http://orcid.org/0000-0002-9646-1412
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ABSTRACT
A methodology of modeling chip geometry of flat helical end milling based on a variable flow stress machining theory is presented in this article. The proposed model is concerned with the variation of the width of cut thickness. The nonuniform chip thickness geometry is discretized into several segments based on the radial depth of cut. The chip geometry for each segment is considered to be constant by taking the average value of the maximum and minimum chip thickness. The maximum chip thickness for each chip segment is computed based on the current width of cut, feed per tooth and the cutter diameter. The subsequent radial depth of cut is subtracted from the discretized size of the width of cut to obtain the minimum chip thicknesses. The forces for each segment are summed to obtain the total forces acting on the system of the workpiece and the tool. The cutting forces can be predicted from input data of work material properties, cutter configuration and the cutting conditions used. The validation of the proposed model is achieved by correlating experimental results with the predicted results obtained.
Nomenclature
| b | = | axial depth of cut |
| Δb | = | discrete axial depth of cut |
| DC | = | cutter diameter |
| F | = | frictional force at tool–chip interface |
| FC | = | cutting force |
| FN | = | normal force to AB |
| FT | = | thrust force |
| ft | = | feed rate (mm/tooth) |
| FR | = | radial force |
| FS | = | shear force |
| FX,Y,Z | = | component of cutting forces in three orthogonal directions |
| ic | = | inclination angle |
| kAB | = | shear flow stress on AB |
| kchip | = | shear flow stress at tool–chip interface |
| N | = | normal force at tool–chip interface |
| n | = | strain hardening index |
| Nf | = | number of flutes on the cutter |
| R | = | resultant force |
| RC | = | end milling cutter radius |
| rd | = | radial depth of cut |
| Δrd | = | discrete radial depth of cut |
| T | = | temperature |
| T | = | time |
| Δt | = | time increment of machining process |
| t1 | = | undeformed chip thickness |
| t2 | = | chip thickness |
| tavg | = | average chip thickness |
| tmax | = | maximum chip thickness |
| tmin | = | minimum chip thickness |
| Tmod | = | velocity-modified temperature |
| U | = | cutting speed (m min−1) |
| VCh | = | chip velocity |
| VS | = | shear velocity |
| w | = | width of cut |
| α | = | rake angle |
| βhx | = | helix angle |
| ϵ | = | uniaxial strain |
| = | uniaxial strain rate | |
| = | constant in velocity-modified temperature | |
| ηc | = | chip flow angle |
| θ | = | angle made by R with AB/cutting angle |
| θp | = | pitch angle |
| θst | = | entry angle |
| θex | = | exit angle |
| Δθ | = | angular increment |
| λ | = | mean friction angle |
| = | constant in velocity-modified temperature | |
| σ | = | uniaxial effective flow stress |
| σ1 | = | value of σ at ϵ = 1 |
| τint | = | shear stress at tool-chip interface |
| Φ | = | shear angle |
| ψ | = | lag angle |
| Ω | = | spindle speed in revolutions per minute |