1 Introduction
2 The planar process force model
2.1 Dexel based cutting model for computation of the chip thickness
2.2 Cutting forces
3 Simulation results
3.1 Static force simulation
Parameter | Symbol | Value and unit |
---|---|---|
Tool radius | \({{r}}_{{T}}\) | \(0.01\left[{m}\right]\) |
Depth of cut | \({a}\) | \(0.01[{m}]\) |
Tangential cutting coefficient | \({{k}}_{{t}}\) | \({10}^{8}\left[{N}/{m}^{2}\right]\) |
Radial cutting coefficient | \({{k}}_{{r}}\) | \(0.6\cdot {k}_{t}\) |
Number of teeth | \({N}\) | \(1\) |
Feed rate | \({{v}}_{{x}}\) | \(0.01\left[{m}/{s}\right]\) |
Spindle speed | \({\Omega}\) | \(2000\left[{rev}/{min}\right]\) |
3.2 Dynamic force simulation
3.2.1 Single degree of freedom (SDOF) vibration model
3.2.2 Transient results
3.2.3 Process stability lobes
3.3 Real-time capability
4 Conclusion and outlook
Parameter | Symbol | Value and unit |
---|---|---|
Tool radius | \({r}_{T}\) | \(0.01\left[{m}\right]\) |
Depth of cut | \({a}\) | \(0.01[{m}]\)/\(0.03[{m}]\) |
Tangential cutting coefficient | \({k}_{t}\) | \({10}^{8}\left[{N}/{m}^{2}\right]\) |
Radial cutting coefficient | \({k}_{r}\) | \(0.6\cdot {k}_{t}\) |
Number of teeth | \({N}\) | \(10\) |
Feed rate | \({v}_{x}\) | \(0.02\left[{m}/{s}\right]\) |
Spindle speed | \({\Omega}\) | \(600\left[{rev}/{min}\right]\) |
Damping ratio | \({D}\) | \(0.1\) |
Natural eigenfrequency | \({\omega}_{0}\) | \(500\left[{rad}/{s}\right]\) |
Stiffness | \({k}_{0}\) | \({10}^{7}\left[{N}/{m}\right]\) |
Simulation time step size | \(\Delta t\) | \(0.0002[{s}]\) |
\(\Delta t\) | 0.001 [s] | |||||||
---|---|---|---|---|---|---|---|---|
\({\Omega}[\frac{rev}{min}]\) | 100 | 200 | 500 | 1000 | 2000 | 5000 | 10,000 | |
N = 2 | RTF | 0.1 | 0.08 | 0.08 | 0.1 | 0.14 | 0.3 | 0.53 |
ND | 505 | 319 | 218 | 205 | 202 | 200 | 200 | |
N = 10 | RTF | 0.24 | 0.2 | 0.2 | 0.27 | 0.39 | 0.82 | 1.46 |
ND | 487 | 316 | 217 | 205 | 202 | 201 | 200 |
\(\Delta t\) | 0.0002 [s] | |||||||
---|---|---|---|---|---|---|---|---|
\({\Omega}[\frac{rev}{min}]\) | 100 | 200 | 500 | 1000 | 2000 | 5000 | 10,000 | |
N = 2 | RTF | 1.02 | 0.63 | 0.41 | 0.33 | 0.32 | 0.43 | 0.63 |
ND | 1826 | 984 | 488 | 315 | 228 | 205 | 202 | |
N = 10 | RTF | 2.77 | 1.84 | 1.26 | 1.04 | 0.89 | 1.21 | 1.96 |
ND | 1725 | 957 | 484 | 323 | 228 | 205 | 202 |