The estimation of the diameter error in bar turning: a comparison among three cutting force models

Machining accuracy is considerably affected by the deflection of the machine-tool-workpiece system under the action of the cutting force. A new model to estimate a bar diameter error due to the deflection of the tool, of the workpiece-holder and of the workpiece was defined by the authors, starting from a cutting force model. This work deals with a comparison among the bar diameter errors that are calculated by means of the developed model involving three different cutting force models. The considered cutting force models were the specific cutting resistance, the Kronenberg cutting force and the unified-generalised mechanics of the cutting force model developed by Armarego. The numerical results were compared with those obtained by experimental tests carried out through a parallel lathe. The results show that the Armarego's cutting force model provides values of the force components and, therefore, the values of the resulting bar diameter errors are closest to the experimental ones.Nomenclature a The longitudinal position of the tool, [mm] - a_pn The nominal depth of cut, [mm] - a_p The real depth of cut, [mm] - b The width of area of cut, [mm] - A The tool-workpiece interference area of cut, [mm²] - AB The generalised cutting edge vector - A_r The area of the workpiece cross section, [mm²] - c_s The spindle compliance, [mm/N] - c_t The tailstock compliance, [mm/N] - c_tht The tangential toolholder compliance, [mm/N] - c_thr The radial toolholder compliance, [mm/N] - D The workpiece diameter, [mm] - E The modulus of elasticity, [N/mm²] - f The feed, [mm/r] - F_rad The radial component of the cutting force, [N] - F_feed The feed component of the cutting force, [N] - F_{tan g} The tangential component of the cutting force, [N] - F_i The resultant of F_feed and F_{tan g}, [N] - G The shear modulus, [N/m²] - h The thickness of the area of the cut, [mm] - I The workpiece moment of inertia, [mm⁴] - L The workpiece length, [mm] - P_i The plane containing the inflected curve of the workpiece - P_f The tool assumed working plane - P_n The cutting edge normal plane - P_nG The generalised cutting edge normal plane - P_r The tool reference plane - r_l The chip length ratio - R The workpiece radius, [mm] - R_b The tailstock reaction force, [N] - R_s The spindle reaction force, [N] - S The shape factor - v_c The cutting speed, [mm/min] - v_e The resultant cutting speed, [mm/min] - v_f The feed speed, [mm/min] - v_ch The chip speed, [mm/min] - v_sh The shear speed, [mm/min] - w(z) The total deflection of the workpiece axis, [mm] - w_a The total displacement of the workpiece axis from z reference axis measured in P_i plane, [mm] - (z) The orientation of P_i with respect to F_rad and F_{tan g}, [degree] - The friction angle, [degree] - _n The normal friction angle, [degree] - _nG The generalised normal friction angle, [degree] - The shear factor - _n The normal shear angle, [degree] - _NG The generalised normal shear angle, [degree] - _f The tool side angle, [degree] - _n The tool normal rake angle, [degree] - _nG The generalised tool normal rake, [degree] - _P The tool back angle, [degree] - _c The chip flow angle, [degree] - _cG The generalised chip flow angle, [degree] - _r The tool cutting edge angle, [degree] - _rG The generalised tool cutting edge angle, [degree] - _s1 The tool cutting edge inclination, [degree] - _s2 The inclination of the secondary tool cutting edge [degree] - _sG The generalised tool cutting edge inclination, [degree] - The friction coefficient - The work material shear stress, [MPa] - _r The tool approach angle, [degree] - The approach angle of the secondary cutting edge, [degree]