Application of Matlab to. Injection Molding Quality Control

Transcription

1 Application of Matlab to Injection Molding Quality Control Emlyn Garvey Moldflow Pty. Ltd. Australia David Kazmer University of Massachusetts Amherst United States of America Abstract Injection molding is the most common manufacturing process for production of high volume commercial parts. However, injection molding is characterized by extremely complex process dynamics and material properties, which make it difficult to understand and predict the product quality and can lead to numerous unacceptable quality defects. There are many solutions to these problems Moldflow is recognized as the leading global provider of valueadded solutions to the plastics industry. This paper describes the application of Matlab numerical software in Moldflow s development process, focusing on prototype development and validation of an on-line quality control system for injection molding. As a specific example, one module of this quality control system is discussed in detail. This problem is unique in that quality is multi-dimensional and discrete (not continuous), the process is stochastic (not deterministic), and that quality data is non-uniform and sparse. The described module, Process Window, examines the local multi-dimensional quality surface using statistical methods. Process Window then automatically searches the process space and efficiently locates a defect free process zone suitable for production. Finally, the performance of the Process Window prototype is compared to the Matlab function fmins(), a multi-objective optimization which uses a Simplex search method. Introduction Injection molding of thermoplastics is increasingly regarded as the preferred method for delivering high quality, value added commercial parts. This process allows for high volume production of complex three-dimensional parts, but is plagued by complex process dynamics and material properties, which make it difficult to understand and predict final part quality and lead to numerous unacceptable quality defects. Despite major advances in injection molding manufacturing technology [1-3], there still exists significant obstacles in the manufacturing process, most notably, the achievement and control of molded part quality. Injection molding is a dynamic, non-linear process consisting of four sequential stages: plastication, filling, packing and ejection. In its simplest form an injection molding machine can be regarded as a large hydraulic pump, which, by virtue of a hydraulically controlled ram: transforms solid thermoplastic pellets into molten polymer (plastication), injects molten polymer into the mold cavity (filling), and pressurizes the cavity during polymer solidification (packing). Once the molded part has taken its final shape and allowed to cool, the mold is opened (ejection) and the process repeated. The requirements for molded part quality are many and varied, but ultimately are defined by the customers requirements, quantified as a measure of the parts fit-for-purpose [4] in terms of the key quality characteristics: dimensional tolerance, appearance, and structural integrity. For example, the dimensional tolerances for a laser printer chassis cabinet are more stringent than those for a freezer container. Similarly, the requirements of surface finish for an automotive heater cabinet, typically hidden from view, would be much less than those for an external side mirror housing. The key factors which determine part quality are the geometric design, material properties, and process dynamics. Advances in computer simulation of the molding process have greatly

2 improved the mold design process, but the correct setup and control of the molding machine has only recently begun to be addressed with the goal of achieving consistent high quality production. Injection molding machines have changed dramatically in recent years, progressing from simple open-loop control systems to present stateof-the-art machines incorporating sophisticated closed-loop and adaptive controllers. This has resulted in huge advancements in terms of machine performance and repeatability, however, to date the objective has been to control the machine and not the part quality. Controlling part quality directly is the key to further advances in injection molding. To this end, a greater understanding of the correlation of part quality with the process control parameters; such as injection stroke, injection speed, and packing pressure is required. Approach The control of part quality must be a vital consideration during each stage in the production cycle, from product design through production. Analysis The rapid advancements and affordability of computer technology has enabled Computer Aided Engineering (CAE) software to forever change the plastic design process. This area forms the core of Moldflow s products, including a complete design suite to optimize the design of molded plastic parts in terms of part quality, production time and cost [5]. Using CAE software, a mold designer is able to simulate the molding process during the conceptual and detailed stages of product development, before expensive die cutting has commenced. In this way the designer can preempt potential problems in the part design before production, and optimize the process for efficiency and cost. This can provide enormous savings in the product design stage, however, the manufacturing stage essentially remains a manual process, in that the setting-up and control of the molding equipment relies on the abilities of the equipment operator. Production To improve the manufacturing process, Moldflow is developing Intelligent Process Control (IPC) technology to optimize machine setup and provide on-line control of part quality [6]. Moldflow s IPC system comprises of two parts: MF/OPTIM, an extension of the existing CAE software suite to optimize the molding machine setup in terms of the specific part, material and machine combination; and MF/SmartMold, an intelligent analysis and control system for molding machines, which uses the MF/OPTIM results to configure the machine, then automatically monitors and controls part quality during production. As shown in Figure 1, Process Window, which forms the basis of this report, is an integral part of the MF/SmartMold software system. Using the MF/OPTIM results as a starting processing state, MF/SmartMold intelligently shifts the process to a region producing acceptable quality parts (as defined by the molder and in terms of certain quality attributes) and then determines a processing window - or region of acceptable molding - by performing an automatic experimental validation of the surrounding process space. This process window determination enables on-line development of a process quality model which is subsequently used for automatic production quality monitoring and control. START Use results from MF/ OPTIM Mold Part Evaluate part quality Part OK? Yes Determine Process Window Production Quality Monitor (PQM) No Die Set Adjust machine control parameters Check process using quality issue rule-base Isolate quality issue Figure 1: MF/Smartmold Structure Technical Usage Matlab has been used frequently throughout the product development for system prototyping as well as results analysis. This extensive usage

3 enabled the development team to more easily gain insight and rapidly develop solutions due to these Matlab characteristics: 1) a high level language allowing rapid software development, 2) vast function library enabling access to advanced, previously inaccessible functions, and 3) efficient management and manipulation of large and complex data sets. Table 1 highlights some specific instances in which Matlab was recognized as a vital tool in product development. Table 1: Uses of Matlab in Prototyping and Analysis Task Description Filtering high and low frequency noise of process data Automatic manipulation, inspection, analysis of larger matrices (on the order of 10 by 5,000) Estimation of process effects and errors from process data Function fitting, design optimization Display and communication of complex functions and data Estimation of plant dynamics Design of discrete controller Toolbox Signal Processing Built-In Math Polynomial Functions Optimization Graphics System Identification Control System As an example of the compactness and adaptability of Matlab code, consider the prototype code listed in figure 2. This code exemplifies the power and versatility enabled by the Matlab language. The application is a straightforward design of experiments (DOE). In line 1, a DOE is entered into the environment as a matrix: each row represents an experimental run, while each column indicates the value of the process variable (low or high). In this case, a full factorial design of experiments was utilized [7]. 1: DOE=[ ;-1-1 1;-1 1-1;-1 1 1; ; 1-1 1; 1 1-1; 1 1 1]; 2: nx=size(doe,2); 3: for i=1:nx 4: lo(:,i)=find(doe(:,i)==-1); 5: hi(:,i)=find(doe(:,i)==1); 6: end 7: Y=Process_Out(DOE); 8: for i=1:nx 9: dydx(i)=(y(hi(:,i))-y(lo(:,i))) /size(lo,1); 10: end Figure 2: A Sample of Prototype Code Line 2 finds the number of process variables in the experimental design. Lines 4 through 6 find the low and high run numbers from the experiment for each process parameter their use will be explained shortly. Once the setup is complete, the manufacturing process is performed, or simulated, and the results gathered in array Y. It is useful to note that Y can be a vector with the result of each experimental run, or a matrix with any number of observations. Line 9 then calculates the effect of each process variable on the desired result. This is performed by using the arrays lo and hi to lookup the correct runs in array Y, find the difference between the low and high levels, then divide by the number of observations. It is important to note the power and flexibility of these few lines. First, the code is completely flexible. The engineer need only enter the experimental design the find function will automatically locate and guarantee that the correct indices which are used. Moreover, the size and shape of the array, defined by the number of process variables and number of runs in the experimental array, can be arbitrary the code adapts to any experimental approach. Second, the code is incredibly compact, was quickly coded, and can be easily understood. The same functionality coded in C required over two hundred lines. Finally, the full Matlab library of functions is available to support results analysis and decision support. Having constructed a working Process Window prototype in Matlab, the next stage was to integrate the developed system into the MF/SmartMold program. MF/SmartMold is a dedicated software application designed for a Pentium PC, running QNX real-time operating system and X/Motif

4 Quality Index graphical interface. The program comprises the following major C/C++ software modules: Graphical User Interface (GUI), Adaptive Controller, Data Acquisition (DAQ), and Quality Control (QC) utilizing expert system technology. To integrate the Process Window prototype, the Matlab meta-language was converted to C code and incorporated into the Quality Control subsystem. The completed C module was almost ten times the prototype size (in terms of program lines of code) to perform the same task, which clearly demonstrates the conciseness and power of the Matlab language. Matlab inherently provides complex array manipulations and operators, such as a*b and a.*b, which are not present in procedural languages such as C, and had to be explicitly programmed into the MF/SmartMold system. Example The goal of Process Window is to define a region around an optimal operating point which will produce quality parts. Injection molded part quality, however, is most frequently defined with multiple criteria, each of which may have unique dependence upon several process variables. As such, it is very difficult to completely understand all of the process-to-quality relationships. Figure 3 shows a subset of a simple quality model Shot Size 10 0 Figure 3: Subset of Product Quality Response not be repeatable with significant material property, operator, or controller variation. Finally, the quality index is an aggregate measure of how many defects are present in the molded parts a quality index of 100 indicates no defects. However, a better understanding involves mapping the process to quality relation for each quality criteria, then superimposing the state spaces to find the actual molding process window. Considering these details, the resolution of the process window is very difficult, especially considering the cost of acquiring data. Each observed data point for the quality model requires feedback from the product quality molded at specified molding conditions. Given the time required to enact a process change and the need for multiple samples due to issues with process repeatability, roughly 4,500 parts would be required to obtain the surface shown in Figure 3. This quantity is, in itself, on the order of a production lot costing tens of thousands of US dollars. Moldflow s approach for defining the Process Window is illustrated below in Figure 4. The first and most critical assumption is that the procedure will start from a process point which produces high quality parts. This requirement will be met through the utilization of Die Set, described in Figure 1, which couples operator feedback, machine control, and a molding expert system [8] to produce one good part. This model is, in fact, a gross oversimplification of the molding process as the product quality depends not only upon shot size and pack pressure but also additional process parameters such as ram velocity, melt temperature, etc. which can not be simultaneously charted. Worse, the process may

5 START Use process state determined in Die Set stage Modify process parameters according to DOE Mold Parts Input molded parts quality and record process history All moldings OK? No Yes Re-evaluate part quality by interpolating molding state space Determine process shifts for each control variable in terms of each quality attribute Move to new process state END Optimum process state and limits are as determined in DOE Figure 4: Process Window Structure A second input to Process Window is the coefficient of variation for each of the critical molding process parameters. This data is used in determining the required breadth of the Process Window necessary to produce quality parts, even in the presence of significant stochastic process variation. As such, the process capability is monitored and assessed during the initial start-up of the application. With these inputs, Process Window proceeds by automatically generating an experimental design, perturbing the molding process, and producing a series of molded parts. The user then assesses each molded part according to the application s critical quality criteria. This approach enables any number and types of quality to be considered the experimental design will develop the local quality model on-line for each quality criteria. As previously stated, the process dynamics or operator feedback may vary significantly while defining the Process Window. Each bit of quality data is permanently stored and subsequently used for quality verification. This is accomplished by dynamically building a multi-dimensional data space, then using data in nearby cells to estimate the actual quality characteristics of the molded part. If the quality feedback is significantly different from the expected value, then the operator is asked to verify the molded part quality. Once the molded part quality has been entered and verified for the experimental design, the process shifts for each process control variable is determined. The methodology has been developed to resolve conflicting process shifts as well as the existence of no solutions, however the details will not be discussed here. After the process shifts have been determined, the operating point is moved and another DOE begun. The process continues until all molded parts produced by the experimental design are acceptable, i.e. every quality criteria has been met. It is vital to remember that the levels of perturbation have been chosen to encompass the representative process variation. If all parts in the experimental design meet the quality criteria, then all parts molded during production should meet the quality standards, even in the presence of process inconsistencies. The results of Process Window are passed to MF/Smartmold s Production Quality Monitor, which monitors and controls the molding process to assure product quality. The Process Window was tested with the quality model described by Figure 3. Using the methods previously described, an adequate process window was able to be defined if given an initial operating point which produced good parts or was close to producing good parts. On the average, this method required a total of 30 parts to be molded. If the same procedure was started at a bad operating point, no adequate solution would typically be found. This is to be expected given the needs and assumptions made during development. It is clearly possible to formulate this same problem as a minimization suitable for fmins(), a Matlab multi-variable optimization routine based on the Simplex search method. As a matter of fact, fmins() was typically able to find an adequate solution irrespective of the initial starting position. This is to be expected, given the ability of the

6 Simplex to walk, expand, and contract the search zone to better operating regimes. Unfortunately, this method typically required over 600 parts to be sampled, far too many for commercial feasibility end-users would vastly prefer a sub-optimal solution. Conclusions One component of a quality control system for injection molding has been described. This system has been developed and prototyped in Matlab then commercially implemented in the C programming language. The use of Matlab enabled for rapid development and an approach which is more robust than would have been developed given the tight time and cost constraints of system development. The completed C module was almost ten times the prototype size (in terms of program lines of code) to perform the same task, which clearly demonstrates the conciseness and power of the Matlab language. Some of the subtleties of implementing a quality control system for injection molding have been discussed: multiple and diverse quality criteria, multiple control variables, complex and stochastic process dynamics, operator faults, and high cost of sampling. Each of these items was explicitly considered during system development. Using specific assumptions conformant to adjacent modules of MF/Smartmold, the Process Window requires only 30 samples to define an adequate process regime this compares favorably to a general Simplex approach which requires several hundred samples and can not be considered a feasible approach. 4. DeVor, R. E, Chang, T., Sutherland, J., W., Statistical Quality Design and Control: Contemporary Concepts and Methods, Macmillan Publishing Company, New York, Austin, C., Industrial Metamorphosis, Proceedings from the 1994 Annual Technical Meeting of the Society of Plastics Engineers, v. 52, pp. 1626, Rowland, J. C., Kazmer, D. O., An On-line Quality Monitoring System for Thermoplastic Injection Molding, Proceedings from the 1996 Annual Technical Meeting of the Society of Plastics Engineers, v. 54, Box, G.E.P., Hunter, W.G., Hunter, J.S., Statistics for Experimenters, John Wiley & Sons, New York, Giarranto, J. C., Culbert, C., Savely, R. T., The State of the Art for Current and Future Expert System Tools, ISA Transactions, v. 29, n. 1, pp , References 1. O Bryan, J. E., Proportional Valves, Microprocessors, and Closed-Loop Control Keeps Plastics Molders Competitive, Hydraulic and Pneumatics, v. 42, n. 3, pp. 95, Agrawal, A. R., Pandelidis, I. O., Pecht, M., Injection-Molding Process Control A Review, Polymer Engineering and Science, v. 27, pp. 18, Ma, C., Y., A Design Approach to A Computer-Controlled Injection-Molding Machine, Polymer Engineering and Science, v. 14, n. 11, pp. 768, 1974.