Available online at www.sciencedirect.com Procedia CIRP (2012) 56 – 59 5th CIRP Conference on High Performance Cutting 2012 Development of novel anisotropic boring tool for chatter suppression Norikazu Suzukia,*, Kohei Nishimurab, Ryo Watanabea, Takashi Katoa and Eiji Shamotoa a Department of Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan b Okuma Corporation, 5-25-1, Shimooguchi, Oguchi-cho, Niwa-gun, Aichi 480-0193, Japan * Corresponding author Tel.: +81-52-789-4491; fax: +81-52-789-3107 E-mail address: nsuzuki@mech.nagoya-u.ac.jp Abstract A novel chatter suppression method in boring operation is proposed in the present study The anisotropic boring tool with a step portion and notches on the cylinder periphery is designed, which has anisotropic dynamic characteristics Since the direct and the cross transfer function components of the proposed tool are designed to cancel out each vibration, the nominal compliance of the boring tool in cutting process can be reduced significantly Hammering tests of the developed tool clarified that appropriate anisotropic frequency response function is roughly attained by the proposed design The developed tool was subsequently applied to turning experiments, and it was clarified that the stability limit in the radial depth of cut significantly increases by using the proposed boring tool as compared to the ordinary boring tool © 2012 Authors by Elsevier B.V.and/or Selection and/or peer-review under responsibility of Professor Konrad Wegener 2012 The Published byPublished Elsevier BV Selection peer-review under responsibility of Prof Konrad Wegener Keywords: chatter; boring; stability; dynamics; anisotropy; Introduction Self-excited chatter vibration in cutting sometimes causes excessive tool damage and surface deterioration, resulting in low productivity in manufacturing As lower compliance, i.e., higher stiffness, of the mechanical structure can lead to better chatter stability, the design of the stiffer mechanical structures is essentially important [1] However, it is often difficult to increase the stiffness of mechanical structures depending on the geometry constraint of the tool structure and/or the workpiece structure Boring operation is a particularly difficult cutting process in suppressing chatter vibration due to the low stiffness of slender boring tool geometry, whose diameter has to be smaller than that of the machined hole Although the stability limit might be increased by optimizing several conditions, such as spindle speed, insert geometry, depth of cut, and so on [2], this optimization does not always work effectively It is sometimes difficult to utilize the high stability pocket with large depth/width of cut due to several reasons, such as insufficiently-high spindle speed, influence of unexpected other vibration modes, and so on Process damping is also only available to increase the chatter stability in inefficiently-low cutting speed area [3] In order to increase chatter stability essentially, a novel design methodology to increase dynamic process stiffness in boring operation is proposed in the present study The anisotropic boring tool with a step portion and simple notches is designed to attain suitable anisotropic transfer function, which leads to low nominal compliance in cutting process The paper describes the basic idea of the proposed method Subsequently, the development of the proposed boring tool is presented, and its chatter suppression effect is verified through a series of turning experiments Chatter Stability in Boring Operation 2.1 Chatter stability analysis model Figure shows the boring process with chatter vibration, where the workpiece rotates and the tool is fed along the axial direction without rotation Note that the cutting mechanics of the boring process is essentially same as that of general turning and rather complicated with respect to that of plunge cutting The cantilevered 2212-8271 © 2012 The Authors Published by Elsevier B.V Selection and/or peer-review under responsibility of Professor Konrad Wegener http://dx.doi.org/10.1016/j.procir.2012.04.008 57 Norikazu Suzuki et al / Procedia CIRP (2012) 56 – 59 slender boring tool is assumed to become the most flexible structure, and thus its dynamics is dominant to the chatter stability As the tool is flexible in the plane perpendicular to the axial direction, it assumes that chatter vibration generates only in the depth of cut direction (x-axis direction) and the cutting direction (yaxis direction) in this study Workpiece Rotation direction fp :Principal force ft :Thrust force x Tool fp η Chip flow direction by Colwell's law dr x(t) Radial depth of cut x(t-T) Present dynamic displacement ft Vibration direction y Previous dynamic displacement x ε z z Phase shift y bd f b Front view b :Cutting width bd :Regenerative width f :Feed rate Top view Fig Boring process with chatter vibration When the mechanical structure vibrates, relative displacement between the tool and the workpiece fluctuates The uncut chip area varies due to not only the present displacement (outer modulation) but also the past displacement (inner modulation) left on the surface in the previous rotation The variation of the uncut area causes the cutting force fluctuation, and this dynamic force induces the present vibration As this processdynamics interaction builds up the closed-loop system, unstable vibration, i.e., self-excited chatter vibration, can generate Figure shows a block diagram of the plunge cutting process with the regenerative chatter vibration s (t ) = bx(t ) − bd x(t − T ) (1) where T is a spindle revolution period, b is a cutting width, bd (≤ b ) is a regenerative width The dynamic cutting force is assumed to be proportional to the dynamic uncut chip area s Then, the dynamic cutting force components, fx(t) and fy(t), can be expressed as: − K f cosηs(t )½ ° ½° f x (t )ẵ Kf = = f x (t )đ đ ắ đ ắ ắ K r cos °¿ ¯ f y (t )¿ ° − K s(t ) ° r ¯ ¿ (2) where Kf is the cutting constant in the chip-flow direction, Kr is the constant ratio of the force in chipflow direction to the principal force The chip flow angle η is derived from Colwell’s law Although the variation of the chip flow direction due to dynamic displacement affects the cutting force fluctuation simultaneously, this influence is ignored in the analysis for simplification [4] The transfer function of the most flexible mechanical structure G(jωc) relates the forces and the relative displacement While the fluctuation of the relative displacement between the tool and the workpiece in the cutting direction (y-axis direction) does not fundamentally affect the cutting force variation, that in the depth-of-cut direction (x-axis direction) induces the cutting force fluctuation directly The displacement in xaxis direction is derived as follows; x( jω c ) = G xx ( jω c ) f x ( jω c ) + G xy ( jω c ) f y ( jω c ) G xy ( jω c ) Ã Đ f x ( j c ) = ăă G xx ( j c ) + K r cos áạ â = ( j c ) f x ( jω c ) (3) where ωc is a chatter frequency, Φ is the one dimensional (1D) “equivalent transfer function” for the boring operation By using this equivalent transfer function, the formulation of the chatter stability analysis can be treated simply as a one degree-of-freedom system [5] The stability limit in the critical regenerative width bd_lim can be calculated by solving the following simple 1D equation f x ( jωc ) = ( ) − K f bd _ lim + f − bd _ lim e − jωcT cosηΦ( jωc ) f x ( jωc ) (4) 2.2 Design of anisotropic transfer function Fig Block diagram of boring process with chatter vibration The dynamic uncut chip area s(t) can be derived from the displacement x(t) as follows: The equivalent transfer function consists of the direct / cross components Thus, its dynamic compliance can be controlled by designing the ratio of the direct / cross components of the transfer function in an appropriate manner When both components are homothetic and the Norikazu Suzuki et al / Procedia CIRP (2012) 56 – 59 = − K r cos η Cp G xy º = G yy »¼ êcos ô sin = x p Zero compliance leads to not only completely stabile process for self-excited chatter vibration but also less forced vibration In order to attain the ideal transfer function, following design methodology is proposed in the present study At first, anisotropic tool structure is designed Here diagonal components of the transfer function, Gpp and Gqq, are designed to be homothetic in a mode coordinate system, which is represented by pq Although the homothetic ratio is not 1, their natural frequencies are same Off-diagonal components, Gpq and Gqp, are also designed to become zero Subsequently, the anisotropic tool structure is turned In a coordinate system with a rotation angle θ, which is represented by xy, the diagonal and the off-diagonal components, Gxx and Gxy, are derived from Gpp and Gqq as shown in following Eq (6) êG xx ôG yx sin êG pp ô cos ằẳ G qp (6) G pq º ªcos θ G qq ằẳ ôơ sin sin cos »¼ Namely, the ratio of Gxx to Gxy can be adjusted by the homothetic ratio of Gqq to Gpp and the rotation angle θ By means of this adjustment, the dynamic compliance of the equivalent transfer function can be down efficiently After several trial-and-error of the tool geometry design, it was found that the ratio of Gqq to Gpp of less than can be attained but it is tough to attain the ratio of more than When the ratio of Gqq to Gpp is 2, the minimum ratio of Gxx to Gxy can be obtained at the rotation angle θ of about 148° Figure demonstrates a simple example It assumes that Gyy=Gqq is twice greater than Gxx=Gpp in the normal coordinate system ( θ = 0° ), and they are homothetic When the mode coordinate system rotates with an angle of θ =148° , the ratio of Gxy to Gxx becomes about -0.35 In terms of Eq (5), the appropriate constant ratio of Gxy to Gxx depends on the cutting force ratio Kr and the chip flow angle η Both Kr and η vary depending on several conditions, such as tool/workpiece materials and cutting conditions According to authors’ experience, Kr is considered to distribute roughly from 0.2 to 1.0 in many case It is also considered that the chip flow angle kp Tool Cq kp p kq 1750 2000 1750 2000 Frequency Hz x 1500 180 1750 2000 1750 2000 Frequency Hz (b) Gxy(jω) 1750 2000 -180 1500 1500 180 -180 1500 (a) Gxx(jω) q θ Cq -180 1500 kq Cp y Compliance μm/N yq 1500 180 Phase deg Holder Compliance μm/N (5) Phase deg G xx ( jω c ) K r cos η θ = 0㼻 θ = 148㼻 =0 Compliance μm/N ∴ G xy ( jω c ) G xy ( jω c ) Compliance μm/N Φ ( jω c ) = G xx ( jω c ) + changes from 0° to 60° Then, the appropriate constant ratio of the transfer function is considered to distribute from -1.0 to -0.1 in practice Phase deg ratio satisfies following Eq (5), the dynamic compliance becomes zero, i.e., both the direct and the cross components cancel out each other Phase deg 58 1750 2000 Frequency Hz (c) Gyx(jω) 1500 180 1750 2000 -180 1500 1750 2000 Frequency Hz (d) Gyy(jω) Fig Schematic illustrations of coordinate systems and influence of relative rotation angle on anisotropy of transfer function Development of Anisotropic Boring Tool By utilizing finite element analysis, boring tool shape is designed Figure shows the designed anisotropic tool In order to increase Gqq with respect to Gpp, a step hone is fabricated at the top end of the cantilevered boring tool holder Small notches are also machined at the bottom, and both natural frequencies in p-axis and q-axis are adjusted to be in an agreement The ratio of projection length to the diameter (L/D) is set to be 4, and a rotation angle θ is set to be 148° Because of this anisotropic geometry, desired anisotropic transfer function can be attained Subsequently, the proposed boring tool was fabricated, and it was confirmed that the diagonal and the cross transfer function compliances become homothetic and the ratio of 1.8 was attained Fig Schematic illustration of designed anisotropic tool The Fourier response function (FRF) of developed tool is measured by a hammering test Figure 59 Norikazu Suzuki et al / Procedia CIRP (2012) 56 – 59 , , , ( ) demonstrates the vector diagrams of the equivalent transfer function Φ and both components Gxx and Gxy The FRF of ordinary boring tool with same projection length is also shown for comparison Kr is set to be 0.914 based on after-mentioned steel machining experiments The chip flow angle η of 60° is also assumed means stable and the corresponding area is described in blue color Unstable radial depth of cut conditions in the experiment are marked by crosses, while stable radial depth of cut conditions are marked by circles (a) Ordinary tool (a) Developed tool (b) Developed tool (b) Ordinary tool Fig 5.Fourier response functions measured by hammering tests Fig Experimental results and predicted chatter stability limits Note that the equivalent transfer function of the developed tool is smaller than that of the ordinary tool, while the diagonal component of the developed tool is almost three times greater than that of the ordinary tool Because of this equivalent transfer function, the developed tool should be more stable in chatter even though its nominal compliance is larger As shown in Fig 7, the experimental results roughly correspond to analytical results While the maximum stable radial depth of cut in the ordinary tool is less than 0.06 mm, that in the developed tool becomes more than 0.8 mm In terms of the analytical results, the chatter stability in the radial depth of cut increases about 15 times by using the developed tool than the ordinary tool Experimental Verification Conclusion The experimental verification was conducted Figure shows turning experimental setups with the ordinary tool and the developed tool The steel workpiece (JIS: SS400) was machined by the carbide tool with a nose radius of mm The specific cutting force Kf of 2.27 GPa was measured in other cutting experiments The feed rate was set to be 0.2 mm/rev The novel chatter suppression method in boring process by utilizing the anisotropy in the transfer function is proposed in the present study The design methodology of the boring tool is presented, and the anisotropic boring tool was developed The experimental investigation verified significant chatter suppression effect of the proposed method in boring operation References (a) Ordinary tool (b) Developed tool Fig Experimental setup with ordinary and developed tools Figure shows the experimental results and the analytical results The black solid line describes stability boundary calculated in stability analysis Predicted chatter gain margin is also shown, which indicate chatter stability quantitatively [6] The gain margin of larger than means unstable and the corresponding area is described in red color, while the gain margin of less than [1] Tlusty J Manufacturing Process and Equipment, Prentice Hall; 1999 [2] Altintas Y Manufacturing Automation Cambridge Univ Press; 2000 [3] Altintas Y, Eynian M, Onozuka H Identification of dynamic cutting force coefficients and chatter stability with process damping CIRP Annals – Manufacturing Technology; 2008, 57, p 371-374 [4] Eynian M, Altintas Y Chatter stability of general turning operations with process damping J Manu Sci Eng; 2009, 131, 041005 [5] Suzuki N, Nishimura K, Shamoto E, Yoshino K Effect of cross transfer function on chatter stability in plunge cutting J Adv Mech Des Sys Manu; 2010, 4, 5, p 883-891 [6] Shamoto E, Akazawa K Analytical prediction of chatter stability in ball end milling with tool inclination, CIRP Annals – Manufacturing Technology; 2009, 58, p 351-354 ... illustrations of coordinate systems and influence of relative rotation angle on anisotropy of transfer function Development of Anisotropic Boring Tool By utilizing finite element analysis, boring tool. .. the anisotropic boring tool was developed The experimental investigation verified significant chatter suppression effect of the proposed method in boring operation References (a) Ordinary tool. .. mm/rev The novel chatter suppression method in boring process by utilizing the anisotropy in the transfer function is proposed in the present study The design methodology of the boring tool is presented,