit that calculates the shape of the parison in the pushout step by time-integrating the first physical model of the parison.
The first physical model includes a plurality of connected mass points and a viscoelastic body that expands and deforms along the expansion and contraction direction of the viscoelastic model by connecting the mass points with each other by a viscoelastic model. It is a assumed physical model based on the motion equation of the mass point.
The force acting on the parison is generated by at least the force generated by the viscoelastic model acting on the parison, the gravity acting on the parison, and the suction of air between the parison and the mold. A simulation device that includes the force received from the airflow. The simulation apparatus according to claim 1, wherein the force acting on the parison further includes a repulsive force when the parison collides with the mold and a frictional force when the parison and the mold come into contact with each other. .. The simulation apparatus according to claim 1 or 2, wherein the force acting on the parison further includes a force for generating a bending moment between the viscoelastic models adjacent to each other. Any of claims 1 to 3, further comprising a radius calculation unit that calculates a change in the radius of the parison based on the degree of extension of the parison based on the shape of the parison calculated by the first shape calculation unit. The simulation apparatus according to item 1. Any of claims 1 to 4, further comprising a thickness calculation unit that calculates a change in the thickness of the parison based on the degree of elongation of the parison based on the shape of the parison calculated by the first shape calculation unit. The simulation apparatus according to item 1. A curvature calculation unit that calculates the curvature of the parison based on the angle between the viscoelastic models adjacent to each other,
The simulation according to any one of claims 1 to 5, further comprising a buckling determination unit for determining whether or not the parison buckles based on the curvature of the parison calculated by the curvature calculation unit. apparatus. A second physical model generation unit that generates a second physical model of the parison in a blowing step of blowing air into the parison after being extruded into the mold to expand the parison.
A second shape calculation for calculating the shape of the parison in the blow process based on the shape of the parison after the pushout process calculated by the first shape calculation unit and the second physical model of the parison. The simulation apparatus according to any one of claims 1 to 6, further comprising a unit. The second physical model is a physical model in which the parison is assumed to be a viscoelastic body or an elastic body.
The forces acting on the parison are the gravity acting on the parison, the pressure due to the air blown into the parison, the repulsive force when the parison collides with the mold, and the parison and the mold. The simulation apparatus according to claim 7, which includes a frictional force when the devices come into contact with each other. The flow path in the mold from which the parison is extruded has a straight pipe shape or a meandering pipe shape.
The first shape calculation unit is configured to calculate the shape of the parison in the flow path in the mold having the straight pipe shape or the meandering pipe shape, claims 1 to 8. The simulation apparatus according to any one of the above items. In suction blow molding, in which a parison, which is a substantially tubular molten resin, is extruded into the mold while sucking out air in the mold, and air is blown into the parison extruded into the mold to form a resin molded product. A simulation method for simulating the shape of the parison.
A step of generating a first physical model of the parison in a push-out step in which the parison is extruded into the mold by an extruder, and
A step of calculating the shape of the parison in the pushout step by time-integrating the first physical model of the parison is provided.
The first physical model includes a plurality of connected mass points and a viscoelastic body that expands and deforms along the expansion and contraction direction of the viscoelastic model by connecting the mass points with each other by a viscoelastic model. It is a assumed physical model based on the motion equation of the mass point.
The force acting on the mass point is generated by at least the force generated by the viscoelastic model acting on the parison, the gravity acting on the parison, and the suction of air between the parison and the mold. A simulation method that includes the force received from the airflow. In suction blow molding, in which a parison, which is a substantially tubular molten resin, is extruded into the mold while sucking out air in the mold, and air is blown into the parison extruded into the mold to form a resin molded product. A program that simulates the shape of the parison.
A step of generating a first physical model of the parison in a push-out step in which the parison is extruded into the mold by an extruder, and
A step of calculating the shape of the parison in the pushout step by time-integrating the first physical model of the parison is provided.
The first physical model includes a plurality of connected mass points and a viscoelastic body that expands and deforms along the expansion and contraction direction of the viscoelastic model by connecting the mass points with each other by a viscoelastic model. It is a assumed physical model based on the motion equation of the mass point.
The force acting on the mass point is generated by at least the force generated by the viscoelastic model acting on the parison, the gravity acting on the parison, and the suction of air between the parison and the mold. A program that includes the force received from the airflow. In suction blow molding, in which a parison, which is a substantially tubular molten resin, is extruded into the mold while sucking out air in the mold, and air is blown into the parison extruded into the mold to form a resin molded product. A storage medium for storing a program for simulating the shape of the parison.
A step of generating a first physical model of the parison in a push-out step in which the parison is extruded into the mold by an extruder, and
A step of calculating the shape of the parison in the pushout step by time-integrating the first physical model of the parison is provided.
The first physical model includes a plurality of connected mass points and a viscoelastic body that expands and deforms along the expansion and contraction direction of the viscoelastic model by connecting the mass points with each other by a viscoelastic model. It is a assumed physical model based on the motion equation of the mass point.
The force acting on the mass point is generated by at least the force generated by the viscoelastic model acting on the parison, the gravity acting on the parison, and the suction of air between the parison and the mold. A storage medium that stores a program, including the force received from the airflow.

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