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- 1. Affects of Cutting Parameters (Chatter Theory) Dynamics of High Performance/ High Speed Machining
- 2. SECTION OBJECTIVES <ul><li>Define Cutting Forces and Parameters. </li></ul><ul><li>Explain Chatter Theory </li></ul><ul><li>Explain Process Damping </li></ul><ul><li>Affects of cutting parameters </li></ul><ul><li>Case study </li></ul>
- 3. The Cutting Force <ul><li>The cutting force F is in the first approximation proportional to the chip area obtained as chip width b times chip thickness h , </li></ul><ul><li>F = K s b h (1) , </li></ul><ul><li>where the coefficient K s is the force per unit chip area, the “specific force” determined primarily by the work piece material. </li></ul><ul><li>There are other influences such as tool geometry, tool material, cutting speed and chip thickness such that it is easier to cut thicker chips, but these are not strong and for most purposes can be neglected. </li></ul><ul><li>So, we will assume the force to be proportional to both b and h. </li></ul><ul><li>A Table of specific forces (discussed briefly) is included, using N/mm 2 as the dimension. </li></ul>
- 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
- 7. Definitions: <ul><li>Chatter: </li></ul><ul><ul><li>A self-excited vibration between the tool and work piece in cutting. </li></ul></ul><ul><ul><li>It can create large forces, damage tools and work pieces, and create unacceptable surfaces. </li></ul></ul><ul><ul><li>Particularly problematic in high-speed high-power machining. </li></ul></ul><ul><li>High-Performance/High-Speed: </li></ul><ul><ul><li>Machining with such a spindle speed that the tooth passing frequency can approach the dominant natural frequency of the system. </li></ul></ul>
- 8. Stable Chatter
- 9. High-Speed Benefits <ul><li>Along with losses and limitations, there are important benefits from phenomena which occur only in high-speed milling. </li></ul><ul><li>An especially important phenomenon is that of “stability lobes” (stability pockets). </li></ul><ul><li>Stability lobes permit dramatically larger axial depths of cut at high spindle speeds, but the spindle speed must be carefully selected. </li></ul>
- 10. Basis for Analysis: The Stability Chart Process Damping Region Full Stability Chart
- 11. Chatter Mechanism <ul><li>Most undesirable vibrations in milling are self-excited chatter vibrations. </li></ul><ul><li>What mechanism is responsible for transforming the steady input of energy (from the spindle drive) into a vibration? </li></ul><ul><li>The primary mechanism is- </li></ul><ul><li>“ Regeneration of Waviness”. </li></ul>
- 12. Regeneration of Waviness
- 13. Cutting Force and Chip Thickness <ul><li>The wavy surface leads to variable chip thickness, variable force, and vibration </li></ul><ul><li>The variable part of the cutting force depends on the current vibration and the previously generated surface </li></ul><ul><li>Depending on conditions (K s , b, spindle speed) this vibration either grows or diminishes </li></ul><ul><li>Diminishes - stable cut, no chatter </li></ul><ul><li>Grows - unstable cut, chatter </li></ul>
- 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)
- 21. Chatter characteristics. <ul><li>The chatter frequency is usually close to, but not equal to the natural frequency. </li></ul><ul><li>The lobes are more tightly packed at the left (smaller speed change for the same phase change). </li></ul><ul><li>Large stable zones exist in the high speed ranges. </li></ul><ul><li>Surprisingly, the largest such gap occurs where the tooth passing frequency is equal to the natural frequency . Why? </li></ul><ul><li>When tooth frequency matches natural frequency, the surface waves and the tooth vibration are in phase. The chip thickness looks the same as if there were no vibration. </li></ul>
- 22. Comparison of stable and unstable cut spectra (frequency content)
- 23. Process Damping <ul><li>Chatter vibrations are inhibited at low speeds by “process damping”. </li></ul><ul><li>Interference between the rake face of the tool and the tool path produces a net damping force. </li></ul>
- 24. General Tendencies <ul><li>Feed Rate </li></ul><ul><ul><li>By itself will not determine if a give cut chatters. </li></ul></ul><ul><ul><li>If a cut chatters higher feed rates will chatter more than lower feed rates. </li></ul></ul><ul><li>Number of teeth </li></ul><ul><ul><li>For a given width and depth of cut a cutter with more teeth will chatter at lower depths of cut. </li></ul></ul><ul><ul><li>For example, a 4 tooth cutter with similar length, diameter and cutting parameters will chatter at roughly half the depth of a 2 tooth cutter. </li></ul></ul><ul><ul><li>Increasing the number of teeth will generally shift the stability pockets to a lower speed. </li></ul></ul><ul><li>Width (a or a r ) and Depth (b or a e ) of cut. </li></ul><ul><ul><li>Along with material machinability is the biggest influence for chatter. </li></ul></ul><ul><ul><li>Generally the product of a and b will be constant for a given chatter limit, e.g., doubling depth usually requires reducing width by ½ if at the chatter limit. </li></ul></ul><ul><li>Direction of cut </li></ul><ul><ul><li>Both width of cut and direction will influence chatter limit. </li></ul></ul><ul><ul><li>For long slender cutters the direction of cut is not as influential as it is for shorter and larger indexable cutters. </li></ul></ul>

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