optimization-driven design of dies for profile extrusion: parameterization, strategy, and performance.

The extrusion of plastic and rubber profiles is an important processing department with unplasticized PVC (uPVC)
It is widely used in the construction industry and composite rubber sealing profiles, which occupies a large market in automobile production.
Tyretreads and side walls are also produced as profile extrusion and form another important department.
Figure 1 shows the typical assembled windows system in uPVC, clarifying the complexity of the profile and the exact details and dimensions needed to ensure that the parts are assembled together and work properly.
The design of profile molds is very complex and important, because these bring great challenges.
This work extends the computational design optimization approach to help designers with results that are at least as good as those obtained using traditional methods, but with significant economic benefits.
The current focus is onuPVC profile molds, but the methods described are rich and flexible enough to be applied to other types of molds as well.
There are two main types of Profile extrusion molds.
The first includes streamlined molds, which are widely used to produce profiles in upvc;
These molds need to produce profiles with complex and detailed features as shown in the figure
1. high productivity.
The streamlined mold provides a smooth transition in the geometry of the mold (flow channels).
It is usually possible to distinguish four main areas along the flow direction: the entrance area, the pre-formed area, the adapter area and the parallel area.
These areas can be supplemented by more areas, such as protected areas.
As the material flows from the extruder to the land it exports, these step-by-step introduce more details of the cross-section of the profile.
The extruded profile is then cooled and solidified to the calibration device.
The mold is made up of a pile of platforms located on the pins.
Profiles usually have hollow internal chambers, so the internal components of the mold are required to form these chambers.
There are two main construction methods: Core-
Plates and torpedoIn core-
Platform structure, cut the inside and outside profile of the mold cavity in each plate by wire discharge machining (wEDM)
It includes the formation of an internal core to support them and a streamlined spider arm.
Therefore, many cavities can be cut out from each plate.
Another option would be to use a torpedo core that runs through many plates and is supported by a spider arm in the middleposition.
In this case, only one cavity needs to be cut for each plate.
These two methods may be combined to take advantage of core-
On the downstream flat panel, it provides high accuracy on the land size and torpedo on the upstream, which reduces the amount required for wEDM processing.
In further elaboration, separate parts that form the core shaft can be connected from the mold surface by screws.
An example is shown in Figure 1. 2.
In wEMD, different cutting paths can be specified on both sides of the board.
The wire guide then slopes the surface and connects the profile to the relative surface through the straight line surface.
Restrictions on certain manufacturing by WEDM;
The cutting path is specified according to the line and arc entity with CI continuity, and the minimum arc radius is related to the wire diameter.
These considerations suggest a representation (parameterizing)
Mold Design as described below.
The second main type is the simpler plate mold, which is fixed on the front of the mold body with an interchange plate with an appropriate shape cut.
These are widely used for extrusion of composite rubber profiles, as well as stagnation or recycling flow of sudden 90 shrinkage
Just because of the flow properties of these compounds, especially the obvious wall sliding, the flow behind the plate is avoided.
Calibration is usually not used, and the extruded prolife is carried out on the conveyor belt through the oven, where it is cured and reaches the final form.
Although wEDM may not be used in this case, the geometry can be described with the contours of a plane parallel surface formed by a line and an arc entity and connected by a regular surface.
Further special mold types can also be described in this way.
The traditional method of calculating mold design optimization profile mold development relies on the experience of the designer to carry out the initial design, followed by the mold construction and extrusion test.
Based on the results, the designer decides what modifications need to be made and runs further trials.
It can take ten or more cycles. The die run-
In the occupied extrusion production line that could have been used for production, the use of materials and workshop resources requires skilled staff time and introduces delays and uncertainties in time --to-market.
Analysis of calculated traffic (
Computational fluid dynamics (CFD)
Used to reduce the number of necessary physical development tests;
But there is still a need for the designer to explain the CFD results and decide the required modifications.
In further development, CFD simulation is combined with computational optimization to automatically and step-by-step design modifications to achieve specific performance.
In the case of uPVC, the potential of computer methods in mold design can be explained, of which approximately 25 million tons are used worldwide each year (1).
It can be estimated that this includes the development of thousands of new molds every year, and the cost of each mold is about 15-20,000[euro](
Does not include the calibration device)(2).
About half the situation due to running
At the stage of development.
The economic potential of computer methods in helping to produce improved initial designs, thereby reducing the number of required workshop trials is evident.
In addition, computer optimization can reduce the time required by designers-
Expensive resources-
This is the focus of the current work.
The purpose of this is not to eliminate human factors in the design;
This is unrealistic and undesirable.
The designer\'s experience is always important in properly setting up the computational optimization process.
This paper describes the computational shape optimization environment of the profile mold, which is related to the special functions and construction methods of the streamlined mold used in the profile in uPVC and other thermoplastic plastics and comes from the environment.
The design goal is to inspect the mold: that is, to ensure that the quantity of material delivered to all parts of the mold outlet is correct to obtain the correct wall thickness and feature size in the finished product profile.
The adjustment of the mold outlet is not considered to compensate for the expansion of the extrusion, so when the calibration is used, these procedures are particularly relevant, such as in the production of upvc profiles, or when the extrusion is not calibrated at the time of expansion.
Calculate the shape optimization environment will be presented in line with the classic (3)three-
Part structure composed of simulation package;
Optimization algorithm;
Optimize the modules, stand between the two, control them, and exchange information.
The user interface will also be linked to the central optimization module.
The simulation package provides a numerical solution for the flow inside the mold.
Therefore, in post-processing operations, one or more scalar measures of mold performance will be evaluated.
These are called objective functions (OFs)
, The calculation optimization process will (usually)
In this way, the OFs correspondence can be minimized in order to find the best design.
In addition, for the gradient
An optimization-based approach is used here to calculate the sensitivity.
These are the rate of change of OFs relative to the design variable (DVs)
, In this case, related to certain key dimensions of the mold cavity.
By optimizing the module, the OF and sensitimetric values are passed from the simulation package to the optimization algorithm, which calculates the updated value OF the DVs.
These are passed back to the optimization model and then to the simulation package to simulate the modified design.
The central optimization module is more than just exchanging information.
It controls how the optimization algorithm is used to update the DVs, which is the optimization strategy.
It also rebuilds the mold geometry based on the updated DVs to prepare for the next flow simulation.
In this process, it uses a mold parametric scheme, which is a logical process of rebuilding the entire geometry from a compact data set.
In order to achieve such a design environment, many details need to be considered, which will be described in the section below.
The calculation of mold design the element of the design environment parameterized the geometry of the mold cavity includes the identification of the characteristic dimensions or spatial coordinates of the mold cavity, from which it can be automatically reconstructed by its entire geometry, computer program.
DVs are selected according to these parameters, and the optimization process adjusts these parameters to the best iterative process.
Therefore, at each stage of optimization, the updated mold cavity geometry is created and discrete through the grid Gree analysis.
Two methods are described.
First, the grid itself is parameterized (4-9).
The flow domain is discrete with a structured grid and generated using macro-cell technology.
Coordinates of macro nodes-
Select the element as a parameter, in part or all as a DVs.
In each optimization cycle, adjust the grid according to the new macro
Element coordinates;
The mesh is deformed but remains the same in topology.
This method has been successfully used to optimize molds where the number of DVs is a single number.
While computational efficiency is high, the use of a fixed topology limits possible design modifications in more complex molds.
Another drawback is that the optimized result is the mesh, not the CAD model needed for mold manufacturing.
In the second method, the CAD model is parameterized.
For relatively simple molds, a small number of key dimensions (such as land length or land clearance height) are sufficient to parameterized the design (10-13)
These changes can be used to modify the CAD model and then send to the grid generator for re-grid division in each optimization cycle.
For more complex streamline molds that are of particular interest here, a more powerful and flexible approach is needed.
It is clear that describing the geometry of the mold can produce the classification profile shown in Figure 1
More information is needed.
By considering the method of streamline mold manufacturing, Ascheme based on key points is introduced.
The detailed description is described below, and a more brief description has been given before (14-19).
Representing the geometry of the mold based on the key points, a plane profile describing the wedge-cut path has been mentioned, or, more generally, the perimeter of the cross-section of the mold cavity, three can be constructed through a straight line surface-
Geometric dimensions of cavity.
Therefore, the parameterized of these profiles provides a description of three
Dimension geometry.
It is very troublesome to deal with them directly according to the lines and arc entities that make up them in the CAD model, because acontour usually participates in the order of hundreds of entities, in these operations, it is difficult to maintain the required CIcontinuity.
A more convenient way is to create key points (20)
As shown in the figure.
3, showing the partial circumference of the cross-section of the adie cavity made of lines and arcs.
The line adjacent to the arc is projected to intersect the key point.
The key point data records the coordinates of this point and arcradius.
Typically, the data available in the CAD model is the coordinates of the connection between the line and the arc.
Then, by extrapolation from the endpoint of aline, the key point coordinates can be found. [X. sub. I]= [b. sub. I-1]+ [t. sub. I-1](|[b. sub. I-1]-[a. sub. I]|/2cos[[gamma]. sub. I])with 2[[gamma]. sub. I]=[cos. sup. -1]([n. sub. I-1]. [n. sub. I])(1)
Radius and length from [r. sub. I]= |[r. sub. I]-[b. sub. I-1]|2sin[[gamma]. sub. I]and[s. sub. I]= 2[[gamma]. sub. I][r. sub. I](2)
For all arcs to repeat the process, the key points are stored in an ordered list and agree on the direction around each closed profile.
DVs will be expressed according to the main points, as described later.
In the reconstruction of 2D contour geometry from key points, the established CAD model must meet the standards of the software used.
In the current work, this is AutoCAD.
The data generated from the key points are the starting and ending points of the lines that arcand connects them, and the center point of the arc.
Use [, handle key points in ordera. sub. I]= [X. sub. I]+ [t. sub. I][[gamma]. sub. I]tan[[gamma]. sub. I][b. sub. I-1]= [X. sub. I]-[t. sub. I-1][[gamma]. sub. I]tan[[gamma]. sub. I][c. sub. I]= [X. sub. I][+ or -][[gamma]. sub. I]([n. sub. I-1]. [n. sub. I])/(2[cos. sup. 2][[gamma]. sub. I])(3)
In the expression in the center of the arc, use a plus sign when the arc is an external angle, as shown in key point I, use a minus sign when the arc is an internal angle, as shown in I 1.
Figure 4a shows an example of a relatively simple parameterized mold cavity profile, in which case, on a surface of the adapter plate in the astreamline mold.
In some cases, the CADmodel needs to be modified. In Fig. 4 detail (b)
The initial IGES of the feature indicates that using a semi-arc, the key points, details cannot be obtained from the semi-arc (c).
In the modification, a single arc is divided into two parts and is divided by zero-
The length line makes it possible to create two key points, details (d).
This model is clean.
Up, automatically process the creation of key point data in a specially written preprocessor (20), Fig. 5a.
The process of converting the profile back to the dxf cad model is also automatically completed;
See the flow chart in the figure. 5b.
When the 3D geometry of the mold cavity needs to be established, the straight grain surface is constructed between the contours of the two plane parallel surfaces of the mold plate, corresponding to the way the wEDM wire cutting machine is made.
Create a straight grain surface between so-
Called construction edge.
They can be either a line or an arc, or they can be made up of many lines and arcs.
To determine the endpoint of the line, define the parameter curve on the two construction edges to be connected and parallel to x-y plane. [alpha](u)= [[[alpha]. sub. x](u), [[alpha]. sub. x](u)][beta](u)=[[beta]. sub. x](u), [[beta]. sub. x](u)][
Less than or equal to]u [
Less than or equal to]1 (4)
The parameter representation of the straight surface is X (u, v)= (1 -v)[alpha](u)+ v[beta](u)(5)where 0 [
Less than or equal to]v [
Less than or equal to]
1 parameter z-
The direction of the surface is separated.
Obviously, adding and parameterized build edges is always optional, but the right choice will be clear.
In response to this, the proposed geometric parametric approach is suitable for 2D and 3D design strategies.
In principle, three can be optimized-
Based on the 3D flow simulation, the dimension mold geometry is drawn directly, which is effective for relatively simple molds.
However, the complexity of the mold cavity required to produce a typical uPVC profile is evident in the three-
Size treatment can be expected.
The note falls under the following heading: flow simulation.
In the optimization process, the mesh division and flow simulation will be repeated multiple times as the design moves in the optimal direction.
Therefore, the calculation requirements involved must be carefully considered.
To represent the details of the features in the profile currently of interest, the grid with an element edge length of 0.
15mm was found to be satisfactory, resulting in about 30,000 nodes in the Ross section (20).
Using even highly heterosexual elements, elongated in the direction of flow, 3D analysis requires about a hundred layers of elements with about 3 million nodes.
Based on the flow analysis of generalized Newton flow, there are four unknown nodes on each node ---
Three velocity components and pressure (
For thermal analysis of the opposite sex)--
Causes a problem in the order of 12 million degrees of freedom.
While such an analysis is entirely possible, computing costs can become significant when it is repeated multiple times.
Another approach is based on the assumption of the flow developed on each cross section.
This approximation makes sense because the Reynolds number is low and the flow will be close to development in a slowly changing cross-section channel.
In the comparison of full 3D (isothermal)
Simulate the mold cross section with a cone 4:1 shrinkage with a set of developed flow solutions (21)
Discover the interior half angle for up to 40 [degrees]
The calculated pressure fell to an agreement within 10%.
For molds that shrink from square to L, similar results were found
Forming section (22).
In the developed process solution, there is only one unknown Node per node--
Extrusion direction speed--
Causing problems with about 30,000 unknowns on the cross section.
Although multiple 2D analyses are required, the computational requirements are much lower than 3D processing.
In working section mold optimization, the use of the development flow assumption on the mold cross section has been well established (23-25).
In these work, the optimization of the mold is confirmed by comparison with the 3D flow simulation and the experimental test.
The number of DVs and the convergence of optimization.
Complex uPVC profile optimization typically requires dozens of dvs.
As the number of DVs increases, it becomes more and more difficult to achieve the convergence of optimization, and when there is a coupling between them, it is very difficult, as is the case here.
The coupling and coupling effects will be discussed further below, where it is clear that it has a significant effect on convergence even in smaller 2D problems.
In 3d processing, the coupling is extended to more DVs, and serious convergence difficulties can be foreseen.
If convergence can be achieved, multiple iterations are required, each involving a solution for large flow analysis, as described above.
This is unlikely to provide
Effective method.
By contrast, decomposing optimization into a large number of 2D problems reduces the number of DVs in each problem, thus providing a more robust process that greatly reduces the computational requirements.
Use of dead balance to avoidCross-
In the current work, the flow strategy in 2D method optimization includes balancing the mold to ensure that the correct amount of material is delivered to the various spaces of the outlet, to produce the required wall thickness and characteristic dimensions in the profile produced.
Other objectives in the optimization have been described (26)
In particular, including obtaining uniform extrusion-
Directional flow rate on the cross section of the mold outlet (4),(5), (27).
This is appropriate when exit is a scaled version of the desired profile and causes a flat draw-
Go to the cinema.
In order to achieve this goal, the flow distribution must be controlled by changing the length of land in different parts of the supply profile because of the lateral dimensions (in the lands)are fixed.
This is impractical for the type of mold considered here, where the land length is uniform and corresponds to the thickness of the downstream mold plate (s).
Therefore, in the current work, DVs are related to the lateral dimensions of the flow channel.
The optimized outlet cross section is not scaled according to the required profile, the speed on the outlet of the mold is uneven, and the resulting uneven stretching
One accepted result of this approach is failure.
Further objectives identified for mold optimization include minimizing dwell time or degradation and minimizing pressure drop.
The limitation of the pressure drop can also be considered as an asa constraint on the design.
Further limitations may include limits on the rate of melting deformation or shear stress, as well as the lower limit of the length of the land.
Including these other attributes leads to multi-objective and constraint optimization problems that are not considered here.
Instead, they may be checked after the optimization is completed, and if it is found to be unsatisfactory, the optimization may run again with the different processing conditions or ranges of DVs.
The assumption that the flow is developed on the mold cross section means that there is no pressure gradient and velocity component on the cross section plane.
In order to apply this consistently across multiple sections, it is necessary to cross
Minimize traffic, which leads to the use of avoidcross-flow strategy (ACFS)
Balance mold (23-25).
In fact, the lateral velocity component cannot be completely eliminated in a gradually thinner mold cavity, But ACFS provides a way to control them and balance the mold.
It works as follows.
The cross section of the desired final profile is divided into multiple partitions, separated by the dividing line relative to the obvious features, such as angle or thickness change.
The partition will correspond to the independent function of the configuration file required to control the dimension.
Calculate the area of each partition as a percentage of the total cross-section.
Call the score area of partition p, Ap.
The part is mapped to the die outlet and mapped to the cross section of the interface between the die plates.
On each cross section, ideally, the score of the total flow through partition p is this score Ap (
Strictly speaking, this involves the assumption of a constant density stream).
Partitions can be visualized as a cross section of a virtual channel that provides the correct amount of material to achieve the same quality within each partition of the finished outline.
In the 2D method, the horizontal dimension optimization of parallel land is performed first.
Then optimize the other cross sections in turn (
Based on the development traffic assumption again)
Working behind death
In the process, some of the dimensions that have been optimized go back to the upstream cross-section.
This limits the upstream part and avoids sudden changes in geometry, simplifying the selection and handling of DVs.
As the level of detail decreases, the number of partitions required for the upstream cross-section usually decreases.
Combining smaller downstream partitions into larger upstream partitions will provide an appropriate flow rate fraction.
When optimizing each cross-section individually, the assumption of the maximum weak coupling between upstream and downstream locations is implied;
In particular, the dependence of critical traffic on upstream details is weak.
In fact, the length of the land is several times larger than the horizontal size (the land gap).
In the prevention of low Reynolds numbers, the developed flow will be obtained within the flow length of one or two land clearances and will therefore be present on most land lengths.
In addition, most of the pressure drop through the mold will occur on land, so there is a major impact on the flow distribution.
The most critical part of optimizing the design first is effective using the development process assumptions.
Although in true 3D flow coupling, there is a principle coupling between all points, but the details of the further parts of the mold have less and less impact on the outlet flow balance.
Optimize the upstream part according to ACFS, minimize the flow components in the transverse plane, and maximize the applicability of the developed flow assumptions.
In particular, the strategy will avoid the rapid and unrecoverable redistribution of materials when entering land or land protected areas.
The process assumptions for ACFS and development are consistent internally.
Any approximation in the resulting design will be small and offset by the computational advantages of this method.
For the specified flow rate, the uniqueness of the optimized design simulation is performed without a pressure gradient.
Therefore, there may be multiple solutions corresponding to various combinations of channel size and pressure gradient;
For example, the same flow rate can obtain a high pressure gradient in a narrow channel, or a lower pressure gradient in more open channels.
In the above process, shipping as many sizes as possible from the mold outlet back to the upstream section will eliminate this possibility and avoid unnecessary sudden geometric changes along the mold cavity.
Also, avoiding too many restrictions on DVs will help avoid multiple solutions.
Experience has shown that these rarely occur, and, where multiple of the best points are found, it is easy to choose a reference solution based on lower value, easy to manufacture, etc.
Ability to repair mold size in this step-
Wiseway brings some back to the upstream section compared to the 3D method, which is a further advantage of 2D.
In 3D optimization, all DVDs are optimized at the same time, and it is more likely that multiple optima will appear.
Selection of partitions and location of partitions typical partition examples of uPVC profile cross section as shown in Fig. 6.
A geometric simple area, such as a wall of uniform thickness, is represented by a single partition.
Detail features that control size precisely are critical form small partitions.
For the profile cross-section of the illustration, a total of 39 partitions are considered necessary.
Partitions are limited by dividers.
These are related to key points, but they are used directly.
In some cases, the way forward as the end of the demarcation line is not satisfactory;
Then, some partitions may not be shut down by partitions as required by the integrated partition flow rate.
The study of all possible cases found that the three methods of defining the separator are necessary, and the definition of the separator and the creation of the partition are carried out in specially written preprocessing software. 20.
The geometric modifications required during the optimization process may cause the voltage divider to reposition in response to a change in D [F. sub. s]
, As described below.
O definition [F. sub. s]
The mold balance is expressed as a mathematical optimization problem. F. sub. s]
The mold performance and design quality must be defined as measured. Local (partition)and global O[F. sub. s]
Selected here [F. sub. p]= ([Q. sub. p]-[A. sub. p]/[A. sub. p])x 100% [
Mathematical expressions that cannot be reproduced in ASCII](6)
In the optimal local O [F. sub. s], [F. sub. p]
When the fraction of the total volume flow rate is zero ,[Q. sub. p]
, The partition p passing through the cavity cross section is equal to the corresponding area fraction Ap in the desired profile.
By defining the inverse weighting of the area score, the definition forces all partitions to have the same percentage accuracy.
This is usually appropriate, but can be modified to increase or decrease the accuracy of the target in some partitions.
The global of F is equal to the deviation mode between the fractional flow rate and the expected value on all partitions, p = 1. . . , nPart. O[F. sub. s]
This type of application is already in (26)
And added constraints (penalty)
On a land too short10-13).
DV types based on key points use key points directly because DVs are rarely convenient or efficient.
To develop a practical program to track the work of experienced designers in an industrial environment.
In addition, it is necessary to pay attention to the following limitations of mold design and manufacture: 1.
Keep the standard corner radius where needed. 2.
Define the minimum corner radius associated with the wire diameter of the wEDM wire cutter. 3.
Keep parallel channel walls if necessary. 4.
Maintain CI continuity of the profile.
Common types of geometry modifications are shown in the figure. 7.
Determine that constraints can be met and implement all required design modifications using the following four types of dv: Type 1: Single Key point modifications.
Specify the movement vector, and define the movement limit that allows the moving endpoint.
Alternatively, or at the same time, the arc radius may change and the moving limit defines the maximum and minimum allowable range.
This basic type of DV is rarely used.
Type 2: movement of multiple key points.
This is the most commonly used type.
Select a set of key points, along with the amove vector, and move the limit. In Fig.
While maintaining parallelism, use the 7a set of key points to move the channel wall.
Type 3: feature extension.
Select a set of key points and determine the entry point.
Within the specified range of movement, the key points move to or away from the center point. In Fig.
This is used to change the feature size while maintaining the feature shape. In Fig.
7 CA corner radius changed.
In another example using the 3DV type, it is applied to profile features with specific requirements, fig. 8.
This is on the adapter board, the flow channel convergence, due to the limitation of the wEDM wire cutting angle, it is necessary to incorporate cerbs into the design.
These are manually initially defined, and maintenance of their size is necessary in optimization.
As shown in the figure, it is possible to scale type 3 DV using features with two key points.
Type 4: generic type.
This can be useful when assigning multiple geometry modifications to a single DV.
Any combination of type 1-3 may be used.
The definition of various DVs with moving limits and vectors is performed manually through a specially written preprocessing program that operates key points (20).
This provides visual feedback on geometric changes generated by the largest and least defined modifications, allowing analysts to confirm their applicability. Gradient-
The optimization algorithm based on optimization is the mathematical process of calculating the new DVs value and making it move in the optimal direction.
Minimizing F for solving unconstrained optimization problems (s)s [member of][R. sup. nDV][S. sub. i. sup. L][
Less than or equal][s. sub. i][
Less than or equal to][S. sub. i. sup. U]i =, . . . ,nDV (7)Here, F(s)
Depending on the optimization strategy used, global or local can be represented.
S is a vector of DVs with dimensions that represent the number of DVs associated with.
Every DV, anupper ,[S. sub. i. sup. U]And lower ,[S. sub. i. sup. L]
Was designated.
These are called movement restrictions or side constraints.
The vector of the DVs and its movement limits define the design space. F(s)
Is a smooth implicit scalar function of DVs;
Re-calculate the values based on the results of the flow simulation. Values of F(s)
The system response is formed and the response surface is formed.
Partial derivative [s. sub. i]
Known as the sensitivity or gradient of the response surface, it is used to find the best response surface.
In the current work, DVs are continuous, gradient
Therefore, in order to improve the efficiency, the optimization-based method is selected.
The basic concept of iteration is expressed [s. sub. k]= [s. sup. k-1]+ [[alpha]. sup. k][r. sup. k](8)
Iteration k on DVs [vectors. sup. k-1]
Update in the design space of the unit vector direction [r. sup. k]by a distance[[alpha]. sup. k].
Moving direction]r. sup. k]
Recalculate level 4 using sensitivity values and line search, using different methods in various algorithms.
The structure of the design optimization environment allows for free selection and can change the merged algorithm with minimal effort.
Therefore, the details of the algorithm are not included;
They are available in standard work.
In the present workden-Fletcher-
Olfletcher-
Using the Reeves method, from DOT (
Design optimization toolspackage (28).
Sensitivity is obtained by finite difference;
That is to say, DV values are disturbed, repeated flow simulation and repeated flow simulationevaluated.
The finite difference method is chosen because it is simple and can be implemented independently of the specific simulation package used.
Using an alternative approach to the direct differential method, integrate the calculation of sensitivity into the simulation software, see (6).
Flow Simulation of constant temperature flow developed on the cavity cross section was performed using in-
Generation of housing grid and finite element (FE)software (2).
Therefore, assuming that a constant temperature generalized Newton flow is developed, independent terms and gravity terms are ignored, the conservation law equation solved is [eth]/[[eth]. sub. x]([mu][eth][v. sub. z]/[[eth]. sub. x])+[eth]/[[eth]. sub. y]([mu][eth][v. sub. z]/[[eth]. sub. y])= dp/[d. sub. z](9)
The cross section is located in x-
The Y plane and z are the direction of flow, and P is the uniform pressure on the cross section. Viscosity [mu]
Expressing the quality of uPVC with truncated power law [mu]= [[mu]. sub. 0][[gamma]. sup. n-1], [gamma]>[[gamma]. sub. min]; [mu]= [[mu]. sub. 0][[gamma]. sub. min. sup. n-1], [gamma][
Less than or equal to][[gamma]. sub. min](10)[[mu]. sub. 0]
The coefficient of consistency specified at the processing temperature is [T. sub. 0], and [gamma]
Is the shear rate.
The second is the power law index.
When the shear rate is close to zero, apply a minimum value to the alternative shear rate to avoid infinite viscosity.
It is believed that the solution has nothing to do with the values chosen in the order [s][gamma]. sub. min]= [10. sup. -3][s. sup. -1].
It is widely believed that wall sliding often occurs in uPVC.
This is represented by the nonlinear Navi law associated with wall shear stress [j][tau]. sub. w]
Speed to slide [v. sub. zs][[tau]. sub. w]= [C. sub. 0][v. sub. zs. sup. m](11)[C. sup. 0]
The sliding coefficient assessed at temperature is that nr is the sliding index.
The use of Navi\'s law is reasonable, because it is generally believed that the sliding of uPVC is due to the presence of a low viscosity cleaning layer on the mold wall (29).
The power law and Na-Law parameters of window profile grade uPVC byon-are determinedLine flow measurement (30)
, See Table 1, providing values for polished diesel surfaces ,[R. sub. a]= 0. 13[micro]
Typical commercial use.
By comparing the offlow simulation with the extrusion test, the suitability of these values is confirmed (20).
The above figures reflect the significant contribution of slip, which is particularly important in places of death.
The developed flow solution dpldz must be specified.
The total flow rate and flow rate within each partition can then be obtained by integrating [v. sub. z]
On cross section
In order to obtain the solution of the specified total flow rate, it is necessary to iterate over the dpldz.
However, in the simulation of the flow rate change, there is only a small change in the distribution of fractional flow ,[Q. sub. p], werefound.
Change the flow rate through the cross section in the figure6 by -[+or -]
20% resulting in the greatest change of any [Q. sub. p]of 3%.
The change is less than 1% in 39 partitions [20].
Therefore, forward-looking convergence of process flow rates can be set, resulting in a computational economy.
To satisfactorily address the flow distribution in a typical profile feature, elements with an edge length of 0.
15mm was found to be sufficient, resulting in a grid of about 30,000 elements on the cross section and about 10 linear elements on the wall thickness.
Grid Generation and solving (
A function call)took 120 s(Pentium4, 2. 8 GHz).
The process simulation is only briefly introduced here, and the current focus is on other features of the design optimization environment.
The way this structure is structured is that in the case of minimal variation, any one of many simulation packages using different physical models or numerical techniques can be merged.
How to apply optimization strategy control optimization algorithm to D [V. sub. s].
For issues involving a large number of DVs, especially when there is a coupling between them, this can have a significant impact on robustness and efficiency.
In the current work, some strategies have been studied.
Global optimization strategy (GOS).
Optimization is driven by global minimisation of F.
Sensitivity is obtained by disturbing each DV separately, which requires the Newcastle 1 function to call the peroptimization loop.
Up to 50 DVs may be required on a single flowchannel cross section when trying to optimize more than 5-
10 at the same time.
One of the important factors is the coupling between regions;
Changes to traffic through one partition usually change the traffic of all other partitions.
Two types of coupling are identified.
Local coupling occurs between adjacent partitions, which may cause local changes in values to be negative or positive.
The weaker global coupling comes from the distribution of traffic changes on all partitions.
The results show that GOS is not robust and stable enough to optimize complex uPVC profiles in industrial environments.
Sequential Optimization Strategy (SOS).
Compared to local OFs, Fp, the design is optimized to update the DVs in turn, while the others remain the same.
Again, the Newcastle 1 function calls arerequired for each optimization cycle.
Compared with GOS, the strategy proves a more robust convergence, with the degree of coupling affecting the convergence speed but not the stability.
The parallel decoupling optimization strategy parallel decoupling scheme is driven by local OFs, but unlike SOS, after all DVs are disturbed at the same time, the local sensitivity is evaluated by finite difference, so, only two function calls are required for each cycle, providing a substantial computational economy.
In order to extract only the sensitivity value of one DV, the effect of interfering with all other DV must be eliminated.
This is done using a flow rate change that occurs in an artificial reference partition that introduces the mold cross section.
This is a small, isolated area that is not included in the associated DV in the flow simulation.
Changes are made to all DVs areas at the same time during an optimization cycle, and the effects of coupling must be considered again.
This is achieved by modifying DVchanges to consider the traffic increment generated by coupling, which can be obtained from changes in the reference partition.
The program shows good consistency.
For more details, see (20).
In conclusion, SOS proved to be the most robust, as failure to optimize a partition would not interfere with subsequent optimization and was corrected in further cycles.
However, considering the overall performance of computational costs, robustness, and required manual inputs, the parallel decoupling optimization strategy becomes the first choice and is applied to commercial mold optimization;
However, before describing this case study, an overview of the optimization process is provided for clarity.
Optimization Process overview optimization process overview for each diecross section provided by the diagram9.
Optimization begins with the iges cad model of the mold cavity created by the designer and embodies his best estimate of the desired geometry.
Pre-processing of the selected mold cross section starts by creating key points from the CAD model, using software polygons-PRE2D.
This contains manual tools for model cleanup, including any arcs that handle a diface angle close to 180 [degrees]
As shown in the figure. 4. Key point data-
Then, a list of each profile of the cross section will be automatically created. An initial (developed)
The flow simulation of the cross section is followed.
Use Poly again
PRE2D, performs partitions by creating delimiters based on key points and arc centers.
When using the software DIEVAL fractionalareas ,[A. sub. i]
, Initially calculate the partition on the required profile to provide the target flow rate through the partition on the mold cross section.
The partition on the finished profile is mapped to the mold cross section, and dieval provides the fractional flow rate according to the initial flow simulation ,[Q. sub. i]
And calculate the global, F, and partition ,[F. sub. p], OF values.
With this information and taking into account the form of the partition, the designer uses POLYPRE2D to specify the DV type associated with each Partition and Its mobility restrictions.
Typically, a DV is associated with each partition, although it may not be available in some casesa partitions, it remains the same during the optimization process.
The preprocessing also includes the input of the processing conditions, the flow characteristic data, and the parameters of the control grid division, solution and optimization.
Enter the auto-optimization loop to create a dxf cad model for the 2 Dflow domain based on the current key point value.
Domain grid partitioning and flow solutions are carried out.
Evaluate and check for convergence of OFs.
According to experience, the convergence criteria for global OF and all local OFs are 3% and 1%, respectively.
If the convergence is not complete, DVs are disturbed, which is a repeated flow analysis and sensitivity is evaluated by limited differences.
Pass the sensitivity and DV values to the optimization algorithm that updates the DVs.
The parametric module updates the list of key points and rebuilds the geometry.
The next loop starts with creating a new mesh from the updated DXF model.
Case study: the application in the initial design, zoning, and DV selection of streamlined molds now provides an example of a medium complex profile mold optimization.
This creates a fixed window profile as shown in the figure. 10.
The mold consists of six plates using a combination of torpedo and core
Plate structure, similar (
But not the same)
As shown in Figure 12.
The first task of the designer is to specify the initial design and then make important decisions in many aspects that affect the success of the optimization.
First, select five parts for optimization, as shown in the figure. 11.
The upstream parts are not optimized because the impact of these parts on mold balance is minimal.
Next, select partition and DVs.
The results are shown in the figure.
12, where the number identifying the partition is given.
Now describe the selected mold cavity part that works backwards from the mold outlet.
The first part represents the parallel land of dieexit.
To control the final details of the 46 partitions of the profile, each partition has a related DV.
Most of them are type 2 and consist of key points.
The exception is the partition associated with partitions 1, 7, 8, 22, 26, 34, 38, 40, 42 and 43 of type 3, where the zoom function is required.
In the second section, the only change introduced in the land area is the intranet to allow the placement of torpedo brackets.
Only two DVs associated with web partitions 1 and 2 are required.
All other sizes are returned from Part 1.
In mold 3, the structure from torpedo to core has changed
Therefore, on Section 3, the outer wall was broken.
Select DVs on these separate sections, a total of eight.
The exterior wall thickness and network size of the upper and lower parts are shipped back from the second part.
Section 4 is located in the adapter area where a large change in the cross section occurs.
The whole area is divided into 23 partitions, each with a DV.
Finally, the form of section V is simpler and lacks details of the introduction downstream.
The cross section is represented by 10 partitions, each with a DV.
However, constraints are introduced in manufacturing requirements.
To simplify the programming of wEDM, left and right outer boundaries should be flush with lines.
In addition, only the external boundary of the wall can be modified.
The appropriate specification of the DV type satisfies these constraints.
Specified for all selected DVs movelimits based on the results of experience, manufacturing constraints and preliminary flow simulations.
The results of computerized optimization and the comparison with the \"manual\" optimization results of automatic computerized optimization have now been presented and compared with the \"manual\" process.
In this design, the designer is guided by the flow simulation value (
Local and global)
Calculated on the same partition as the one used in the automatic process.
According to his judgment, design changes are made manually on the CAD model.
Due to the selection of automatically optimized DVs, manual and automatic programs can be compared directly, taking into account the type of changes that designers usually make.
Evaluation results under the following heading: design quality.
This is measured by the value.
In the first part, the automatic process will be global F = 0.
76%, compared with 0. 88% manually.
Comparison of local values [F. sub. p]As shown in the figure. 13.
The substantial improvements to the original highly unbalanced design are obvious, and the value of automatically optimizing production is getting lower and lower.
Similar results and conclusions were drawn in other sections.
Similarity of design.
Of course, it is possible to obtain equal values from different geometric modifications, and it makes sense to compare the final form of the geometry generated by the two processes.
A typical example is provided in Figure 14.
Although the difference can be seen in the feature details, the wall thickness has a considerable response.
However, a check on the value indicates that although both manual and automatic programs meet the convergence criteria, the latter results in a lower value.
The modifications here may seem small, but the high sensitivity of the flow rate to the size change should be taken into account.
This can be explained by the flow solution developed by the analysis of the apower law liquid through the too wide slit.
For a given pressure gradient (
Includes wall slides that simplify the discussion)
This predicts the flow rate associated with the slit gap of the power (2n + 1)/n. With n = 0.
28, as here, for example, a decrease of a10 % of Clearance Height corresponds to a flow rate change of 45%.
Computing requirements.
The calculation requirements can be evaluated by the number of function calls, and other calculations are relatively small.
Figure 15 shows the change OF global OF to function call during the first part OF the manual and automatic process optimization process.
The automatic program uses a parallel decoupling optimization scheme. two function calls are required for each optimization cycle, while only one function call is required manually.
Automatic optimization, however, implements about twice the F per cycle, so the number of function calls that reach convergence is very similar.
In both cases, F decreases in the direction of convergence in a monotonous manner, which proves the skill of the designer and also proves the effectiveness of automatic optimization.
A similar diagram was obtained to optimize the other parts.
To achieve convergence, the number of function calls depends on the number of DVs and the degree of coupling between them.
For the first part, the automatic program requires seven redesign cycles, the second part requires only one cycle, the fourth part requires five cycles, the third part requires four cycles, and the fifth part requires five cycles.
User interaction.
For comparative purposes, by tracking the work of experienced designers in an industrial environment, the time involved in performing manual and automatic optimization was assessed. A break-
Table 2 gives the required tasks and time.
An important quantity here is the number of manual redesign cycles, iiman, which designers need to enter on each cycle.
This does not exist in the automatic program.
Table 2 shows pre-
The processing time automatically optimized is more than twice the manual time (
The time for each chip part depends on the number of partitions and DVs, and the time quoted is the average).
However, in each cycle of the automatic process, the elimination of designer input greatly exceeds the pre-processing, with a total time of 225 minutes compared to the manual 1500 minutes.
Also, this input is only needed at the beginning of the process, not as inconvenient to propagate as manual optimization.
The conclusion describes the automatic computer optimization scheme of Profile extrusion die in detail.
This provides for the first time a method for handling complex types of dierequi for the production of uPVC profiles containing multiple complex features.
These techniques are based on the manufacturing methods of this mold and the experience and practice of skilled designers.
The design and optimization strategies are compared and discussed, thus developing an efficient, robust and practical computing design environment in the industrial environment.
Its use has been demonstrated in an application of a typical uPVC window profile, and compared to the work of the designer to manually modify the CAD model based on the results of the flow simulation, the automatic program has been demonstrated
This is a relevant comparison to assess the benefits of the current work.
The results show that the computational optimization design has at least the same effect as the manual adjustment, and most significantly, the time required by the designer has been reduced by nearly 7 times, resulting in important economic development.
Automatic optimization provides a CAD model for manufacturing molds, providing a good starting point for the physical extrusion test required for final adjustment.
The scope of this stage will mainly depend on the extent to which the underlying simulation captures the flow phenomenon in the mold.
The use of the developed flow solution eliminates the modeling of stretching and stickinessElastic effect.
Other differences may be caused by the assumption of constant temperature flow.
To include these, 3D CFD is necessary in combination with 3D optimization.
The view was expressed that technical difficulties and cost implications made the situation unattractive or not feasible.
However, the 2D method has proven to be effective and any limitation can be overcome to some extent by calibration optimization based on experimental results.
For example, if traffic in the inflow partition is found to be lower than predicted in the extrusion test, the target traffic can be increased and the optimization can be re-run.
Although the focus here is on the design of streamlined molds for the production of complex uPVC profiles, the optimization strategy, the proposed parametric method of key points of mold design is powerful and flexible, other types of molds can be applied in 2D or 3D methods.
This paper will incorporate the background in a broad review of profile mold design in the references. 31.
Confirm that gratefullyackinformed Kommerling Kunststoff is a cooperation.
To: J. F. T. Pittman; e-mail:j. f. t. Pitman in Swanseaac.
British Commission for Research in Engineering and Physical Sciences, UK;
Contract award No. : epsrc gr/M 95820 (
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