basic Lagrangian dynamics question (setup of problem)
I am currently a grad student. Part of my PhD work will be to formulate a mathematical model of a manufacturing process using Lagrangian dynamics. I am just beginning to delve into the world of variational mechanics, having never had a formal course in the subject. The process involves a stationary tool (rigid) which rotates about a fixed axis and contacts a metal plate that is moving in the x-direction at some feed rate, fr (similar to a milling operation). The plate material is reinforced with abrasive "spheres" which come into contact with the tool at a rate that is dependent on tool rotation speed, material feed rate, percent reinforcement, etc. and result in wear of the tool.
I'm in the formative stages, but I just wanted to be clear on how many degrees of freedom (n) this problem entails. N is the number of "particles" and m indicates the number of kinematical constraints. My mechanics book relates n to N and m by the expression n = 3N -m. Does N = 2 (the rotating tool + the abrasive particle moving at fr which the tool comes in contact with)? Or is there another N I am neglecting (such as the other components of the material? What about m?
Visualize the abrasive particle carving a straight portion of the tool into a curved shape as it makes contact. My ultimate goal is to determine the shape of this curve......
Thanks for any help you can offer me! I will probably be posting a lot more in the coming year as I progress. The experimental work is somewhat complete.....I am trying to obtain some sort of mathematical model which validates the shapes I have observed. This is my first of what will be many attempts....