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ABSTRACT
In this paper, a numerical model was used based on the tool-piece geometric intersection, which enables the determination of a roughness profile as a function of feed, tool radii and tool eccentricity in side milling processes. Average roughness Ra and peak-to-valley roughness Rt were obtained for a group or family of tools, defined by an average radius value and a standard deviation value of all tool radii. The Monte Carlo method was used to generate N random combinations of radius values for each family, according to a normal distribution. The model was validated by means of experimental tests. For each family of tools, roughness distributions were obtained at different feed values and for different eccentricity values. It was found that the higher eccentricity, the more asymmetrical roughness distributions become.
Acknowledgments
The authors thank Mr. Alejandro Domínguez-Fernández and Mr. Ramón Casado-López for their contributions to measurements and simulations.
Funding
The authors thank the Spanish Ministry of Education and Science for funding the project (DPI2007-66546).
| Nomenclature | ||
| Ad | = | Axial depth of cut, mm |
| C | = | Geometric center of a milling tool |
| E | = | Tool eccentricity, mm |
| EDM | = | Electrical discharge machining |
| f | = | Feed per tooth, mm·tooth−1 |
| fn | = | Feed per revolution |
| HRC | = | Rockwell hardness C |
| k | = | Number that identifies each tool tooth |
| N(R, σ2) | = | Normal distribution of average radius R and standard deviation σ, min−1 |
| nt | = | Number of tool teeth |
| O | = | Rotation center of a milling tool |
| P | = | Tooth end of a milling tool |
| R | = | Average tool radius, mm |
| Ra | = | Average roughness, µm |
| Rd | = | Radial depth of cut, mm |
| Rek | = | Effective radius of each tool k |
| Rk | = | Radius of each tool k |
| Rki | = | Radius of each tool k corresponding to coordinate xi |
| Rt | = | Total or peak-to-valley roughness, µm |
| vc | = | Cutting speed, m·min−1 |
| WNr | = | German number for steels according to EN 10027-2:1992-09 |
| xi | = | x position of a discrete point along axis X |
| yi | = | y position along axis Y of each discrete point xi along axis X |
| θk | = | Position angle of geometric center C of a milling tool with respect to rotation center O |
| θki | = | Position angle corresponding to coordinate xi |
| σ | = | Standard deviation of tool radii or runout, mm |
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