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.(adsbygoogle = window.adsbygoogle || []).push({});

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....

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Basic Lagrangian dynamics question (setup of problem)

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**