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# Mold cooling system efficiency

Articles

Mikhail Bulatov, Doctor of Engineering, professor of Moscow State University of Mechanical Engineering.
Vladimir Duvidzon, chief designer of AB Universal Engineering Company Ltd.

An efficient mold cooling system must ensure the removal of QM heat that entered the mold with TPM melt during an injection molding cycle. This heat removal will allow the mold to cool to a temperature at which one can remove the casting from the mold without damage:

$Q_{M}=-\frac{c_{p}\cdot&space;m\cdot&space;(T_{e}-T_{m})}{\tau_{c}}&space;\;\;\;\;\;&space;(1),$

where QМ has the dimension of $\inline&space;\frac{kJ}{s}$; cp is the average heat capacity of the polymeric material within mold temperature range,$\inline&space;\frac{kJ}{kg\cdot&space;K}$; m is the weight of casting, kg; Tm is the mold temperature, K; Te is the end casting temperature before its removal from the mold, K; τ is the injection molding cycle time, s. The melt entering the mold has the injection temperature (Ti) and should cool to the end casting temperature before its removal from the mold (Te).

Intensity and uniformity of cooling of a casting depend on the location of cooling channels relative to shaping surfaces (retainer, die), the number of channels and their shape, coolant (HTF) flow rate in the cooling channels and other factors.
Insufficient cooling increases the casting cooling time τ0 with respect to the calculated value, and hence the molding cycle time τc and the casting cost [1]:

$\tau_{c}=\tau_{ih}+\tau_{0}&space;\;\;\;&space;(2),$

where τih is the time of injection, hold and handling, s;

$\tau_{0}=-\frac{\delta&space;}{\pi&space;^{2}\cdot&space;\alpha&space;}\cdot&space;\ln&space;\left&space;(&space;(\frac{4}{\pi})\cdot&space;\left&space;(&space;\frac{T_{e}-T_{m}}{T_{i}-T_{m}}&space;\right&space;)&space;\right&space;)\;\;\;(3),$

where τ0 is the cooling time, s; δ is the wall thickness of the TPM part, m; α is the thermal diffusivity of TPM, m2/s; Te, Tm, Ti are the end casting temperature, the mold temperature, and the temperature of melt being injected in the mold, respectively, °С.

Thus, it can be argued that a 1°C increase in mold wall temperature increases cooling time by 2% (3).

The heat quantity QF that the cooling system is able to withdraw is

$Q_{F}=K_{T}\cdot&space;F\cdot&space;(T_{m}-T_{e})\;\;\;&space;(4),$

where КТ is heat transfer coefficient, $\inline&space;\frac{kJ}{m^{2}\cdot&space;s\cdot&space;\degree\!C}$; F is the area of heat transfer surface of the cooling channels, m2. The melt entering the mold has the injection temperature (Ti) and should cool to the mold temperature (Tm).

The cooling system design is efficient if

$Q_{F}\geq&space;Q_{M}\;\;\;(5).$

Important properties of molded parts such as operational strength (internal stress level), surface quality (shine), dimensional accuracy and absence of warping depend directly on the temperature of the shaping parts during injection molding and on a correctly designed cooling system of the mold (uniform cooling).

Performability of cooling channels
Let us consider the principles of keeping a proper performance of cooling channels.

Principle 1. Coolant flow rate in the cooling system of the mold must be higher than the calculated minimum allowed rate.
But how we determine this minimum allowed coolant flow? To do this, we have to know how much heat we must remove (1) and set the allowed temperature difference at the inlet of the cooling (thermostatic control) circuit of the mold and the mold outlet. The higher are the requirements for part quality, the smaller this difference is, usually within 3…5 ºC. To maintain the desired temperature of the shaping parts in the mold and coolant circulation in the cooling channels (l/min), thermostatic devices are used [2].

Principle 2. During mold operation, it is necessary to keep the same design mode of cooling system operation.
Process water circulating in the cooling system usually contains poorly soluble compounds. With increasing temperature, some of these form scale composed of hardness salts. Eventually, heat transfer surfaces of cooling channels become covered in scale; their flow area decreases (Fig. 1).

Calculation of molding cycle time adopted in specialized technical literature does not take into account the fact that cooling channels become overgrown with time by solid deposit (scale, corrosion, bio-products) and does not describe how it affects the cooling process. However, solid deposit on heat transfer surfaces of cooling channels hampers heat dissipation from the casting.

Cooling with scale formation
When using molds with process water as coolant (HTF), various heterogeneous processes (phase transformations, chemical and electrical reactions of sorption and other processes) are accelerated at the heat transfer surface of cooling channels. When predicting cooling system operation, absence of data on scaling processes necessary for reliable quantitative estimates does not allow for operational control of τcool value, i.e. for keeping the value of heat transfer coefficient over the minimum allowed value [КТ]:

$K_{T}=\left&space;(&space;\frac{\delta_{w}}{\lambda_{w}}+\frac{\delta_{s}(\tau)}{\lambda_{s}}+\frac{1}{\alpha(\tau&space;)}&space;\right&space;)^{-1}\geq&space;[K_{T}]\;\;\;(6),$

where λw, λs is the thermal conductivity of shaping parts (retainer, die, cores) of the mold and that of scale, respectively, $\inline&space;\frac{W}{m\cdot\degree\!C}$ (Fig. 2); α is the heat transfer coefficient for the given coolant flow parameters, $\inline&space;\frac{kJ}{m^{2}\cdot&space;s\cdot&space;\degree\!C}$.

Тm, Тw, Тs are the temperatures of mold (mold/melt contact surface), of cooling channels/scale contact surface, and at the boundary scale/coolant, respectively, °С; qz is the specific heat of the melt, W/m2·s; Rc (Rк) is the internal channel dimension, m; δw is the distance from the heat transfer surface of the cooling channel of the die (contact with coolant) to the shaping surface of the die (contact with melt), m.

Decrease in cooling efficiency
As scale layer thickness δs increases during mold operation, the value of heat transfer coefficient КТ and the heat QF (4) that the cooling system is able to remove decrease.

Solving these problems requires highly effective methods of reducing the rate of solid salt deposit formation at the heat transfer surfaces of cooling channels in molds.

The problem of heat transfer control is to maintain a predetermined [KТ] value for long-term operation of the mold, and to determine the runlife Tγ of mold cooling channels. When KТ decreases below [KТ], and cooling time  is thus increased, it becomes uneconomical to use the mold for injection molding.

The rate of change of the sum of thermal resistances $\inline&space;\left&space;(&space;\frac{\delta_{s}(\tau}{\lambda_{s}}+\frac{1}{\alpha(\tau)}&space;\right&space;)$ determines КТ(τ) behavior.

The interaction of metallic heat transfer surface of cooling channels of i.e. a die with water can induce processes such as metal corrosion and crystallization of salts from the solution. The generated products form a so-called contact layer on the heat transfer surface of cooling channels. During mold operation, the layer becomes more and more uniform. When moving away from the metal surface, we can consider scale structure as uniform since the time when the formed primary scale layer screens the effect of geometric and energetic non-uniformity of the heat transfer surface (Fig. 3).

δs,r is the removable scale layer; δs(τ) is the non-removable scale layer; δw(τ) is the layer of corrosion products; δs,0 is the primary deposit (scale) layer that screens the geometric/energetic relief of heat transfer surface of cooling channels.

To calculate the change in thickness of the deposited layer in time δs(τ) that leads to mold heating Тm(τ), we assume that at the initial time  (τ=0) no solid deposit is present on the walls of cooling channels (δs=0), and wall temperature of a channel ТW(z) equals the temperature of cooling water [3]. Fig. 4 shows the temperature control scheme [4]. In the diagram, two circuits with circulating water are designated. The first is the water cooling system of the workshop, and the second is the temperature control system. First, the mold is heated to a predetermined temperature using a thermostat. During the process of injection molding, the thermostat maintains a constant temperature of cooling water in the mold at the entrance to the cooling channels. During molding, water temperature at inlet and outlet of the cooling channels of the mold is additionally measured.

Predicting the cooling system performance
To evaluate the efficiency of a cooling system, we propose to use ε value that reflects the relative variation of injection molding cycle time (Fig. 5).

ε = τcc,0 where τc,0 and τc are injection molding cycle times without and with scale in cooling channels.

In the initial period of mold operation, a certain reduction of cycle time τc is due to the formation of a primary scale layer with a thickness δs,0 (Fig. 3b) on the heat transfer surface of cooling channels. At the stage of primary layer growth, insular deposit structure is formed [5], increasing the roughness of heat transfer surface. Due to water turbulence in the boundary layer, heat transfer is enhanced, and the heat transfer coefficient α(τ) increases by 10…15 %. At this stage, heat removal is improved, and cycle time τc decreases by 15…20 % compared to that for a clean heat transfer surface τc,0.

However, after only 300 hours of mold operation, as shows the graph in Fig. 5, cooling time increases by 10 % compared to the cooling time at the start of measurement, and after 600 hours, by 20 %. Further mold operation is not efficient, and it is necessary to clean the channels.
In continuous mold operation (24 hours a day), 300 hours equals only 12.5 days. Accordingly, 600 hours is only 25 days. If the mold is used occasionally but the water is constantly stored in cooling channels, scaling processes slow down but do not stop during idle periods.
Thus, we can formulate the third principle of maintaining cooling channels operability.

Principle 3. A cooling time increase by 20 % of the design value requires economically viable preventive cleaning of mold cooling channels from solid deposit.
Currently, considerable experience in the use of various antiscale methods is gained [5].
Mechanical self-cleaning filters installed at water inlet to mold cooling channels, as well as corrosion and scaling inhibitors introduced in water cooling system of the workshop (Fig. 4) allow for highly efficient (ε ≈ 1.0, Fig. 5) mold operation for a long time (Тγ > 600 h).
Distilled water used as coolant in the second circuit (thermostatic temperature control, Fig. 4) makes it possible to increase continuous operation time of the mold Тγ to 800…900 hours.

Principle 4. To maintain the performance of cooling channels in the mold at a required level, it is necessary to use antiscale methods.

Chosen antiscale methods must keep the scaling rate in mold cooling channels below the maximum allowed value.

References
1. N. I. Basov, V. A. Braginsky, Yu. V. Kazankov. Calculation and design of shaping tools for the manufacture of parts from polymeric materials. — Moscow: Khimiya, 1991. — 352 pages.
2. Thermostats and coolers in industrial processes: designing, choosing, and using. Edited by P. Gorbach. — Saint-Petersburg, Professiya Pilot Production Unit, 2012 — 352 pages.
3. E. A. Zyukov, M. A. Bulatov, V. G. Duvidzon. Calculation of thermal modes and mold operation prediction for injection molding of plastics. // Izvestiya of MSTU “MAMI” journal — 2014 — №2 (20) — vol. 3 — pp. 106–116.
4. M. A. Bulatov, V. G. Duvidzon. Reliability of mold cooling systems. // Mold + Tooling for Plastic Processing — October 2008 — pp. 16–18.
5. M. A. Bulatov. Complex processing of multicomponent liquid systems (Theory and technique of deposit control). — Moscow: Mir — 2012, 3rd edition — 302 pages.

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