Machine-tool Vibration

A₁ a₂ amplification factor amplitude angular frequency assumed axis b₁ beam c₁ chatter frequency chip chip-thickness coefficient chip-thickness variation effect cutter cutting conditions cutting edge cutting force cutting process cutting speed cutting-force component damper damping ratio deflection degree of freedom depth of cut differential equation direction displacement disturbing force disturbing frequency elementary vibratory system equation of motion equivalent stiffness equivalent system example exciting force experimental experiments feed forced vibration frame frequency ratio function harmonic response locus hence horizontal hysteretic hysteretically damped kg/mm lathe lathe tool machine-tool magnification factor mass method milling modes of vibration natural frequency negative obtained occur penetration phase angle position rake angle resonance curve rev/min shaft shown in fig solution spindle spring constant stability chart static surface theory thickness tool torsion spring torsional vibration Type B chatter unbalance undamped unstable speed ranges V₁ values vibration absorber