Machining modeling Goals for part production by machining Dimensionally accurate part Desired surface finish No chatter (unstable behavior) Acceptable tool life Dynamometer testing Surface location error (SLE) Force model Stability Stable Frequency domain SLE Time domain simulation Tool wear Frequency domain stability Modal fitting Frequency response function (FRF) Chatter Receptance coupling modeling Modal testing

Research opportunities Predictions and experiments differ due to uncertainties. What are some opportunities for improvement in machining modeling? Typically empirical. Can be described using Johnson-Cook constitutive model (or similar). 𝐹 𝑡 = 𝑘 𝑡𝑐 𝑏ℎ 𝑖 + 𝑘 𝑡𝑒 𝑏 Composition  microstructure  tool geometry  force Dynamometer testing Surface location error (SLE) Force model Stability Frequency domain SLE Time domain simulation Tool wear Frequency domain stability Empirical. Tool life often described by power law (Taylor 1906). 𝐶= 𝑣 𝑝 𝑓 𝑡 𝑞 𝑇 Composition  microstructure  tool geometry  wear rate Modal fitting Frequency response function (FRF) Damping is empirical. 𝑚 𝑥 𝑥 𝑡 + 𝑐 𝑥 𝑥 𝑡 + 𝑘 𝑥 𝑥 𝑡 = 𝐹 𝑥 𝑡 Material properties  geometry  interface  energy dissipation Receptance coupling modeling Modal testing