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Injection molding quality control by integrating weight feedback into a cascade closed-loop control system.

INTRODUCTION

The quality requirements of injection-molded components have become more stringent because of growing plastics applications and increasing customer demands. The quality can be measured in many ways, such as part weight, mechanical properties, dimensional conformity, and aesthetic appearance. Among them, part weight is often selected as a measure of the quality because not only can it be measured precisely, but it is also an important criterion [1, 2]. Research has shown that the variation in part weight is due essentially to changes in part dimensions rather than variations in density [3]. Therefore, consistency of part weight is a good indicator of consistent part dimensions, which is important in precision manufacturing. As such, part weight is a commonly used criterion in quality control on the shop floor in industry.

To produce parts with high quality, considerable research has been conducted to address different aspects of the injection molding injection molding
n.
A manufacturing process for forming objects, as of plastic or metal, by heating the molding material to a fluid state and injecting it into a mold.
 process. Some of the work has studied the control of machine components, such as the hydraulic system Noun 1. hydraulic system - a mechanism operated by the resistance offered or the pressure transmitted when a liquid is forced through a small opening or tube , injection ram, and/or heating bands of the injection barrel [4-6]. Because process variables (or polymer variables) are more closely related to part quality than machine variables [7], the control of process variables, such as cavity pressure, has received extensive attention [8-10].

However, part quality is a collective and lump-sum response to machine and process variables. The control of machine and process variables is not sufficient to guarantee the desired part quality in a consistent manner. Studies on machine performance revealed significant time-varying characteristics in the process (see e.g., [11]). Hence, quality control is needed to achieve quality consistency and accuracy. In general, there are two types of quality control schemes that have been investigated for injection molding: observer-based quality control and direct quality feedback control. The difference between these two schemes is how part quality is obtained. In the first case, a quality model, which estimates the quality from a set of machine and process variables, is used as a "soft sensor Soft sensor or virtual sensor is a common name for software where several measurements are processed together. There may be dozens or even hundreds of measurements. The interaction of the signals can be used for calculating new quantities that need not be measured. " while a real quality sensor is used in the second case.

The work reported in Refs. 12-14 falls into the category of observer-based quality control. Their common feature is that the control action is based on quality estimates rather than actual measurements. As a result, the control performance is highly dependent on the accuracy of the quality models no matter what constitutes the models. However, it is well known that the modeling accuracy is limited by many factors such as inevitable disturbances, incomplete knowledge, or limited resources. Strictly speaking Adv. 1. strictly speaking - in actual fact; "properly speaking, they are not husband and wife"
properly speaking, to be precise
, observer-based quality control does not close the quality loop; it is a comprehensive control of machine and process variables.

To overcome the deficiency in quality modeling and to achieve high performance in quality control, a direct quality feedback should be considered. Chen and Turng investigated online weight control through numerical simulation, combining feedback and feedforward feedforward /feed-for·ward/ (fed-for´ward) the anticipatory effect that one intermediate in a metabolic or endocrine control system exerts on another intermediate further along in the pathway; such effect may be positive or negative.  based on a neural network neural network or neural computing, computer architecture modeled upon the human brain's interconnected system of neurons. Neural networks imitate the brain's ability to sort out patterns and learn from trial and error, discerning and extracting  model [15]. Havard et al. [16] proposed a direct weight feedback control with holding pressure adjusted for each shot. Their experimental results showed that the weight feedback control had a significant benefit on part weight stability over process control and machine control. In the above method, only cycle-to-cycle control was implemented; i.e., some selected machine variables could be changed once in a cycle to regulate the part weight, but there were no adjustments within a cycle to reduce the quality discrepancy DISCREPANCY. A difference between one thing and another, between one writing and another; a variance. (q.v.)
     2. Discrepancies are material and immaterial.
. Long-term shift could be eliminated with such a method, because the average weight would be controlled to the preset preset Cardiac pacing A parameter of a pacemaker that is programmed permanently when manufactured  value. Nevertheless, short-term consistency could not be improved because the machine performance was not changed within each shot.

In this paper, a cascade closed-loop system Noun 1. closed-loop system - a control system with a feedback loop that is active
closed loop

control system - a system for controlling the operation of another system
 with direct quality feedback and disturbance feedforward for online quality control of injection molding is presented. Figure 1 shows the overall control system structure. At the outer loop, the part weight is regulated through manipulating the maximum mold separation (MS) from shot to shot. At the inner loop, the MS is taken as a signature of the process. The maximum MS specified in the outer loop is used to scale the whole MS profile, which covers the later filling and early holding stages. Then the profile, including the MS peak value, is controlled via two separate controllers: namely, cycle-to-cycle switchover switch·o·ver  
n.
A complete shift, as from one system to another.
 control and within-cycle post-filling control. First, the switchover point is adjusted from shot to shot to achieve the required maximum MS value. After the switchover point, the holding pressure is adjusted to duplicate the desirable MS profile, which is normalized by scaling the maximum value to the required peak value. In this way, long-term disturbances are prevented in cycle-to-cycle control, and short-term disturbances are compensated by the within-cycle control. More details on injection molding control using MS can be found in Ref. 17. This paper concentrates on quality modeling, control, and related MS regulation.

[FIGURE 1 OMITTED]

EXPERIMENTAL SETUP

Molding experiments have been conducted to validate the proposed quality control scheme. The experimental injection molding system consists of three components: an injection molding machine Injection molding machine (also known as injection press) - a machine for making plastic parts. Manufacturing products by injection molding process. Consist of two main parts, an injection unit and a clamping unit.  with a mold of two different cavity geometries, a mold temperature control unit, and an advanced control system based on computer networks, as shown in Fig. 2. The machine used in the experiments is a BOY 50T equipped with a Moog servo-valve. The mold temperature control unit is from Sterling (Model No. 8422). The advanced control system includes both hardware and software as follows: (1) data acquisition (DAQ See data acquisition. ) card (AT-MIO-16E-2 from National Instrument), (2) digital injection controller (DIC DIC diffuse intravascular coagulation; disseminated intravascular coagulation.

DIC
abbr.
disseminated intravascular coagulation


Disseminated intravascular coagulation (DIC) 
) that consists of Moog digital and analog modules and a digital signal processing See DSP.

Digital Signal Processing - (DSP) Computer manipulation of analog signals (commonly sound or image) which have been converted to digital form (sampled).
 (DSP (1) (Digital Signal Processor) A special-purpose CPU used for digital signal processing applications (see definition #2 below). It provides ultra-fast instruction sequences, such as shift and add, and multiply and add, which are commonly used in math-intensive ) board that handles machine control during filling, packing/holding, and plastication, (3) signal conditioners Conditioners used on leather take many shapes and forms. They are used mostly to keep leather from drying out and deteriorating.

A very old and widely used conditioner is dubbin.
 (SCM (1) (Software Configuration Management, Source Code Management) See configuration management.

(2) See supply chain management.
5B series), and (4) control algorithms hosted on desktop computers connected through TCP/IP networks. An electronic balance (METTLER TOLEDO Mettler-Toledo is a manufacturer of scales and analytical instruments. It is the combination of two companies: Mettler, based in Switzerland, and Toledo Scale, based in Columbus, Ohio, USA.  AG 104) with a repeatability of 0.1 mg is used to measure part weight.

Six signals are collected at machine side, namely, ram position ([Y.sub.r]), ram speed ([V.sub.r]), nozzle An orifice in an inkjet print head through which ink is sprayed onto the paper. Print heads with six thousand or more nozzles are common in today's printers.
Nozzle 
 pressure ([P.sub.n]), melt temperature ([T.sub.m]), hydraulic pressure ([P.sub.h]), and servo-valve opening ([S.sub.o]). A configurable multicavity plate mold is used in this study. Figure 3 shows the schematic A graphical representation of a system. It often refers to electronic circuits on a printed circuit board or in an integrated circuit (chip). See logic gate and HDL.  diagram of the plate mold geometry marked with different transducers and their positions. The mold has a tapered ta·per  
n.
1. A small or very slender candle.

2. A long wax-coated wick used to light candles or gas lamps.

3. A source of feeble light.

4.
a.
 round sprue sprue, chronic disorder of the small intestine caused by impaired absorption of fat and other nutrients. Two forms of the disease exist. Tropical sprue occurs in central and northern South America, Asia, Africa, and other specific locations.  (the top diameter is 6 mm and the bottom diameter is 8 mm), trapezoidal runners (base dimensions are 4 mm and 5 mm with a height of 5 mm), and two rectangular cavities. The upper cavity is 120 mm long, 40 mm wide, and 1.73 mm thick with a rectangular gate (5 mm long, 3 mm wide, and 1 mm thick). The lower cavity has the same length and width as the upper one, but is 3.36 mm thick. It can be blocked by changing the layout of runners.

[FIGURE 2 OMITTED]

The mold is instrumented, as shown in Fig. 3, in order to collect process data. Four LVDTs, namely, M[S.sub.1] to M[S.sub.4] are mounted at the four corners of the mold along the parting line to measure the displacement, MS. The cavity pressures, P[c.sub.1], P[c.sub.2], P[c'.sub.1], and P[c'.sub.2] are measured by pressure transducers that are flush mounted inside the mold cavity near and far from the gates. The sprue pressure, [P.sub.s], and the runner pressure, [P.sub.r], are also measured at the sprue end and along the trapezoidal runner near the gate, respectively. The mold wall temperature, [T.sub.w], is measured by a J-type thermocouple mounted in the mold, 2 mm beneath the mold wall surface.

[FIGURE 3 OMITTED]

Two different types of resins are used in this study, namely, a semicrystalline polypropylene polypropylene (pŏl'ēprō`pəlēn), plastic noted for its light weight, being less dense than water; it is a polymer of propylene. It resists moisture, oils, and solvents.  (PP, Exxon PP 7032 E2) and an amorphous Unorganized or vague. A lack of structure. For example, the amorphous state of a spot on a rewritable optical disc means that the laser beam will not be reflected from it, which is in contrast to a crystalline state which will reflect light. See crystalline.  polycarbonate A category of plastic materials used to make a myriad of products, including CDs and CD-ROMs.  (PC, Teijin Panlite AD 5503).

All the experiments are conducted through a custom-developed injection molding control program, which was coded jointly in Microsoft Visual C++ and Matlab. The program provides a human-machine interface (HMI (Human Machine Interface) The user interface in a manufacturing or process control system. It provides a graphics-based visualization of an industrial control and monitoring system. ) to set up the references, process conditions, control parameters Control parameters

In a nonlinear dynamic system, the coefficient of the order parameter; the determinant of the influence of the order parameter on the total system. See: Order Parameter.
, and other variables. Furthermore, it carries out the computation in quality control and process control, while the machine control runs in Moog DIC. The sampling periods are 0.2 and 2 ms, and one cycle, for machine level, process level, and quality level controls, respectively.

Before running the automatic quality control, a quality model and process model are obtained for the different combinations of molds and materials given the machine. The quality model is built on a design of experiments (DOE), and the process model is constructed in open-loop experiments. The model parameters are then read into the control program and used to tune control parameters. After the program starts and a part-weight reference is given, the system can automatically adjust process and machine parameters to achieve the target quality, based on the control algorithms in this paper.

Process and Quality Modeling

As shown in Fig. 1, the part weight is regulated through MS, and MS is regulated through switchover point and holding pressure. The holding pressure adjustment is implemented in the within-cycle control, which was published in Ref. 17, so it is not repeated in this paper. To properly design the control system, the process model, which describes the relationship between switchover point and MS, and the quality model, which describes the relationship between MS and part weight, are first obtained in experiments.

Process Modeling

A novel concept of mass-based switchover control is proposed and implemented in this study. The injected in·ject·ed
adj.
1. Of or relating to a substance introduced into the body.

2. Of or relating to a blood vessel that is visibly distended with blood.



injected

1. introduced by injection.

2. congested.
 mass is calculated based on Eq. 1,

[m.sub.inj] = A([[l.sub.0]/[[v.sub.0](T, p)]] - [[l.sub.s]/[[v.sub.s](T, p)]]) (1)

where [m.sub.inj] is the injected mass, A is the area of the barrel's cross section, [l.sub.0] is the ram position at the start of filling, [l.sub.s] is the ram position at switchover, and [v.sub.0] and [v.sub.s] are the corresponding specific volumes at the start of filling and switchover, respectively. Parameters [v.sub.0] and [v.sub.s] are functions of temperature and pressure and can be calculated from the resin's pvT (pressure-specific volume-temperature) property given the melt temperature and pressure. In this study, the material's pvT property is modeled by a two-domain, modified Tait equation [18].

In contrast to the conventional, single switchover parameter, such as time, pressure, or ram position, mass-based switchover is determined based on multiple variables including pressure, temperature, and ram position. Note that the injected mass is the exact physical variable that needs to be controlled in the process. It provides more reliable control of the MS than do the conventional, single variable (i.e., time-, position-, or pressure-based) switchover method.

Conceivably con·ceive  
v. con·ceived, con·ceiv·ing, con·ceives

v.tr.
1. To become pregnant with (offspring).

2.
, the mass-based switchover point affects the maximum mold separation in the current shot. Based on several independent experiments conducted using the same experimental set-up, the data points in the diagram of maximum MS versus injected mass at switchover roughly fall into a straight line, as shown in Fig. 4. Therefore, a pure proportional element is readily employed to model the effect of mass-based switchover on the maximum mold separation at an operating point, as shown in Eq. 2. The proportional gain, [K.sub.SM], can be obtained in open-loop experiments.

[DELTA]M[S.sub.max] = [K.sub.SM][DELTA][m.sub.inj]. (2)

Quality Modeling

As reported in Ref. 19, part weight is highly correlated with mold separation. However MS alone cannot account for all of the variations in part weight, which are a collective result of the process conditions. For example, additional experiments by the authors have revealed that melt temperature and mold temperature also affect the correlation between part weight and MS.

To obtain the quality model and investigate the temperature effects, a DOE was conducted. Three process parameters, namely, mold temperature, [T.sub.w], melt temperature, [T.sub.m], and holding pressure, [P.sub.p], are selected. In this DOE, all process parameters have two levels. The other important process conditions used in the experiments include: injection velocity at 35 mm/s, holding time at 5 s, cooling time (Law) such a lapse of time as ought, taking all the circumstances of the case in view, to produce a subsiding of passion previously provoked.
- Wharton.

See also: Cooling
 at 25 s, and a position-based switchover point at 20.5 mm. The responses are maximum MS and part weight. The results of the full-factorial experiment with two replicates are given in Table 1.

[FIGURE 4 OMITTED]

From the experimental data, the coefficients in Eq. 3 are fitted, and the values are listed in Table 2.

[W.sub.t] = [Wt.sub.0] + [a.sub.1][MS] + [a.sub.2][[T.sub.m]] + [a.sub.3][[T.sub.w]] + [a.sub.4][MS][[T.sub.w]] + [a.sub.5][MS][[T.sub.w]] (3)

[MS] = [[MS - 35]/20], [T.sub.w] = [[T.sub.w] - 70/5], [[T.sub.m]] = [[T.sub.m] - 310/5]. (4)

Based on the fitted model, the temperature effects on the correlation between part weight and maximum mold separation can be visually examined in Fig. 5. It shows that the linear correlation between part weight and maximum MS still dominates. At the same time, the temperatures affect both the slope and the interception of the correlating line. This means that different maximum MS's correspond to the same weight at different temperatures. For instance, it requires a larger mold separation to achieve the same part weight when higher temperatures are used.

Controller Design

On the basis of the schematic closed-loop quality control diagram in Fig. 1, Fig. 6 shows the global nonlinear A system in which the output is not a uniform relationship to the input.

nonlinear - (Scientific computation) A property of a system whose output is not proportional to its input.
 block diagram A chart that contains squares and rectangles connected with arrows to depict hardware and software interconnections. For program flow charts, information system flow charts, circuit diagrams and communications networks, more elaborate graphical representations are usually used.  of the quality control system. Note that the within-cycle post-filling control is not included. Because the internal states of the post-filling control are not affected by any cycle-to-cycle updates, it is separable sep·a·ra·ble  
adj.
Possible to separate: separable sheets of paper.



sep
 from the cycle-to-cycle control and designed independently as reported in Ref. 17. The design of the quality controller and mold separation controller are based on Fig. 6.

[FIGURE 5 OMITTED]

In Fig. 6, [G.sub.1] ([z.sup.-1]) and [G.sub.2] ([z.sup.-1]) are the weight and MS controllers, respectively. The function f ([m.sub.inj],[P.sub.p]) models the dependence of the maximum mold separation on switchover point and holding pressure. The function g ([T.sub.m], [T.sub.w], M[S.sub.max]) expresses part weight in terms of mold temperature, melt temperature, and the maximum mold separation. The equation, M[S.sub.max] = h([Wt.sub.ref], [T.sub.m], [T.sub.w]) is converted from Wt = g([T.sub.m], [T.sub.w], M[S.sub.max]). The symbol [z.sup.-1] is the backward shift operator on the shot sequence.

Note that there is a one-cycle delay in the MS feedback loop due to the intrinsic nature of cycle-to-cycle control. A two-cycle delay exists in the weight feedback loop because of the need to measure part weight after the cycle. The whole system can be divided into several subparts as follows.

[FIGURE 6 OMITTED]

Weight controller:

M[S.sub.max_ref.sup.fb] = [G.sub.1]([z.sup.-1])[[Wt.sub.ref] - Wt[z.sup.-2]] (5)

where M[S.sub.max_ref.sup.fb] is the feedback component of the maximum MS reference.

MS controller:

[m.sub.inj] = [G.sub.2]([z.sup.-1])[M[S.sub.max_ref.sup.fb] + M[S.sub.max_ref.sup.did] - M[S.sub.max][z.sup.-1]] (6)

where M[S.sub.max_ref.sup.did] is the disturbance input decoupling Decoupling

The occurrence of returns on asset classes diverging from their normal pattern of correlation.

Notes:
Take for example stock and corporate bond returns, which normally rise and fall together.
 or feedforward component of the maximum MS reference.

Disturbance input decoupling or feedforward compensator:

M[S.sub.max_ref.sup.did] = h([Wt.sub.ref], [T.sub.m], [T.sub.w]) - M[S.sub.max_ref.sup.0] (7)

where [MS.sub.max_ref.sup.0] is the maximum MS reference corresponding to the required weight under nominal conditions.

Process (MS) object:

M[S.sub.max] = f([m.sub.inj], [P.sub.p]). (8)

Quality (weight) object:

Wt = g(M[S.sub.max], [T.sub.m], [T.sub.w]). (9)

Equations 5 and 6 are already in linear form and Eqs. 7-9 can be linearized. Next, a linear operating point model can be obtained. It is expressed in Eqs. 10-14,

[DELTA]M[S.sub.max_ref.sup.fb] = -[G.sub.1]([z.sup.-1])[DELTA]Wt[z.sup.-2] (10)

[DELTA][m.sub.ing] = [G.sub.2]([z.sup.-1])[[DELTA]M[S.sub.max_ref.sup.fb] + [DELTA]M[S.sub.max_ref.sup.ff] - [DELTA]M[S.sub.max][z.sup.-1]] (11)

[DELTA]M[S.sub.max_ref.sup.did] = - [[^.b.sub.1]/[^.a.sub.1]] [DELTA][T.sub.m] - [[^.c.sub.1]/[^.a.sub.1]][DELTA][T.sub.w] (12)

[DELTA]M[S.sub.max] = [K.sub.SM][DELTA][m.sub.inj] + [K.sub.SP][DELTA][P.sub.p] (13)

[DELTA]Wt = [a.sub.1][DELTA]M[S.sub.max] + [b.sub.1][DELTA][T.sub.m] + [c.sub.1][DELTA][T.sub.w] (14)

where [^.a.sub.1], [^.b.sub.1], and [^.c.sub.1] are estimates of [a.sub.1], [b.sub.1], and [c.sub.1], respectively. The coefficient, [K.sub.SP], equals [partial derivative]f/[[partial derivative][P.sub.p]]. From these equations, the state block diagram of the operating point model for the closed-loop quality feedback control can be readily drawn in Fig. 7, which has the same structure as Fig. 6.

The weight variation is related to the extra inputs through

[DELTA]Wt([1/[a.sub.1]] + [1/[a.sub.1]] [K.sub.SM][G.sub.2][z.sup.-1] + [K.sub.SM][G.sub.2][G.sub.1][z.sup.-1]) = [K.sub.SP][DELTA][P.sub.p] + (1 - [K.sub.SM][G.sub.2][z.sup.-1]) ([[b.sub.1]/[a.sub.1]] [DELTA][T.sub.m] + [[c.sub.1]/[a.sub.1]][DELTA][T.sub.w]) - [K.sub.SM][G.sub.2]([[^.b.sub.1]/[^.a.sub.1]][DELTA][T.sub.m] + [[^.c.sub.1]/[^.a.sub.1]][DELTA][T.sub.w]). (15)

Equation 15 shows that the temperature effects on weight variations can be eliminated entirely if the parameter estimates match their true values and if the MS controller, [G.sub.2], is selected as an integrator. Thus [G.sub.2] takes the following form,

[G.sub.2]([z.sup.-1]) = 1/[[^.K.sub.SM](1 - [z.sup.-1])] (16)

where [^.K.sub.SM] is the estimate of [K.sub.SM].

The weight controller, [G.sub.1], also needs to be an integrator to eliminate steady state errors. A proportional element is added to provide additional degrees of freedom to improve system performance. Thus, it takes the form of a PI controller, as

[FIGURE 7 OMITTED]

[G.sub.1]([z.sup.-1]) = [K.sub.P] + [[K.sub.1]/1 - [z.sup.-1]] (17)

where [K.sub.P] and [K.sub.1] are the proportional gain and integration gain, respectively. The characteristic equation of the system is

[z.sup.3] - (1 + [epsilon])[z.sup.2] + [([a.sub.1][K.sub.P] + [a.sub.1][K.sub.1])(1 - [epsilon]) + [epsilon]] z(1 - [epsilon])[a.sub.1][K.sub.P] = 0 (18)

where [epsilon] = 1 - [[K.sub.SM]/[^.K.sub.SM]]. The controller gains, [K.sub.P] and [K.sub.1], are determined under the nominal condition, [epsilon] = 0. Note that there are only two design parameters in Eq. 18, but it has three characteristic roots. Thus, not all characteristic roots can be freely placed. There is one constraint in this pole-placement, namely,

[z.sub.1] + [z.sub.2] + [z.sub.3] = 1 (19)

where [z.sub.1], [z.sub.2], and [z.sub.3] are the characteristic roots. It is still possible to put all three roots in stable positions (within the unit cycle on the complex z-plane) by selecting proper [K.sub.P] and [K.sub.1]. For instance, if the characteristic roots are 0.4, 0.3, and 0.3, the corresponding controller gains are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ]. (20)

When [a.sub.1] is not available, it is replaced by its estimate [^.a.sub.1]. This method is used to determine the values of the controller parameters in the experiments.

With both controllers properly designed based on the process and quality models, the closed-loop quality control system performance, such as the dynamic stiffness and robust stability, can be readily analyzed. The analysis can be found in Ref. 20 and is not included in this paper due to its length. Instead, several molding experiments have been conducted to verify the performance of the proposed quality control scheme.

Experimental Results

Two resins and two different mold geometries were used in the experiments. The resins were polypropylene and polycarbonate and the tool was the configurable multicavity rectangular mold, both described previously in the Experimental Setup section. The performance of the closed-loop quality control is compared with that of the prevailing cavity pressure based control, which is regarded as the most advanced method in the industry.

The process conditions in the experiments, which are tabulated in Table 3 where the references for weight and cavity pressure are listed, were used in the closed-loop quality control and cavity-pressure based control. In the experiments with a two-cavity mold, the weight reference is the combined part weight, the cavity pressure reference is the threshold value for switchover from filling to holding, and the pressure measured by P[c.sub.1] is used in all cases. As shown in Fig. 3, the thickness of the two cavities is different, and thus the mold-filling process is not balanced. To reduce the effect of unbalanced filling, the injection speed was increased to 40 mm/s. The melt temperature was increased as well to achieve filling at high speeds. The second cavity and its large thickness, combined with the increased melt temperature, required a longer cooling time. As a counteraction, the mold temperature was decreased to shorten the cooling time.

During the molding experiments, the melt and mold temperatures were purposely pur·pose·ly  
adv.
With specific purpose.


purposely
Adverb

on purpose
USAGE: See at purposeful.

Adv. 1.
 varied to evaluate the performance of different control methods. That is why two values are listed in Table 3 for each temperature setting. Typical recorded temperature points in the experiments with PC using a single cavity and PP using the two-cavity configuration are shown in Fig. 8, where the melt temperature setting was decreased by 5[degrees]C after 50 shots, and then the mold temperature setting was increased by 5[degrees]C after another 50 shots.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

The process and quality models shown in Eqs. 2 and 3 were obtained in the modeling experiments. In the experiments with the single cavity, the MS measured by M[S.sub.2] was adopted for process-level MS control, while M[S.sub.3] was used for the same purpose in the experiments with the two-cavity configuration. The estimates of the important parameters, [K.sub.SM] and [a.sub.1], in the process and quality models are given in Table 4.

[FIGURE 10 OMITTED]

To favor robust system stability, slightly larger values than the estimates in Table 4 were used to calculate the controller parameters. The closed-loop poles were placed at 0.4, 0.3, and 0.3 for fast and stable responses. Even though two poles are at the same location, the root loci loci

[L.] plural of locus.

loci Plural of locus, see there
 do not leave the real axis under small parameter uncertainty when a larger [^.K.sub.SM] value is used [20]. The resulting controllers in the different experiments are given in Eqs. 21 and 22.

[FIGURE 11 OMITTED]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (22)

In Figs. 9-11, the weights obtained using cavity-pressure based control, direct weight feedback control without disturbance input decoupling, and direct weight feedback control with disturbance input decoupling are shown sequentially in (a), (b), and (c), respectively, for comparison. In the direct weight feedback control without disturbance input decoupling, the path from the temperature disturbances to the MS reference was cut off. Thus, the only control action was from feedback. The same controller parameters were used for direct weight feedback controls with and without disturbance input decoupling. Table 5 summarizes the statistical information including the mean and standard deviation of the part weight in each of the experiments with different control methods.

The experimental results in Table 5 and Figs. 9-11 clearly suggest that the direct weight feedback controls achieved more consistent and accurate part weight, and thus part quality, than cavity pressure based control when encountering the same temperature disturbances. The direct weight feedback control can regulate the part weight to its reference, but the weight cannot be directly assigned in process-level cavity pressure based control. In the two investigated schemes of direct quality feedback control, the disturbance input decoupling further improved the performance by reducing both the transition period and the magnitude of weight variations when the melt or mold temperatures were changed. The benefit of disturbance input decoupling is gained by counteracting the temperature effects on the part weight before they take place. Additionally, the quality improvement obtained in all experiments with the different mold geometries and resins builds confidence in generalizing the proposed method.

CONCLUSIONS

A direct quality feedback control system has been proposed and implemented for injection molding in this paper. It had a cascade structure and combined both feedback and feedforward controls. At the outer quality loop, the quality index, part weight, was measured online and regulated by manipulating the maximum mold separation. Next, the mold separation was controlled at an inner loop by changing the mass-based switchover and holding pressure. Both cycle-to-cycle control and within-cycle control were adopted to eliminate long-term and short-term quality variations. The cycle-to-cycle control included updating the references for the maximum mold separation and mass-based switchover point in each shot. Corresponding weight and MS controllers were designed using the pole-placement method based on the resultant process and quality models. The details of these models, including structure and parameters, were also presented.

The proposed closed-loop quality feedback control was evaluated in experiments by using different resins and mold configurations. The experimental results showed that closed-loop quality control can achieve much better part quality in terms of weight consistency and accuracy than cavity pressure based control, which is regarded as the most prevailing and advanced method in the injection molding industry.

Compared with process and machine controls for injection molding, direct quality feedback control has additional benefits, such as 100% quality inspection and automatic process tuning. Its successful application on the shop floor will depend on the development of quality sensors and measurement equipment. There are on-going research efforts to develop and apply innovative sensors to monitor the process and detect part quality [21, 22]. It is desirable to see more automated devices, including robotics robotics, science and technology of general purpose, programmable machine systems. Contrary to the popular fiction image of robots as ambulatory machines of human appearance capable of performing almost any task, most robotic systems are anchored to fixed positions , machine vision, and nondestructive sensors, to be used in injection molding. In the face of extensive competition from the global market, the degree of automation has to be improved for injection molding.

ACKNOWLEDGMENTS

The authors thank Professor Kuo K. Wang of Cornell University Cornell University, mainly at Ithaca, N.Y.; with land-grant, state, and private support; coeducational; chartered 1865, opened 1868. It was named for Ezra Cornell, who donated $500,000 and a tract of land. With the help of state senator Andrew D.  and Dr. Daniel F. Caulfield of the Forest Products Laboratory, USDA-Forest Service, for their technical support.

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Zhongbao Chen, Lih-Sheng Turng

Polymer Engineering Center, Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, Wisconsin Madison is the capital of the U.S. state of Wisconsin and the county seat of Dane County. It is also home to the University of Wisconsin–Madison.

The 2006 population estimate of Madison was 223,389, making it the second largest city in Wisconsin, after Milwaukee, and
 53706-1572

Correspondence to: Lih-Sheng Turng; e-mail: turng@engr.wisc.edu

Contract grant sponsor: National Science Foundation; contract grant number: EEC-0332696.
TABLE 1. DOE results for quality modeling (resin: PC).

[T.sub.m]     [T.sub.w]                               [MS.sub.max]
([degrees]C)  ([degrees]C)  [P.sub.p] (MPa)  Wt (g)   ([micro]m)

315           75            5                10.1101  69.45
                                             10.0211  52.07
315           75            4                 9.7185  21.33
                                              9.7097  15.18
315           65            5                10.0611  50.24
                                             10.0169  42.11
315           65            4                 9.7472  16.51
                                              9.7372  13.75
305           75            5                 9.8964  34.99
                                              9.9247  32.51
305           75            4                 9.6509   5.01
                                              9.6797  10.61
305           65            5                 9.8846  22.79
                                              9.9486  29.39
305           65            4                 9.6436   1.14
                                              9.6789   5.51

TABLE 2. Coefficient values in the quality model built upon experiments.

[Wt.sub.0]   9.92888
[a.sub.1]    0.18818
[a.sub.2]   -0.03621
[a.sub.3]   -0.04112
[a.sub.4]   -0.01408
[a.sub.5]   -0.01412

Coefficient unit: gram.

TABLE 3. Process conditions in the closed-loop quality control
experiments.

                                     PP
Process conditions      Single cavity  Two cavity   PC

[T.sub.m] ([degrees]C)  200, 205       210, 215     310, 315
[T.sub.w] ([degrees]C)   35, 40         30, 35       60, 65
[V.sub.r] (mm/s)         35             40           35
[P.sub.p] (Mpa)           5.0            5.0          4.5
[t.sub.pack] (s)          4.0            4.0          5.0
[t.sub.cool] (s)         20             25           25
W[t.sub.ref] (g)/         7.05/18.5     20.35/11.5    9.80/13.5
  P[c.sub.ref] (MPa)

TABLE 4. The estimates of [K.sub.SM] and [a.sub.1] in the process and
quality models.

Experiments        [K.sub.SM] ([micro]m/g)  [^.a.sub.1] (g/[micro]m)

PC, single cavity  25.0                     0.00941
PP, single cavity  38.0                     0.00381
PP, two cavity     40.0                     0.00927

TABLE 5. Comparison of the performance of different control methods.

Experiments     Control method*  [Wt.sub.ref] (g)  Mean (g)  StDev (g)

PC, one cavity  Pc               N/A                9.7878   0.0294
                Wt Fb             9.80              9.8001   0.0085
                Wt Fb+DID         9.80              9.8022   0.0058
PP, one cavity  Pc               N/A                6.9537   0.0119
                Wt Fb             7.05              7.0500   0.0070
                Wt Fb+DID         7.05              7.0525   0.0040
PP, two cavity  Pc               N/A               20.3686   0.0338
                Wt Fb            20.35             20.3518   0.0124
                Wt Fb+DID        20.35             20.3507   0.0096

Experiments     Control method*  Max (g)  Min (g)

PC, one cavity  Pc                9.8689   9.7410
                Wt Fb             9.8207   9.7716
                Wt Fb+DID         9.8150   9.7865
PP, one cavity  Pc                6.9769   6.9308
                Wt Fb             7.0638   7.0265
                Wt Fb+DID         7.0611   7.0386
PP, two cavity  Pc               20.4141  20.2773
                Wt Fb            20.3820  20.3167
                Wt Fb+DID        20.3719  20.3169

* Pc, Cavity pressure based control; Wt Fb, direct weight feedback
control; Wt Fb+DID, direct weight feedback control plus disturbance
input decoupling.
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Date:Jun 1, 2007
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