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大連交通大學(xué)2017屆本科生畢業(yè)設(shè)計（論文）外文翻譯
Optimization of Conformal Cooling Channels with Array of Baffles for Plastic Injection Mold
NOMENCLATURE
α = Thermal diffusivity of polymer (m2/s)
σT = Standard deviation of temperature distribution
d = Diameter of baffle (mm)
hc = Heat transfer coefficient (W/m2°C)
km = Thermal conductivity of mold material (W/m°C)
kp = Thermal conductivity of polymer (W/m°C)
q = Instantaneous heat flux (W/m2) s = Thickness of molded part (mm) tc = Cooling time (s)
Tavg = verage temperature through part’s thickness (°C)
Te = Ejection temperature (°C) Ti = Injection temperature (°C) Tm = Mold temperature (°C)
Tmax= Maximum temperature at center line of thickness (°C)
Tps = Molded part surface temperature (°C)
Tw = Coolant temperature (°C)
x = The pitch of baffles in x direction (mm)
y = The pitch of baffles in y direction (mm)
z = Distance from baffle’s tip to cavity surface (mm)
? KSPE and Springer 2010
1. Introduction
Injection molding has been the most popular method for making plastic product due to high efficiency and manufacturability. The injection molding process includes three significant stages: filling and packing stage, cooling stage and ejection stage. Among these stages, cooling stage is very important one because it mainly affects the productivity and molding quality. It is well known that more than two thirds of the molding cycle is taken up by cooling process. An appropriate design of cooling channel reduces cooling time, increases the productivity and minimizes undesired defects such as sink marks, differential shrinkage, thermal residual stress and warpage.
For many years, the importance of cooling stage in injection molding has drawn a great attention from researchers and mold designers. They have been struggling for the improvement of the cooling system in the plastic injection mold. This field of study can be divided into two groups: optimizing conventional cooling channels (straight-drilled cooling lines) and finding new
(a) straight-drilled channel
(b) SFF conformal channel
(c) channels with the array of baffles Fig. 1 Kinds of cooling channels
architecture for injection mold cooling channels (conformal cooling channels). The first group focuses on how to optimize the configuration of the cooling system in terms of shape, size and location of cooling lines.1-15 The second group investigates the way
to build the cooling layout namely conformal cooling channels that conform to the mold cavity surface and examines the effectiveness of this cooling system. Solid free-from fabrication (SFF) or rapid prototype (RP) techniques have been proposed to build this complex cooling system. It was reported that cooling quality is
better than that of conventional cooling channels.16-24 Along with
SFF technique, milled groove conformal cooling channels made by CNC milling machine has also been proposed by Sun Y. F. et al.25,26 Although these kinds of cooling channels offer an even cooling performance, there are still high manufacturing costs for medium
and large-sized mold.
In order to improve the performance of the cooling system and to reduce mold making cost, this paper presents a kind of conformal cooling channel in the plastic injection mold by using an array of baffles. The difference between this cooling channels layout and the others is depicted in Fig. 1. Baffles are alternative cooling devices
that are used to cool some small regions in the mold’s core which normally lack cooling.27 A series of baffles in cooling circuit for core of a box mold was suggested.28 For medium and large-sized molds with free-form cavity’s surfaces, if a constant distance from the tip of the baffles to mold cavity’s surface is maintained, this kind of cooling circuits can be considered as conformal cooling channels. Unfortunately, it still lacks of study of how well this conformal cooling system performs and how to optimize its
configuration in order to obtain minimum cooling time, even cooling and reasonable mold making cost. In addition, cooling design is often based on designer’s experience and tuition. When molding geometry becomes more complex, experience-based and trial-and-error approaches would be time-consuming and less
feasible.3,5,11,13 Therefore, our study focuses on a systematic method
(a) Real construction of the array of baffles cooling channels
(b) Modeling of array of baffles cooling channels in CAE software
Fig. 2 Deployment and configuration of the cooling channels with array of baffles
for optimizing the configuration of the proposed cooling channel including coolant temperature, the pitch (x and y), the distance z and the diameter d of the baffle. The combination of analytical method, design of experiment (DOE), finite difference method and CAE tool was used to derive approximate equations showing the relation among cooling channels’ design variables, mold material and process parameters for a given polymer. Cooling time and optimum cooling channels’ configuration of a given injection molding part can be determined easily at early design stage.
The remainder of the paper is organized as follows. Section 2 introduces the deployment and configuration of the array of baffles in cooling channels. Section 3 describes the physical and mathematical model of heat transfer within the polymer and the mold. Mathematical solution in Section 3 is validated in Section 4. Section 5 proposes optimization method, and Section 6 illustrates two case studies to test the facility and feasibility of the proposed method for a plastic cover and an automotive plastic part. Finally, some conclusions and discussions of future work are given in Section 7.
2. Deployment and configuration of array of baffles in cooling channels
A baffle is a cooling channel drilled perpendicular to a main cooling line with a thin plate separating the drilled hole into two semicircular channels. The plate forces the coolant to flow down in one side and up in the other side (see Fig. 1(c) and Fig. 2(a)). By
changing the direction of the coolant flow in cooling channels, the baffle creates turbulence around the bend and increases the heat transfer coefficient. Nevertheless, pressure drop increases, and more pump power is required in comparison to straight or smooth cooling channels. There are two kinds of baffles: normal baffle and spiral baffle (Fig. 2(a)). The first one is simple, but it is difficult to mount the thin plate (divider) exactly in the center of the channels and the temperature distributions in both sides of the baffle are different. The other one is a bit more complex, but it is easy to place the divider at the center of cooling channels; the turbulent effect and temperature distribution are improved. In this study, it is assumed that the flow rate of coolant is large enough to achieve effective turbulent flow, and an increase in flow rate makes little difference to the rate of heat extraction. For this reason, both types of baffles are treated the same in terms of heat extraction.
Baffles are arranged as a two-dimensional array including rows and columns. The configuration of the proposed cooling channels includes the pitch (x and y) between the baffles, the distance from a baffle’s tip to the cavity surface (z) and the diameter of the baffle (d) (Fig. 2). The diameter of the main cooling line is proportional to d. The baffle’s tip conforms to the cavity surface in order to remove heat from hot polymer evenly. The baffle channels are machined by drilling method which reduces the manufacturing cost.
3. Physical-mathematical model and numerical solution
This section addresses the mathematical relation among cooling channels’ configuration, temperature distribution in the mold and molded part, cooling time and process parameters. Without losing the generality, a cooling cell (see Fig. 3) is extracted and examined instead of considering the whole mold. Four lateral faces of the cooling cell are treated as adiabatic. With this physical model, the simulation time is reduced significantly since the number of elements decreases. Assuming that the cavity surface of the cooling
(a) (b)
Fig. 3 Physical model of a cooling cell (a), and typical temperature distribution (b)
? The minimum Reynolds’ number in cooling channels should be more than 10,000.
? The thermal effect derived from the crystallization process is ignored.
In this study, the coupling of cycle-averaged and one- dimensional transient approach was applied since it is computationally efficient and sufficiently accurate for mold design purpose.11,35 Heat transfer in the mold is treated as cycle-averaged
steady state, and 3D FEM simulation was used for analyzing the temperature distribution. The cycle-averaged approach is applied because after a certain transition period from the beginning of the molding operation, the steady-state cyclic heat transfer within the mold is achieved. The fluctuating component of the mold temperature is small compared to the cycle-averaged component so that cycle-averaged temperature approach is computationally more
efficient than periodic transition analysis.37 Heat transfer in polymer
(molding) is considered as transient process, and finite difference method was applied.
The temperature distribution in the molding is modeled by following equation:
cell has a small curvature, this surface can be considered as a planar face.
?T = α
?t
? 2T
?z
(1)
In physical aspect, heat transfer in cooling process is complicated. To simplify the mathematical model, the following assumptions are made in this study:
? Physical properties of mold material are constant.
? The heat flux in mold-polymer interface is constant on each element of mold cavity surface.1
? Constant cycle-averaged mold temperature is used.
? Only packing and cooling phases are considered because the filling phase is short.29,30
The partial difference equation (1) can be solved conveniently by finite difference method. Laasonen method,38 unconditionally stable scheme, was used to solve Eq.(1). Due to the nature of thermal contact resistance between polymer and mold, a convective boundary condition39 was applied instead of isothermal boundary condition. This boundary condition expresses the nature of heat transfer in mold-polymer interface better than isothermal boundary condition.
? Thermal analysis for polymer is performed in one dimension
h ?T ? T ? = ?k ?T
(2)
because the thickness of the molding is small in comparison to
c ps m
? ?
p ?z
planar dimension.31-36
? Natural convection between ambient air and exterior mold faces is ignored because it takes less than 5% of overall heat loss.7
? Cooling effect of main cooling lines is ignored because most of the heat is removed by the baffles.
The inversion of the heat transfer coefficient (HTC) is called thermal contact resistance (TCR). It is reported that TCR between the polymer and the mold is not negligible. TCR is the function of a gap, roughness of contact surface, time and process parameters. The values of TCR are very different,29,34,40-45 and they are often obtained by experiment. In this study, HTC is set to 10,000 W/m2°C
1. Smith, A. G., Wrobel, L. C., McCalla, B. A., Allan, P. S. and Hornsby, P. R., “A computational model for the cooling phase of injection moulding,” Journal of Materials Processing Technology, Vol. 195, No. 1-3, pp. 305-313, 2008.
2. Sridhar, L. and Narh, K. A., “Finite size gap effects on the modeling of thermal contact conductance at polymer-mold wall interface in injection molding,” Journal of Applied Polymer Science, Vol. 75, No. 14, pp. 1776-1782, 2000.