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2019-08-28

Y. C. LAM [a]L. W. SEOW [b]

Cavity balance is the process of changing the flow front of the cavity through thickness and design changes, thus achieving the desired filling pattern.

This paper reports a preliminary study on the development of two-cavity balancing automation methods

Size cavity.

In order to shorten the development time of the product and improve the quality of the product, the purpose of automatic cavity balance is.

This will reduce the level of expert knowledge necessary for successful mold and part design.

The automatic space balancing program was developed using the concept of the flow path. The hill-

The hill climbing algorithm is used to generate the flow path on the cavity filling pattern.

In the previous work, this method replaces the flow path generated using the DC path assumption and finds that this method is more generic and more suitable for automation.

Special considerations or procedures are not required to overcome the information that exists in the cavity.

This method has been implemented in a computer program running as an external loop of the Moldflow software.

Through the analysis of the model, the feasibility and robustness of the method are proved.

1 Introduction plastic injection molding is the process of injecting hot moltenpolymer into the mold.

After cooling, the solidified part of the concave cavity shape inside the mold is popped up.

With the turn of the century, through the innovation of machine technology, improved process control and the introduction of a series of new plastics, injection molding has become the main manufacturing process for producing large quantities of parts at the lowest cost.

The active research and application of computer accelerate the transformation of injection molding from process to process.

Since the 1970s, design engineers have been using computer software to predict fill pressure, fill mode and temperature in plastic injection molding.

Because the mold is expensive and difficult to make, designers rely on software to accurately predict the processing, cooling and warping behavior.

Recently, the research of plastic injection molding mainly focuses on the optimization algorithm. Lee and Kim [1]

Use improved complex methods to reduce warping by optimizing the thickness of different surfaces.

The warpage is further reduced by obtaining the best process conditions.

The optimal injection gate position was studied by pendlidis and Zou [2]

Who defines the best position with a mass function consisting of temperature difference, outer packaging and friction heating term.

Simulated annealing and hill-

Then the optimal node is found by climbing the mountain.

In a later paper, process variables were also optimized3]. Lee and Kim [4]

The optimum gate position was also studied using the evaluation criteria for warping, welds and melting lines, and izod impact strength.

By allowing designers to select some gatelocations first, intensive search programs are avoided.

Then use riteria to do a local search on the node to determine the quality of the node. Jong and Wang [5]

Describes the optimal design of the gate system that supplies the melt to the injection gate in multiple gatespart mold.

Although cavity balance is an important first step in the design of plastic parts that can improve the quality of the finished product, it has not received the attention it deserves.

The main drawback is the time and manpower required to iterate to an acceptable solution for the balanced cavity.

Lack of experience and complex part geometry can easily lead to too long development time.

One of the main reasons why cavity balance requires experience is the need to assume or predict the flow path in the cavity and identify the dominant flow path.

Dominant flow pathis is defined as the simplest route of plastic flow between gate and last point filling [6].

This is done by checking the parts to see how the polymer will flow, or by running the initial flow analysis and looking at the resulting fill pattern.

For parts with uniform thickness, the process is very simple due to similar flow resistance at all locations.

However, this will become a complex problem when there are different thicknesses that must be judged.

With the help of computers, the time required for this heuristic process is greatly reduced.

Nevertheless, the balanced flow within the cavity will still pose a challenge to inexperienced designers or complex parts.

Therefore, in seeking the method of automatic cavity balancing, the optimization program must overcome the difficulty of flow path visualization and balancing.

In our previous work7]

A straight flow path is assumed.

It provides good results for a simple two-cavity balance

Size object.

A major disadvantage in the use of DC path assumptions [7]

It is difficult to apply complex geometric assumptions.

While it works for simple geometry, it has great limitations due to its inherent simplicity.

When applying this hypothesis to say automotive components, it is difficult to predict that the actual flow path is far from a straight line.

Therefore, in order to develop a robust automatic cavity balancing technique, an improved approach to approximate flow paths is needed.

A simple and effective technique, often called Hill-

In this study, the flow path is determined by climbing algorithm. Thehill-

Mountain climbing search is a kind of deterministic search.

It guarantees that the global optimum can only be found if the search space is convex, which is usually correct for the current problem.

Flow path generated using hill-will be displayed

The mountain climbing algorithm combined with the optimization program provides an effective method for space balance.

In this paper, we will describe how the mountain is

The mountain climbing algorithm is adopted to determine the flow path.

Subsequently, the determined flow path through the optimization program will be used to achieve a balanced space.

Several aspects of the optimization program will also be studied.

Approximate using 2 flow paths of HILL-

Climbing Method-

Mountain climbing is well known in optimization theory, and it comes from a series of search methods used to find the target state in solution space.

A good description of the different techniques that can be classified under hill

The climb can be found in the text of Schwefel [8].

Basically, the mountain-

The climbing method can be described by using a popular analogy from a mountaineer who tries to find peaks in adense fog without a map.

In theory, if the climber keeps moving in the steepest direction, he will eventually reach the top of the mountain.

Similarly, when looking for the maximum value defined by the target function, the method can start at a random position and use the information provided by the surrounding gradient to locate the maximum value.

The maximum value will then be the point at which the negative gradient is represented by moving in all directions.

However, the process of locating the maximum is not always simple.

Method of mountain-

As we all know, climbing is subject to certain restrictions, the most critical of which is made up of harsh terrain such as the terrain shown in Figure 11.

In particular, it may be affected by the largest, plateau or ridge in the area.

The local maximum is the second peak in the search space, which is achieved by drawing the algorithm to that peak.

When the algorithm converges to the local maximum, the solution is not only a sub-

It also prevents the algorithm from finding the true global maximum. If thehill-

Crawling algorithm is an algorithm to find the global maximum in an unknown search space. then, inevitably, every solution found needs to be tested and verified. on the other hand, the plateau is a relatively flat space.

So the mountain-

Since there are multiple directions to take the best steps for the next step, the mountain climbing algorithm can be easily found in this area.

If the steps taken are small and turn-led, the problem is more complicated. off errors.

Finally, there is no difference between the ridge and the saddle point.

The algorithm effectively finds itself at the edge where each step moves down, although it is not a local or global maximum.

So, obviously, the mountain-

If the search space contains the above features, the crawling algorithm is not a reliable way to locate the global maximum.

Although some techniques have been proposed from backtracking to random jumping, these are only supplementary measures, which cannot guarantee the efficient and effective convergence of the algorithm to the optimal.

However, it is worth noting that the limitation of the method stems from the solution space of the application of the method.

For example, if the solution space is a concentric hypersphere, the method can generate a global maximum in one step.

In this way, in the use of mountains-

Effective crawling algorithm must have a prior internal knowledge of the features of the search space.

This can determine the success or failure of the algorithm.

For plastic injection molding, the flow path can be derived from the TIME profile of the fill pattern generated by the fill analysis.

The flow path can be traced back to the injection door from a point on the boundary, rather than tracking the flow path from the injection door to the boundary.

To explain how to use hill to locate the flow path

Climbing algorithm, let\'s consider the filling time profile of a single gatedcavity shown in the figure2.

One can observe that the outline of the plot can be framed as the solution space of the objective function.

If this is the case, then the global minimum of the fill time is the injection node (

Fill time = 0. 0)

By applying thehill-

Climb the algorithm from any position within the space. (

Note the term Hill.

Since the actual process is downhill, the climb is used here as a general term

Climb, and the minimum position is not the maximum position.

In addition, the search direction is the direction of the fastest decline).

For current applications, use thehill-

The climbing strategy is not to find the global minimum, but at the door.

Interested is the path taken by the algorithm to reach the minimum value. As the hill-

The mountain climbing algorithm moves along the direction of the most rapid descent to the injection node, and the trajectory from the boundary position to the gate represents a strong recommendation for the path taken by the flow when the melt is injected into the cavity.

This is based on the fact that during the filling process, it is known that the melt fills the part with the least resistance before the other part.

It can then be assumed that at any point in the filling phase, the previous position of melting can be determined by the filling direction of the fastest flow.

On the fill time line chart, the fastest flow is the direction of the steepest gradient, which is exactly the path that hill tracks

Mountain climbing algorithm in the process of reaching the global minimum.

So, from the fill time profile generated by the fill analysis, hill-

The climbing algorithm can be used to track the flow path from any position within the cavity.

As mentioned earlier, Hill-when faced with bad terrain-

There are some defects in the algorithm.

However, a significant advantage of the filling pattern in plastic injection molding is that it does not cause bad terrain to the algorithm.

First, a strong global minimum is defined in the search space.

This is represented by the jectionnode.

Second, it is impossible for the plateau to exist because it needs to melt almost instantly to fill certain areas.

Third, the ridges produced by multiple gates are basically welds.

In order to avoid difficulties caused by welds (ridges)

Multiple doors (

Multiple local minimum values)

, Physical domain (search space)

Can be divided into separate sub along the welddomains. (

The function of child creation

Domains can be easily implemented.

In fact, it is available in commercial software such as mobile flow. )

Therefore, within each individual

Domain, there is only one injection door.

The difficulties of the Ridgesare are also avoided because they are now the boundary of the submarinedomains.

Therefore, the fill mode is indeed well defined terrain, which makes itideal suitable for simple Hills

Climbing algorithm.

Strong and simple mountain-

Therefore, the climbing method becomes an advantage when determining the flow path.

As an example

3 shows the filling time isograms of the quarterly portion of the uniform thickness plate. Shown in Fig.

3 is the path generated using hill-

Climbing algorithm.

The initial position of the algorithm is at the boundary node of the model.

From here, Hill-

Use the mountain climbing algorithm to trace the path back to the injection node in the lower left corner.

It can be seen that the generated path is a good representation of the flow path.

When flowing to the top right corner, the flow path is usually straight towards the end.

The change in direction near the edge can be explained by the outer packaging on the side.

The edge is first populated because it has a distance from the injection node.

As a result, the extra meltwill is pushed up to the corner.

Therefore, the molten particles moving on the path shown in the figure

3. due to excessive packaging, an indirect change will be experienced.

So use the mountain-

Through the climbing algorithm, the flow path can be generated effectively and the change of flow direction can be modeled.

Its benefits far outweigh the additional computer time required compared to the linear flow path assumption in our previous work [7].

Using thehill-generated flow path

For automatic balancing, the mountain climbing algorithm will now be adopted.

3 The method of optimizing the automatic cavity balance of the program is based on the same principle as described in our previous paper [7].

The optimization procedure for cavity balance is basically unchanged.

The only difference is that using hill-generated flow path

The climbing algorithm is now used, not the DC path.

Therefore, the optimization program will only briefly discuss the details included in [here]7].

Figure month shows the generatingflow Road Mountain in the algorithm flow chartClimbing Method.

The specific steps are as follows: 1.

All boundary nodes BN are considered. 2.

Coordinates of BN ([X. sub. i], [Y. sub. i])are stored in([X. sub. c], [Y. sub. c]). 3.

Determine points (NP)

Calculate next time in radius r.

NP is the number of points on the perimeter of a circle with a radius of r ([X. sub. c], [Y. sub. c])as the center.

Calculate the fill time for these points.

Search within the 5-degree interval, NP is equal (360/5 = 72).

For numerical examples included in this article, r is equal to 5mm, I. e.

About 2.

Large size 5%.

The value of the selected NP and r depends on the accuracy required by the flow path, the higher the NP value, the lower the r value, and the resolution of the flow path will increase as the calculation cost increases accordingly. 4.

Calculation of filling time]f. sub. j]of point ([X. sub. j],[Y. sub. j]).

The fill time is calculated by interpolation from the fill time at the element node. 5.

Min minimum filling time ([f. sub. j])from j = 1, . . . ,NP. 6.

Coordinates of points ([X. sub. m], [Y. sub. m])

Store the minimum fill time in the array ([X. sub. c], [Y. sub. c]). 7. If ([X. sub. c], [Y. sub. c])

Not the injection node, repeat the calculation from step 3. 8.

If all boundary node BN is not processed, the calculation is repeated from step 2. 3.

1 Flow Path concept flow path is the path tracked by particles when injected into the mold through the gate.

For simple geometry that is not inserted, unbalanced flow will indicate that the flow path changes direction once a boundary is encountered.

The flow path may look like the picture3.

By changing the thickness along these flow paths, thus changing their flow rate, the cavity balance can be achieved.

It should be noted that the resulting thickness distribution may cause difficulty in mold manufacturing.

The average process can be used to distribute the thickness evenly, and/or the thickness requirements of the balanced cavity can be relaxed to reduce the manufacturing cost.

Similarly, if changes in part thickness cannot be accepted due to functional requirements, these requirements should be applied as constraints.

The resulting cavity may not be \"balanced\" as it would ideally be, but one can expect a more balanced cavity. 3.

2 update the parameters to adjust the thickness along the flow path, and there is a direct linear relationship between the flow and the thickness assumption.

The updated equation can be expressed as follows :[Z. sub. new]= [lgroup][frac{[t. sub. node]}{[t. sub. ref]}][rgroup]X[Z. sub. old](1)where [Z. sub. new]

Is it the updated thickness ,[Z. sub. old]

Is the thickness of the present ,[t. sub. node]

The filling time when the cutting edge is melted to fill the node, and ,[t. sub. ref]

The filling time when the melt frontier fills the reference node.

Time to fill in ,[t. sub. ref]

, Used as a reference to compare all other fill times.

If the initial thickness distribution is uniform and the filling time of the flow path boundary node with this length is selected [t. sub. ref]

, This will result in an increase in the thickness of all other flow paths.

Conversely, if the fill time of the longest flow path is selected as [, the thickness of the other flow paths is reducedt. sub. ref].

The fill time of any other flow path can be used.

In this case, the thickness of the flow path longer than the reference flow path increases, and the thickness of the flow path shorter than the reference flow path decreases.

In this paper, the filling time of the shortest path is [t. sub. ref].

It should be noted that the program for flow path determination, optimization and thickness update acts as an external run of the Moldflow software that simulates the injection process. 3.

3 optimization criteria a feature of flow during injection molding is that the pressure at the advancing melting front is equal to zero.

In the unbalanced flow, the pressure accumulates at the edges as the melting fills the edges first and continues to wrap as shown2.

However, this is not the case with unbalanced flows.

When the flow front reaches the boundary at the same time, no excessive packaging will occur.

In addition, the pressure at the boundary node is the pressure at the flow front.

Therefore, the pressure on the boundary node should be equal to zero before the balance gap is filled.

Therefore, the above conditions can be used as a standard for terminating the optimization routine.

Obviously, in reality, it is very likely that a flow frontier will be generated, reaching each boundary node at exactly the same time, and there will be some overfilling.

In this case, a tolerance is set according to which if the pressure on the boundary node is less than 1% of the maximum pressure of the cavity, the pressure on the boundary node is assumed to be zero.

The condition of convergence is the goodness of the hundred %, in which the goodness is given by, goodness = [lgroup][frac{N}{[N. sub. total]}][rgroup]X 100 (2)

Where N is the number of zero-pressure boundary nodes, and ,[N. sub. total]

Total number of boundary nodes. 4.

The first model of case study Model 1 (shown in Fig. 5)

The quarterly plate model representing the square cavity door at the corner.

The injection node is located in the lower left corner of the model.

The edge to be balanced is the top and right edge.

The desired optimization is 100%.

Figure 5a and B respectively show the filling pattern of the plate with uniform thickness distribution before balance and the filling pattern after balance.

The desired optimization was achieved in 15 iterations.

The thickness distribution after equilibrium is shown in the figure. 6.

The darker area indicates the thicker part.

Similar to the results obtained using the linear flow path assumption, the flow leader can form to the upper right corner of the cavity with a long path.

Model shown in Figure 2

7 is created with inserts that hinder the movement of molten logistics.

The last point to fill is in the top left corner-handcorner.

The injection node is represented by a black square in the middle.

The optimization routine is configured to balance the cavity of all edges indicated by the dark border.

As before, the optimization is set to 100%.

Convergence is achieved in 33 iterations.

The thickness distribution is shown in the figure. 8.

The darker area indicates the thicker part.

You can clearly see that a traffic leader is formed on the left.

As expected, because this is the last point to fill. 5.

Use hill-observe an interesting result

The climbing algorithm that produces the flow path is the final flow path pattern of the equilibrium cavity.

Figure 1 shows a result like this.

9 quarter plate model.

The injection node is represented by a black square in the lower left corner. From Fig.

The final flow path pattern seems to show abranch-like behavior.

The leading flow path that coincides with the flowleader extends from the injection node to the last node filled in the upper right corner.

In addition, the secondary flow path extending from the mainstream path to the edge of the cavity.

This information is useful because the dominant flow path is often used when analyzing and optimizing processing conditions.

This information is interesting because it shows that the leading flow path acts as a line-

Source of materials.

It also highlights very inaccurate pictures represented by the DC path assumption.

Without this algorithm, it would be difficult for human analysts to come up with a similar approximation of cavity balance.

As mentioned earlier, 100% of excellence is not required in practice.

A satisfactory solution is most likely 90% or less.

Therefore, the number of iterations that converge to an acceptable solution can be significantly reduced.

For example

10 shows the progress of optimization criteria for cavities with aninsert.

Although the initial convergence rate was slow, the optimization degree increased significantly from 11 iterations, and the optimization degree of 87 times increased significantly.

8% is achieved in only 9 iterations.

The remaining 13 iterations cost 100% of the optimization.

Therefore, if the optimization is set to 85%, the number of iterations will be reduced by 40%.

Therefore, setting a lower optimization will always translate into a reduction in the number of iterations, resulting in a solution.

Figure 10 shows a slight decrease in optimization over 15 iterations.

The reason is that the pattern of the process path is relatively stable from the first iteration to the 14 iterations.

In 15 iterations, the flow path pattern around the inserted area changed.

This disturbance resulted in a slight decrease in subsuperiority.

The simple DC path assumption is inaccurate.

It must be modified as an insert, and it is not easy to automate changes to the insert or cavity.

By contrast, the mountain-

The method is simple, effective and stable, and can be used in various types of cavities.

Its advantage is its ability to fix parts with one or more plug-ins. Shown in Fig.

11 is the flow path pattern generated by Hill

Cavity climbing method with insert (Model 3).

Obstacles such as insertion will not cause problems to the algorithm.

It automatically tracks the path around the obstacle.

Therefore, it is an ideal tool for flow visualization.

Also, the ability to export the flow path from the fill mode is important.

Its ability so far is not limited to the 2D shape shown, but can be extended to 2.

5 calculate the flow path by local coordinates based on a single finite element. 6.

The conclusion proposes a method of using Hill-

Climbing algorithm.

It overcomes the difficulty of the Assumption of the direct flow path by exporting the flow path from the filling pattern of the cavity.

Especially on the mountain --

The climbing algorithm is automated and can solve the existence of one or more inserts without modifying its formula.

Combine the generated flow path with the optimization routine developed in our previous work [7]

The automatic cavity balance has achieved excellent results.

Several 2d models with different levels of complexity were successfully balanced using this method.

The method has proven to be robust and effective with the potential to easily scale from 2D to 2. 5D parts.

Month confirm the author thanks to the limited company that supports Moldflow. Ltd.

Especially sir.

Peter Kennedy, director, provided valuable help and exciting discussions.

The project was supported by the anARC collaborative research grant, and the second author thanked Monash University for its financial support in the form of an aMonash graduate scholarship, as well as the Australian government\'s scholarship for overseas graduate studies(a. )

School of Mechanical and production engineering, Nanyang University of Science and Technology, Singapore 639798 (b. )Holden Ltd.

241 Salmon Street, Port Melbourne 3207, Victoria, Australia reference (1. )B. H. Lee and B. H. Kim, Polym-Plast. Technol. Eng. , 34,793-811 (1995). (2. )I.

Panda and Q. Zou, Polym. Eng. Sci. , 30, 873 (1990). (3. )I.

Panda and Q. Zou, Polym. Eng. Sci. , 30, 883 (1990). (4. )B. H. Lee and B. H.

Mr. Jin, professional and technical staff

Paper, 41,554 (1995). (5. )W. R. Jong and K. K.

36. 385 (China)1990). (6. )

Mobile flow traffic training manual, released 9. 5, 1998. (7. )L. W. Seow and Y. C.

Lin, material processing technology, 72,333 (1996). (8. )H. P.

John Willie Anderson, evolution and best searchNew York (1995).

Cavity balance is the process of changing the flow front of the cavity through thickness and design changes, thus achieving the desired filling pattern.

This paper reports a preliminary study on the development of two-cavity balancing automation methods

Size cavity.

In order to shorten the development time of the product and improve the quality of the product, the purpose of automatic cavity balance is.

This will reduce the level of expert knowledge necessary for successful mold and part design.

The automatic space balancing program was developed using the concept of the flow path. The hill-

The hill climbing algorithm is used to generate the flow path on the cavity filling pattern.

In the previous work, this method replaces the flow path generated using the DC path assumption and finds that this method is more generic and more suitable for automation.

Special considerations or procedures are not required to overcome the information that exists in the cavity.

This method has been implemented in a computer program running as an external loop of the Moldflow software.

Through the analysis of the model, the feasibility and robustness of the method are proved.

1 Introduction plastic injection molding is the process of injecting hot moltenpolymer into the mold.

After cooling, the solidified part of the concave cavity shape inside the mold is popped up.

With the turn of the century, through the innovation of machine technology, improved process control and the introduction of a series of new plastics, injection molding has become the main manufacturing process for producing large quantities of parts at the lowest cost.

The active research and application of computer accelerate the transformation of injection molding from process to process.

Since the 1970s, design engineers have been using computer software to predict fill pressure, fill mode and temperature in plastic injection molding.

Because the mold is expensive and difficult to make, designers rely on software to accurately predict the processing, cooling and warping behavior.

Recently, the research of plastic injection molding mainly focuses on the optimization algorithm. Lee and Kim [1]

Use improved complex methods to reduce warping by optimizing the thickness of different surfaces.

The warpage is further reduced by obtaining the best process conditions.

The optimal injection gate position was studied by pendlidis and Zou [2]

Who defines the best position with a mass function consisting of temperature difference, outer packaging and friction heating term.

Simulated annealing and hill-

Then the optimal node is found by climbing the mountain.

In a later paper, process variables were also optimized3]. Lee and Kim [4]

The optimum gate position was also studied using the evaluation criteria for warping, welds and melting lines, and izod impact strength.

By allowing designers to select some gatelocations first, intensive search programs are avoided.

Then use riteria to do a local search on the node to determine the quality of the node. Jong and Wang [5]

Describes the optimal design of the gate system that supplies the melt to the injection gate in multiple gatespart mold.

Although cavity balance is an important first step in the design of plastic parts that can improve the quality of the finished product, it has not received the attention it deserves.

The main drawback is the time and manpower required to iterate to an acceptable solution for the balanced cavity.

Lack of experience and complex part geometry can easily lead to too long development time.

One of the main reasons why cavity balance requires experience is the need to assume or predict the flow path in the cavity and identify the dominant flow path.

Dominant flow pathis is defined as the simplest route of plastic flow between gate and last point filling [6].

This is done by checking the parts to see how the polymer will flow, or by running the initial flow analysis and looking at the resulting fill pattern.

For parts with uniform thickness, the process is very simple due to similar flow resistance at all locations.

However, this will become a complex problem when there are different thicknesses that must be judged.

With the help of computers, the time required for this heuristic process is greatly reduced.

Nevertheless, the balanced flow within the cavity will still pose a challenge to inexperienced designers or complex parts.

Therefore, in seeking the method of automatic cavity balancing, the optimization program must overcome the difficulty of flow path visualization and balancing.

In our previous work7]

A straight flow path is assumed.

It provides good results for a simple two-cavity balance

Size object.

A major disadvantage in the use of DC path assumptions [7]

It is difficult to apply complex geometric assumptions.

While it works for simple geometry, it has great limitations due to its inherent simplicity.

When applying this hypothesis to say automotive components, it is difficult to predict that the actual flow path is far from a straight line.

Therefore, in order to develop a robust automatic cavity balancing technique, an improved approach to approximate flow paths is needed.

A simple and effective technique, often called Hill-

In this study, the flow path is determined by climbing algorithm. Thehill-

Mountain climbing search is a kind of deterministic search.

It guarantees that the global optimum can only be found if the search space is convex, which is usually correct for the current problem.

Flow path generated using hill-will be displayed

The mountain climbing algorithm combined with the optimization program provides an effective method for space balance.

In this paper, we will describe how the mountain is

The mountain climbing algorithm is adopted to determine the flow path.

Subsequently, the determined flow path through the optimization program will be used to achieve a balanced space.

Several aspects of the optimization program will also be studied.

Approximate using 2 flow paths of HILL-

Climbing Method-

Mountain climbing is well known in optimization theory, and it comes from a series of search methods used to find the target state in solution space.

A good description of the different techniques that can be classified under hill

The climb can be found in the text of Schwefel [8].

Basically, the mountain-

The climbing method can be described by using a popular analogy from a mountaineer who tries to find peaks in adense fog without a map.

In theory, if the climber keeps moving in the steepest direction, he will eventually reach the top of the mountain.

Similarly, when looking for the maximum value defined by the target function, the method can start at a random position and use the information provided by the surrounding gradient to locate the maximum value.

The maximum value will then be the point at which the negative gradient is represented by moving in all directions.

However, the process of locating the maximum is not always simple.

Method of mountain-

As we all know, climbing is subject to certain restrictions, the most critical of which is made up of harsh terrain such as the terrain shown in Figure 11.

In particular, it may be affected by the largest, plateau or ridge in the area.

The local maximum is the second peak in the search space, which is achieved by drawing the algorithm to that peak.

When the algorithm converges to the local maximum, the solution is not only a sub-

It also prevents the algorithm from finding the true global maximum. If thehill-

Crawling algorithm is an algorithm to find the global maximum in an unknown search space. then, inevitably, every solution found needs to be tested and verified. on the other hand, the plateau is a relatively flat space.

So the mountain-

Since there are multiple directions to take the best steps for the next step, the mountain climbing algorithm can be easily found in this area.

If the steps taken are small and turn-led, the problem is more complicated. off errors.

Finally, there is no difference between the ridge and the saddle point.

The algorithm effectively finds itself at the edge where each step moves down, although it is not a local or global maximum.

So, obviously, the mountain-

If the search space contains the above features, the crawling algorithm is not a reliable way to locate the global maximum.

Although some techniques have been proposed from backtracking to random jumping, these are only supplementary measures, which cannot guarantee the efficient and effective convergence of the algorithm to the optimal.

However, it is worth noting that the limitation of the method stems from the solution space of the application of the method.

For example, if the solution space is a concentric hypersphere, the method can generate a global maximum in one step.

In this way, in the use of mountains-

Effective crawling algorithm must have a prior internal knowledge of the features of the search space.

This can determine the success or failure of the algorithm.

For plastic injection molding, the flow path can be derived from the TIME profile of the fill pattern generated by the fill analysis.

The flow path can be traced back to the injection door from a point on the boundary, rather than tracking the flow path from the injection door to the boundary.

To explain how to use hill to locate the flow path

Climbing algorithm, let\'s consider the filling time profile of a single gatedcavity shown in the figure2.

One can observe that the outline of the plot can be framed as the solution space of the objective function.

If this is the case, then the global minimum of the fill time is the injection node (

Fill time = 0. 0)

By applying thehill-

Climb the algorithm from any position within the space. (

Note the term Hill.

Since the actual process is downhill, the climb is used here as a general term

Climb, and the minimum position is not the maximum position.

In addition, the search direction is the direction of the fastest decline).

For current applications, use thehill-

The climbing strategy is not to find the global minimum, but at the door.

Interested is the path taken by the algorithm to reach the minimum value. As the hill-

The mountain climbing algorithm moves along the direction of the most rapid descent to the injection node, and the trajectory from the boundary position to the gate represents a strong recommendation for the path taken by the flow when the melt is injected into the cavity.

This is based on the fact that during the filling process, it is known that the melt fills the part with the least resistance before the other part.

It can then be assumed that at any point in the filling phase, the previous position of melting can be determined by the filling direction of the fastest flow.

On the fill time line chart, the fastest flow is the direction of the steepest gradient, which is exactly the path that hill tracks

Mountain climbing algorithm in the process of reaching the global minimum.

So, from the fill time profile generated by the fill analysis, hill-

The climbing algorithm can be used to track the flow path from any position within the cavity.

As mentioned earlier, Hill-when faced with bad terrain-

There are some defects in the algorithm.

However, a significant advantage of the filling pattern in plastic injection molding is that it does not cause bad terrain to the algorithm.

First, a strong global minimum is defined in the search space.

This is represented by the jectionnode.

Second, it is impossible for the plateau to exist because it needs to melt almost instantly to fill certain areas.

Third, the ridges produced by multiple gates are basically welds.

In order to avoid difficulties caused by welds (ridges)

Multiple doors (

Multiple local minimum values)

, Physical domain (search space)

Can be divided into separate sub along the welddomains. (

The function of child creation

Domains can be easily implemented.

In fact, it is available in commercial software such as mobile flow. )

Therefore, within each individual

Domain, there is only one injection door.

The difficulties of the Ridgesare are also avoided because they are now the boundary of the submarinedomains.

Therefore, the fill mode is indeed well defined terrain, which makes itideal suitable for simple Hills

Climbing algorithm.

Strong and simple mountain-

Therefore, the climbing method becomes an advantage when determining the flow path.

As an example

3 shows the filling time isograms of the quarterly portion of the uniform thickness plate. Shown in Fig.

3 is the path generated using hill-

Climbing algorithm.

The initial position of the algorithm is at the boundary node of the model.

From here, Hill-

Use the mountain climbing algorithm to trace the path back to the injection node in the lower left corner.

It can be seen that the generated path is a good representation of the flow path.

When flowing to the top right corner, the flow path is usually straight towards the end.

The change in direction near the edge can be explained by the outer packaging on the side.

The edge is first populated because it has a distance from the injection node.

As a result, the extra meltwill is pushed up to the corner.

Therefore, the molten particles moving on the path shown in the figure

3. due to excessive packaging, an indirect change will be experienced.

So use the mountain-

Through the climbing algorithm, the flow path can be generated effectively and the change of flow direction can be modeled.

Its benefits far outweigh the additional computer time required compared to the linear flow path assumption in our previous work [7].

Using thehill-generated flow path

For automatic balancing, the mountain climbing algorithm will now be adopted.

3 The method of optimizing the automatic cavity balance of the program is based on the same principle as described in our previous paper [7].

The optimization procedure for cavity balance is basically unchanged.

The only difference is that using hill-generated flow path

The climbing algorithm is now used, not the DC path.

Therefore, the optimization program will only briefly discuss the details included in [here]7].

Figure month shows the generatingflow Road Mountain in the algorithm flow chartClimbing Method.

The specific steps are as follows: 1.

All boundary nodes BN are considered. 2.

Coordinates of BN ([X. sub. i], [Y. sub. i])are stored in([X. sub. c], [Y. sub. c]). 3.

Determine points (NP)

Calculate next time in radius r.

NP is the number of points on the perimeter of a circle with a radius of r ([X. sub. c], [Y. sub. c])as the center.

Calculate the fill time for these points.

Search within the 5-degree interval, NP is equal (360/5 = 72).

For numerical examples included in this article, r is equal to 5mm, I. e.

About 2.

Large size 5%.

The value of the selected NP and r depends on the accuracy required by the flow path, the higher the NP value, the lower the r value, and the resolution of the flow path will increase as the calculation cost increases accordingly. 4.

Calculation of filling time]f. sub. j]of point ([X. sub. j],[Y. sub. j]).

The fill time is calculated by interpolation from the fill time at the element node. 5.

Min minimum filling time ([f. sub. j])from j = 1, . . . ,NP. 6.

Coordinates of points ([X. sub. m], [Y. sub. m])

Store the minimum fill time in the array ([X. sub. c], [Y. sub. c]). 7. If ([X. sub. c], [Y. sub. c])

Not the injection node, repeat the calculation from step 3. 8.

If all boundary node BN is not processed, the calculation is repeated from step 2. 3.

1 Flow Path concept flow path is the path tracked by particles when injected into the mold through the gate.

For simple geometry that is not inserted, unbalanced flow will indicate that the flow path changes direction once a boundary is encountered.

The flow path may look like the picture3.

By changing the thickness along these flow paths, thus changing their flow rate, the cavity balance can be achieved.

It should be noted that the resulting thickness distribution may cause difficulty in mold manufacturing.

The average process can be used to distribute the thickness evenly, and/or the thickness requirements of the balanced cavity can be relaxed to reduce the manufacturing cost.

Similarly, if changes in part thickness cannot be accepted due to functional requirements, these requirements should be applied as constraints.

The resulting cavity may not be \"balanced\" as it would ideally be, but one can expect a more balanced cavity. 3.

2 update the parameters to adjust the thickness along the flow path, and there is a direct linear relationship between the flow and the thickness assumption.

The updated equation can be expressed as follows :[Z. sub. new]= [lgroup][frac{[t. sub. node]}{[t. sub. ref]}][rgroup]X[Z. sub. old](1)where [Z. sub. new]

Is it the updated thickness ,[Z. sub. old]

Is the thickness of the present ,[t. sub. node]

The filling time when the cutting edge is melted to fill the node, and ,[t. sub. ref]

The filling time when the melt frontier fills the reference node.

Time to fill in ,[t. sub. ref]

, Used as a reference to compare all other fill times.

If the initial thickness distribution is uniform and the filling time of the flow path boundary node with this length is selected [t. sub. ref]

, This will result in an increase in the thickness of all other flow paths.

Conversely, if the fill time of the longest flow path is selected as [, the thickness of the other flow paths is reducedt. sub. ref].

The fill time of any other flow path can be used.

In this case, the thickness of the flow path longer than the reference flow path increases, and the thickness of the flow path shorter than the reference flow path decreases.

In this paper, the filling time of the shortest path is [t. sub. ref].

It should be noted that the program for flow path determination, optimization and thickness update acts as an external run of the Moldflow software that simulates the injection process. 3.

3 optimization criteria a feature of flow during injection molding is that the pressure at the advancing melting front is equal to zero.

In the unbalanced flow, the pressure accumulates at the edges as the melting fills the edges first and continues to wrap as shown2.

However, this is not the case with unbalanced flows.

When the flow front reaches the boundary at the same time, no excessive packaging will occur.

In addition, the pressure at the boundary node is the pressure at the flow front.

Therefore, the pressure on the boundary node should be equal to zero before the balance gap is filled.

Therefore, the above conditions can be used as a standard for terminating the optimization routine.

Obviously, in reality, it is very likely that a flow frontier will be generated, reaching each boundary node at exactly the same time, and there will be some overfilling.

In this case, a tolerance is set according to which if the pressure on the boundary node is less than 1% of the maximum pressure of the cavity, the pressure on the boundary node is assumed to be zero.

The condition of convergence is the goodness of the hundred %, in which the goodness is given by, goodness = [lgroup][frac{N}{[N. sub. total]}][rgroup]X 100 (2)

Where N is the number of zero-pressure boundary nodes, and ,[N. sub. total]

Total number of boundary nodes. 4.

The first model of case study Model 1 (shown in Fig. 5)

The quarterly plate model representing the square cavity door at the corner.

The injection node is located in the lower left corner of the model.

The edge to be balanced is the top and right edge.

The desired optimization is 100%.

Figure 5a and B respectively show the filling pattern of the plate with uniform thickness distribution before balance and the filling pattern after balance.

The desired optimization was achieved in 15 iterations.

The thickness distribution after equilibrium is shown in the figure. 6.

The darker area indicates the thicker part.

Similar to the results obtained using the linear flow path assumption, the flow leader can form to the upper right corner of the cavity with a long path.

Model shown in Figure 2

7 is created with inserts that hinder the movement of molten logistics.

The last point to fill is in the top left corner-handcorner.

The injection node is represented by a black square in the middle.

The optimization routine is configured to balance the cavity of all edges indicated by the dark border.

As before, the optimization is set to 100%.

Convergence is achieved in 33 iterations.

The thickness distribution is shown in the figure. 8.

The darker area indicates the thicker part.

You can clearly see that a traffic leader is formed on the left.

As expected, because this is the last point to fill. 5.

Use hill-observe an interesting result

The climbing algorithm that produces the flow path is the final flow path pattern of the equilibrium cavity.

Figure 1 shows a result like this.

9 quarter plate model.

The injection node is represented by a black square in the lower left corner. From Fig.

The final flow path pattern seems to show abranch-like behavior.

The leading flow path that coincides with the flowleader extends from the injection node to the last node filled in the upper right corner.

In addition, the secondary flow path extending from the mainstream path to the edge of the cavity.

This information is useful because the dominant flow path is often used when analyzing and optimizing processing conditions.

This information is interesting because it shows that the leading flow path acts as a line-

Source of materials.

It also highlights very inaccurate pictures represented by the DC path assumption.

Without this algorithm, it would be difficult for human analysts to come up with a similar approximation of cavity balance.

As mentioned earlier, 100% of excellence is not required in practice.

A satisfactory solution is most likely 90% or less.

Therefore, the number of iterations that converge to an acceptable solution can be significantly reduced.

For example

10 shows the progress of optimization criteria for cavities with aninsert.

Although the initial convergence rate was slow, the optimization degree increased significantly from 11 iterations, and the optimization degree of 87 times increased significantly.

8% is achieved in only 9 iterations.

The remaining 13 iterations cost 100% of the optimization.

Therefore, if the optimization is set to 85%, the number of iterations will be reduced by 40%.

Therefore, setting a lower optimization will always translate into a reduction in the number of iterations, resulting in a solution.

Figure 10 shows a slight decrease in optimization over 15 iterations.

The reason is that the pattern of the process path is relatively stable from the first iteration to the 14 iterations.

In 15 iterations, the flow path pattern around the inserted area changed.

This disturbance resulted in a slight decrease in subsuperiority.

The simple DC path assumption is inaccurate.

It must be modified as an insert, and it is not easy to automate changes to the insert or cavity.

By contrast, the mountain-

The method is simple, effective and stable, and can be used in various types of cavities.

Its advantage is its ability to fix parts with one or more plug-ins. Shown in Fig.

11 is the flow path pattern generated by Hill

Cavity climbing method with insert (Model 3).

Obstacles such as insertion will not cause problems to the algorithm.

It automatically tracks the path around the obstacle.

Therefore, it is an ideal tool for flow visualization.

Also, the ability to export the flow path from the fill mode is important.

Its ability so far is not limited to the 2D shape shown, but can be extended to 2.

5 calculate the flow path by local coordinates based on a single finite element. 6.

The conclusion proposes a method of using Hill-

Climbing algorithm.

It overcomes the difficulty of the Assumption of the direct flow path by exporting the flow path from the filling pattern of the cavity.

Especially on the mountain --

The climbing algorithm is automated and can solve the existence of one or more inserts without modifying its formula.

Combine the generated flow path with the optimization routine developed in our previous work [7]

The automatic cavity balance has achieved excellent results.

Several 2d models with different levels of complexity were successfully balanced using this method.

The method has proven to be robust and effective with the potential to easily scale from 2D to 2. 5D parts.

Month confirm the author thanks to the limited company that supports Moldflow. Ltd.

Especially sir.

Peter Kennedy, director, provided valuable help and exciting discussions.

The project was supported by the anARC collaborative research grant, and the second author thanked Monash University for its financial support in the form of an aMonash graduate scholarship, as well as the Australian government\'s scholarship for overseas graduate studies(a. )

School of Mechanical and production engineering, Nanyang University of Science and Technology, Singapore 639798 (b. )Holden Ltd.

241 Salmon Street, Port Melbourne 3207, Victoria, Australia reference (1. )B. H. Lee and B. H. Kim, Polym-Plast. Technol. Eng. , 34,793-811 (1995). (2. )I.

Panda and Q. Zou, Polym. Eng. Sci. , 30, 873 (1990). (3. )I.

Panda and Q. Zou, Polym. Eng. Sci. , 30, 883 (1990). (4. )B. H. Lee and B. H.

Mr. Jin, professional and technical staff

Paper, 41,554 (1995). (5. )W. R. Jong and K. K.

36. 385 (China)1990). (6. )

Mobile flow traffic training manual, released 9. 5, 1998. (7. )L. W. Seow and Y. C.

Lin, material processing technology, 72,333 (1996). (8. )H. P.

John Willie Anderson, evolution and best searchNew York (1995).

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