Conduction Heat Transfer in Manufacturing Processes

1. Conduction Heat Transfer in Manufacturing Processes P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Heat Transfer due to micro-molecular Movements!!!

2. The thermal energy balance equation The thermal energy balance equation for the volume V is then However, since the integrals are equal the arguments are also equal. The most general form of the differential thermal energy balance equation is This is called the differential thermal energy balance equation. The fact is that it is not the heat generated by a machining process that does the damage, it’s the increase in temperature.

3. Constitutive Equation for The Heat Flux • Fourier law of conduction in vector form is used as constitutive equation to replace heat flux vector in terms of primitive properties.

4. The Conduction Equation Incorporation of the constitutive equation into the energy equation above yields: Dividing both sides by Cpand introducing the thermal diffusivity of the material given by

5. Thermal Diffusivity,  Thermal Diffusivity of general Tools • Thermal diffusivity includes the effects of properties like mass density, thermal conductivity and specific heat capacity. • The physical significance of thermal diffusivity is associated with the diffusion of heat generated in shear zone into the medium (tool body/chip body/work) with time. • The higher thermal diffusivity coefficient signifies the faster penetration of the heat into the medium and the less time required to remove the heat from the solid. • Thermal diffusivity, which is involved in all unsteady heat-conduction problems, is a property of the solid object. • The time rate of change of temperature depends on its numerical value.

6. This is often called the heat equation. For a homogeneous material: This is a general form of heat conduction equation. Valid for all geometries. Selection of geometry depends on nature of application.

7. Geometry of Machining Systems : Heat Generation • Anyone who is even casually involved with a machining process knows that cutting tools generate large amounts of heat. In fact, much of the power drawn at the spindle motor winds up as heat which is concentrated in a very small area at the cutting edge of the tool, and in the chip itself • Heat is generated in three ways (locations); • by the deformation of the metal in the shear zone ahead of the cutting edge, • at the point of separation when the metal is physically pulled apart • by the friction of the chip as it rubs along the surface of the tool as it is pushed out of the way..

8. General conduction equation based on Cartesian Coordinates For an isotropic and homogeneous material:

9. Geometry of Drilling Operation

10. General conduction equation based on Polar Cylindrical Coordinates

11. General conduction equation based on Polar Spherical Coordinates Y X