1. The Minimum Work/Energy for Manufacturing
P M V Subbarao
Professor
Mechanical Engineering Department
The Most Important Bench Mark…

2. Types of Work Transfers in Manufacturing
Moving Boundary work (displacement work)
Extrusion
Metal cutting
Forging
Shaft work
Electrical work
Steam/gas work

3. Study of Pressure-Volume Diagrams.
The rapid rise in pressure during initial ram travel is due to the initial compression of the billet to fill the extrusion container.
For direct extrusion, the metal begins to flow through the die at the maximum pressure.
This pressure is called as the breakthrough pressure.
• As the billet extrudes through the die the pressure required to maintain flow progressively decreases with decreasing length of the billet in the container.
• At the end of the stroke, the pressure rises up rapidly and it is usual to stop the ram travel so as to leave a small discard in the container.

4. Innovative Design to modify Pressure volume Diagram

5. Thermodynamic definition of Plastic Deformation Work
Themodynamically simple displacement work :
A bar of initial length l0 is subjected to a force F acting upon an area A0 and an extrusion dl occurs, the work consumed is:
Work consumed by unit volume of extruded material is:

6. Most Generic Extrusion Work
Stress and strain are tensors.
The generalized work consumed can be represented as:

7. Effective Strain & Stress
Effective stress and strain are defined for each extrusion case as:
Von Mises proposed an expression for effective stress as:
i are called as principle stresses and obtained as roots of a cubic equation :

8. Effective Strain & Stress
The simplified form of specific work equation is

9. Specific work done during Extrusion of Axi-symmetric incompressible solids

10. Common Models for Extrude Materials
Ductile aluminum alloys are most preffered material for extrusion.
For infinitesimally slow extrusion.

11. Impact of Thermodynamic Analysis of Extrusion

12. Displacement Work during Metal Cutting
Themodynamically simple displacement work :
The total cutting work consumed in machining can be defined as the sum of shear work and friction work.
Also defined as primary shear work and secondary shear work.

13. Simple model for Primary Shear Work
Primary shear work is estimated as:
The layer to be removed of thickness t1 transforms into the chip of thickness t2 as a result of shear deformation that takes place along a certain unique plane AO.
This plane is inclined to the cutting plane at an angle ϕ.
This is called as single shear plane model.
This plane moves with at velocity Vs parallel to Fs relative to Tool

14. Comprehensive model for Primary Shear Work
Plastic zone LOM is limited by shear line OL, along which the first plastic deformation in shear occurs.
Shear line OM along which the last shear deformation occurs.

15. Visualization of Cutting as A Work
Line LM is “the surface of the cut” .
The plastic zone LOM includes “a family of shear lines along which growing shear deformation are formed successively.”
This shape of the deformation (plastic) zone is based on the multiple experimental studies and this is more than a very serious statement.
Based on this model the specific work consumption is:

16. Model for Specific Work during Cutting
Based on previous model the specific work consumption is:

17. Effective Plastic Zone Stress during Metal Cutting

18. Generation of Shaft Work
Energy transmission with a rotating shaft is very common in engineering practice.
A force F acting through a moment arm rs,p generates a torque T of

19. Flowing Fluid Work

20. Flowing Fluid Work in a Polytropic Process

22. The Faraday’s Work : An Amazing form of Work Transfer
Consider a conducting rod PQ moving at a steady speed V perpendicular to a field with a flux density B.
An electron (negative charge e) in the rod will experience a force (= BeV) that will push it towards the end P.

23. Description of Work done by A Conductor
The same is true for other electrons in the rod, so the end P will become negatively charged, leaving Q with a positive charge.
As a result, an electric field E builds up until the force on electrons in the rod (unit length) due to this electric field (= Ee) balances the force due to the magnetic field
Force per unit charge on Rod of unit length:

24. Identification of A Novel Force
For a rod of length L, define the EMF as :
What happens when the EMF drives a current in an external circuit?
To do this, imagine that the rod moves along a pair of parallel conductors that are connected to an external circuit

25. Electrical Loading of Conductor
The EMF will now cause a current to flow in the external resistor R.
This means that a similar current flows through the rod itself giving a magnetic force, BIL to the left.

26. Quantification of the Faraday’s Work
L is now the separation of the two conductors along which the rod PQ moves.
An equal and opposite force (to the right) is needed to keep PQ moving at a steady speed.
In a time dt, the rod moves a distance dx = Vdt
Infinitesimal Work done on the rod

27. The Pairs of Work Transfers
Energy dissipated in R = power x time = EMF× I× t
Giving : B × I × L ×V × t = EMF × I × t
or, as before, EMF = B × V × L ?