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Cutting Vibrations
CHAPTER EIGHT
Cutting Vibrations Contents 8.1 Classification of Cutting Vibrations and Their Sources 8.2 Forced Vibrations in Milling Operations 8.3 Mechanisms of Self-Excitation in Metal Cutting 8.4 Stability of Chatter 8.5 Methods for Improving Machine Tool Stability References
147 149 151 154 158 161
8.1 CLASSIFICATION OF CUTTING VIBRATIONS AND THEIR SOURCES The structural machining system consisting of the machine tool, the cutting tool and the workpiece mounted in the fixture (see Fig. 5.5) have very complicated dynamic characteristics, and as a consequence vibrations can frequently occur under certain undesirable machining conditions. In all types of machining processes, the three classes of mechanical vibrations can be distinguished in such a structural system: free (natural), forced, and self-excited vibrations [13], as shown in Fig. 8.1, and defined by the differential equation of a damped motion, Eq. (8.1). 8 0 Free vibrations > > > > FðtÞ ω 5 ω0 ; x0 -0 > > < Forced vibrations mxðtÞ € 1 kxðtÞ _ 1 cxðtÞ 5 (8.1) F½xðtÞ ω 5 ωF ; x0 5 const > > > > Self -excited vibrations > > : ω ωF ; x0 -N where m is mass of the vibration system (kg), k is the damping ratio (Ns/m), c is the rigidity constant (N/m), ω is the angular frequency of free vibrations (rad/s), ω0 is the angular frequency of self-excited vibrations (rad/s), ωF is the angular frequency of forced vibrations (rad/s), and x0 is amplitude of vibration (mm). Free (also natural or transient) vibrations appear when the mechanical system is displaced from its equilibrium and is allowed to vibrate freely. They can result from impulses transferred to the structure through its foundation; from rapid reversals of reciprocating masses, such as machine tables; the initial engagements of the cutting Advanced Machining Processes of Metallic Materials. DOI: http://dx.doi.org/10.1016/B978-0-444-63711-6.00008-9
© 2017 Elsevier B.V. All rights reserved.
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(A) c
k
fnd x0
m
(B) F = F0 sin 2πft X = X0 sin (2πft + φ)
c
k
f
F
A m
fn
x
(C)
FS
fn
FV
S
X
M
Figure 8.1 The three classes of mechanical vibrations: free (A), forced (B) and self-excited (C) [1].
tool into the workpiece; or, in the case of multi-axis CNC machine tools, from an incorrect tool path definition that leads to a collision between the cutting tool and the workpiece. The result is a motion with an amplitude decaying and a frequency equal to the natural damped frequency fnd of the system (Fig. 8.1A). Forced vibrations result from external, periodic force F(t) acting on the system (i.e., are sourced from external harmonic excitations). The principal sources of forced vibrations are unbalanced rotating shafts and the periodically changing component of the cutting force during the intermittent engagement of multi-tooth milling cutters, or through the foundations near the machine tool. However, forced vibrations are also transmitted, e.g., from unbalanced bearings or cutting tools, or by other machine tools through the workshop floor. The resulting motion reaches a steady state in which the amplitude A of sinusoidal vibrations is constant and the frequency of vibrations f is equal to the frequency of the exciting force (Fig. 8.1B). For a case when f 5 fn, a resonance is obtained at which the amplitude of vibrations exceed the maximum value. In general, forced vibrations occur at all kinds of machine tools where periodic forces are generated. Forced vibrations can produce machined surfaces with wavy patterns in finish grinding and boring as well as caused the shift of the machined
Cutting Vibrations
surface (over- or undercut effect) in slab milling, and nonflatness of the machined surface in end milling with helical cutters. Self-excited vibrations usually result from a dynamic instability of the cutting process, and develop due to the built up mechanism providing for a closed-loop relationship in the system. Self-excited vibrations extract energy to start and grow from the interaction between the cutting tool and the workpiece during the machining process. This mechanism is capable of modulating a steady, nonperiodical energy source and generating a periodic force Fv through the vibration system S (Fig. 8.1C), since it sustains the vibration. The characteristic features of self-excited vibrations are: (1) the amplitude increases until it stabilizes on a constant value; (2) the frequency of the vibration is equal to or close to the natural frequency of the system; (3) there is no independent, external periodic force; and (4) there is a steady energy force from which the system derives a periodic force through its vibration. This phenomenon is commonly referred as machine tool chatter and, typically, if large tool/work engagements are attempted, oscillations suddenly build up in the structure. They effectively limit metal removal rates and the conditions for the limit of stability are of decisive interest.
8.2 FORCED VIBRATIONS IN MILLING OPERATIONS As mentioned earlier, forced vibrations in machine tools are most often caused by cyclic variations in the cutting forces. Such variations will occur in end milling, which is a significant operation in the aerospace industries, and in face milling where the frequency of the forced vibration equals the product of the tool rotational frequency and the number of teeth on the milling cutter. Moreover, they can appear in broaching operations for which the number of active teeth oscillates between two integers (for instance between 4 and 5 when the ratio of the hole diameter to the pitch of broaching tool is equal to 4.54). It is obvious that similar to the single-degree-of-freedom system, the behaviour of a complex structure with many degrees of freedom, characteristic for the machine tools, can also be illustrated by the harmonic response locus of the system [2]. This is due to the fact the periodic forces are not sinusoidal but have significant harmonics (similar to that shown in Fig. 8.3A) and the tool has the same frequency as the periodicity of the force. Fig. 8.2 shows the resonance (A) and phase (B) curves and the relevant harmonic response locus in polar coordinates (C). Because a complex structure exhibits several different resonances or natural frequencies, the frequency response curve will also have several peaks corresponding to each resonance (two peaks at approximately 60 Hz and 80 Hz in Fig. 8.2A and B). Moreover, each resonance produces a separate loop of approximately circular form in the polar harmonic response locus shown in Fig. 8.2C.
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(B)
(A)
Phase angle φ f, (°)
Amplitude ratio
10
5
0 0
40
80
180
90
160
120
0 0
40
Frequency, Hz
80
120
160
Frequency, Hz
(C) In-phase axis 100
90
80
55 70
57.5 bh
72.5
60 Hz
75
76
ah
Out-of-phase axis
68
52.5
40 50
67
66 65.5
61
62
63 65 64.5
63.5 64
Figure 8.2 Frequency (A, B) and polar (C) response of a machine tool structure [2].
The surface error produced in end milling with cutters having four helical teeth due to force variation (Fig. 8.3A) is shown in Fig. 8.3C. Every tooth starts through a surface starting at line AA and ending at line BB. As the cutting edge CE rotates, it climbs on line AA and imprints the sinusoidal vibration (B) exiting by the force (A) on the surface S through the succession of points 1, 2, . . ., 6. As a result, the waved surface is produced as shown in detail (D). In practice, each resonance has a corresponding mode of vibration or mode shape that the structure adopts or, in other words, the amplitude and relative phases of various points on the structure will be different. For example, the modes of vibration which result in relative displacement of the tool and workpiece, causing a detrimental effect on the surface finish or surface error of the workpiece, can be determined by special computing algorithms or structural analysis programs based on the finite element method [1,2]. In the case of
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(A)
Y F
(C) Fav a
Time
φ
(B) y
(D)
6
3
A
Yav
1
2
4
5
B
b
6 5
Y
Time
4 3 2
Surface profile
1
s
B
CE
A
Figure 8.3 Development of surface error by end-milling cutter with helical teeth and nonregenerative approach according to Tlusty [1]: (A) force variation; (B) corresponding vibration of the tool in the Y direction shown in (C); and (D) imprints the vibration on surface S.
a three-dimensional structure of a machine tool the exciting forces applied at certain points and direction result in the displacements at another points in different directions, so the resulting frequency response curve will be referred to as a crossfrequency response.
8.3 MECHANISMS OF SELF-EXCITATION IN METAL CUTTING The basic cause of chatter is the dynamic interaction of the cutting process and the machine tool structure, which behaves as a closed-loop feedback system. However, so-called primary chatter can be caused by the cutting process itself (i.e., by intensive friction between the tool and the workpiece and thermo-mechanical effects resulting in instabilities of chip formation) [3]. In consequence, a deflection of the structure caused by an accidental disturbance in the cutting process usually alters the uncut chip thickness, and then the cutting force, and initiates self-sustaining vibrations. In general, chatter occurs in metal cutting if the chip width is too large with respect to the dynamic stiffness of the system. The cutting force becomes periodically variable, reaching considerable amplitudes, the machined surface becomes undulated, and the chip thickness varies in the extreme so much that it becomes dissected. Chatter is easily recognized by the harmful noise associated with these vibrations and by the characteristic chatter marks left on the machined surface. Such unstable cutting with large peak values of the variable cutting force is mostly unacceptable because of
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a real occurrence of tool breakage or machine part failure. Moreover, the limit of the chip width can substantially reduce the metal removal rate. In practice, the most significant cutting parameter for generating chatter is the width of cut b (width of chip). The limiting value of blim depends on the dynamic characteristics of the machine tool structure, the workpiece material, and its configuration (thin-walled structures are mostly sensitive to chatters), cutting speed and feed, and the geometry and construction of the tool. Especially, a high degree of tool overhang can, together with the undesirable mechanical properties of the workpiece material, lead to excessive vibrations in the tool shaft, which in turn causes chatter vibrations. Two major effects causing the instability of the closed-loop cutting process structural system are [13]: 1. The mode coupling effect (mode coupling for short overlap), shown in Fig. 8.4. 2. The regenerative effect (or simply regeneration of waviness), shown in Fig. 8.5. Mode coupling is a mechanism of self-excitation that can only be associated with a situation where the relative vibration between the tool and the workpiece can exist simultaneously in at least two directions in the plane of the orthogonal cut. Obviously, mode coupling instability occurs when successive passes of the tool do not overlap, as in screw cutting. Simultaneous vibrations in the X and Y directions with the same frequency and a phase shift between the two vibrations result in an elliptical path of the tool tip relative to the workpiece as shown in Fig. 8.4A. The resultant cutting force Fr does not work during this periodic motion of the tool from point A to point B, because it acts against the motion and takes energy away. During the reverse motion from point B to point A the force drives the tool and imparts energy to its (A)
(B)
C External modulation Fr B
FX A
X
B A
Y
Tool motion relative to workpiece
Internal modulation
X
Figure 8.4 Mode coupling instability: mode coupling effect (A) and regenerative effect (B) [2,3].
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(A)
(C) Milling cutter
Workpiece
(B) Yk
Turning (plunge cut)
ε Y
β
αi Xi
F
ε = 0°
ε = 90°
ε = 180°
Chip thickness variation h
Yk+1
Figure 8.5 Regeneration of surface waviness: (A) shaping; (B) turning; (C) milling [1].
motion and a larger value of the cutting force causes the surplus of energy sustaining the vibrations against damping losses. Regeneration of waviness shown in Fig. 8.5 is possible because in almost all machining operations the tool removes the chip from the surface that was produced in the previous pass. In other words, regenerative instability occurs when successive passes overlap. The tool in the next pass (next revolution of the workpiece in turning or next tooth engagement in milling) encounters a wavy surface and removes a chip with periodically variable thickness (Fig. 8.5C). The newly created surface is again wavy, and in this way the waviness is continually regenerated. In turning, as in diagram (B), the phase ε between the subsequent undulations is determined by the relationship between spindle speed n and frequency of chatter f. The number of waves between subsequent cuts is N1
ε f 5 2π n
(8.2)
where f is the frequency in Hz, n is the spindle rotational speed in rev/sec, and N is the largest integers such that ε/(2π) , 1. In practice, there are N full waves, and a fraction equals ε/2π. The chip thickness variation can be either zero for ε 5 0 or maximum for ε 5 π. In milling, the geometric constraint is much more important
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because the regeneration of waviness is produced by subsequent teeth of the cutter and Eq. (8.2) is changed to Eq. (8.3), hence N1
ε f 5 2π nm
(8.3)
where m is the number of teeth of the milling cutter. It may easily be computed that there are two and a fraction (three and a fraction) waves between subsequent teeth. Moreover, a change of ε by 2π, for N 5 2, requires a 50% change of frequency or the cutting speed. This causes the process stability to be importantly influenced by the geometric conditions.
8.4 STABILITY OF CHATTER As discussed in the previous section, in turning, changing spindle speed affects the level of stability very little, but in milling, especially in high-speed milling, a change of spindle rotational speed may be a very effective means for increasing the limit depth of cut and, correspondingly, the metal removal rate (MRR) [1]. In practice, stability of a machine tool can be represented graphically in the form of a special chart called the stability lobe diagram (SLD), which depicts the effect of the depth of cut in milling, drill diameter, and so on, versus the rotational speed of the tool or workpiece. The SLD visualizes the border between a stable zone (i.e., chatter free) and an unstable zone (i.e., with chatter). In milling operations, both 2D and 3D stability lobes that consider the axial depth of cut or the axial and radial depths of cut together are used [4,5]. An example of a two-dimensional stability chart for an end-milling operation with characteristic unstable ranges shown as lobed areas is presented in Fig. 8.6C. It is shown in a sequence of Fig. 8.8A and B that in milling the waviness, which is cut into the surface during chatter vibrations by a tooth, gets recut by the subsequent tooth. Cases (A1), (A2), and (A3) were recorded for increased spindle speed and it can be seen that for higher spindle speed (A3) only one and a small fraction of a wave occur. In addition, cases (B1) and (B2) illustrate that a substantial variation in chip thickness (twice the vibration amplitude) occurs with one and a half waves between the teeth, for the same amplitude. In contrast, no chip thickness and force variations were obtained with exactly one wave between the teeth being in phase. In the stability diagram shown in Fig. 8.6C, the vertical coordinate is the ratio q 5 blim/bcr, where bcr is the lowest blim obtained for phasing most favourable for chatter generation, and the horizontal scale expresses the value of the number p being the ratio of the tooth frequency over the natural frequency of the system. It should be pointed out that the individual “lobes” in the diagram correspond to a different integer N in Eq. (8.3). The practical interpretation of the graph is to consider the envelope of all the lobes as the boundary between the stable field below the envelope and the chatter field (shaded areas) lying above the envelope. The upturn of the stability
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(A)
(1)
(2)
(3)
(B)
(1)
(2)
q = blim / bcr
(C)
N=0
N=1
q=1
N=2
p=1 p = mn /60 / fn
Figure 8.6 Two-dimensional stability lobe diagram for a milling operation: waviness generation for increased spindle speed (A), variations of chip thickness (B) and stability lobe (C) [1].
boundary on the left end of the horizontal scale is the effect of process damping. In contrast, at the high-speed end, on the right, gaps of increased stability occur. The highest stability, permitting the highest value of stable depth of cut, is obtained with the spindle speed at which the tooth frequency equals the natural frequency of the system (for p 5 1). It can be seen in Fig. 8.6C that peaks of stability are close to values of p 5 1(N 1 1). This means that for low spindle speeds, the peaks of stability are not very high and are localized close to each other. But as the spindle speed approaches the values of n 5 0.5fn/m (and mainly n 5 fn/m), which denotes one wave between the subsequent teeth, substantial increase of the stability may be achieved by exact
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selection of the right rotational speed. In practice, it is necessary to have steplessly variable spindle speed to be able to select the most stable speed. Fig. 8.7 shows how the MRR can be increased (B) by dynamical optimization of the interface between the spindle unit and tool holder using the appropriate stability lobe (A). As a result, when using an end-milling cutter of 19 mm in diameter at a most stable spindle speed of 15,000 m21, it was possible to decrease the radial force down to 1250 N and to increase the material volume removed up to 900 cm3/min. Fig. 8.8A shows an example of a three-dimensional lobe diagram using the spindle rotational speed and the axial and radial depths of cut as coordinates for milling of the thin-walled part. The relationship between the axial and radial depths of cut obtained at the spindle rotational speed of 10,000 rpm is presented in Fig. 8.8B. It should be noted that in high-performance milling operations of thin-walled structures, traditional 2D lobe diagram is not sufficient to correctly predict the stable zones of the
(A)
(B) 1000
5000
860
MRR, cm3/min
800
Radial force, N
3750
2500
1250
0 5000
635 600
540
400 200 0
8000
11,000
14,000
Rotational frequency, min–1
17,000
20,000
10,000
12,500
15000
Rotational frequency, min–1
a
Figure 8.7 Optimized stability chart (A) and corresponding values of MRR (B) [5]. a depth of cut change in every step by 0.5 mm.
Figure 8.8 Three-dimensional stability lobe diagram for a milling operation of a thin-walled plate (A) and the relationship between axial and radial depths of cut for rotational spindle speed of 10,000 rpm (B) [4].
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chatter system. In such cases, the dynamical behaviour variation of the machined part with respect to the tool position [4] or the dynamic behaviour of the chatter system [5] should also be considered. As a result, an optimal pair of axial and radial depths of cut which satisfies the maximum MRR for the chatter-free milling can be obtained. Most of the techniques for predicting and controlling machining chatter are based on the three stability lobe equations in milling as [6]: blim 5
21 2Ks mavg μRe½G
(8.4)
where blim is the limiting stable axial depth of cut, Ks is the material specific power, mavg is the average number of teeth in the cut, and μRe[G] is the real part of the oriented frequency response function (FRF) measured at the tool tip. The second is Eq. (8.3) and the third is as follows: 21 Re½G ε 5 2π 2 2 tan (8.5) Im½G where Im[G] is the imaginary part of the FRF measured at the tool tip. The measurements of the FRF are most commonly based on the impact testing when an instrumented hammer is used to strike the tool tip, and the force of the impact is measured or the “pop-off ” device in which the impact is created by using an explosive device. Another method is the impact excitation technique, in which a magnet and the rotation of the spindle are used to provide the excitation [6]. Once the measured FRF is available, the SLD may be computed using a set of Eqs (8.3) (8.5). The methods of determining stable cutting regions without the requirement of an FRF measurement involve recording the sound spectrum during the cutting process, or a special device that uses the rotating tool and a noncontact actuator to generate the excitation force. The displacement of the tool tip is measured in response to the excitation at the tool pass frequency, and by utilizing once-per-revolution sampling of the displacement at each tachometer impulse, the superimposed real part of the FRF (see Eq. (8.5)) is constructed. Each of these real parts corresponds to the regions where the tooth passing frequency matches the chatter frequency, and therefore corresponds to the most stable regions of the stability diagram. Commercially available software exists [1,6,7] that can be used to simulate the chatter and calculate the cutting power from the MRR (it is proportional to the spindle speed and the axial depth of cut). Moreover, such runs can be automatically programmed over ranges of spindle speeds and depths of cut, resulting in comprehensive graphs of vibration and force amplitudes for all combinations of the axial and radial depth of cuts and spindle speeds. Finally, these lobes can be used for NC programming of optimum machining operations, but the dynamic characteristics of all cutting tools used must be measured. For instance, the machine tool producer, Okuma offers commercial control system
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Figure 8.9 Detection of chatter by microphone (A) and its suppression (C) using Machining Navi software with triangular spindle speed variation (B) [7].
Okuma Navi [7] which, if chatter is detected by built-in sensors or a microphone, changes automatically spindle speed or makes the spindle speed adjustments. The chatter detection and its suppression are schematically illustrated in Fig. 8.9
8.5 METHODS FOR IMPROVING MACHINE TOOL STABILITY During the operation of a machine tool, particularly under computer numerical control (CNC) control (see Fig. 8.9B), it is not always possible to avoid the machining conditions at which chatter may build up. Therefore, in such a situation, improving the stability of a machine tool is necessary. The possibilities of improving machine tool stability are as follows [13,8]: 1. Structural alterations dealing with adding more damping and/or stiffness to the structure in order to reduce the magnitude of the in-phase component of harmonic receptance ah on the operative response locus (see Fig. 8.2C). For example, it is possible to alter the principal directions of the major modes of vibration in such a way that they will not coincide with the cutting forces and/or the directions normal to the cut surface. Moreover, damping is a cumulative effect owing to a number of joints in a machine tool.
Cutting Vibrations
2. Application of a vibration absorber being the mass-spring system added to structure and tuned so that its natural frequency coincides with that of the major vibration mode. Such solution can be especially effective for machine tools with a single dominant mode of vibration. 3. Modification of the regenerative effect which utilizes disturbing the phasing between successive waves cut on the surface by a vibrating tool. This effect can be achieved in several ways. a. The use of special milling cutters with nonuniform tooth spacing, cutters that use teeth with alternating helix (the average chip thickness variation is very small), cutters that either have interrupted or undulated edges (they divide a wide chip into narrower and shorter pieces), and variable-pitch cutters. b. Chatter suppression by the effect of time-varying cutting parameters—width of cut, the spindle speed and mainly time-varying feed rate [3,8]. In the latter case, the stability is higher because a negative feedback loop is introduced into the system. For instance, Fig. 8.10 shows the principle of active chatter elimination by varying the spindle speed to disrupt regenerative effects shown previously in Fig. 8.5. The concept of spindle speed variation (SSV) is similar to the use of cutters with variable pitch, but is more flexible. As shown in Fig. 8.10, the chatter suppression can be obtained by triangular (B) and sinusoidal (C) speed variations. The SSV using triangular form of spindle variation was applied in a Machining Navi system by Okuma (see Fig. 8.9B). c. Active force control by means of active feedback control. For instance, the effect of providing damping force can be generated by a piezoelectric actuator with an inertial mass attached to the controlled cutting tool [8]. The actuator
Figure 8.10 Concept of chatter suppression in end-milling using variable spindle speed of triangular (B) and sinusoidal (C) shapes instead constant (linear) speed (A) [3].
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Figure 8.11 Damped (silent) boring bar (A) and obtainable MRR for different length-to-diameter ratio L/D (B) [9].
resonance can be tuned over a wide frequency range by adjusting the size of the inert mass, so that the actuator can provide an extremely large damping force to suppress undesired forced or self-excited vibration of the cutting tool at the resonance frequency of the actuator. Vibration from machining creates noise and sometimes it is necessary to use damped tools to keep it within the maximum noise level permitted in a workshop. Currently used damped tooling includes so-called silent tools (Fig. 8.11A) that are pretuned to the correct frequency in relation to the tool length that is ordered. This is basically required for the extremely damped boring bar in order to sustain the high material removal rate, as shown in Fig. 8.11B. In general, several techniques are known for enhancing dynamic stiffness and stability (chatter resistance) of long cutting tools and increasing the allowable overhang. The four most widely used and most universal approaches are [3,8]: 1. Use of anisotropic bars with specifically assigned orientations of the stiffness axes. This approach utilizes the development of chatter during cutting by an intermodal coupling in the two-degrees-of-freedom system referred to the orthogonal plane to the bar axis and passing through the cutting zone. A specific orientation of the stiffness axis relative to the cutting force leads to a significant increase of the dynamic stability. 2. Use of high Young’s modulus and/or high damping materials, such as sintered tungsten carbides and machinable sintered tungsten alloys with an added 24 percent of copper or nickel. Solid bars or monolithic tools (drills, milling cutters) made of these materials allow stable cutting with ratios L/D . 7 [10]. 3. Use of passive dynamic vibration absorbers (DVA) with an inertia mass, called pretuned bars. In boring bars, the DVA must be placed in an inertial cavity of much smaller diameter than the bar diameter, inside the tool structure.
Cutting Vibrations
Figure 8.12 Examples of active chatter suppression in boring bars using noncontact magnetic actuator (A) [10] and piezoelectric actuators and LR circuit (B) [11].
4. Use of active vibration control with active vibration dampers. This approach requires vibration sensors and actuators generating forces opposing the deflection of the tool when chatter occurs. The most frequently used are active systems with cavities in the mandrel body filled with variably pressurized oil. In this case, the ultimate L/D ratio increases up to 1012. To measure and control vibrations, advanced machine systems must rely on accurate sensors. A number of direct and indirect sensors have been used to measure also vibrations, including contact strain gauges/accelerometers, capacitive probes, inductive probes, fibre-optic displacement sensors, laser Doppler vibrometers, and acoustic pick-up devices (microphones) [3]. New methods of active damping of chatter include noncontact magnetic actuator instrumented with fibre-optic displacement sensors (Fig. 8.12A), piezoelectric actuators installed in the boring bar (Fig. 8.12B), and the application of the acceleration feedback of machine drives using two accelerometers mounted in x- and y-directions at the ram tip of a CNC milling machine [12]. In case of the boring bar mounted on a CNC lathe shown in Fig. 8.12A, the magnetic force produced by four magnetic units (the actuator) is used for active damping of its bending modes and increasing the dynamic stiffness. In the second case shown in Fig. 8.12B, two piezoelectric actuators are installed with preload in the boring bar. This acts together with an inductorresistant (LR) circuit as a hybrid dynamic absorber. In general, it is possible to suppress chatter in milling by means of an external excitation of the workpiece in the feed direction [13].
REFERENCES [1] G. Tlusty, Manufacturing Processes and Equipment, Prentice Hall, Upper Saddle River, New Jersey, 2000. [2] G. Boothroyd, W.A. Knight, Fundamentals of Machining and Machine Tools, Marcel Dekker, New York, NY, 1989. [3] G. Quintana, J. Ciurana, Chatter in machining process: a review, Int. J. Mach. Tools Manuf. 51 (2011) 363376.
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[4] V. Thevenot, L. Arnaud, G. Dessein, et al., Integration of dynamic variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling, Int. J. Adv. Manuf. Technol. 27 (2006) 638644. [5] A. Tang, Z. Liu, Three-dimensional stability lobe and maximum material removal rate in end milling of thin walled plate, Int. J. Adv. Manuf. Technol. 43 (2009) 3339. [6] S. Smith, Techniques for predicting and controlling chatter, invited paper on the topic of machine tools presented at the 29th NAMRC, University of Florida, 2001. [7] Machining Navi, Okuma. ,www.okuma.co.jp.. [8] Y. Altintas, M. Weck, Chatter stability of metal cutting and grinding, CIRP Ann Manuf Technol 53/2 (2004) 619642. [9] How to reduce vibration in metal cutting, Silent Tools, Sandvik Coromant, Sandviken, Sweden, 2006. [10] X. Liu, F. Chen, Y. Altintas, Magnetic actuator for active damping of boring bars, CIRP Ann Manuf Technol 64 (2015) 369372. [11] J. Munoa, X. Beudaert, K. Erkorkmaz, et al., Active suppression of structural chatter vibrations using machine drives and accelerometers, CIRP Ann Manuf Technol 64 (2015) 385388. [12] A. Matsubara, M. Maeda, I. Yamaji, Vibration suppression of boring bar by piezoelectric actuators and LR circuit, CIRP Ann Manuf Technol 64 (2015) 373376. [13] A. Weremczuk, R. Rusinek, J. Warminski, The concept of active elimination of vibrations in milling process, Procedia CIRP 31 (2015) 8287. [14] H. Voll, K. Gebert, Motor-spindeln fu¨r hohe Spanvolumina, Werkstatt und Betrieb 132 (1999) 5052.
Cutting Vibrations Contents 8.1 Classification of Cutting Vibrations and Their Sources 8.2 Forced Vibrations in Milling Operations 8.3 Mechanisms of Self-Excitation in Metal Cutting 8.4 Stability of Chatter 8.5 Methods for Improving Machine Tool Stability References
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8.1 CLASSIFICATION OF CUTTING VIBRATIONS AND THEIR SOURCES The structural machining system consisting of the machine tool, the cutting tool and the workpiece mounted in the fixture (see Fig. 5.5) have very complicated dynamic characteristics, and as a consequence vibrations can frequently occur under certain undesirable machining conditions. In all types of machining processes, the three classes of mechanical vibrations can be distinguished in such a structural system: free (natural), forced, and self-excited vibrations [13], as shown in Fig. 8.1, and defined by the differential equation of a damped motion, Eq. (8.1). 8 0 Free vibrations > > > > FðtÞ ω 5 ω0 ; x0 -0 > > < Forced vibrations mxðtÞ € 1 kxðtÞ _ 1 cxðtÞ 5 (8.1) F½xðtÞ ω 5 ωF ; x0 5 const > > > > Self -excited vibrations > > : ω ωF ; x0 -N where m is mass of the vibration system (kg), k is the damping ratio (Ns/m), c is the rigidity constant (N/m), ω is the angular frequency of free vibrations (rad/s), ω0 is the angular frequency of self-excited vibrations (rad/s), ωF is the angular frequency of forced vibrations (rad/s), and x0 is amplitude of vibration (mm). Free (also natural or transient) vibrations appear when the mechanical system is displaced from its equilibrium and is allowed to vibrate freely. They can result from impulses transferred to the structure through its foundation; from rapid reversals of reciprocating masses, such as machine tables; the initial engagements of the cutting Advanced Machining Processes of Metallic Materials. DOI: http://dx.doi.org/10.1016/B978-0-444-63711-6.00008-9
© 2017 Elsevier B.V. All rights reserved.
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(A) c
k
fnd x0
m
(B) F = F0 sin 2πft X = X0 sin (2πft + φ)
c
k
f
F
A m
fn
x
(C)
FS
fn
FV
S
X
M
Figure 8.1 The three classes of mechanical vibrations: free (A), forced (B) and self-excited (C) [1].
tool into the workpiece; or, in the case of multi-axis CNC machine tools, from an incorrect tool path definition that leads to a collision between the cutting tool and the workpiece. The result is a motion with an amplitude decaying and a frequency equal to the natural damped frequency fnd of the system (Fig. 8.1A). Forced vibrations result from external, periodic force F(t) acting on the system (i.e., are sourced from external harmonic excitations). The principal sources of forced vibrations are unbalanced rotating shafts and the periodically changing component of the cutting force during the intermittent engagement of multi-tooth milling cutters, or through the foundations near the machine tool. However, forced vibrations are also transmitted, e.g., from unbalanced bearings or cutting tools, or by other machine tools through the workshop floor. The resulting motion reaches a steady state in which the amplitude A of sinusoidal vibrations is constant and the frequency of vibrations f is equal to the frequency of the exciting force (Fig. 8.1B). For a case when f 5 fn, a resonance is obtained at which the amplitude of vibrations exceed the maximum value. In general, forced vibrations occur at all kinds of machine tools where periodic forces are generated. Forced vibrations can produce machined surfaces with wavy patterns in finish grinding and boring as well as caused the shift of the machined
Cutting Vibrations
surface (over- or undercut effect) in slab milling, and nonflatness of the machined surface in end milling with helical cutters. Self-excited vibrations usually result from a dynamic instability of the cutting process, and develop due to the built up mechanism providing for a closed-loop relationship in the system. Self-excited vibrations extract energy to start and grow from the interaction between the cutting tool and the workpiece during the machining process. This mechanism is capable of modulating a steady, nonperiodical energy source and generating a periodic force Fv through the vibration system S (Fig. 8.1C), since it sustains the vibration. The characteristic features of self-excited vibrations are: (1) the amplitude increases until it stabilizes on a constant value; (2) the frequency of the vibration is equal to or close to the natural frequency of the system; (3) there is no independent, external periodic force; and (4) there is a steady energy force from which the system derives a periodic force through its vibration. This phenomenon is commonly referred as machine tool chatter and, typically, if large tool/work engagements are attempted, oscillations suddenly build up in the structure. They effectively limit metal removal rates and the conditions for the limit of stability are of decisive interest.
8.2 FORCED VIBRATIONS IN MILLING OPERATIONS As mentioned earlier, forced vibrations in machine tools are most often caused by cyclic variations in the cutting forces. Such variations will occur in end milling, which is a significant operation in the aerospace industries, and in face milling where the frequency of the forced vibration equals the product of the tool rotational frequency and the number of teeth on the milling cutter. Moreover, they can appear in broaching operations for which the number of active teeth oscillates between two integers (for instance between 4 and 5 when the ratio of the hole diameter to the pitch of broaching tool is equal to 4.54). It is obvious that similar to the single-degree-of-freedom system, the behaviour of a complex structure with many degrees of freedom, characteristic for the machine tools, can also be illustrated by the harmonic response locus of the system [2]. This is due to the fact the periodic forces are not sinusoidal but have significant harmonics (similar to that shown in Fig. 8.3A) and the tool has the same frequency as the periodicity of the force. Fig. 8.2 shows the resonance (A) and phase (B) curves and the relevant harmonic response locus in polar coordinates (C). Because a complex structure exhibits several different resonances or natural frequencies, the frequency response curve will also have several peaks corresponding to each resonance (two peaks at approximately 60 Hz and 80 Hz in Fig. 8.2A and B). Moreover, each resonance produces a separate loop of approximately circular form in the polar harmonic response locus shown in Fig. 8.2C.
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(B)
(A)
Phase angle φ f, (°)
Amplitude ratio
10
5
0 0
40
80
180
90
160
120
0 0
40
Frequency, Hz
80
120
160
Frequency, Hz
(C) In-phase axis 100
90
80
55 70
57.5 bh
72.5
60 Hz
75
76
ah
Out-of-phase axis
68
52.5
40 50
67
66 65.5
61
62
63 65 64.5
63.5 64
Figure 8.2 Frequency (A, B) and polar (C) response of a machine tool structure [2].
The surface error produced in end milling with cutters having four helical teeth due to force variation (Fig. 8.3A) is shown in Fig. 8.3C. Every tooth starts through a surface starting at line AA and ending at line BB. As the cutting edge CE rotates, it climbs on line AA and imprints the sinusoidal vibration (B) exiting by the force (A) on the surface S through the succession of points 1, 2, . . ., 6. As a result, the waved surface is produced as shown in detail (D). In practice, each resonance has a corresponding mode of vibration or mode shape that the structure adopts or, in other words, the amplitude and relative phases of various points on the structure will be different. For example, the modes of vibration which result in relative displacement of the tool and workpiece, causing a detrimental effect on the surface finish or surface error of the workpiece, can be determined by special computing algorithms or structural analysis programs based on the finite element method [1,2]. In the case of
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(A)
Y F
(C) Fav a
Time
φ
(B) y
(D)
6
3
A
Yav
1
2
4
5
B
b
6 5
Y
Time
4 3 2
Surface profile
1
s
B
CE
A
Figure 8.3 Development of surface error by end-milling cutter with helical teeth and nonregenerative approach according to Tlusty [1]: (A) force variation; (B) corresponding vibration of the tool in the Y direction shown in (C); and (D) imprints the vibration on surface S.
a three-dimensional structure of a machine tool the exciting forces applied at certain points and direction result in the displacements at another points in different directions, so the resulting frequency response curve will be referred to as a crossfrequency response.
8.3 MECHANISMS OF SELF-EXCITATION IN METAL CUTTING The basic cause of chatter is the dynamic interaction of the cutting process and the machine tool structure, which behaves as a closed-loop feedback system. However, so-called primary chatter can be caused by the cutting process itself (i.e., by intensive friction between the tool and the workpiece and thermo-mechanical effects resulting in instabilities of chip formation) [3]. In consequence, a deflection of the structure caused by an accidental disturbance in the cutting process usually alters the uncut chip thickness, and then the cutting force, and initiates self-sustaining vibrations. In general, chatter occurs in metal cutting if the chip width is too large with respect to the dynamic stiffness of the system. The cutting force becomes periodically variable, reaching considerable amplitudes, the machined surface becomes undulated, and the chip thickness varies in the extreme so much that it becomes dissected. Chatter is easily recognized by the harmful noise associated with these vibrations and by the characteristic chatter marks left on the machined surface. Such unstable cutting with large peak values of the variable cutting force is mostly unacceptable because of
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a real occurrence of tool breakage or machine part failure. Moreover, the limit of the chip width can substantially reduce the metal removal rate. In practice, the most significant cutting parameter for generating chatter is the width of cut b (width of chip). The limiting value of blim depends on the dynamic characteristics of the machine tool structure, the workpiece material, and its configuration (thin-walled structures are mostly sensitive to chatters), cutting speed and feed, and the geometry and construction of the tool. Especially, a high degree of tool overhang can, together with the undesirable mechanical properties of the workpiece material, lead to excessive vibrations in the tool shaft, which in turn causes chatter vibrations. Two major effects causing the instability of the closed-loop cutting process structural system are [13]: 1. The mode coupling effect (mode coupling for short overlap), shown in Fig. 8.4. 2. The regenerative effect (or simply regeneration of waviness), shown in Fig. 8.5. Mode coupling is a mechanism of self-excitation that can only be associated with a situation where the relative vibration between the tool and the workpiece can exist simultaneously in at least two directions in the plane of the orthogonal cut. Obviously, mode coupling instability occurs when successive passes of the tool do not overlap, as in screw cutting. Simultaneous vibrations in the X and Y directions with the same frequency and a phase shift between the two vibrations result in an elliptical path of the tool tip relative to the workpiece as shown in Fig. 8.4A. The resultant cutting force Fr does not work during this periodic motion of the tool from point A to point B, because it acts against the motion and takes energy away. During the reverse motion from point B to point A the force drives the tool and imparts energy to its (A)
(B)
C External modulation Fr B
FX A
X
B A
Y
Tool motion relative to workpiece
Internal modulation
X
Figure 8.4 Mode coupling instability: mode coupling effect (A) and regenerative effect (B) [2,3].
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(A)
(C) Milling cutter
Workpiece
(B) Yk
Turning (plunge cut)
ε Y
β
αi Xi
F
ε = 0°
ε = 90°
ε = 180°
Chip thickness variation h
Yk+1
Figure 8.5 Regeneration of surface waviness: (A) shaping; (B) turning; (C) milling [1].
motion and a larger value of the cutting force causes the surplus of energy sustaining the vibrations against damping losses. Regeneration of waviness shown in Fig. 8.5 is possible because in almost all machining operations the tool removes the chip from the surface that was produced in the previous pass. In other words, regenerative instability occurs when successive passes overlap. The tool in the next pass (next revolution of the workpiece in turning or next tooth engagement in milling) encounters a wavy surface and removes a chip with periodically variable thickness (Fig. 8.5C). The newly created surface is again wavy, and in this way the waviness is continually regenerated. In turning, as in diagram (B), the phase ε between the subsequent undulations is determined by the relationship between spindle speed n and frequency of chatter f. The number of waves between subsequent cuts is N1
ε f 5 2π n
(8.2)
where f is the frequency in Hz, n is the spindle rotational speed in rev/sec, and N is the largest integers such that ε/(2π) , 1. In practice, there are N full waves, and a fraction equals ε/2π. The chip thickness variation can be either zero for ε 5 0 or maximum for ε 5 π. In milling, the geometric constraint is much more important
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because the regeneration of waviness is produced by subsequent teeth of the cutter and Eq. (8.2) is changed to Eq. (8.3), hence N1
ε f 5 2π nm
(8.3)
where m is the number of teeth of the milling cutter. It may easily be computed that there are two and a fraction (three and a fraction) waves between subsequent teeth. Moreover, a change of ε by 2π, for N 5 2, requires a 50% change of frequency or the cutting speed. This causes the process stability to be importantly influenced by the geometric conditions.
8.4 STABILITY OF CHATTER As discussed in the previous section, in turning, changing spindle speed affects the level of stability very little, but in milling, especially in high-speed milling, a change of spindle rotational speed may be a very effective means for increasing the limit depth of cut and, correspondingly, the metal removal rate (MRR) [1]. In practice, stability of a machine tool can be represented graphically in the form of a special chart called the stability lobe diagram (SLD), which depicts the effect of the depth of cut in milling, drill diameter, and so on, versus the rotational speed of the tool or workpiece. The SLD visualizes the border between a stable zone (i.e., chatter free) and an unstable zone (i.e., with chatter). In milling operations, both 2D and 3D stability lobes that consider the axial depth of cut or the axial and radial depths of cut together are used [4,5]. An example of a two-dimensional stability chart for an end-milling operation with characteristic unstable ranges shown as lobed areas is presented in Fig. 8.6C. It is shown in a sequence of Fig. 8.8A and B that in milling the waviness, which is cut into the surface during chatter vibrations by a tooth, gets recut by the subsequent tooth. Cases (A1), (A2), and (A3) were recorded for increased spindle speed and it can be seen that for higher spindle speed (A3) only one and a small fraction of a wave occur. In addition, cases (B1) and (B2) illustrate that a substantial variation in chip thickness (twice the vibration amplitude) occurs with one and a half waves between the teeth, for the same amplitude. In contrast, no chip thickness and force variations were obtained with exactly one wave between the teeth being in phase. In the stability diagram shown in Fig. 8.6C, the vertical coordinate is the ratio q 5 blim/bcr, where bcr is the lowest blim obtained for phasing most favourable for chatter generation, and the horizontal scale expresses the value of the number p being the ratio of the tooth frequency over the natural frequency of the system. It should be pointed out that the individual “lobes” in the diagram correspond to a different integer N in Eq. (8.3). The practical interpretation of the graph is to consider the envelope of all the lobes as the boundary between the stable field below the envelope and the chatter field (shaded areas) lying above the envelope. The upturn of the stability
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(A)
(1)
(2)
(3)
(B)
(1)
(2)
q = blim / bcr
(C)
N=0
N=1
q=1
N=2
p=1 p = mn /60 / fn
Figure 8.6 Two-dimensional stability lobe diagram for a milling operation: waviness generation for increased spindle speed (A), variations of chip thickness (B) and stability lobe (C) [1].
boundary on the left end of the horizontal scale is the effect of process damping. In contrast, at the high-speed end, on the right, gaps of increased stability occur. The highest stability, permitting the highest value of stable depth of cut, is obtained with the spindle speed at which the tooth frequency equals the natural frequency of the system (for p 5 1). It can be seen in Fig. 8.6C that peaks of stability are close to values of p 5 1(N 1 1). This means that for low spindle speeds, the peaks of stability are not very high and are localized close to each other. But as the spindle speed approaches the values of n 5 0.5fn/m (and mainly n 5 fn/m), which denotes one wave between the subsequent teeth, substantial increase of the stability may be achieved by exact
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selection of the right rotational speed. In practice, it is necessary to have steplessly variable spindle speed to be able to select the most stable speed. Fig. 8.7 shows how the MRR can be increased (B) by dynamical optimization of the interface between the spindle unit and tool holder using the appropriate stability lobe (A). As a result, when using an end-milling cutter of 19 mm in diameter at a most stable spindle speed of 15,000 m21, it was possible to decrease the radial force down to 1250 N and to increase the material volume removed up to 900 cm3/min. Fig. 8.8A shows an example of a three-dimensional lobe diagram using the spindle rotational speed and the axial and radial depths of cut as coordinates for milling of the thin-walled part. The relationship between the axial and radial depths of cut obtained at the spindle rotational speed of 10,000 rpm is presented in Fig. 8.8B. It should be noted that in high-performance milling operations of thin-walled structures, traditional 2D lobe diagram is not sufficient to correctly predict the stable zones of the
(A)
(B) 1000
5000
860
MRR, cm3/min
800
Radial force, N
3750
2500
1250
0 5000
635 600
540
400 200 0
8000
11,000
14,000
Rotational frequency, min–1
17,000
20,000
10,000
12,500
15000
Rotational frequency, min–1
a
Figure 8.7 Optimized stability chart (A) and corresponding values of MRR (B) [5]. a depth of cut change in every step by 0.5 mm.
Figure 8.8 Three-dimensional stability lobe diagram for a milling operation of a thin-walled plate (A) and the relationship between axial and radial depths of cut for rotational spindle speed of 10,000 rpm (B) [4].
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Cutting Vibrations
chatter system. In such cases, the dynamical behaviour variation of the machined part with respect to the tool position [4] or the dynamic behaviour of the chatter system [5] should also be considered. As a result, an optimal pair of axial and radial depths of cut which satisfies the maximum MRR for the chatter-free milling can be obtained. Most of the techniques for predicting and controlling machining chatter are based on the three stability lobe equations in milling as [6]: blim 5
21 2Ks mavg μRe½G
(8.4)
where blim is the limiting stable axial depth of cut, Ks is the material specific power, mavg is the average number of teeth in the cut, and μRe[G] is the real part of the oriented frequency response function (FRF) measured at the tool tip. The second is Eq. (8.3) and the third is as follows: 21 Re½G ε 5 2π 2 2 tan (8.5) Im½G where Im[G] is the imaginary part of the FRF measured at the tool tip. The measurements of the FRF are most commonly based on the impact testing when an instrumented hammer is used to strike the tool tip, and the force of the impact is measured or the “pop-off ” device in which the impact is created by using an explosive device. Another method is the impact excitation technique, in which a magnet and the rotation of the spindle are used to provide the excitation [6]. Once the measured FRF is available, the SLD may be computed using a set of Eqs (8.3) (8.5). The methods of determining stable cutting regions without the requirement of an FRF measurement involve recording the sound spectrum during the cutting process, or a special device that uses the rotating tool and a noncontact actuator to generate the excitation force. The displacement of the tool tip is measured in response to the excitation at the tool pass frequency, and by utilizing once-per-revolution sampling of the displacement at each tachometer impulse, the superimposed real part of the FRF (see Eq. (8.5)) is constructed. Each of these real parts corresponds to the regions where the tooth passing frequency matches the chatter frequency, and therefore corresponds to the most stable regions of the stability diagram. Commercially available software exists [1,6,7] that can be used to simulate the chatter and calculate the cutting power from the MRR (it is proportional to the spindle speed and the axial depth of cut). Moreover, such runs can be automatically programmed over ranges of spindle speeds and depths of cut, resulting in comprehensive graphs of vibration and force amplitudes for all combinations of the axial and radial depth of cuts and spindle speeds. Finally, these lobes can be used for NC programming of optimum machining operations, but the dynamic characteristics of all cutting tools used must be measured. For instance, the machine tool producer, Okuma offers commercial control system
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Figure 8.9 Detection of chatter by microphone (A) and its suppression (C) using Machining Navi software with triangular spindle speed variation (B) [7].
Okuma Navi [7] which, if chatter is detected by built-in sensors or a microphone, changes automatically spindle speed or makes the spindle speed adjustments. The chatter detection and its suppression are schematically illustrated in Fig. 8.9
8.5 METHODS FOR IMPROVING MACHINE TOOL STABILITY During the operation of a machine tool, particularly under computer numerical control (CNC) control (see Fig. 8.9B), it is not always possible to avoid the machining conditions at which chatter may build up. Therefore, in such a situation, improving the stability of a machine tool is necessary. The possibilities of improving machine tool stability are as follows [13,8]: 1. Structural alterations dealing with adding more damping and/or stiffness to the structure in order to reduce the magnitude of the in-phase component of harmonic receptance ah on the operative response locus (see Fig. 8.2C). For example, it is possible to alter the principal directions of the major modes of vibration in such a way that they will not coincide with the cutting forces and/or the directions normal to the cut surface. Moreover, damping is a cumulative effect owing to a number of joints in a machine tool.
Cutting Vibrations
2. Application of a vibration absorber being the mass-spring system added to structure and tuned so that its natural frequency coincides with that of the major vibration mode. Such solution can be especially effective for machine tools with a single dominant mode of vibration. 3. Modification of the regenerative effect which utilizes disturbing the phasing between successive waves cut on the surface by a vibrating tool. This effect can be achieved in several ways. a. The use of special milling cutters with nonuniform tooth spacing, cutters that use teeth with alternating helix (the average chip thickness variation is very small), cutters that either have interrupted or undulated edges (they divide a wide chip into narrower and shorter pieces), and variable-pitch cutters. b. Chatter suppression by the effect of time-varying cutting parameters—width of cut, the spindle speed and mainly time-varying feed rate [3,8]. In the latter case, the stability is higher because a negative feedback loop is introduced into the system. For instance, Fig. 8.10 shows the principle of active chatter elimination by varying the spindle speed to disrupt regenerative effects shown previously in Fig. 8.5. The concept of spindle speed variation (SSV) is similar to the use of cutters with variable pitch, but is more flexible. As shown in Fig. 8.10, the chatter suppression can be obtained by triangular (B) and sinusoidal (C) speed variations. The SSV using triangular form of spindle variation was applied in a Machining Navi system by Okuma (see Fig. 8.9B). c. Active force control by means of active feedback control. For instance, the effect of providing damping force can be generated by a piezoelectric actuator with an inertial mass attached to the controlled cutting tool [8]. The actuator
Figure 8.10 Concept of chatter suppression in end-milling using variable spindle speed of triangular (B) and sinusoidal (C) shapes instead constant (linear) speed (A) [3].
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Figure 8.11 Damped (silent) boring bar (A) and obtainable MRR for different length-to-diameter ratio L/D (B) [9].
resonance can be tuned over a wide frequency range by adjusting the size of the inert mass, so that the actuator can provide an extremely large damping force to suppress undesired forced or self-excited vibration of the cutting tool at the resonance frequency of the actuator. Vibration from machining creates noise and sometimes it is necessary to use damped tools to keep it within the maximum noise level permitted in a workshop. Currently used damped tooling includes so-called silent tools (Fig. 8.11A) that are pretuned to the correct frequency in relation to the tool length that is ordered. This is basically required for the extremely damped boring bar in order to sustain the high material removal rate, as shown in Fig. 8.11B. In general, several techniques are known for enhancing dynamic stiffness and stability (chatter resistance) of long cutting tools and increasing the allowable overhang. The four most widely used and most universal approaches are [3,8]: 1. Use of anisotropic bars with specifically assigned orientations of the stiffness axes. This approach utilizes the development of chatter during cutting by an intermodal coupling in the two-degrees-of-freedom system referred to the orthogonal plane to the bar axis and passing through the cutting zone. A specific orientation of the stiffness axis relative to the cutting force leads to a significant increase of the dynamic stability. 2. Use of high Young’s modulus and/or high damping materials, such as sintered tungsten carbides and machinable sintered tungsten alloys with an added 24 percent of copper or nickel. Solid bars or monolithic tools (drills, milling cutters) made of these materials allow stable cutting with ratios L/D . 7 [10]. 3. Use of passive dynamic vibration absorbers (DVA) with an inertia mass, called pretuned bars. In boring bars, the DVA must be placed in an inertial cavity of much smaller diameter than the bar diameter, inside the tool structure.
Cutting Vibrations
Figure 8.12 Examples of active chatter suppression in boring bars using noncontact magnetic actuator (A) [10] and piezoelectric actuators and LR circuit (B) [11].
4. Use of active vibration control with active vibration dampers. This approach requires vibration sensors and actuators generating forces opposing the deflection of the tool when chatter occurs. The most frequently used are active systems with cavities in the mandrel body filled with variably pressurized oil. In this case, the ultimate L/D ratio increases up to 1012. To measure and control vibrations, advanced machine systems must rely on accurate sensors. A number of direct and indirect sensors have been used to measure also vibrations, including contact strain gauges/accelerometers, capacitive probes, inductive probes, fibre-optic displacement sensors, laser Doppler vibrometers, and acoustic pick-up devices (microphones) [3]. New methods of active damping of chatter include noncontact magnetic actuator instrumented with fibre-optic displacement sensors (Fig. 8.12A), piezoelectric actuators installed in the boring bar (Fig. 8.12B), and the application of the acceleration feedback of machine drives using two accelerometers mounted in x- and y-directions at the ram tip of a CNC milling machine [12]. In case of the boring bar mounted on a CNC lathe shown in Fig. 8.12A, the magnetic force produced by four magnetic units (the actuator) is used for active damping of its bending modes and increasing the dynamic stiffness. In the second case shown in Fig. 8.12B, two piezoelectric actuators are installed with preload in the boring bar. This acts together with an inductorresistant (LR) circuit as a hybrid dynamic absorber. In general, it is possible to suppress chatter in milling by means of an external excitation of the workpiece in the feed direction [13].
REFERENCES [1] G. Tlusty, Manufacturing Processes and Equipment, Prentice Hall, Upper Saddle River, New Jersey, 2000. [2] G. Boothroyd, W.A. Knight, Fundamentals of Machining and Machine Tools, Marcel Dekker, New York, NY, 1989. [3] G. Quintana, J. Ciurana, Chatter in machining process: a review, Int. J. Mach. Tools Manuf. 51 (2011) 363376.
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[4] V. Thevenot, L. Arnaud, G. Dessein, et al., Integration of dynamic variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling, Int. J. Adv. Manuf. Technol. 27 (2006) 638644. [5] A. Tang, Z. Liu, Three-dimensional stability lobe and maximum material removal rate in end milling of thin walled plate, Int. J. Adv. Manuf. Technol. 43 (2009) 3339. [6] S. Smith, Techniques for predicting and controlling chatter, invited paper on the topic of machine tools presented at the 29th NAMRC, University of Florida, 2001. [7] Machining Navi, Okuma. ,www.okuma.co.jp.. [8] Y. Altintas, M. Weck, Chatter stability of metal cutting and grinding, CIRP Ann Manuf Technol 53/2 (2004) 619642. [9] How to reduce vibration in metal cutting, Silent Tools, Sandvik Coromant, Sandviken, Sweden, 2006. [10] X. Liu, F. Chen, Y. Altintas, Magnetic actuator for active damping of boring bars, CIRP Ann Manuf Technol 64 (2015) 369372. [11] J. Munoa, X. Beudaert, K. Erkorkmaz, et al., Active suppression of structural chatter vibrations using machine drives and accelerometers, CIRP Ann Manuf Technol 64 (2015) 385388. [12] A. Matsubara, M. Maeda, I. Yamaji, Vibration suppression of boring bar by piezoelectric actuators and LR circuit, CIRP Ann Manuf Technol 64 (2015) 373376. [13] A. Weremczuk, R. Rusinek, J. Warminski, The concept of active elimination of vibrations in milling process, Procedia CIRP 31 (2015) 8287. [14] H. Voll, K. Gebert, Motor-spindeln fu¨r hohe Spanvolumina, Werkstatt und Betrieb 132 (1999) 5052.