1. Affects of Cutting Parameters (Chatter Theory) Dynamics of High Performance/ High Speed Machining

4. Mechanical and Thermal Properties of Selected Work piece Materials Column Heads represent the following: UTS, ultimate tensile strength, N/mm 2 (Mpa) K s , specific force, N/mm 2 k, thermal conductivity, N/(sec °C)  =k/(  c), thermal diffusivity, mm 2 /sec T m , melting temperature, °C (  c), specific heat per volume, N/(mm 2 °C) T s , shear plane temperature, °C

5. Metal Removal Rate MRR = b*a*f f = n*m*c b = axial depth of cut n = spindle speed a = radial depth of cut m = number of teeth (width of cut) c = chip load f = feed or feed rate v =  *d*n v = cutting speed d = cutting diameter 1) From the point of view of cutting speed v and chip load c the limit is dictated by tool life and breakage and potential increase of MRR depends mainly on improving tool materials. 2) From the point of view of the depth of cut b and number of teeth m cutting simultaneously the limit is caused by chatter and improvement of MRR is possible by higher dynamic stiffness of the machine tool as formulated by the condition of limit of stability. This condition is the primary reason for the dimensions and shapes of the machine tool structural components.

6. Simplified Formulations

8. Stable Chatter

10. Basis for Analysis: The Stability Chart Process Damping Region Full Stability Chart

12. Regeneration of Waviness

14. Derivation of Limit of Stability

15. Where k is stiffness,  is damping ratio,  is orientation factor, and K s is specific force. This is a design criterion. The actual structural systems are more complex, with several prominent modes. The criterion is then For a SDOF system: Limit of Stability Computation “ Oriented” FRF: Limit width of chip:

16. Limit of Stability Computation (cont.) Where: b lim = limit axial width of cut for no chatter K s = cutting stiffness m = direction orientation factor -> m =cosb (b=70º, m=0.34) Re[G] = real part of the transfer function. b lim is smallest (b lim,crit ) when Re[G] is minimum EXAMPLE: Plunge turning 1035 steel, K s =300,00 lb/in 2 Assume common z=0.04, b=70º and choose a large, easy to remember stiffness k=1 Mlb/in. For p times less stiffness b lim,crit =0.8 in/p e.g. if stiffness 10 times less, b lim,crit =0.080 in

17. Directional Orientation  = cutting force angle f = feed direction F = cutting force n = cutter rotation N = normal of cut u = directional orientation factor X = X-axis Y = Y-axis

18. Oriented Frequency Response Function (FRF)

19. Formation of the Stability Lobe Diagram from the Real Part of the FRF Critical limit depth of cut (b cr )

20. Stability Chart (Lobing Diagram)

22. Comparison of stable and unstable cut spectra (frequency content)