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    Thermal expansion of a nozzle cause by melt plastic flow
    will result in size variation, even exceeding mechanical load
    limit thus deformation. When design a nozzle, precise
    calculation and modification are necessary for assembly length
    and operation length, where the operation length is the total
    length of the assembly length and the thermal expansion.
    Nozzle length is calculated as: /[1 ( )] dF dF L LTT α =+− (mm),
    where LF is the mold dimension (mm) in room temperature;
    Ld is the nozzle dimension in room temperature;  is the
    thermal expansion coefficient (for steel, between 20o
    C and
    200 o
    C,  is 13×10-6
    ); Td is nozzle operation temperature (
    o
    C);
    TF is mold operation temperature (
    o
    C).
    The design process of an equilibrium runner is shown
    below:
    Step1. Determine the arrangement and the structure of  
    the runner plate by cavity configuration;
    Step2. Select an appropriate section shape of the branch-
    runner by relevant knowledge of the runner plate;
    Step3. Transfer standard runner plate model into model
    library;
    Step4. Determine the dimensions of the major runner  
    structure;
    Step5. Determine the dimensions of each branch-runners
    layer;
    Step6. Check the runner dimensions and equilibrium, and  
    determine the optimum runner section dimensions;
    Step7. Modify the standard hot-runner plate model;
    Step8. Complete the hot-runner plate model and save it.
    IV.   KNOWLEDGE CONNECTION OF TEMPERATURE
    SIMULATION AND ANALYSIS OF HOT-RUNNER
    A. Knowledge Expression of Hot-runner Temperature
    Control
    Even temperature distribution on hot-runner plate is one
    of the key factors to guarantee a successful application of the
    hot-runner technology. Therefore, heating elements should be
    located on both sides of the hot-runner as evenly as possible.
    Thermal expansion factors of the runner plate also need to be
    considered. Heating power of a hot-runner plate is calculated
    as: Where, P is the required power, kW;
    θ  is the required
    temperature of the hot-runner plate, o
    C; assuming temperature
    base point is 40 o
    C; m is the mass of the hot-runner plate, kg; t
    is the hours of heating (from 40 o
    C toθ  o
    C), h;
    η  is the
    efficiency, which is determined by the assembly situation and
    the heat insulation situation between the heater and the hot-
    runner plate. Usually,
    η  is between 0.2 and 0.3.
    B. Hot-runner Temperature field Simulation Analysis
    Hot-runner Temperature field analysis requires the
    establishment of a mathematical model of a transient
    temperature field. The state of temperature during a plastic
    injection process is very complicated, so that in a real hot-
    runner temperature field analysis, four aspects of the heat
    exchange need to be considered, namely, internal heat
    exchange of the melt, heat change between the melt and the
    hot-runner system, internal heat exchange within the hot-
    runner system, and heat exchange between the hot-runner
    system and the coolant. In order to simplify the design model,
    these assumptions should be made before analysis:
    (1) No variation of plastic melt character, i.e. the density,
    the specific heat at constant pressure and thermal conductivity
    coefficient are constants.
    (2) Heaters on the hot-runner plate have been located on
    both sides of the runner plate symmetrically. The heater
    evenly heats up along the outside of the runner, and the
    ambient temperature of the melt in the runner is evenly
    distributed. In all geometrical models, melts form
    axisymmetric objects about the runner axes.
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