a is a schematic control diagram depicting a preferred control scheme for the injection molding system of
b is a global nonlinear state block diagram further illustrating the control scheme depicted in
c is the operating point state block diagram of the control scheme of
To review the foregoing discussion in greater detail,
However, since mold separation alone cannot account for all variations in part weight—for example, studies by the inventors have found that melt temperature and mold temperature also affect the correlation between part weight and mold separation—the inner loop is further used to enhance weight (and thus quality) control. At the inner loop, which may be regarded as a process control loop, the maximum mold separation is used to scale the whole mold separation profile during filling and holding and the whole mold separation profile is taken as a signature of the injection molding process. The mold separation profile, including the maximum mold separation MSRef, is controlled via both cycle-to-cycle control of switchover S/O and within-cycle holding control (i.e., control of holding pressure Pp). First, the switchover point S/O is adjusted from cycle to cycle (based on injected mass) to at least partially achieve the required maximum mold separation MSRef. After the switchover point S/O, the holding pressure Pp is adjusted to duplicate the desirable mold separation profile, which is normalized by scaling the maximum mold separation value of the profile to the required maximum value. In this way, long-term disturbances are prevented in cycle-to-cycle control, and short-term disturbances are compensated for by the within-cycle control.
Referring to
Control of switchover S/O within the switchover controller 200 can be based on parameters such as time during injection, injector pressure, or ram position. However, switchover S/O is most preferably controlled in accordance with the mass of the injected plastic, since this parameter is believed to have a more direct bearing on mold separation MS than time, pressure, or position alone: experiments have found that if maximum mold separation is plotted versus injected mass at switchover, the resulting data points fall roughly along a straight line, indicating that a simple proportional model can be used to define the relationship between these parameters. Injected mass may then be calculated in accordance with:
where minj is the injected plastic mass, A is the cross-sectional area of the injector barrel 108, l0 is the position of the ram 116 at the start of filling, ls is the position of the ram 116 at switchover S/O, and v0 and vs are respectively the specific volumes of the plastic at the start of filling and at switchover. Parameters v0 and vs are functions of temperature and pressure, and can be calculated from the chosen plastic's pvT (pressure-specific volume-temperature) property relationship given the melt temperature Tm and pressure P. The plastic's pvT properties can be conveniently modeled by a two-domain, modified Tait equation, as described in Cheng, H. H., C. A. Hieber, and K. K. Wang, Polym. Eng. Sci. 31, 1571 (1991).
Then, as discussed above, a pure proportional element can be employed to model the maximum mold separation MSmax:
ΔMSmax=KΔminj (2)
As discussed above, melt temperature Tm and mold temperature Tw are further variables apart from mold separation that also have an impact on part weight. Studies by the inventors have found that there is a roughly linear correlation between part weight and maximum mold separation, but at the same time, melt temperature Tm and mold temperature Tw affect both the slope and the interception of the correlating line. A simple relationship between these variables can be expressed as:
Wt=Wt
0
+a
1
[MS]+a
2
[Tm]+a
3
[Tw]+a
4
[MS][Tm]+a
5
[MS][Tw] (3)
wherein the coefficients a1, a2, a3, a4, and a5 can also be experimentally determined for a given injection molding system 100. Equation (3), and the derived coefficients, can then be programmed into or otherwise used in the compensator 204 Turning to
MS
max
ref
fb
=G
1(z−1)[Wtref−Wtz−2] (4)
where MSmax
m
inj
=G
2(z−1)[MSmax
where MSmax
MS
max
ref
did
=h(Wtref,Tm,Tw)−MSmax
where MSmax
MS
max
=f(minj,Pp) (7)
Wt=g(MSmax,Tw,Tm) (8)
Equations (5) and (6) are already in linear form and Eqs. (6) to (8) can be linearized. Next, a linear operating point model can be obtained, as expressed in Eqs. (9) to (13):
where â1,{circumflex over (b)}1, and ĉ1 are estimations of a1,b1, and c1, respectively. The coefficient KSP equals
From these equations, the state block diagram of the operating point model for closed-loop quality feedback control can be readily drawn in
To eliminate the temperature effects on weight variations, the mold separation controller G2(z−1) is preferably designed to be an integrator:
where {circumflex over (K)}SM is the estimation of KSM. In the ideal situation, the weight variation due to temperature changes can be eliminated entirely.
The weight controller G1(z−1) is designed to keep the system stable and have good dynamic performance. It preferably takes the form of a PI controller, as
where KP and KI are the proportional gain and integration gain, respectively. The characteristic equation of the system is
z
3−(1+ε)z2+[(a1KP+a1KI)(1−ε)+ε]z−(1−ε)a1KP=0 (17)
where
The controller gains KP and KI are determined under the nominal condition ε=0. Note that there are only two design parameters in Eq. (17), 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
1
+z
2
+z
3=1 (18)
where z1, z2, and z3 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). For instance, if the characteristic roots are 0.4, 0.3, and 0.3, the corresponding controller gains are
With all 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.
Since the foregoing discussion and accompanying drawings merely relate to preferred versions of the invention, it should be understood that the invention may take other forms as well. As one example, since the injection molding system 100 is merely a simplified schematic depiction, the invention may be implemented in injection molding systems having radically different appearance from the one depicted. The measured parameters used for control (e.g., mold separation MS, holding pressure Pp, mold temperature Tw, and melt temperature Tm) can be measured by one or more sensors at locations other than those depicted. Further, the control relationships and physical process modeling relationships discussed above may be replaced with other appropriate arrangements.
The invention is not intended to be limited to the preferred versions of the invention described above, but rather is intended to be limited only by the claims set out below. Thus, the invention encompasses all different versions that fall literally or equivalently within the scope of these claims.
This invention was made with United States government support awarded by the following agencies: NSF (National Science Foundation) Grant No(s).: 0332696 The United States has certain rights in this invention.