Heat transfer is carried out by means of heat conduction under direct contact of body parts with a different temperature.

Differential equation of transient heat conduction used for this phenomenon simulation in QForm UK has a form:

or in compact form

Here: D - Laplace operator, T - temperature field [K], t- time [s], k - heat transfer coefficient [W/(m K)], ρ - density [kg/m3], c - specific heat [J/(kg K)], qG - power of distributed volumetric heat source [W/m3].

In QForm UK the volumetric heat source power is the sum of external heat source unit power qV (can be given in the initial data and used for simulation of different methods of workpiece heating) and heat generation due to plastic deformation qp.

In order to solve the heat conduction differential equation it is necessary to establish the initial conditions T0 and boundary conditions. They distinguish the boundary conditions of first kind (temperature distribution over body surface for every moment of time - are not used in QForm UK); of second kind (values of heat flux for every point of body surface and every moment of time). QForm UK uses either heat flux through an entire surface or specific heat flux per unit area. The boundary conditions of the third kind include an ambient temperature and law of heat transfer between the body surface and environment).

For determination of boundary conditions of the third kind Fourier's law is used (the amount of heat going per unit time through unit area of isothermal surface is proportional to the temperature gradient):

Here n - the normal to the surface of heat transfer, qn - the thermal flux through the heat transfer surface that is determined by the sum of convection heat transfer and radiation heat transfer at surface of workpiece and tool [W/m2].

For deriving the finite element method relations the variational formulation of heat conduction equation is used in a form

Here is used a compact form:

Variational formulation is equivalent to heat conduction differential equation with regard to boundary conditions of the third kind at body surface.

Convection heat transfer occurs in the case of solid body contact with gas (or liquid) having different temperature. In QForm UK Newton-Richmann law is used for the description of convection heat transfer.

where h - heat transfer coefficient [W/(m2K)], T1 - temperature of body (workpiece or tool), TC - environment temperature. Ambient temperature in QForm UK is considered as constant or time dependent and is set in initial data.

For simulation of workpiece contact with tool through lubricant the lubricant temperature is not accounted for, and Newton-Richmann law is used in the following form:

where α - heat transfer coefficient [W/(m2K)] which takes into account the complex of coefficients of heat transfer between the workpiece and lubrication and between lubrication and the tool, T1 - the workpiece temperature, T2 - the tool temperature, b - pause coefficient which shows how many times it is necessary to reduce a heat transfer rate in the absence of tight contact between the workpiece and the tool. Pause coefficient is taken into consideration when simulating the heat problem(heating and cooling of the workpiece and tool without forced movement of dies by process equipment for plastic deformation of the workpiece).

Radiation heat transfer occurs without direct contact between bodies. In this case heat transfer is performed in the form of electromagnetic waves. Radiation heat flux at the surface is determined from the formula:

Here ε - the real body emissivity factor that is determined as the ratio of given body emissivity to absolutely black body emissivity at the same temperature, σ0=5.67·10-8 [W/(m2K4) - Stefan-Boltzmann constant

For workpiece heat conductivity simulation it is required to set the initial temperature and to select the material in Workpiece parameters. The materials database contains values of density, thermal conductivity and specific heat for the chosen material. These quantities may be constant or set as tabulated function of temperature. When selecting a new material or obtaining precise experimental values the database item can be edited.

For a tool thermal problem simulation it is required to set the initial temperature and to select the material in Tool parameters. The tool materials database contains values of density, thermal conductivity and specific heat for the selected material. These quantities may be constant or set as tabulated function of temperature. When selecting a new material or obtaining precise experimental values in the item of the database can be edited.

It is possible to simulate different heat transfer conditions between the workpiece and the tool:

•No heat exchange

•Constant temperature of the tool

•Coupled calculation of heat condition of workpiece and tool with account for lubricant properties

•Simple heat transfer of workpiece and tool whilst accounting for lubricant properties

Specific features of all variants will be discussed later in other sections.

See also:

Additional options of simulation

Tool parameters

For simulation of heat transfer between the lubricant and the tool it is necessary to activate on the tab Tool parameters the line Lubricant and then select the required lubricant. Lubricant database contains the values of heat transfer coefficient and pause coefficient for selected lubricant. This values can be constant only. When selecting a new material or obtaining precise experimental values the database can be edited.

See also:

Additional options of simulation

Coefficients of transformation of deformation energy and friction into heat energy are specified on the tab Simulation Parameters in General – Heat Generation Efficiency. By default, these values are equal to 0.95.

The heat flux density in the workpiece volume as a result of conversion of deformation into heat qdef[W/ m 3] is calculated by the formula:

η - coefficient of conversion of deformation into heat

σ - stress intensity [Pa]

έ - strain rate [c-1]

The heat flux density at the contact surface of workpiece and tool as a result of converting friction into heat q fr [ W/ m2] is calculated by the formula:

η - coefficient of conversion of friction into heat

τ - tangential stresses [Pa]

ΔVτ is the sliding speed of the workpiece relative to the tool [m/s].

Half of the heat generated by friction goes into the workpiece and half into the tool.

For simulation of heat transfer from the workpiece and the tool to environment it is required to activate on the tabBoundary conditionsthe sectionEnvironment and to select the required environment. Theenvironment database contains values for environment temperature, emissivity factor and heat emission coefficient. These values may be constant or a set as tabulated function of process time. When selecting a new environment or obtaining precise experimental values the database can be edited.

See also:

Diffusion processes

The parameters for external heat flux to the workpiece are specified on the tabBoundary conditions. For this purpose it is required to specify the kind of boundary condition (Heat rate, Heat rate per unit area, Heat rate per unit volume), to define the area of boundary conditions validity and to set the required parameters values.