- Email: [email protected]
Active damping of milling chatter vibration via a novel spindle system with an integrated electromagnetic actuator
Precision Engineering 57 (2019) 203–210
Contents lists available at ScienceDirect
Precision Engineering journal homepage: www.elsevier.com/locate/precision
Active damping of milling chatter vibration via a novel spindle system with an integrated electromagnetic actuator
T
Shaoke Wana,b,c, Xiaohu Lia,b,∗, Wenjun Sua,b, Junpeng Yuana,b, Jun Honga,b, Xiaoliang Jinc a
Key Laboratory of Education Ministry for Modern Design & Rotor-Bearing System, Xi'an Jiaotong University, Xi'an, Shaanxi, China School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, China c Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada b
ARTICLE INFO
ABSTRACT
Keywords: Active damping Milling chatter vibration Electromagnetic actuator
Self-excited vibration, widely referred to as chatter, has always been a limitation and challenge in machining. To suppress milling chatter vibration and improve surface finishes, a novel spindle system is proposed in this study. A noncontact electromagnetic actuator with two degrees of freedom is developed and integrated into the designed spindle system compactly. A differential driving mode is utilized for the electromagnetic actuator to obtain a linear output of actuator force, making the actuator more applicable for vibration control. Displacement sensors mounted near the actuator measure the vibration of the rotating spindle shaft and provide feedback signals for the developed proportional-derivative controller. The active damping performance of the designed spindle system with an integrated electromagnetic actuator, in both x and y directions, is also validated with impact tests and milling experiments, and a maximum increase (by factors of 3.67 and 2.89 in x and y directions, respectively) of dynamic stiffness at the first modal frequency is obtained. Milling experiment results with and without active damping also illustrate that milling chatter vibration has been well damped actively with the developed spindle system.
1. Introduction Chatter vibrations result from regenerative dynamic chip thickness during machining, are always a major productivity limitation, and lead to poor, wavy surface finishes, decreasing the life of mechanical components [1]. Consequently, chatter suppression techniques have become one of the major concerns in machining in the past few decades. Because cutting stability is affected by the dynamic parameters of machine tools, system damping enhancement has been one of the ideas promoted to suppress chatter vibration [2]. Damping can be increased passively and actively. Because of their simplicity and reliability, passive damping techniques have been presented for chatter suppression by many researchers. Yang attached a tuned mass damper [3,4] to a specific support of the workpiece during the milling process and improved machining stability. However, the tuned mass damper required adjustment for different workpiece structures. Burtscher [5] presented a tuned mass damper fixed onto the spindle head of a machine tool, and variable mass was utilized to adapt its eigenfrequency to the dominant frequency of the machine tool, but the dimension of the mass damper was large. Hamed [6] designed a tunable vibration absorber set composed of mass, spring, and dashpot
∗
elements and aimed to suppress regenerative chatter by adjusting the supported position on the extension of the tool and the stiffness of the spring in the milling process, but only theoretical results were shown and no prototype was presented. Matsubara [7] proposed a support system with a pivot mechanism providing damping of the vibration modes for thin-wall milling. Fei [8] proposed a moving damper during the milling process, improving the system chatter stability, but it was also designed for thin-wall milling. Though passive dampers entail reasonable cost and have the advantage of simplicity, a large space is needed, the damping effect is limited when dynamic properties vary, and the dampers are difficult to integrate into the machine tool. In active damping, an active control force is introduced to the cutting system with specific actuators, and parameters related to cutting vibration are measured with sensors as a feedback signal. The active damping of chatter vibration has been widely performed in boring [9–14] and turning processes [15–17], and the control force mostly acts on the tool directly to obtain an excellent damping effect. However, the rotating tool limits the possibilities for directly applying an active control force on the tool during the milling process. Similar to the applications of piezoelectric actuators in Refs. [9–12,16], Monnin's [18,19] active spindle with four piezoelectric actuators applied a
Corresponding author. No. 28 Xianning West Road, Xi'an, Shaanxi, 710049, China. E-mail address: [email protected] (X. Li).
https://doi.org/10.1016/j.precisioneng.2019.04.007 Received 13 December 2018; Received in revised form 22 April 2019; Accepted 22 April 2019 Available online 26 April 2019 0141-6359/ © 2019 Elsevier Inc. All rights reserved.
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
control force on the outer ring of spindle bearings to control chatter vibration. However, the extra heat in the bearings caused by the applied radial force could not be ignored, and the active control force cannot be acted on the rotating tool or spindle shaft directly. Moreover, the nonlinear hysteresis of the piezoelectric actuators could not be ignored. Because electromagnetic actuators can generate noncontact magnetic forces and almost no hysteresis exists, they have already been utilized in boring [13,14] and turning [17], where electromagnetic actuators are attached to the boring bar or to the turning tool holder. Active spindles supported with active magnetic bearings (AMBs) have also been proposed by Gourc [20] and Knospe [21] to increase the stability of the milling process. However, the industrial application of spindles supported with AMBs is limited by low radial cutting load capacity, and two control loops are needed for the operation of a high-speed rotating spindle shaft and control of the tool's vibration, posing challenges to reliability. Given the advantages of electromagnetic actuators for active damping of the cutting process and the disadvantage of active spindles supported with AMBs, a novel spindle system is developed for active damping of milling chatter vibration. An electromagnetic actuator is developed and integrated into the spindle system compactly. The milling process is modeled with two radial degrees of freedom, so the electromagnetic actuator is designed to apply a noncontact control force on the rotating spindle shaft in both x and y directions. Displacement sensors are also integrated to measure the vibration displacements of the spindle shaft. A simple and effective proportionalderivative (PD) controller is then developed, and velocity feedback is used for active damping of the spindle system, thereby damping milling chatter vibration effectively. Modal tests and cutting experiments are also performed, and the results demonstrate an increase of dynamic stiffness at the modal frequency and that the milling chatter vibration is well controlled actively. The rest of the paper is organized as follows. Section 2 presents the developed spindle system integrated with an electromagnetic actuator and the working principle of the actuator. Active damping with the PD controller is proposed in Section 3. Experiments are presented in Section 4, and the conclusions are drawn in Section 5.
Table 1 Parameters of the designed spindle. Maximum speed
Power
Torque
Bearing type
Bearing preload
Lubrication
24,000 rpm
3.5 kW
1.4 Nm
7006C/ 7005C
480 N
Grease
tool directly. Fig. 1 shows the configurations of the designed spindle system. An electromagnetic actuator is integrated into a conventional motorized spindle supported with two sets of angular contact ball bearings and placed between the front bearings and the tool. The built-in motor offers speed and torque. In the spindle system, angular contact ball bearings ensure stiffness and rotation accuracy of the whole spindle system, and the electromagnetic actuator is utilized to generate a noncontact electromagnetic force on the rotating spindle shaft to actively damp tool vibration. In each radial direction, two displacement sensors are arranged symmetrically to measure the vibration of the rotating shaft accurately. The structure of the designed prototype is quite compact and quite similar to that of a fabricable industrial product. The electromagnetic actuator can apply a noncontact force on the high-speed rotating spindle shaft with almost no hysteresis, and there is no rotating stability problem for the spindle shaft supported only with AMBs as reported in Refs. [20,21]. An encoder is also mounted at the end of the spindle for the closed-loop control of spindle speed. In addition, some other information about the designed spindle is given in Table 1. Due to small-scale components are utilized, the power and torque of the prototype are lower than a typical commercial milling spindle system, and its dimensions and stiffness are also smaller than the typical ones. However, the presented active damping method and configuration of system is suitable for a commercial milling system, in which a larger dimension of actuator with high actuator capacity can be installed. 2.2. Electromagnetic actuator design Fig. 2(a) shows a schematic of the designed electromagnetic actuator. A rotator core, a stator core, and coil windings around the stator core constitute the actuator. There are eight stator poles with a symmetric layout, and the two adjacent poles together make up a combining electromagnet. When current is applied in the coil windings, a magnetic field emerges in the combining electromagnet. The magnetic field intensity H and flux density B are usually utilized to describe the strength of magnetic field, and their relationship is given [22].
2. Spindle system integrated with an electromagnetic actuator 2.1. Configuration of the developed spindle system During the milling process, chatter vibration occurs between the tool and the workpiece. Because the workpiece can usually be assumed to be rigid, the main idea is to damp the vibrations of the tool to obtain better surface finishes. Actively damping the vibration of a rotating tool is best accomplished by applying an active control force on the rotating
B = µ 0 µr H,
Fig. 1. Configurations of the developed spindle system integrated with an electromagnetic actuator. 204
(1)
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 2. Schematics of (a) the electromagnetic actuator and (b) the working principle.
where µ 0 = 4 × 10 7V s /(A m) is magnetic permeability of vacuum and µr is the relative permeability, which depends on the medium in which the magnetic field acts. The flux is assumed as running entirely along the magnetic circuit with cross-sectional area A , where the cross sections in the iron and air gap are equal and equal to the cross section of the stator poles. The magnetic circuit follows the form
H ds = li Hi + 2c0 Ha = NI ,
driving mode utilized in a noncontact electromagnetic loading device presented by the authors in Ref. [23] is utilized to obtain a linear output force. The working principle is shown in Fig. 2(b): Two symmetric combining electromagnets are operated together, and one of them is driven with the sum of the bias current i 0 and the control current ic and the other one with i 0 ic . The air gaps of the upper and lower combining electromagnets are denoted as c0 s and c0 + s , respectively. The total force applied on the rotator core or the spindle shaft is calculated with Eq. (7) and is given by
(2)
where li and Hi are the length and field intensity of the magnetic circuit in the stator and rotator core, respectively, c0 and Ha are the air gap and field intensity in the air gap, respectively, and N and I are the coil turns and the current, respectively. With Eqs. (1) and (2), the total flux density in one combining electromagnet is obtained from the expression
B = µ0
NI , ( l i / µ r , i + 2c 0 / µr , a )
Fa = F+
k=
ks =
(5)
(6)
For one combining electromagnet, the electromagnetic force generated by one stator pole is f /2 . With Eqs. (1) and (4), and given the angle between two adjacent poles 2 , the total electromagnetic force generated by one pair of combining electromagnets is expressed as
µ0 AN 2I 2 cos , 4c0 2
(9)
ks s
(10)
4ki 0 c02
cos ,
4ki02 c03
cos .
(11)
It is found that the force generated by the two symmetric combining electromagnets has a linear relationship with the control current ic . This configuration makes it possible to generate both positive and negative forces by adjusting the direction of the control current ic , which is very beneficial for active damping of milling chatter vibration. Meanwhile, with the configuration shown in Fig. 2(a), the force in both x and y directions is generated individually with the four pairs of symmetric combining electromagnets, and vibration of the two degrees of freedom can both be damped. The final designed solid model of the electromagnetic actuator and the fabricated assemblies are shown in Fig. 3. The key parameters of the proposed electromagnetic actuator are listed in Table 2.. The rotator is designed as an armillary to be installed in the spindle system shown in Fig. 1. It should also be noted that both the stator core and the rotator are fabricated with very thin, isolated silicon steel sheet (with a 0.35 mm thickness), reducing eddy current in the stator and rotator produced by the magnetic fields and enabling the actuator to work for a long time without a significant temperature rise. Different from what was done in Ref. [13], in which a permanent magnet was utilized to offer bias magnetic fields, a specific current amplifier as shown in Fig. 4 is designed to output the desired control current to the actuator with control voltage signal vc , and the bias current i 0 can be adjusted with the designed amplifier. The output control current ic and input control
where Va = 2c0 Aa and Aa is the cross-sectional area along the magnetic circuit, which equals the cross-sectional area of the stator pole, A , rather than the curved surface area. With the principle of virtual displacement, the attraction force is derived as
F=
(8)
in which
The attraction force of the combining electromagnet is generated at the boundary of media with different permeabilities. The energy stored in the air gap is expressed as
B 2 Aa Ea = a , c0 µ0
1 µ AN 2 , 4 0
Fa = ki ic
ki =
f=
(i 0 i c ) 2 )cos , (c 0 + s ) 2
For the application of the electromagnetic actuator in this study, the rotator core is mounted on the spindle shaft, and, during the milling c0 , so Eq. (8) can be simplified and linearized as process s
(3)
(4)
1 Ea = Ba Ha Va, 2
(i 0 + i c ) 2 (c 0 s ) 2
with
where µr , i and µr , a are the relative permeability in iron and air, re1 in iron (the stator core spectively. Given that µr , a ≈ 1 in air and µr , i and rotator core), Eq. (3) is replaced with
NI B = µ0 , 2c 0
F = k(
(7)
The generated electromagnetic force is adjusted by altering the current applied in the coil windings. However, the relationship between the current I and the electromagnetic force F is nonlinear, as shown in Eq. (7). In control theory, the actuator is usually desired to be linear for the convenience of controller design. In this study, the same differential 205
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 5. Schematic of active damping of vibration in the milling process. Fig. 3. Electromagnetic actuator. (a) Solid model. (b) Fabricated stator and rotator assemblies.
The electromagnetic actuator then applies a control force to damp the vibration of the tool tip when chatter occurs. However, the control force Fa (t ) cannot directly act on the tool tip, so the vibration of the tool tip should be suppressed indirectly. Displacement sensors mounted near the electromagnetic actuator measure the vibration signals s1 (t ) in x and y directions, and the controller outputs control signals to each of two amplifiers and then the control current is applied to the actuator, causing the control forces to act on the rotating spindle shaft to damp the vibration in the x and y directions indirectly. AMBs in rotating machinery are used to control an unstable rotor and allow it to rotate about an equilibrium point [22]. Similar to the application of AMBs, deployment of an electromagnetic actuator here provides a restoring control force similar to the mechanical spring and damper to control the milling vibration. Obviously, the simplest approach one might set up for the desired control force can be described by the expression
Table 2 Electromagnetic actuator parameters. Parameter
Value
Air gap, c0 Pole cross-sectional area, A Number of coil turns for two adjacent poles, N Angle between the two adjacent poles, 2 Bias current, i 0 Maximum coil current, Imax Maximum force
0.5 mm 190 mm2 80 45° 5A 10 A 150 N
f=
Ks
(12)
Cs,
where K and C denote the stiffness and damper, respectively. With Eq. (10), the control current can be designed with the expression
K
ic (s ) =
ks ki
s
C s, ki
(13)
A well-known control law PD controller, with proportional and differential feedback with control parameters Kp and K d , respectively, can then be utilized for vibration control:
Fig. 4. Designed amplifier for the electromagnetic actuator.
voltage signal vc also have a linear relationship within a 1,200 Hz bandwidth, which is designed as 1 A/V, and the maximum current output is 10 A. When the frequency of the control voltage exceeds 1,200 Hz, the output current decreases with the increase of frequency, leading to the decrease of the electromagnetic force. It should be noted that the designed current amplifier is not the only factor limits the system's bandwidth. As reported in Ref. [22], when the operating frequency of current is larger than 2 kHz, serious eddy current emerges in the stator and rotator, which significantly decreases the electromagnetic force, and the current coefficient ki is not a constant value anymore, and it can keep constant at maximum 1.4 kHz with a 0.35 mm thickness of silicon steel sheet. When a larger bandwidth of the actuator system is desired, an improved circuit design of current amplifier and structure of stator and rotator is needed. A nonlinear controller is also helpful to suppress the vibration at higher frequency, in which the actuator has a non-linear output.
Kp =
K
ks
Kd =
C . ki
ki
, (14)
With Eq. (14), it can be found that both the equivalent stiffness and damping can be adjusted with Kp and K d , respectively. Fig. 6 shows the control block diagram. With transfer functions between the vibrations of the tool tip and the measuring position, Gs2, s1 (s = x , y ),considered, the vibration of the tool tip can be well controlled by minimizing the vibration of the acting position of the electromagnetic actuator indirectly. Because the PD controller does not require the dynamics of the controlled system, the transfer functions Gs2, Fc and Gs1, Fa shown in the block diagram need not be identified in actual operation. 4. Experiments and discussion The prototype of designed spindle system integrated with an electromagnetic actuator (shown in Fig. 1) was fabricated and mounted on a three-axis machine tool (Fig. 7(a)). In each direction, two eddy current displacement sensors are used to measure the vibration, with a sensitivity 8 V/mm and maximum measuring range 1 mm, and its dynamic attenuation coefficient is less than 1% in 0–1 kHz and 5% in 0–10 kHz, which can satisfy the measuring requirements. In this section, the performance of the fabricated prototype is tested with a series of experiments.
3. Active damping of chatter vibration in the milling process Fig. 5 presents the schematic of active damping of vibration in the milling process with the designed electromagnetic actuator integrated into the spindle system. During the milling process, cutting forces Fc (t ) excite the vibration of the tool tip (s2 (t ), (s = x , y ) ) in both x and y directions, and a regenerative effect occurs that might lead to chatter under certain cutting conditions, limiting the critical cutting depth [1]. 206
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 6. Control block diagram with a PD controller.
4.1. Plant identification Because the electromagnetic actuator has two degrees of freedom, and control forces are applied in x and y directions with each measured vibration signal, respectively, the coupling effects between each degree of freedom should be tested firstly. Transfer functions between the vibrations of the tool tip and measuring position, Gs2, s1 (s = x , y ), were also measured. A sinusoidal sweep voltage signal with an amplitude of 1 V and a range from 10 to 1,200 Hz was applied to the amplifiers for x and y directions, respectively, and the corresponding response signals in both directions were measured simultaneously. Fig. 8 shows the response in the two directions when the excitation was applied in the x and y directions, and the open-loop frequency responses from the command current to the response displacement were also measured. It can be found that the amplitudes of the direct displacement response are higher than the those of the cross displacement response when the sinusoidal sweep excitation was applied in x and y directions, respectively, and the amplitudes of the cross frequency response are much lower than those of the direct frequency response. Consequently, coupling between the two degrees of freedom of the electromagnetic actuator can be ignored, and the actuator can be controlled individually with the control block diagram in Fig. 6. Transfer functions between the tool tip and the measuring position in both x and y directions were then measured with an impact test, the experimental setup of which is shown in Fig. 7(b). A dummy tool with an overhang of 35 mm and a diameter of 7 mm was mounted on the spindle for the convenience of measurement. Impact excitation was applied on the tip of the dummy tool with a PCB 086C03 hammer, and
Fig. 8. Measured displacement responses and frequency responses from sinusoidal sweep current (i x , i y ) to the measured displacements ( x , y ). (a) displacement responses in x direction and (b) y direction with excitation in x direction; (c) frequency responses in x direction and (d) y direction with excitation in x direction; (e) displacement responses in x direction and (f) y direction with excitation in y direction; (g) frequency responses in x direction and (h) y direction with excitation in y direction.
the displacement sensor installed in the spindle and an additional displacement sensor were utilized to measure the corresponding response at measuring position 1 and tool tip 2 simultaneously. The tests were performed in both x and y directions, and the LMS modal measurement and analysis system was used for the measurement and signal processing. The obtained transfer functions between the two positions are shown in Fig. 9. Considering the measurement error and noise, and the advantage of PD controller that does not require actuate dynamics of the controlled system, an approximate linear relationship with Gx2, x1 5 and Gy2 , y1 5 were defined. Therefore, the vibration of tool tip could be well suppressed indirectly with the designed control block diagram shown in Fig. 6. 4.2. Improvement of stiffness and damping of spindle system The static stiffness of the developed spindle system are measured
Fig. 7. Experimental setup. (a) three-axis machine tool with proposed spindle system; (b) setup for impact test; (c) setup for static stiffness measuring. 207
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 9. Measured transfer functions between the tool tip and sensor measuring position in (a) x direction; and (b) y direction.
with the setup shown in Fig. 7 (c). Without proportional feedback control, the stiffness values are 1.879 and 1.891 N/μm in x and y directions, respectively. With proportional feedback control and tuning of the proportional controller parameter Kp , the static stiffness values increase to 2.07 and 2.18 N/μm in the two directions, respectively. To validate the active damping performance of the designed spindle system, in both x and y directions, the proportional controller parameter was set as Kp = 0 and only the differential feedback controller was activated. The frequency response functions (FRFs) of the tool tip in both x and y directions were then measured with and without active damping. Though the damping of the spindle system could be improved with a higher differential controller parameter K d , unstable vibration will also occur as a result of noise from the feedback signal, so an appropriate value should be tuned (here, being set as K d = 18) in both x and y directions. Fig. 10 shows the measured FRFs with the impact test. It can be found that the first modal frequency and second modal frequency in the two directions are very close to each other, indicating symmetrical dynamics of the developed spindle system. In the x direction, both the first modal (960 Hz) and second modal (1410 Hz) are damped with active damping, and the dynamic stiffness values are increased by factors of 3.67 and 1.78, respectively. Similarly, the first modal (961 Hz) and second modal (1414 Hz) are also damped with in dynamic stiffness in the y direction increasing by factors of 2.89 and 2.75, respectively.
Fig. 11. Vibration signals before and after adaptive filtering: (a) time domain signals and (b) spectrum of signals.
actuator during the milling process was validated. In the milling process, a carbide end mill with the same diameter and overhang of the dummy tool utilized in the impact test was chosen, and the number of teeth was three. The workpiece material was AL6061, and the milling speed, radial cutting depth, axial cutting depth, and feed rate were set as 10,000 rpm, 3.5 mm, 2.5 mm, and 300 mm/min, respectively. During the milling operation, a Brüel & Kjær data acquisition system was used to measure the vibration signal with an accelerometer fixed on the spindle. In the milling process, the displacement sensors not only detect the vibration, but also the run-outs which are due to the tool rotation, geometrical error and sensor's installation error. The spindle speed frequency and its harmonics caused by the run-outs lead to the unnecessary excitation of actuator, and significantly affect the performance of active damping. In order to eliminate these undesired harmonics in the detected signals, an adaptive filter presented by the authors in Ref. [24] was used, with which the spindle speed frequency and its harmonics can be effectively filtered out. Fig. 11 shows the detected signals before and after filtering, and the spindle speed is 5,000 rpm and the milling process is stable. It is found that the amplitude of signals decrease significantly after filtering (Fig. 11(a)), and the
4.3. Milling test results Milling experiments were also performed with and without active damping on the three-axis machine tool (shown in Fig. 7 (a)), and the performance of the spindle system integrated with an electromagnetic
Fig. 10. Frequency response functions measured at the tool tip with and without active damping in (a) the x direction and (b) the y direction. 208
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 12. Milling experiment results without active damping ((a) workpiece surface; (c) acceleration signal in the time domain; (e) spectrum of acceleration signal) and with active damping ((b) workpiece surface; (d) acceleration signal in the time domain; (f) spectrum of acceleration signal).
comparison shown in Fig. 11(b) also show that the spindle rotation frequency and its harmonics are effectively filtered out, which means the harmonics in the detected signals will not affect the output of controller for the active damping of milling chatter. The details of the proposed adaptive filter was presented in Ref. [24], and the order and step size factor of the active filter have been carefully redesigned to achieve the desired filtering performance. In addition, a low-pass filter was also utilized to filter out the high-frequency noise in the detected signals. Fig. 12 shows the surface finishes and corresponding vibration signal characteristics in both the time and frequency domains without and with active damping. Serious chatter marks can be easily seen without active damping (Fig. 12(a)), while the surface finishes (Fig. 12(b)) are much better with active damping. Meanwhile, the magnitude of vibration decreases with the active damping force introduced to the milling process (Fig. 12(c) and (d)). The spectra shown in Fig. 12(e) and (f) also prove that chatter vibration has been well suppressed with the active damping force.
first modal frequency is obtained in the x direction. Milling experiments with and without active damping also illustrate that milling chatter vibration can be well damped actively with the developed spindle system. The dynamic characteristics of the system are not considered with a PD controller, and an advanced controller that can address the dynamics of the milling process will be developed in the future. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant No. 51575434 and the Key National Science and Technology Projects of China (No. 2017ZX04013001) and Natural Science Basic Research Plan in Shaanxi Province of China (No. 2018JM5163). The authors express their gratitude for the support. References [1] Quintana G, Ciurana J. Chatter in machining processes: a review. Int J Mach Tool Manuf 2011;51(5):363–76. [2] Munoa J, Beudaert X, Dombovari Z, Altintas Y, Budak E, Brecher C, Stepan G. Chatter suppression techniques in metal cutting. CIRP Ann 2016;65(2):785–808. [3] Yang Y, Dai W, Liu Q. Design and implementation of two-degree-of-freedom tuned mass damper in milling vibration mitigation. J Sound Vib 2015;335:78–88. [4] Yang Y, Munoa J, Altintas Y. Optimization of multiple tuned mass dampers to suppress machine tool chatter. Int J Mach Tool Manuf 2010;50(9):834–42. [5] Burtscher J, Fleischer J. Adaptive tuned mass damper with variable mass for chatter avoidance. CIRP Ann 2017;66(1):397–400. [6] Moradi H, Bakhtiari-Nejad F, Movahhedy MR, Vossoughi G. Stability improvement and regenerative chatter suppression in nonlinear milling process via tunable vibration absorber. J Sound Vib 2012;331(21):4668–90. [7] Matsubara A, Taniyama Y, Wang J, Kono D. Design of a support system with a pivot mechanism for suppressing vibrations in thin-wall milling. CIRP Ann 2017;66(1):381–4. [8] Fei J, Lin B, Yan S, Ding M, Xiao J, Zhang J, Zhang X, Ji C, Sui T. Chatter mitigation using moving damper. J Sound Vib 2017;410:49–63. [9] Tanaka H, Obata F, Matsubara T, Mizumoto H. Active chatter suppression of slender boring bar using piezoelectric actuators. JSME Int J., Ser. C 1994;37(3):601–6. [10] Redmond JM, Barney P, Smith D. Development of an active boring bar for increased chatter immunity. Smart structures and materials, vol. 3044. International Society for Optics and Photonics; 1997. p. 295–307. Industrial and Commercial Applications of Smart Structures Technologies. [11] Andrén L, Håkansson L. Active vibration control of boring bar vibrations. 2004. [12] Albertelli P, Elmas S, Jackson MR, Bianchi G, Parkin RM, Monno M. Active spindle system for a rotary planing machine. Int J Adv Manuf Technol 2012;63(9–12):1021–34. [13] Chen F, Lu X, Altintas Y. A novel magnetic actuator design for active damping of
5. Conclusions To suppress milling chatter vibration and improve surface finishes, a novel spindle system is presented in this paper. A noncontact electromagnetic actuator with two degrees of freedom is developed and integrated into the designed spindle system compactly. A differential driving mode is utilized for the electromagnetic actuator to obtain a linear relationship between the control current and the output force, making the actuator more suitable for vibration control. Displacement sensors mounted near the actuator measure the vibration of the rotating spindle shaft and provide feedback signals for the developed PD controller. To actively damp the vibration of the tool tip effectively, transfer functions between the tool tip and the sensors' measuring position on the spindle shaft in both x and y directions are considered in the control block diagram and measured with an impact test. The active damping performance of the designed spindle system, in both x and y directions, is also validated with impact tests and milling experiments. The measured FRFs of the tool tip with and without active damping show that the spindle system is well damped in both x and y directions, and a maximum increase (by a factor of 3.67) of dynamic stiffness at the 209
Precision Engineering 57 (2019) 203–210
S. Wan, et al. machining tools. Int J Mach Tool Manuf 2014;85:58–69. [14] Lu X, Chen F, Altintas Y. Magnetic actuator for active damping of boring bars. CIRP Ann - Manuf Technol 2014;63(1):369–72. [15] Kakinuma Y, Enomoto K, Hirano T, Ohnishi K. Active chatter suppression in turning by band-limited force control. CIRP Ann - Manuf Technol 2014;63(1):365–8. [16] Ma H, Wu J, Yang L, Xiong Z. Active chatter suppression with displacement-only measurement in turning process. J Sound Vib 2017;401:255–67. [17] Chen M, Knospe CR. Control approaches to the suppression of machining chatter using active magnetic bearings. IEEE Trans Control Syst Technol 2007;15(2):220–32. [18] Monnin J, Kuster F, Wegener K. Optimal control for chatter mitigation in milling—Part 1: modeling and control design. Control Eng Pract 2014;24:156–66. [19] Monnin J, Kuster F, Wegener K. Optimal control for chatter mitigation in milling—Part 2: experimental validation. Control Eng Pract 2014;24:167–75.
[20] Gourc E, Seguy S, Arnaud L. Chatter milling modeling of active magnetic bearing spindle in high-speed domain. Int J Mach Tool Manuf 2011;51(12):928–36. [21] Knospe CR. Active magnetic bearings for machining applications. Control Eng Pract 2007;15(3):307–13. [22] Schweitzer G, Maslen EH. Magnetic bearings: theory, design, and application to rotating machinery. Berlin: Springer; 2009 Jan. [23] Wan, S., Hong, J., Su, W., Li, X., Sun, Y., Chen, W. Measurement of dynamic performances of high-speed rotating spindle by non-contact electromagnetic loading device. In ASME 2017 international mechanical engineering congress and exposition (pp. V002T02A095-V002T02A095). American Society of Mechanical Engineers. [24] Wan S, Li X, Chen W, Hong J. Investigation on milling chatter identification at early stage with variance ratio and Hilbert–Huang transform. Int J Adv Manuf Technol 2018;95(9–12):3563–73.
210
Contents lists available at ScienceDirect
Precision Engineering journal homepage: www.elsevier.com/locate/precision
Active damping of milling chatter vibration via a novel spindle system with an integrated electromagnetic actuator
T
Shaoke Wana,b,c, Xiaohu Lia,b,∗, Wenjun Sua,b, Junpeng Yuana,b, Jun Honga,b, Xiaoliang Jinc a
Key Laboratory of Education Ministry for Modern Design & Rotor-Bearing System, Xi'an Jiaotong University, Xi'an, Shaanxi, China School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, China c Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada b
ARTICLE INFO
ABSTRACT
Keywords: Active damping Milling chatter vibration Electromagnetic actuator
Self-excited vibration, widely referred to as chatter, has always been a limitation and challenge in machining. To suppress milling chatter vibration and improve surface finishes, a novel spindle system is proposed in this study. A noncontact electromagnetic actuator with two degrees of freedom is developed and integrated into the designed spindle system compactly. A differential driving mode is utilized for the electromagnetic actuator to obtain a linear output of actuator force, making the actuator more applicable for vibration control. Displacement sensors mounted near the actuator measure the vibration of the rotating spindle shaft and provide feedback signals for the developed proportional-derivative controller. The active damping performance of the designed spindle system with an integrated electromagnetic actuator, in both x and y directions, is also validated with impact tests and milling experiments, and a maximum increase (by factors of 3.67 and 2.89 in x and y directions, respectively) of dynamic stiffness at the first modal frequency is obtained. Milling experiment results with and without active damping also illustrate that milling chatter vibration has been well damped actively with the developed spindle system.
1. Introduction Chatter vibrations result from regenerative dynamic chip thickness during machining, are always a major productivity limitation, and lead to poor, wavy surface finishes, decreasing the life of mechanical components [1]. Consequently, chatter suppression techniques have become one of the major concerns in machining in the past few decades. Because cutting stability is affected by the dynamic parameters of machine tools, system damping enhancement has been one of the ideas promoted to suppress chatter vibration [2]. Damping can be increased passively and actively. Because of their simplicity and reliability, passive damping techniques have been presented for chatter suppression by many researchers. Yang attached a tuned mass damper [3,4] to a specific support of the workpiece during the milling process and improved machining stability. However, the tuned mass damper required adjustment for different workpiece structures. Burtscher [5] presented a tuned mass damper fixed onto the spindle head of a machine tool, and variable mass was utilized to adapt its eigenfrequency to the dominant frequency of the machine tool, but the dimension of the mass damper was large. Hamed [6] designed a tunable vibration absorber set composed of mass, spring, and dashpot
∗
elements and aimed to suppress regenerative chatter by adjusting the supported position on the extension of the tool and the stiffness of the spring in the milling process, but only theoretical results were shown and no prototype was presented. Matsubara [7] proposed a support system with a pivot mechanism providing damping of the vibration modes for thin-wall milling. Fei [8] proposed a moving damper during the milling process, improving the system chatter stability, but it was also designed for thin-wall milling. Though passive dampers entail reasonable cost and have the advantage of simplicity, a large space is needed, the damping effect is limited when dynamic properties vary, and the dampers are difficult to integrate into the machine tool. In active damping, an active control force is introduced to the cutting system with specific actuators, and parameters related to cutting vibration are measured with sensors as a feedback signal. The active damping of chatter vibration has been widely performed in boring [9–14] and turning processes [15–17], and the control force mostly acts on the tool directly to obtain an excellent damping effect. However, the rotating tool limits the possibilities for directly applying an active control force on the tool during the milling process. Similar to the applications of piezoelectric actuators in Refs. [9–12,16], Monnin's [18,19] active spindle with four piezoelectric actuators applied a
Corresponding author. No. 28 Xianning West Road, Xi'an, Shaanxi, 710049, China. E-mail address: [email protected] (X. Li).
https://doi.org/10.1016/j.precisioneng.2019.04.007 Received 13 December 2018; Received in revised form 22 April 2019; Accepted 22 April 2019 Available online 26 April 2019 0141-6359/ © 2019 Elsevier Inc. All rights reserved.
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
control force on the outer ring of spindle bearings to control chatter vibration. However, the extra heat in the bearings caused by the applied radial force could not be ignored, and the active control force cannot be acted on the rotating tool or spindle shaft directly. Moreover, the nonlinear hysteresis of the piezoelectric actuators could not be ignored. Because electromagnetic actuators can generate noncontact magnetic forces and almost no hysteresis exists, they have already been utilized in boring [13,14] and turning [17], where electromagnetic actuators are attached to the boring bar or to the turning tool holder. Active spindles supported with active magnetic bearings (AMBs) have also been proposed by Gourc [20] and Knospe [21] to increase the stability of the milling process. However, the industrial application of spindles supported with AMBs is limited by low radial cutting load capacity, and two control loops are needed for the operation of a high-speed rotating spindle shaft and control of the tool's vibration, posing challenges to reliability. Given the advantages of electromagnetic actuators for active damping of the cutting process and the disadvantage of active spindles supported with AMBs, a novel spindle system is developed for active damping of milling chatter vibration. An electromagnetic actuator is developed and integrated into the spindle system compactly. The milling process is modeled with two radial degrees of freedom, so the electromagnetic actuator is designed to apply a noncontact control force on the rotating spindle shaft in both x and y directions. Displacement sensors are also integrated to measure the vibration displacements of the spindle shaft. A simple and effective proportionalderivative (PD) controller is then developed, and velocity feedback is used for active damping of the spindle system, thereby damping milling chatter vibration effectively. Modal tests and cutting experiments are also performed, and the results demonstrate an increase of dynamic stiffness at the modal frequency and that the milling chatter vibration is well controlled actively. The rest of the paper is organized as follows. Section 2 presents the developed spindle system integrated with an electromagnetic actuator and the working principle of the actuator. Active damping with the PD controller is proposed in Section 3. Experiments are presented in Section 4, and the conclusions are drawn in Section 5.
Table 1 Parameters of the designed spindle. Maximum speed
Power
Torque
Bearing type
Bearing preload
Lubrication
24,000 rpm
3.5 kW
1.4 Nm
7006C/ 7005C
480 N
Grease
tool directly. Fig. 1 shows the configurations of the designed spindle system. An electromagnetic actuator is integrated into a conventional motorized spindle supported with two sets of angular contact ball bearings and placed between the front bearings and the tool. The built-in motor offers speed and torque. In the spindle system, angular contact ball bearings ensure stiffness and rotation accuracy of the whole spindle system, and the electromagnetic actuator is utilized to generate a noncontact electromagnetic force on the rotating spindle shaft to actively damp tool vibration. In each radial direction, two displacement sensors are arranged symmetrically to measure the vibration of the rotating shaft accurately. The structure of the designed prototype is quite compact and quite similar to that of a fabricable industrial product. The electromagnetic actuator can apply a noncontact force on the high-speed rotating spindle shaft with almost no hysteresis, and there is no rotating stability problem for the spindle shaft supported only with AMBs as reported in Refs. [20,21]. An encoder is also mounted at the end of the spindle for the closed-loop control of spindle speed. In addition, some other information about the designed spindle is given in Table 1. Due to small-scale components are utilized, the power and torque of the prototype are lower than a typical commercial milling spindle system, and its dimensions and stiffness are also smaller than the typical ones. However, the presented active damping method and configuration of system is suitable for a commercial milling system, in which a larger dimension of actuator with high actuator capacity can be installed. 2.2. Electromagnetic actuator design Fig. 2(a) shows a schematic of the designed electromagnetic actuator. A rotator core, a stator core, and coil windings around the stator core constitute the actuator. There are eight stator poles with a symmetric layout, and the two adjacent poles together make up a combining electromagnet. When current is applied in the coil windings, a magnetic field emerges in the combining electromagnet. The magnetic field intensity H and flux density B are usually utilized to describe the strength of magnetic field, and their relationship is given [22].
2. Spindle system integrated with an electromagnetic actuator 2.1. Configuration of the developed spindle system During the milling process, chatter vibration occurs between the tool and the workpiece. Because the workpiece can usually be assumed to be rigid, the main idea is to damp the vibrations of the tool to obtain better surface finishes. Actively damping the vibration of a rotating tool is best accomplished by applying an active control force on the rotating
B = µ 0 µr H,
Fig. 1. Configurations of the developed spindle system integrated with an electromagnetic actuator. 204
(1)
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 2. Schematics of (a) the electromagnetic actuator and (b) the working principle.
where µ 0 = 4 × 10 7V s /(A m) is magnetic permeability of vacuum and µr is the relative permeability, which depends on the medium in which the magnetic field acts. The flux is assumed as running entirely along the magnetic circuit with cross-sectional area A , where the cross sections in the iron and air gap are equal and equal to the cross section of the stator poles. The magnetic circuit follows the form
H ds = li Hi + 2c0 Ha = NI ,
driving mode utilized in a noncontact electromagnetic loading device presented by the authors in Ref. [23] is utilized to obtain a linear output force. The working principle is shown in Fig. 2(b): Two symmetric combining electromagnets are operated together, and one of them is driven with the sum of the bias current i 0 and the control current ic and the other one with i 0 ic . The air gaps of the upper and lower combining electromagnets are denoted as c0 s and c0 + s , respectively. The total force applied on the rotator core or the spindle shaft is calculated with Eq. (7) and is given by
(2)
where li and Hi are the length and field intensity of the magnetic circuit in the stator and rotator core, respectively, c0 and Ha are the air gap and field intensity in the air gap, respectively, and N and I are the coil turns and the current, respectively. With Eqs. (1) and (2), the total flux density in one combining electromagnet is obtained from the expression
B = µ0
NI , ( l i / µ r , i + 2c 0 / µr , a )
Fa = F+
k=
ks =
(5)
(6)
For one combining electromagnet, the electromagnetic force generated by one stator pole is f /2 . With Eqs. (1) and (4), and given the angle between two adjacent poles 2 , the total electromagnetic force generated by one pair of combining electromagnets is expressed as
µ0 AN 2I 2 cos , 4c0 2
(9)
ks s
(10)
4ki 0 c02
cos ,
4ki02 c03
cos .
(11)
It is found that the force generated by the two symmetric combining electromagnets has a linear relationship with the control current ic . This configuration makes it possible to generate both positive and negative forces by adjusting the direction of the control current ic , which is very beneficial for active damping of milling chatter vibration. Meanwhile, with the configuration shown in Fig. 2(a), the force in both x and y directions is generated individually with the four pairs of symmetric combining electromagnets, and vibration of the two degrees of freedom can both be damped. The final designed solid model of the electromagnetic actuator and the fabricated assemblies are shown in Fig. 3. The key parameters of the proposed electromagnetic actuator are listed in Table 2.. The rotator is designed as an armillary to be installed in the spindle system shown in Fig. 1. It should also be noted that both the stator core and the rotator are fabricated with very thin, isolated silicon steel sheet (with a 0.35 mm thickness), reducing eddy current in the stator and rotator produced by the magnetic fields and enabling the actuator to work for a long time without a significant temperature rise. Different from what was done in Ref. [13], in which a permanent magnet was utilized to offer bias magnetic fields, a specific current amplifier as shown in Fig. 4 is designed to output the desired control current to the actuator with control voltage signal vc , and the bias current i 0 can be adjusted with the designed amplifier. The output control current ic and input control
where Va = 2c0 Aa and Aa is the cross-sectional area along the magnetic circuit, which equals the cross-sectional area of the stator pole, A , rather than the curved surface area. With the principle of virtual displacement, the attraction force is derived as
F=
(8)
in which
The attraction force of the combining electromagnet is generated at the boundary of media with different permeabilities. The energy stored in the air gap is expressed as
B 2 Aa Ea = a , c0 µ0
1 µ AN 2 , 4 0
Fa = ki ic
ki =
f=
(i 0 i c ) 2 )cos , (c 0 + s ) 2
For the application of the electromagnetic actuator in this study, the rotator core is mounted on the spindle shaft, and, during the milling c0 , so Eq. (8) can be simplified and linearized as process s
(3)
(4)
1 Ea = Ba Ha Va, 2
(i 0 + i c ) 2 (c 0 s ) 2
with
where µr , i and µr , a are the relative permeability in iron and air, re1 in iron (the stator core spectively. Given that µr , a ≈ 1 in air and µr , i and rotator core), Eq. (3) is replaced with
NI B = µ0 , 2c 0
F = k(
(7)
The generated electromagnetic force is adjusted by altering the current applied in the coil windings. However, the relationship between the current I and the electromagnetic force F is nonlinear, as shown in Eq. (7). In control theory, the actuator is usually desired to be linear for the convenience of controller design. In this study, the same differential 205
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 5. Schematic of active damping of vibration in the milling process. Fig. 3. Electromagnetic actuator. (a) Solid model. (b) Fabricated stator and rotator assemblies.
The electromagnetic actuator then applies a control force to damp the vibration of the tool tip when chatter occurs. However, the control force Fa (t ) cannot directly act on the tool tip, so the vibration of the tool tip should be suppressed indirectly. Displacement sensors mounted near the electromagnetic actuator measure the vibration signals s1 (t ) in x and y directions, and the controller outputs control signals to each of two amplifiers and then the control current is applied to the actuator, causing the control forces to act on the rotating spindle shaft to damp the vibration in the x and y directions indirectly. AMBs in rotating machinery are used to control an unstable rotor and allow it to rotate about an equilibrium point [22]. Similar to the application of AMBs, deployment of an electromagnetic actuator here provides a restoring control force similar to the mechanical spring and damper to control the milling vibration. Obviously, the simplest approach one might set up for the desired control force can be described by the expression
Table 2 Electromagnetic actuator parameters. Parameter
Value
Air gap, c0 Pole cross-sectional area, A Number of coil turns for two adjacent poles, N Angle between the two adjacent poles, 2 Bias current, i 0 Maximum coil current, Imax Maximum force
0.5 mm 190 mm2 80 45° 5A 10 A 150 N
f=
Ks
(12)
Cs,
where K and C denote the stiffness and damper, respectively. With Eq. (10), the control current can be designed with the expression
K
ic (s ) =
ks ki
s
C s, ki
(13)
A well-known control law PD controller, with proportional and differential feedback with control parameters Kp and K d , respectively, can then be utilized for vibration control:
Fig. 4. Designed amplifier for the electromagnetic actuator.
voltage signal vc also have a linear relationship within a 1,200 Hz bandwidth, which is designed as 1 A/V, and the maximum current output is 10 A. When the frequency of the control voltage exceeds 1,200 Hz, the output current decreases with the increase of frequency, leading to the decrease of the electromagnetic force. It should be noted that the designed current amplifier is not the only factor limits the system's bandwidth. As reported in Ref. [22], when the operating frequency of current is larger than 2 kHz, serious eddy current emerges in the stator and rotator, which significantly decreases the electromagnetic force, and the current coefficient ki is not a constant value anymore, and it can keep constant at maximum 1.4 kHz with a 0.35 mm thickness of silicon steel sheet. When a larger bandwidth of the actuator system is desired, an improved circuit design of current amplifier and structure of stator and rotator is needed. A nonlinear controller is also helpful to suppress the vibration at higher frequency, in which the actuator has a non-linear output.
Kp =
K
ks
Kd =
C . ki
ki
, (14)
With Eq. (14), it can be found that both the equivalent stiffness and damping can be adjusted with Kp and K d , respectively. Fig. 6 shows the control block diagram. With transfer functions between the vibrations of the tool tip and the measuring position, Gs2, s1 (s = x , y ),considered, the vibration of the tool tip can be well controlled by minimizing the vibration of the acting position of the electromagnetic actuator indirectly. Because the PD controller does not require the dynamics of the controlled system, the transfer functions Gs2, Fc and Gs1, Fa shown in the block diagram need not be identified in actual operation. 4. Experiments and discussion The prototype of designed spindle system integrated with an electromagnetic actuator (shown in Fig. 1) was fabricated and mounted on a three-axis machine tool (Fig. 7(a)). In each direction, two eddy current displacement sensors are used to measure the vibration, with a sensitivity 8 V/mm and maximum measuring range 1 mm, and its dynamic attenuation coefficient is less than 1% in 0–1 kHz and 5% in 0–10 kHz, which can satisfy the measuring requirements. In this section, the performance of the fabricated prototype is tested with a series of experiments.
3. Active damping of chatter vibration in the milling process Fig. 5 presents the schematic of active damping of vibration in the milling process with the designed electromagnetic actuator integrated into the spindle system. During the milling process, cutting forces Fc (t ) excite the vibration of the tool tip (s2 (t ), (s = x , y ) ) in both x and y directions, and a regenerative effect occurs that might lead to chatter under certain cutting conditions, limiting the critical cutting depth [1]. 206
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 6. Control block diagram with a PD controller.
4.1. Plant identification Because the electromagnetic actuator has two degrees of freedom, and control forces are applied in x and y directions with each measured vibration signal, respectively, the coupling effects between each degree of freedom should be tested firstly. Transfer functions between the vibrations of the tool tip and measuring position, Gs2, s1 (s = x , y ), were also measured. A sinusoidal sweep voltage signal with an amplitude of 1 V and a range from 10 to 1,200 Hz was applied to the amplifiers for x and y directions, respectively, and the corresponding response signals in both directions were measured simultaneously. Fig. 8 shows the response in the two directions when the excitation was applied in the x and y directions, and the open-loop frequency responses from the command current to the response displacement were also measured. It can be found that the amplitudes of the direct displacement response are higher than the those of the cross displacement response when the sinusoidal sweep excitation was applied in x and y directions, respectively, and the amplitudes of the cross frequency response are much lower than those of the direct frequency response. Consequently, coupling between the two degrees of freedom of the electromagnetic actuator can be ignored, and the actuator can be controlled individually with the control block diagram in Fig. 6. Transfer functions between the tool tip and the measuring position in both x and y directions were then measured with an impact test, the experimental setup of which is shown in Fig. 7(b). A dummy tool with an overhang of 35 mm and a diameter of 7 mm was mounted on the spindle for the convenience of measurement. Impact excitation was applied on the tip of the dummy tool with a PCB 086C03 hammer, and
Fig. 8. Measured displacement responses and frequency responses from sinusoidal sweep current (i x , i y ) to the measured displacements ( x , y ). (a) displacement responses in x direction and (b) y direction with excitation in x direction; (c) frequency responses in x direction and (d) y direction with excitation in x direction; (e) displacement responses in x direction and (f) y direction with excitation in y direction; (g) frequency responses in x direction and (h) y direction with excitation in y direction.
the displacement sensor installed in the spindle and an additional displacement sensor were utilized to measure the corresponding response at measuring position 1 and tool tip 2 simultaneously. The tests were performed in both x and y directions, and the LMS modal measurement and analysis system was used for the measurement and signal processing. The obtained transfer functions between the two positions are shown in Fig. 9. Considering the measurement error and noise, and the advantage of PD controller that does not require actuate dynamics of the controlled system, an approximate linear relationship with Gx2, x1 5 and Gy2 , y1 5 were defined. Therefore, the vibration of tool tip could be well suppressed indirectly with the designed control block diagram shown in Fig. 6. 4.2. Improvement of stiffness and damping of spindle system The static stiffness of the developed spindle system are measured
Fig. 7. Experimental setup. (a) three-axis machine tool with proposed spindle system; (b) setup for impact test; (c) setup for static stiffness measuring. 207
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 9. Measured transfer functions between the tool tip and sensor measuring position in (a) x direction; and (b) y direction.
with the setup shown in Fig. 7 (c). Without proportional feedback control, the stiffness values are 1.879 and 1.891 N/μm in x and y directions, respectively. With proportional feedback control and tuning of the proportional controller parameter Kp , the static stiffness values increase to 2.07 and 2.18 N/μm in the two directions, respectively. To validate the active damping performance of the designed spindle system, in both x and y directions, the proportional controller parameter was set as Kp = 0 and only the differential feedback controller was activated. The frequency response functions (FRFs) of the tool tip in both x and y directions were then measured with and without active damping. Though the damping of the spindle system could be improved with a higher differential controller parameter K d , unstable vibration will also occur as a result of noise from the feedback signal, so an appropriate value should be tuned (here, being set as K d = 18) in both x and y directions. Fig. 10 shows the measured FRFs with the impact test. It can be found that the first modal frequency and second modal frequency in the two directions are very close to each other, indicating symmetrical dynamics of the developed spindle system. In the x direction, both the first modal (960 Hz) and second modal (1410 Hz) are damped with active damping, and the dynamic stiffness values are increased by factors of 3.67 and 1.78, respectively. Similarly, the first modal (961 Hz) and second modal (1414 Hz) are also damped with in dynamic stiffness in the y direction increasing by factors of 2.89 and 2.75, respectively.
Fig. 11. Vibration signals before and after adaptive filtering: (a) time domain signals and (b) spectrum of signals.
actuator during the milling process was validated. In the milling process, a carbide end mill with the same diameter and overhang of the dummy tool utilized in the impact test was chosen, and the number of teeth was three. The workpiece material was AL6061, and the milling speed, radial cutting depth, axial cutting depth, and feed rate were set as 10,000 rpm, 3.5 mm, 2.5 mm, and 300 mm/min, respectively. During the milling operation, a Brüel & Kjær data acquisition system was used to measure the vibration signal with an accelerometer fixed on the spindle. In the milling process, the displacement sensors not only detect the vibration, but also the run-outs which are due to the tool rotation, geometrical error and sensor's installation error. The spindle speed frequency and its harmonics caused by the run-outs lead to the unnecessary excitation of actuator, and significantly affect the performance of active damping. In order to eliminate these undesired harmonics in the detected signals, an adaptive filter presented by the authors in Ref. [24] was used, with which the spindle speed frequency and its harmonics can be effectively filtered out. Fig. 11 shows the detected signals before and after filtering, and the spindle speed is 5,000 rpm and the milling process is stable. It is found that the amplitude of signals decrease significantly after filtering (Fig. 11(a)), and the
4.3. Milling test results Milling experiments were also performed with and without active damping on the three-axis machine tool (shown in Fig. 7 (a)), and the performance of the spindle system integrated with an electromagnetic
Fig. 10. Frequency response functions measured at the tool tip with and without active damping in (a) the x direction and (b) the y direction. 208
Precision Engineering 57 (2019) 203–210
S. Wan, et al.
Fig. 12. Milling experiment results without active damping ((a) workpiece surface; (c) acceleration signal in the time domain; (e) spectrum of acceleration signal) and with active damping ((b) workpiece surface; (d) acceleration signal in the time domain; (f) spectrum of acceleration signal).
comparison shown in Fig. 11(b) also show that the spindle rotation frequency and its harmonics are effectively filtered out, which means the harmonics in the detected signals will not affect the output of controller for the active damping of milling chatter. The details of the proposed adaptive filter was presented in Ref. [24], and the order and step size factor of the active filter have been carefully redesigned to achieve the desired filtering performance. In addition, a low-pass filter was also utilized to filter out the high-frequency noise in the detected signals. Fig. 12 shows the surface finishes and corresponding vibration signal characteristics in both the time and frequency domains without and with active damping. Serious chatter marks can be easily seen without active damping (Fig. 12(a)), while the surface finishes (Fig. 12(b)) are much better with active damping. Meanwhile, the magnitude of vibration decreases with the active damping force introduced to the milling process (Fig. 12(c) and (d)). The spectra shown in Fig. 12(e) and (f) also prove that chatter vibration has been well suppressed with the active damping force.
first modal frequency is obtained in the x direction. Milling experiments with and without active damping also illustrate that milling chatter vibration can be well damped actively with the developed spindle system. The dynamic characteristics of the system are not considered with a PD controller, and an advanced controller that can address the dynamics of the milling process will be developed in the future. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant No. 51575434 and the Key National Science and Technology Projects of China (No. 2017ZX04013001) and Natural Science Basic Research Plan in Shaanxi Province of China (No. 2018JM5163). The authors express their gratitude for the support. References [1] Quintana G, Ciurana J. Chatter in machining processes: a review. Int J Mach Tool Manuf 2011;51(5):363–76. [2] Munoa J, Beudaert X, Dombovari Z, Altintas Y, Budak E, Brecher C, Stepan G. Chatter suppression techniques in metal cutting. CIRP Ann 2016;65(2):785–808. [3] Yang Y, Dai W, Liu Q. Design and implementation of two-degree-of-freedom tuned mass damper in milling vibration mitigation. J Sound Vib 2015;335:78–88. [4] Yang Y, Munoa J, Altintas Y. Optimization of multiple tuned mass dampers to suppress machine tool chatter. Int J Mach Tool Manuf 2010;50(9):834–42. [5] Burtscher J, Fleischer J. Adaptive tuned mass damper with variable mass for chatter avoidance. CIRP Ann 2017;66(1):397–400. [6] Moradi H, Bakhtiari-Nejad F, Movahhedy MR, Vossoughi G. Stability improvement and regenerative chatter suppression in nonlinear milling process via tunable vibration absorber. J Sound Vib 2012;331(21):4668–90. [7] Matsubara A, Taniyama Y, Wang J, Kono D. Design of a support system with a pivot mechanism for suppressing vibrations in thin-wall milling. CIRP Ann 2017;66(1):381–4. [8] Fei J, Lin B, Yan S, Ding M, Xiao J, Zhang J, Zhang X, Ji C, Sui T. Chatter mitigation using moving damper. J Sound Vib 2017;410:49–63. [9] Tanaka H, Obata F, Matsubara T, Mizumoto H. Active chatter suppression of slender boring bar using piezoelectric actuators. JSME Int J., Ser. C 1994;37(3):601–6. [10] Redmond JM, Barney P, Smith D. Development of an active boring bar for increased chatter immunity. Smart structures and materials, vol. 3044. International Society for Optics and Photonics; 1997. p. 295–307. Industrial and Commercial Applications of Smart Structures Technologies. [11] Andrén L, Håkansson L. Active vibration control of boring bar vibrations. 2004. [12] Albertelli P, Elmas S, Jackson MR, Bianchi G, Parkin RM, Monno M. Active spindle system for a rotary planing machine. Int J Adv Manuf Technol 2012;63(9–12):1021–34. [13] Chen F, Lu X, Altintas Y. A novel magnetic actuator design for active damping of
5. Conclusions To suppress milling chatter vibration and improve surface finishes, a novel spindle system is presented in this paper. A noncontact electromagnetic actuator with two degrees of freedom is developed and integrated into the designed spindle system compactly. A differential driving mode is utilized for the electromagnetic actuator to obtain a linear relationship between the control current and the output force, making the actuator more suitable for vibration control. Displacement sensors mounted near the actuator measure the vibration of the rotating spindle shaft and provide feedback signals for the developed PD controller. To actively damp the vibration of the tool tip effectively, transfer functions between the tool tip and the sensors' measuring position on the spindle shaft in both x and y directions are considered in the control block diagram and measured with an impact test. The active damping performance of the designed spindle system, in both x and y directions, is also validated with impact tests and milling experiments. The measured FRFs of the tool tip with and without active damping show that the spindle system is well damped in both x and y directions, and a maximum increase (by a factor of 3.67) of dynamic stiffness at the 209
Precision Engineering 57 (2019) 203–210
S. Wan, et al. machining tools. Int J Mach Tool Manuf 2014;85:58–69. [14] Lu X, Chen F, Altintas Y. Magnetic actuator for active damping of boring bars. CIRP Ann - Manuf Technol 2014;63(1):369–72. [15] Kakinuma Y, Enomoto K, Hirano T, Ohnishi K. Active chatter suppression in turning by band-limited force control. CIRP Ann - Manuf Technol 2014;63(1):365–8. [16] Ma H, Wu J, Yang L, Xiong Z. Active chatter suppression with displacement-only measurement in turning process. J Sound Vib 2017;401:255–67. [17] Chen M, Knospe CR. Control approaches to the suppression of machining chatter using active magnetic bearings. IEEE Trans Control Syst Technol 2007;15(2):220–32. [18] Monnin J, Kuster F, Wegener K. Optimal control for chatter mitigation in milling—Part 1: modeling and control design. Control Eng Pract 2014;24:156–66. [19] Monnin J, Kuster F, Wegener K. Optimal control for chatter mitigation in milling—Part 2: experimental validation. Control Eng Pract 2014;24:167–75.
[20] Gourc E, Seguy S, Arnaud L. Chatter milling modeling of active magnetic bearing spindle in high-speed domain. Int J Mach Tool Manuf 2011;51(12):928–36. [21] Knospe CR. Active magnetic bearings for machining applications. Control Eng Pract 2007;15(3):307–13. [22] Schweitzer G, Maslen EH. Magnetic bearings: theory, design, and application to rotating machinery. Berlin: Springer; 2009 Jan. [23] Wan, S., Hong, J., Su, W., Li, X., Sun, Y., Chen, W. Measurement of dynamic performances of high-speed rotating spindle by non-contact electromagnetic loading device. In ASME 2017 international mechanical engineering congress and exposition (pp. V002T02A095-V002T02A095). American Society of Mechanical Engineers. [24] Wan S, Li X, Chen W, Hong J. Investigation on milling chatter identification at early stage with variance ratio and Hilbert–Huang transform. Int J Adv Manuf Technol 2018;95(9–12):3563–73.
210