sensors Article

A Novel Hybrid Error Criterion-Based Active Control Method for on-Line Milling Vibration Suppression with Piezoelectric Actuators and Sensors Xingwu Zhang 1,2 , Chenxi Wang 1 , Robert X. Gao 2 , Ruqiang Yan 2,3 , Xuefeng Chen 1, * and Shibin Wang 1 Received: 6 December 2015; Accepted: 4 January 2016; Published: 6 January 2016 Academic Editor: Vittorio M.N. Passaro 1

2 3

*

State Key Laboratory for Manufacturing System Engineering, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China; [email protected] (X.Z.); [email protected] (C.W.); [email protected] (S.W.) Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106, USA; [email protected] (R.X.G.); [email protected] (R.Y.) School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China Correspondence: [email protected]; Tel./Fax: +86-29-8266-3689

Abstract: Milling vibration is one of the most serious factors affecting machining quality and precision. In this paper a novel hybrid error criterion-based frequency-domain LMS active control method is constructed and used for vibration suppression of milling processes by piezoelectric actuators and sensors, in which only one Fast Fourier Transform (FFT) is used and no Inverse Fast Fourier Transform (IFFT) is involved. The correction formulas are derived by a steepest descent procedure and the control parameters are analyzed and optimized. Then, a novel hybrid error criterion is constructed to improve the adaptability, reliability and anti-interference ability of the constructed control algorithm. Finally, based on piezoelectric actuators and acceleration sensors, a simulation of a spindle and a milling process experiment are presented to verify the proposed method. Besides, a protection program is added in the control flow to enhance the reliability of the control method in applications. The simulation and experiment results indicate that the proposed method is an effective and reliable way for on-line vibration suppression, and the machining quality can be obviously improved. Keywords: active control; hybrid error criterion; milling process; vibration suppression

1. Introduction With the development of manufacturing application requirements, machining quality and precision are more critically required nowadays. However, processing vibration seriously affects the stability of cutting processes, and hence machining quality and precision. Kayhan et al. compared the machining quality between two components, in which the quality of one component is seriously reduced by chatter vibration [1]. Novakov et al. indicated by experiment that the chatter vibration will reduce the lifetime of cutting tools about 50%–80% [2]. Therefore, it’s significant to control the machining vibration to improve the machining quality and reliability of machine tools. There are mainly three methods for decreasing the influence of cutting vibration. The first one is to adjust the processing parameters in a stable region. As shown in Figure 1, the machining condition can be adjusted by changing the cutting depth and spindle speed. If the processing state is located in the green region, i.e., point A, the machining process will be stable and the machining quality will be satisfactory. However, if the processing state is located in the red region, the machining process will fail due to the chatter vibration. Unfortunately, nobody can

Sensors 2016, 16, 68; doi:10.3390/s16010068

www.mdpi.com/journal/sensors

Sensors 2016, 16, 68

2 of 12

Sensors 2016, 16, 68

2 of 12

guarantee the whole process will will always located inin the becauseititrelies relies on can guarantee the machining whole machining process always located thestable stableregion, region, because on experience the processing varies during whole machiningprocess. process. experience and theand processing state state varies during thethe whole machining

Chatter vibration A Current

Stable

Figure 1.1.Cutting themachining machiningprocess. process. Figure Cuttinglobe lobe of the

The second method is to optimize the structures and passive vibration control. For example, in

The second method is to optimize the structures and passive vibration control. For example, order to guarantee processing quality, some thin wall components in aerospace engineering are in order to guarantee processing quality, some thin wall engineering manufactured by real-time cutting compensation. That is, components the influences in of aerospace the deformation will be are manufactured by real-time cutting compensation. That is, the influences of the deformation will be simulated precisely first and then an opposite cutting compensation set in the machining process. simulated precisely first and then an opposite cuttingsimulation compensation set in the machining process. However, this needs a very precise and expensive with low-adaptability. The third However, thisisneeds a very precise and expensive simulation with low-adaptability. The method method real-time active vibration control, which can accomplish on-line control of thethird cutting vibrations to guarantee thecontrol, machining process be stable. It is an adaptive andofefficient way tovibrations deal is real-time active vibration which cantoaccomplish on-line control the cutting with this the problem, and thus has attracted many researchers’ and engineers’ attentionway [3,4].toDue to with to guarantee machining process to be stable. It is an adaptive and efficient deal their excellent vibration reduction performance, active vibration control methods have been applied this problem, and thus has attracted many researchers’ and engineers’ attention [3,4]. Due to their in many industrial areas, such as machine tools, airplanes, ships, cars and hard disks, etc. Taking excellent vibration reduction performance, active vibration control methods have been applied in machine tools as an example, Kakinuma implemented chatter vibration suppression by developing a many industrial areas, such as machine tools, airplanes, ships, cars and hard disks, etc. Taking machine hybrid control method and verified this method by experiments [5]. Hesselbach achieved noise and tools vibration as an example, Kakinuma implemented chatter vibration by system developing hybrid reduction for machining of composite boards by an suppression active clamping baseda on control method and verified this method experiments [5]. Hesselbach achieved noise vibration piezo-stack actuators, although a specialby work fixture is needed. [6]. Monnin proposed twoand different reduction forcontrol machining of composite an active clamping system based [7,8]. on piezo-stack optimal strategies and appliedboards chatterby vibration control for milling processes Long actuators, although a special workcontrol fixturesystem is needed. [6].onMonnin proposed different optimal control developed an active vibration based feedback controllertwo synthesis with a robust mixed sensitivity method for peripheral milling processes [9]. Xu achieved field balancing and strategies and applied chatter vibration control for milling processes [7,8]. Long developed an active harmonic vibration for high-speed rotors based on active magnetic bearings and two vibration control systemsuppression based on feedback controller synthesis with a robust mixed sensitivity method control methods, synchronous current reduction approach and repetitive control algorithm for peripheral milling processes [9]. Xu achieved field balancing and harmonic vibration[10]. suppression Apart from machine tools, active control methods have also been applied in other mechanical for high-speed rotors based on active magnetic bearings and two control methods, synchronous current engineering areas and obtained satisfactory effects. For example, in the area of vehicles, Kwak reduction approach and repetitive control algorithm [10]. proposed a hardware-in-the-loop system to estimate the efficiency of active vibration control of Apart machine tools, active control have also been in [11]. otherNguyen mechanical lateral from vibrations of railway vehicles by amethods magneto-rheological fluidapplied damper engineering areas and obtained satisfactory effects. For example, in the area of vehicles, Kwak proposed implemented a semi-active vehicle seat-suspension system based on a novel neuro-fuzzy controller a hardware-in-the-loop system to estimate the efficiency of active vibration control of lateral vibrations and achieved a satisfactory performance verified by experiments [12,13]. Sun investigated the problem of vibration in vehicularfluid active suspension by implemented simulation, in which the of railway vehicles by a suppression magneto-rheological damper [11].systems Nguyen a semi-active adaptive robust control strategy is used realizeneuro-fuzzy the disturbance suppression Li investigated vehicle seat-suspension system based on atonovel controller and [14]. achieved a satisfactory the adaptive sliding control [12,13]. problemSun for nonlinear active via the Takagi-Sugeno performance verified by mode experiments investigated thesuspension problem of vibration suppression in fuzzy approach [15]. vehicular active suspension systems by simulation, in which the adaptive robust control strategy is used to realize the disturbance suppression [14]. Li investigated the adaptive sliding mode control problem for nonlinear active suspension via the Takagi-Sugeno fuzzy approach [15]. Military equipment and other basic applications have also been explored. Daley introduced a new hybrid active/passive mounting system in vibration reduction of large marine machinery

Sensors 2016, 16, 68

3 of 12

rafts [16]. Structural vibration and structure-borne noise in water of a submerged finite cylindrical shell is investigated by an active vibration method based on macro fiber composites and an optimal control algorithm [17]. Zhang constructed a dynamic frequency characteristics active control method for vibration optimization of beam-plate systems and scaled underwater vehicle models [18,19]. Chamroon investigated active vibration control in multimode rotor-dynamic systems based on dynamic strain feedback and an optimal model-based controller synthesis [20]. Li presented an active control simulation of the acoustic and vibration response of a vibro-acoustic cavity of an airplane based on a PID controller and an Eulerian model [21]. Lin proposed a self-organizing fuzzy controller for active suspension systems, in which the optimal parameters could be obtained by the developed hybrid self-organizing fuzzy and radial basis function neural network controller [22]. Ferrari applied a positive position feedback algorithm in active vibration control of single-input single-output and multi-input multi-output systems and successfully mitigated the vibration of the first four natural modes of a sandwich plate [23]. Sun proposed a novel 3-D quasi-zero-stiffness system and applied it in active vibration control with satisfactory results [24]. Wu studied the accelerometer configuration measurement model for active control of vibration isolation platforms [25]. Her implemented vibration analysis of composite laminate plates bonded with piezoelectric patches for active control systems [26]. Although many control algorithms have been developed and many practical achievements have been made for vibration control, the efficiency, adaptability and anti-interference ability need to be addressed further. Since time-domain control algorithms are mainly used in these systems, the real-time performance is strict both for the control algorithm and hardware devices. Besides, one single time-domain error criterion is used to determine the control process. Therefore, it is easy to make the control process drop into local optimum results with less adaptability and anti-interference ability. In this paper, a novel hybrid error criterion frequency-domain LMS active control method is proposed to enhance the efficiency, adaptability and anti-interference ability of this kind of method in on-line vibration suppression, and verified on a milling process. First, the control algorithm is constructed in the frequency domain, so it is not sensitive to the real time performance. Then the correction formulations of the weights are derived by the steepest decent procedure. Third, a hybrid error criterion is proposed to improve the adaptability and anti-interference ability of the control algorithm and system. Finally, the control method is verified and investigated by simulation and experiments, and a protection program is added to enhance the reliability of this method in applications. 2. Control Algorithm Design LMS [27] is a classical and typical adaptive signal processing method, whose control scheme is simple and efficient, so it’s suitable for real-time active vibration control. Compared with the time-domain LMS control method, the frequency-domain LMS is not sensitive to the transient response and suitable for active vibration control with a periodic response, so the frequency-domain method is chosen as the core control scheme in this paper. Different from the traditional LMS method, the frequency-domain LMS constructed in this paper has three advantages. First, only one Fast Fourier Transform (FFT) is used in each control cycle and no Inverse Fast Fourier Transform (IFFT) is involved. Second, the control parameters are optimized to improve the efficiency. Third, a new hybrid error criterion is constructed to enhance the adaptability, robustness of the frequency-domain LMS method. 2.1. Control Scheme The frequency-domain LMS control scheme for active vibration control is shown in Figure 2, where, D is the frequency-domain destination signal. E is the error signal. F represents the optimized actuating parameters. y(t) is the time-domain vibration response and Y is the frequency-domain vibration response. “Sampling” represents the vibration data collection process. The control process runs according to the following steps. First, a vibration response y(t) is collected by “Sampling” at a determined sampling rate. Then the time-domain response y(t) is transformed to a frequency-domain signal Y by FFT. The difference between Y and D is then set as input for LMS controller to update

Sensors Sensors 2016, 16,2016, 68 16, 68

4 of 12

4 of 12

determined sampling rate. Then the time-domain response y(t) is transformed to a frequency-domain Y by FFT. The difference between Y and D sent is then input for LMS as the the weights W(n). Next,signal the optimized actuating parameters F are to set theascontrol system controller to update the weights W(n). Next, the optimized actuating parameters F are sent to the secondary vibration source to suppression the original vibration. This control cycle is repeated until control system as the secondary vibration source to suppression the original vibration. This control the difference between D and Y satisfies a preset precision. beprecision. seen from the flow that cycle is repeated until the difference between D and Y satisfiesIta can preset It can becontrol seen from the FFTthe is only used in each and once no IFFT is introduced, so the control flow is simplified and control flowonce that the FFT iscycle only used in each cycle and no IFFT is introduced, so the control flow time is simplified and the control time is reduced. the control is reduced.

Figure 2. Frequency-domain LMS control scheme.

Figure 2. Frequency-domain LMS control scheme. In order to make the control algorithm converge to the target solution, the frequency error and iterative functions should be constructed. The global J in thisthe control scheme error to In the order to make the control algorithm converge tofrequency the targeterror solution, frequency and be minimized by adjusting weights is defined as: the iterative functions should be constructed. The global frequency error J in this control scheme to be minimized by adjusting weights is defined 2 1 n as: 1 2

J 

1

2

 (d

i

 yi ) 

i 1

n ÿ

2

2

D  Y

(1)

1

where, di is the ith element of the D. yi|is the´ith element of the frequency-domain pdi ´signal yi q “ J “destination |D Y| |2 (1) 2 2 vibration response Y. i “1 The global frequency error J in Equation (1) represents the difference between the target signal where, and di isthe thevibration ith element of the destination signal frequency D. yi is the ith element of algorithm the frequency-domain response in the whole concerned range. The control can be effective only Y. in the condition of the frequency error J is to be diminished smoothly in the control vibration response process. the error iterative equation of the weights is constructed to guarantee the convergence. The globalTherefore, frequency J in Equation (1) represents the difference between the target signal The steepest descent method is used to obtain the iterative equation of the weights w(n) of controller:

and the vibration response in the whole concerned frequency range. The control algorithm can be w(n  1)  w (n)  ηJis w(nto ) be diminished smoothly in the (2) control effective only in the condition of the frequency error process.where, Therefore, the iterative equation of the weights is constructed to guarantee the convergence. η is the learning rate and represents the step size. w(n + 1) is the weights in step n + 1 and w(n) is the weights step n. Δw(n) is the The steepest descentinmethod is used togradient obtain vector. the iterative equation of the weights w(n) of controller:

By taking a derivation to w(n) of J, the variation of the weights Δw(n) in each step can be obtained to guarantee the convergence: wpn ` 1q “ wpnq ´ η∆wpnq (2) 1 1 2  ( D  Y )  ( e2 (n)) J 2 2 2 w(represents  the  w(n ethe n)  (n) weights in step n +(3) where, η is the learning rate and step size. + 1) is 1 and w(n) w(n) w(n) w(n)

is the weights in step n. ∆w(n) is the gradient vector. m Bywhere, taking ea(nderivation J, the variation of the weights ∆w(n) in each step can be obtained )   (d ito (n)w(n)  yof i(n )) is the global frequency error in nth iterative step. to guarantee the convergence: i 1 Substituting Equation (3) into Equation (2), the iterative equation of the weights w(n) can be 1 1 obtained as follows: Bp ||D ´ Y||2 q Bp e2 pnqq BJ 2 2 ∆wpnq “ “ w(n  1)  w(n)  ηe (“n) 2 “ ´e2 pnq (4)

Bwpnq

where, epnq “

m ř i “1

Bwpnq

Bwpnq

(3)

pdi pnq ´ yi pnqq is the global frequency error in nth iterative step.

Substituting Equation (3) into Equation (2), the iterative equation of the weights w(n) can be obtained as follows: wpn ` 1q “ wpnq ` ηe2 pnq (4)

Sensors 2016, 16, 68

5 of 12

2.2. Error Criterion Sensors 2016, to 16, 68 5 ofcontrol 12 In order improve the adaptability, anti-interference ability and reliability of the algorithm, a new error criterion is constructed. The global frequency error J in Equation (1) is used 2.2. Error Criterion to update the weights of the control network, while the frequency node error Jn in Equation (5) is order towith improve the error adaptability, combinedIntogether J as the criterionanti-interference in Equation (6):ability and reliability of the control

algorithm, a new error criterion is constructed. The global frequency error J in Equation (1) is used to m update the weights of the control network, while node error Jn in Equation (5) is 1 ÿ the frequency 2 Jn “ in Equation pd j ´ y j q(6): combined together with J as the error criterion

(5) m j “1 1 m Jn  (d j  y j )2 (5)  m where, m denotes the number of characteristic frequencies. d j is the amplitude of the jth characteristic j 1 frequency in the destination signal D, and y j is the amplitude of the jth characteristic frequency in the where, m denotes the number of characteristic frequencies. dj is the amplitude of the jth frequency-domain vibration response of Y: characteristic frequency in the destination signal D, and yj is the amplitude of the jth characteristic frequency in the frequency-domain vibration response of Y:

J ď pre_g & Jn ď pre_n (6) J  pre _ g & J n  pre _ n (6) where, pre_g is the convergence precision of the global frequency error, and pre_n is the convergence where, pre_g is the convergence precision of the global frequency error, and pre_n is the convergence precision of the node error. precision of frequency the frequency node error. There are two advantages ofofthe constructedforfor presented active vibration There are two advantages theerror errorcriterion criterion constructed thethe presented active vibration control method in the domain. First, the the control efficiency cancan be improved andand thethe control control method infrequency the frequency domain. First, control efficiency be improved control be more smooth. global frequency errorfor is used for weight updating eachof the process will process be morewill smooth. The globalThe frequency error is used weight updating in eachinstep step ofmethod the presented method and the objective signal and the real-time signal arethe all in the presented and the objective signal and the real-time vibrationvibration signal are all in frequency frequency domain, so only one FFT is used for vibration response in each iteration, and no IFFT is domain, so only one FFT is used for vibration response in each iteration, and no IFFT is included, included, thus control time is saved. Furthermore, as shown in Figure 3, the time-domain signal thus control time is saved. Furthermore, as shown in Figure 3, the time-domain signal sometimes is sometimes is not in a one-to-one correspondence with the frequency-domain signal, so the global not in a one-to-one correspondence with the frequency-domain signal, so the global frequency error frequency error can precisely reflect the difference between the frequency-domain real-time can precisely reflect the difference between the frequency-domain real-time response and objective. response and objective. Otherwise, the control process may oscillate if the time-domain error is used Otherwise, the control process may oscillate if the time-domain error is used in this situation. in this situation.

(a)

(b)

Figure 3. Illustration of the relationship between time-domain signals and frequency-domain signals.

Figure 3. Illustration of the relationship between time-domain signals and frequency-domain signals. (a) Time-domain signal; (b) Frequency-domain signal. (a) Time-domain signal; (b) Frequency-domain signal.

Second, the proposed error criterion can enhance the adaptability and anti-interference ability of the activeerror control method. many cases, we always and focusanti-interference on the characteristic Second,presented the proposed criterion canInenhance the adaptability ability of frequency node amplitude, if the global frequency error J is alone taken as the error criterion, which the presented active control method. In many cases, we always focus on the characteristic frequency cannot efficiently effect the changes on these characteristic frequency nodes. However, if the node amplitude, if the global frequency error J is alone taken as the error criterion, which cannot frequency node error Jn alone is taken as the error criterion, some unacceptable cases, such as that efficiently effect the changes on these characteristic frequency nodes. However, if the frequency node illustrated in Figure 4, may be obtained. Therefore, the global frequency error J and frequency node errorerror Jn alone is combined taken as the error criterion, unacceptable cases, suchofasthe that illustratedmethod in Figure 4, Jn are together as the errorsome criterion, and the adaptability constructed may can be obtained. Therefore, the global frequency error J and frequency node error J are combined n be enhanced by appropriately adjusting the pre_g and pre_n in Equation (8). Besides, since the together as the error criterion, and the adaptability of the constructed method can be enhanced frequency node may vary slightly in practical cases, the anti-interference ability can be enhanced by by setting a variation range frequency nodesininEquation the error criterion. appropriately adjusting thefor pre_g and pre_n (8). Besides, since the frequency node may

Sensors 2016, 16, 68

6 of 12

vary slightly in practical cases, the anti-interference ability can be enhanced by setting a variation 2016, 16, 68 nodes in the error criterion. 6 of 12 rangeSensors for frequency

Sensors 2016, 16, 68

6 of 12

(a)

(b)

Figure 4. Illustration of the unacceptable case that may occur if the frequency node error is alone

Figure 4. Illustration of the case that may occur if the frequency (a)unacceptable (b) node error is alone taken taken as the error criterion. (a) Destination signal; (b) Vibration signal. as the error criterion. (a) Destination signal; (b) Vibration signal. Figure 4. Illustration of the unacceptable case that may occur if the frequency node error is alone

3. Simulation Experimental taken as and the error criterion. (a) Verification Destination signal; (b) Vibration signal.

3. Simulation and Experimental Verification

In order to verify the effectiveness of the proposed control method, simulations and

3. Simulation and Experimental Verification

experiments are presented in this section. The flow chartcontrol of the control method is shownand in Figure 5. In order to verify the effectiveness of the proposed method, simulations experiments In point order that to verify the effectiveness of the“protection proposed control method, simulations andthis A special should mentioned algorithm”, which is added in are presented in this section. Thebe flow chart of is thethe control method is shown in Figure 5. A special point experiments are presented in this section. TheThe flow chart of the control method isdue shown in Figure 5. algorithm to make it more reliable and safe. control process may diverge to some practical that should be mentioned is the “protection algorithm”, which is added which in this algorithm to make it A special that should be mentioned is the “protection algorithm”, added inmay this reasons andpoint the control parameters may exceed the working range, thus theis devices be more reliable and safe. The control process may diverge due to some practical reasons and the algorithm to make it more reliable and safe. The control process may diverge due to some practical control destroyed by these inappropriate parameters. However, the “protection algorithm” can avoid these reasons the control parameters may exceed the working thus the by devices be parameters mayand exceed the working range, thus the devices mayrange, be destroyed thesemay inappropriate losses in such cases. It will analyze the error in every iterative step, and set the initialized control destroyed by these inappropriate parameters. However, the “protection algorithm” can avoid theseanalyze parameters. However, the “protection algorithm” can avoid these losses in such cases. It will again with new parameters if the control algorithm works in a wrong convergence tendency or losses in such cases. Itstep, will and analyze in every iterative step,with and set theparameters initialized control the error in every iterative set the the error initialized control again new if the control inappropriate control parameters. again with new parameters if the control algorithm works in a wrong convergence tendency or algorithm works in a wrong convergence tendency or inappropriate control parameters. inappropriate control parameters.

Start Start

Initialize the control parameters Initialize the control parameters

Original vibration responses Original acquisition vibration responses acquisition

Optimize the controlled actuating Optimize the parameters controlled actuating parameters Yes Yes

Protection algorithm : algorithm : Dose theProtection control output exceeds the Doseeffective the control output exceeds working range ? the effective working No range ? No

Excite the controlled Excite the controlled object object

Yes Yes

Error Does Error criterion criterion ..Does the vibrationsatisfy satisfy the present present vibration destination destination ??

NoNo

End End

Figure5.5.Flow Flow chart chart of Figure of the the control controlprocess. process.

Figure 5. Flow chart of the control process.

Sensors 2016, 16, 68

7 of 12

Sensors 2016, 16, 68 Sensors 2016, 16, 68

7 of 12 7 of 12

3.1. Spindle Based Simulation 3.1. Spindle Based Simulation 3.1.ASpindle Based Simulation spindle is taken as the control object in this simulation, as shown in Figure 6a. Piezoelectric A spindle is taken as the control object in this simulation, as shown in Figure 6a. Piezoelectric patchesA(M-8557-P1, M + P, Hanover, are simulation, supposed fixed on point A and the acceleration spindle is taken the controlGermany) object in this as shown in Figure patches (M-8557-P1, M as + P, Hanover, Germany) are supposed fixed on point A and6a. thePiezoelectric acceleration sensor is fixed on point Frequency Germany) Response Function (FRF) is on tested and used toacceleration simulate the patches (M-8557-P1, M B. + P, supposed fixed point A and sensor is fixed on point B. Hanover, Frequency Responseare Function (FRF) is tested and usedthe to simulate the controlled spindle (Figure 6b). The control flowFunction runs in the following steps. First, the spindle sensor is fixed on point B. Frequency Response (FRF) is tested and used to simulate theisis controlled spindle (Figure 6b). The control flow runs in the following steps. First, the spindle actuated by the simulated sinusoidal signal, and the responses are collected through FRF. Then controlled spindle (Figure sinusoidal 6b). The control runsresponses in the following steps. First, the spindle isthe actuated by the simulated signal,flow and the are collected through FRF. Then the vibration is collected by the acceleration sensor andand transferred toare the frequency domain byby FFT and fed actuated by simulated sinusoidal signal, and the responses collected through FRF. Then the vibration is the collected by the acceleration sensor transferred to the frequency domain FFT and vibration is collected by the acceleration sensor and transferred to the frequency domain by FFT and back to the LMS control algorithm after comparing with the target signal. Next, the control algorithm fed back to the LMS control algorithm after comparing with the target signal. Next, the control fed back towill LMSofcontrol algorithm after comparing with the them target Next, will optimize athe series control parameters and send them assend input to the FRF of piezoelectric algorithm optimize a series of control parameters and assignal. input tothe thethe FRFcontrol of the algorithm will optimize a series of control parameters and send them as input to the FRF of patch which canpatch be found thebe Mfound + P handbook. the simulated willspindle be actuated piezoelectric whichincan in the M + Finally, P handbook. Finally, thespindle simulated willthe beby patch which can be found in the M + P handbook. Finally, the simulated spindle will be thepiezoelectric original vibration source and the piezoelectric patch together, and the vibration responses will actuated by the original vibration source and the piezoelectric patch together, and the vibration bywill thehybrid vibration source and the piezoelectric patch together, anduntil the vibration be actuated judged by the error This process will be process repeated until the hybrid error criterion responses beoriginal judged by criterion. the hybrid error criterion. This will be repeated the hybrid responses will be judged by the hybrid error criterion. This process will be repeated until the hybrid error criterion is satisfied. is satisfied. error criterion is satisfied. 0.025

Amplitude Amplitude

0.025 0.02 0.02 0.015

0.015 0.01 0.01 0.005

0.005 0

0

0

100

0

100

200

300

400

500

600

700

Amplitude−frequency 300 (a) 400 500 600 curve 700

200

800

900

1000

Frequency/Hz 900 1000

800

Frequency/Hz

(a) Amplitude−frequency curve 4 4

Phase Phase

2 2 0 0 −2 −2 −4 −4

0

100

0

100

200 200

300 300

400

500

600

(b) Phase−frequency curve

(a) (a)

700

(b) Phase−frequency 400 500 600curve700

(b) (b)

800 800

900

1000

Frequency/Hz 900 1000 Frequency/Hz

Figure 6. Spindle and tested FRF (a) spindle (b) FRF. Figure FRF (a) (a)spindle spindle(b) (b)FRF. FRF. Figure6.6.Spindle Spindle and and tested tested FRF 4

Amplitude Amplitude

2

Original vibration response Controlled vibration response Original vibration response

2

Controlled vibration response 0

0 −2

−2 −4 −4

4

Amplitude Amplitude

4 4

2

0

0 −2

−2 −4

0

0

200

400

600

800

1000 Time/s (a) Comparison between original and controlled 200 400 600 800responses1000 (a) Comparison between original and controlled responsesTime/s

−4

0.2 0.2 0.1

Error Error

Error Error

0.2

0 −0.1

0.10 0 −0.1

−0.2 0 0

200 400 600 800 1000 Time/s 200 400 600 800responses1000 (a) Comparison between original and controlled Time/s (a) Comparison between original and controlled responses

−0.1 −0.2

−0.1 −0.2 −0.2

0

0

0.2 0.1 0.1 0

Original Controlled Original Controlled

2

200 200

400 600 curve 400 (b) Error 600 (b) Error curve

(a) (a)

1000 times 800 Iterative 1000 Iterative times

0

800

0

200 200

400

600

400 (b) Error curve 600 (b) Error curve

(b) (b)

800 1000 times 800 Iterative1000 Iterative times

Figure 7. Control result of spindle actuated by: (a) single frequency sinusoidal signal (b) Figure 7. Control result signal. of spindle actuated by: (a) single frequency sinusoidal signal (b) multifrequency sinusoidal Figure 7. Control result of spindle actuated by: (a) single frequency sinusoidal signal (b) multifrequency multifrequency sinusoidal signal. sinusoidal signal.

The control algorithm is tested in this simulation in two cases. First, the simulated spindle is The algorithm is tested in this simulation in two cases. First, the simulated spindle is actuatedcontrol by the original vibration source with a single frequency sinusoidal signal with white noise. The control algorithm is tested in this simulation in two cases. First, signal the simulated spindle is actuated by the original vibration source with a single frequency sinusoidal with white noise. The control results and the error curve can be seen in Figure 7a. Next, the original vibration source actuated by the original with single frequency sinusoidal signalvibration with white noise. The results andvibration the error source curve beaseen in Figure 7a. Next, thecan original source withcontrol a multifrequency sinusoidal signalcan is tested, and the control results be seen in Figure 7b. It The control results and the error curve can be seen in Figure 7a. Next, the original vibration source with a multifrequency sinusoidal signal is tested, and the control results can be seen in Figure 7b. It can be seen from these two figures that the proposed method reached well the control destination. can seeniffrom thesesinusoidal two figures that the proposed method reached well the control destination. with a be multifrequency signal isistested, and the control results can be seen in Figure However, the original vibration source a single frequency sinusoidal signal, the control process7b. However, if the original vibration source is a single frequency sinusoidal signal, the control process

Sensors 2016, 16, 68

8 of 12

68 these two figures that the proposed method reached well the control destination. 8 of 12 It Sensors can be2016, seen16,from Sensors 2016, 16, 68 8 of However, if the original vibration source is a single frequency sinusoidal signal, the control process is12 is more efficient and smooth, whereas if the vibration source has a multifrequency signal, the control Sensors 2016, 16, 68 8 of 12 more Sensors efficient 2016,and 16, 68 smooth, whereas if the vibration source has a multifrequency signal, the 8 ofcontrol 12 process will be somewhat more complex, and will oscillate slightly. However, forsignal, eitherthe thecontrol single is more efficient and smooth, whereas if the vibration source has a multifrequency Sensors 2016, 8 of 12 process will 16, be68 somewhat more complex, and will oscillate slightly. However, for either the single frequency or be multifrequency case, the ifif proposed active vibration method performs very process will somewhat more complex, will oscillate slightly. However, forsignal, either thecontrol single is more efficient and smooth, whereas theand vibration source asuppression multifrequency the is more and smooth, whereas the vibration source hashas a suppression multifrequency signal, the control frequency orefficient multifrequency case, the proposed active vibration method performs very well and achieves satisfactory results. frequency or multifrequency case, the if proposed active vibration performs very process will be somewhat more complex, and will oscillate slightly. However, forsignal, either thecontrol single process will be somewhat more complex, and will oscillate slightly. However, formethod either the single is more efficient and smooth, whereas the vibration source has asuppression multifrequency the well and achieves satisfactory results. well and achieves satisfactory results. frequency or multifrequency case, proposed active vibration suppression method performs very frequency or multifrequency case, the proposed active vibration suppression method performs very process will be somewhat more complex, and will oscillate slightly. However, for either the single 3.2. Milling Machine Tool Based Experiment well and achieves satisfactory results. 3.2. Milling Machine Tool Based Experiment well and achieves satisfactory results. frequency or multifrequency case, the proposed active vibration suppression method performs very 3.2. Milling Machine Tool Based Experiment well and achieves satisfactory results. Theexperimental experimental set-up themilling millingprocess processisiscomposed composedofofsix sixparts, parts,namely, namely,the themilling milling The set-up ofof the 3.2. Milling Machine Tool Based Experiment 3.2. Milling Machine Toolset-up Based Experiment machine tool, workpiece, sensors, data acquisition device, NI-FPGA controller, power amplifier and The experimental of the milling process is composed of six parts, namely, the machine tool, workpiece, sensors, data acquisition device, NI-FPGA controller, power amplifiermilling and The Machine experimental set-up of the milling process is composed of six parts, namely, the milling 3.2. Milling Tool Based Experiment piezoelectric patch, as shown in Figure 8. The sampling rate in this experiment is set as 10,240 Hz. machine workpiece, sensors, data acquisition device, NI-FPGA controller, and The tool, experimental set-up the milling is composed of six parts, power namely, the milling piezoelectric as shown inofFigure The process sampling in this experiment is set asamplifier 10,240 machine patch, tool, workpiece, sensors, data 8. acquisition device, rate NI-FPGA controller, power amplifier and Hz. Due to excellent its excellent real time performance, the real-time NIpower FPGA piezoelectric patch, shown in Figure 8. The sampling rate in thisof experiment isPXI-7853R set asthe 10,240 Hz. machine tool, workpiece, sensors, data acquisition device, NI-FPGA controller, amplifier and The experimental of milling process iscommercial composed six parts, namely, Due to its realastime performance, the commercial real-time PXI-7853R controller [28] piezoelectric patch, asset-up shown in the Figure 8. The sampling rate in thisNI experiment is FPGA set as 10,240 Hz.milling controller [28] has been selected for on-line control and vibration suppression. The proposed Due to its excellent real time performance, the commercial real-time NI PXI-7853R FPGA piezoelectric as shown in Figure 8. The sampling rate in real-time this experiment is set amplifier asFPGA 10,240 Hz. machine tool, workpiece, sensors, data acquisition NI-FPGA controller, power and has been for on-line control and vibration suppression. The proposed LMS Dueselected to itspatch, excellent real time performance, thedevice, commercial NIfrequency-domain PXI-7853R frequency-domain LMS control in Figure programed by Labview and downloaded to controller been for on-line control and vibration suppression. The proposed Due to its[28] excellent real performance, the2 is commercial FPGA piezoelectric patch, as shown inalgorithm Figure 8. by The sampling rate in thisreal-time experiment isPXI-7853R set as 10,240 Hz. controller [28]has been selected for on-line control and vibration suppression. The proposed control algorithm inhas Figure 2selected istime programed Labview and downloaded to theNI FPGA controller to the FPGA controller to optimize the actuating parameters. As the data flow shows in Figure 9, frequency-domain LMS control algorithm in Figure 2 is programed by Labview and downloaded frequency-domain LMS control algorithm in Figure 2 is programed by Labview and downloaded to controller [28] has been selected for on-line control and vibration suppression. The proposed Due tothe itsactuating excellentparameters. real timeAsperformance, commercial NI PXI-7853R optimize the data flow the shows in Figure 9,real-time on-line vibration responsesFPGA areto on-line vibration responses are first collected by sensors and the COCO-80 data acquisition device. the FPGA controller to optimize the actuating parameters. As the data flow shows in Figure 9, thecollected FPGA [28] controller toand optimize parameters. As the shows in proposed Figure 9, frequency-domain control algorithm in Figure 2 is programed bydata Labview and downloaded controller hasLMS been selected for actuating on-line control and vibration suppression. The first by sensors the COCO-80 data acquisition device. Then theflow control parameters areto on-line vibration responses are first collected by sensors and the COCO-80 data acquisition device. Then the control parameters are optimized by the LMS control algorithm in FPGA and displayed on on-line vibration responses are first collected by sensors and the COCO-80 data acquisition device. the FPGA controller to optimize the actuating parameters. As the data flow shows in Figure frequency-domain LMS control algorithm in Figure 2 is programed by Labview and downloaded to optimized by the LMS control algorithm in FPGA and displayed on the computer. Next, the optimized9, Then the control parameters arefirst optimized by LMS control algorithm inthe FPGA andacquisition displayed ondevice. the computer. Next, the optimized actuating parameters are sent todata piezoelectric after Then thevibration control parameters are optimized bythe the LMS control algorithm inflow FPGA and displayed on on-line responses are collected by sensors and the COCO-80 data the FPGA controller tosent optimize the actuating parameters. As the inpatch Figure 9, actuating parameters are to the piezoelectric patch after being amplified by theshows power amplifier. the computer. Next, the optimized actuating parameters are sent to the piezoelectric patch after being amplified by the power amplifier. This control process is repeated until the vibration thecontrol computer. Next, optimized actuating parameters are sent to theinprocess piezoelectric patch after Then thevibration control parameters areuntil optimized by by the LMS control algorithm FPGA and displayed on on-line responses are first collected sensors and COCO-80 data acquisition device. This process is repeated the vibration responses inthe the milling satisfy a preset being amplified by the power amplifier. This control process is repeated until the vibration responses in theNext, milling a preset target value. being amplified by theprocess power amplifier. control process until vibration the computer. optimized actuating parameters are algorithm sentistorepeated theinpiezoelectric patch after Then the control parameters are satisfy optimized byThis the LMS control FPGA andthe displayed on target value. responses in the milling process satisfy a preset target value. responses in the milling process satisfy a preset target value. being amplified by the optimized power amplifier. This control process until thepatch vibration the computer. Next, actuating parameters are sentistorepeated the piezoelectric after responses in the milling a preset target value. being amplified by theprocess powersatisfy amplifier. This control process is repeated until the vibration responses in the milling process satisfy a preset target value.

Figure 8. Set-up of the milling process experimental system.

Figure 8. Set-up of the milling process experimental system.

Figure 8.of Set-up of the milling The detailed information this hardware is: process experimental system.

The information of8.this hardware is: process experimental system. Figure Set-up ofUSA) the milling  detailed Sensor (352C34, PCB, Depew, NY, Thedetailed information of this hardware is: process experimental system. Figure 100 8. Set-up the milling Sensitivity: (±10%) mV/gof (10.2) ‚ Sensor (352C34, PCB, Depew, NY, USA) Thedetailed information this hardware 2is: Measurement range: ±50g pk pk)process experimental system. Figure 8.of Set-up of(±490m/s the milling  Sensor (352C34, PCB, Depew, NY, USA) The detailed information of this hardware is:  Broadband resolution: 0.00015 g rms (0.0015 m/s2 rms)  Sensitivity: (±10%) 100 Sensitivity: (˘10%) 100mV/g mV/g (10.2)  Sensor (352C34, PCB, Depew, NY,(10.2) USA)  Frequency range: (±5%) 0.5 to 10,000 Hz The detailed information of this hardware is: 2 pk) 2 pk) Measurement range: ±50g (±490m/s  Sensitivity: (±10%) 100 mV/g (10.2) Measurement range: ˘50 gpk pk (˘490m/s  Sensor (352C34, PCB, Depew, NY, USA)  Piezoelectric patch (M-8557-P1, M + P) 2 pk) m/s2 2rms) Broadband resolution: 0.00015 gg rms (0.0015  Measurement range: ±50g pkwidth (±490m/s (±10%) 100 mV/g (10.2) Broadband resolution: 0.00015 rms (0.0015 m/s rms)  Sensor (352C34, PCB, NY, USA) Sensitivity: Active length 85Depew, mm, active 57 mm 2 pk) m/s2 rms)  Sensitivity: Frequency range: (±5%) 0.5 to 10,000 Hz Broadband resolution: 0.00015 g rms (0.0015 Measurement range: ±50g pk (±490m/s  (±10%) 100 mV/g (10.2) Frequency range: (˘5%) 0.5 to 10,000 Hz Capacitance 9.3 nF  Piezoelectric patch (M-8557-P1, M +10,000 2 pk) m/s2 rms)  Frequency range: (±5%) 0.5pk to(±490m/s Broadband resolution: 0.00015 gP)rms Hz (0.0015 Measurement Free strain 1800 ppm  range: ±50g ‚ Piezoelectric patch (M-8557-P1, M + P)  Active length 85 mm, active width 57 mm  Piezoelectric patch (M-8557-P1, M + P) Blocking force 923 N 0.00015  Frequency range: (±5%) 0.5 to 10,000 Broadband resolution: g rms Hz (0.0015 m/s2 rms) Capacitance 9.3 nF  Active length 85 mm, active mm  Piezoelectric patch (M-8557-P1, +10,000 P) 57Hz  Frequency range: (±5%) 0.5 M towidth  Free strain 1800 ppm Capacitance 9.3 nF  Active length 85 mm, active width 57 mm  Piezoelectric patch (M-8557-P1, M + P)  Blocking force 923 N Free strain 1800 ppm Capacitance 9.3  Active length 85nF mm, active width 57 mm  Capacitance Blocking force N Free strain 1800 ppm  9.3923 nF

the computer. Next, the optimized actuating parameters are sent to the patch after Then the control parameters are optimized by by the LMScommercial control algorithm inpiezoelectric FPGA and displayed on on-line responses are collected sensors and the COCO-80 data acquisition device. controller [28] has been selected for on-line control and vibration suppression. proposed Due tovibration its excellent real time performance, the real-time NIpower PXI-7853R FPGA piezoelectric patch, as shown infirst Figure 8. The sampling rate in this experiment is setThe as 10,240 Hz. machine tool, workpiece, sensors, data acquisition device, NI-FPGA controller, amplifier and being amplified by the power amplifier. This control process is repeated until the vibration the Next, optimized actuating parameters are algorithm sent by to Labview the patch after Then the control parameters are optimized byFigure the LMS control inpiezoelectric FPGA and displayed on frequency-domain LMS control 2 is programed downloaded to controller [28] has been selected for on-line control and suppression. The proposed Duecomputer. to its excellent real time performance, the commercial NIand FPGA piezoelectric patch, as shown inalgorithm Figure 8. in The sampling rate vibration in thisreal-time experiment isPXI-7853R set as 10,240 Hz. responses in the milling process satisfy a preset target value. being amplified by the power amplifier. This control process is repeated until the vibration the computer. Next, optimized actuating parameters are sent to the piezoelectric patch after FPGA controller toreal optimize the parameters. As the flow and shows in proposed Figure to 9, frequency-domain control algorithm in Figure 2 is programed bydata Labview downloaded controller hasLMS been selected for actuating on-line control and vibration suppression. The Due to its[28] excellent time performance, the commercial real-time Figure 8. Set-up ofathe milling process experimental system. NI PXI-7853R FPGA responses in the milling process satisfy preset target value. being amplified by the power amplifier. This control process is repeated until the vibration on-line vibration responses are first collected by sensors and the COCO-80 data acquisition device. the FPGA controller to optimize the actuating parameters. As the data flow shows in Figure 9, frequency-domain LMS control algorithm in Figure 2 is programed by Labview and downloaded to controller [28] has been selected for on-line control and vibration suppression. The proposed Figure 8. Set-up ofathe milling process experimental system. responses in the milling process satisfy preset target value. Then the control parameters are optimized by the LMS control algorithm in FPGA and displayed on on-line responses areoffirst collected by sensors and As the the COCO-80 dataand acquisition the FPGA controller to control optimize the actuating flow shows in Figure 9, frequency-domain LMS algorithm in Figure 2 is programed bydata Labview downloaded Sensors 2016, 16, 68 9device. of 12 to Thevibration detailed information this hardware is:parameters. Figure 8. Set-up of the milling process experimental system. the computer. Next, the optimized actuating parameters areAs sent todata theinflow piezoelectric patch after Then thevibration control parameters arefirst optimized by by the LMS control algorithm FPGA and displayed on on-line responses are collected sensors and the COCO-80 data acquisition device. the FPGA controller to optimize the actuating parameters. the shows in Figure 9, The detailed information this hardware is: process experimental system. Figure 8.ofSet-up ofUSA) the milling the Sensor (352C34, PCB, Depew, NY, being amplified by the power amplifier. This control process is repeated until the vibration computer. Next, optimized actuating parameters are sent to the piezoelectric patch after Then thevibration control parameters arefirst optimized by by thesensors LMS control algorithm in FPGA and displayed on on-line responses are collected and the COCO-80 data acquisition device. The detailed information of mV/g this hardware is:  Sensitivity: (±10%) 100 (10.2) Active length mm, width mm responses Sensor Depew, NY, USA) in(352C34, theNext, milling process satisfy a preset target value. being amplified by PCB, the85 power amplifier. This control process until vibration the computer. optimized actuating parameters are algorithm sentistorepeated theinpiezoelectric patch after Then the control parameters areactive optimized by57 the LMS control FPGA andthe displayed on The detailed information of this hardware is: 2 pk)  Measurement range: ±50g pk (±490m/s Sensitivity: (±10%) 100 mV/g (10.2) Capacitance 9.3 nF being Sensor (352C34, PCB, Depew, NY, USA) responses in the milling process satisfy a preset target value. amplified by the power amplifier. This control process is repeated until the vibration the computer. Next, optimized actuating parameters are sent to the piezoelectric patch after 2experimental 2 pk)  Sensitivity: Broadband resolution: 0.00015 gpreset rms (0.0015 m/s rms) Figure 8.±50g Set-up milling process Measurement range: pkof(10.2) (±490m/s  (±10%) 100 mV/g Free strain ppm being Sensor PCB, Depew, NY, USA) responses in(352C34, the milling process satisfy athe target value. amplified by 1800 the power amplifier. This control process is system. repeated until the vibration 2experimental 2  Frequency range: (±5%) 0.5 to 10,000 Hz Broadband resolution: 0.00015 g rms (0.0015 m/s rms) Figure 8. Set-up of the milling process system. Measurement range: pk (10.2) (±490m/s pk) value.  Sensitivity: (±10%) mV/g Blocking force 923 100 N ±50g responses in the milling process satisfy a preset target The detailed information this hardware is:  Piezoelectric patch (M-8557-P1, M +10,000 2 pk)  Frequency range: (±5%) 0.5pk to Hz Broadband resolution: 0.00015 gP)rms (0.0015 m/s2experimental rms) Figure 8.of Set-up of(±490m/s the milling process system.  Measurement range: ±50g ‚ Control platform (PXIe-8115RT, NI) The detailed information of this hardware is:  Active length 85 mm, active width 57 mm 2  Piezoelectric patch (M-8557-P1, M + P)  Frequency range: (±5%) 0.5 to 10,000 Hz Broadband resolution: 0.00015 g rms (0.0015 m/sexperimental rms) Figure 8. Set-up the milling process system. Sensor (352C34, PCB, Depew, NY,ofUSA) Capacitance 9.3 nF The detailed information of this hardware is:  Active length 85 mm, active width 57 mm  Piezoelectric patch (M-8557-P1, M + P) Frequency range: (±5%) 0.5 to 10,000 Hz Figure 8. Set-up of the milling process experimental system.  Sensitivity: (±10%) 100 mV/g (10.2) 2.5 GHz dual-core Intel Core i5-2510E processor Sensor (352C34, PCB, Depew, NY, USA)  Free strain 1800 ppm Capacitance 9.3 nF The detailed information of this hardware is: 2  Active length 85 mm, active width 57 mm  Piezoelectric patch (M-8557-P1, M + P) Measurement range: ±50g pk (10.2) (±490m/s pk) MHz DDR3 RAM standard, 4 GB maximum  Sensitivity: (±10%) 100 mV/g 2GB (1 ˆ 2 PCB, GB DIMM) single-channel Sensor (352C34, Depew, NY, USA) 1333  Blocking force 923 N ofactive Free strain 1800 ppm  Capacitance 9.3 nF The detailed information this hardware is: 2 pk) m/s2 rms) Active length 85 mm, width 57 mm Broadband resolution: 0.00015 g rms (0.0015  Measurement range: ±50g pk (±490m/s Sensitivity: (±10%) 100 mV/g 10/100/1000 BASE-TX (gigabit) Ethernet, ExpressCard/34 slot  2016, Sensor Depew, NY,(10.2) USA) Sensors 16, 68(352C34, PCB, 9 of 12 Blocking force 923 N8. Set-up  Measurement Free strain 1800 ppm Capacitance 9.3 nF 2 pk)  Frequency range: (±5%) 0.5 toof(10.2) 10,000 Hz Broadband resolution: 0.00015 g rms (0.0015 m/s2experimental rms) Figure the milling process system. range: ±50g pk (±490m/s  Sensitivity: (±10%) 100 mV/g 191 kHz single PID loop rate, maximum  Sensor (352C34, PCB, Depew, NY, USA) Blocking force 923 N8. Set-up  Free strain 1800 ppm 2experimental Piezoelectric patch (M-8557-P1, M +10,000 2 pk)  Frequency range: (±5%) 0.5 toof(10.2) Hz Broadband resolution: 0.00015 gP)rms (0.0015 m/s rms) I/Osystem. Figure the milling process Measurement range: ±50g pk (±490m/s   Control platform (PXIe-8115RT, NI)  Sensitivity: (±10%) 100 mV/g Integrated hard drive, GPIB, serial, and other peripheral Blocking force 923 N The detailed information of this hardware is:  Active length 85 mm, active width 57 mm 2   Piezoelectric patch (M-8557-P1, M + P) 2 pk)  2.5Measurement Frequency range: (±5%) 0.5pk toof(±490m/s 10,000 Hz Broadband resolution: 0.00015 g rms (0.0015 m/sexperimental rms) GHz dual-core Intel Core i5-2510E processor Figure 8.±50g Set-up the milling process system. range: ‚ NIThe FPGA controller (PXI-7853R, NI) Capacitance 9.3 nF detailed information of this hardware is:  Active length 85 mm, active width 57 mm 2   Sensor Piezoelectric patch (M-8557-P1, M + P)  Frequency range: (±5%) 0.5 to 10,000 Hz 2GB (1 × 2 GB DIMM) single-channel 1333 MHz DDR3 RAM standard, Broadband resolution: 0.00015 g rms (0.0015 m/sexperimental rms) Figure 8. Set-up the milling process system. 4 GB maximum (352C34, PCB, Depew, NY,ofUSA)  Free strain 1800 ppm Capacitance 9.3 nF The detailed information of this hardware is:  Active length 85 mm, active width 57 mm Piezoelectric patch (M-8557-P1, M +USA) P)and Hz 10/100/1000 BASE-TX (gigabit) ExpressCard/34 slot Frequency range: (±5%) 0.5 toEthernet, 10,000 Sensitivity: (±10%) 100 mV/g (10.2) User-defined triggering, timing, decision making in hardware with 25 ns resolution    Sensor (352C34, PCB, Depew, NY,  Blocking force 923 N ofactive Free strain 1800 ppm Capacitance 9.3 nF The detailed information this hardware is: 2  Active length 85 mm, width 57 mm 191 kHz single PID loop rate, maximum   Sensor Piezoelectric patch (M-8557-P1, M + P) Measurement range: ±50g pk (±490m/s pk)  Sensitivity: (±10%) 100 mV/g (10.2) Up(352C34, to eightPCB, analog inputs, independent sampling rates up to 750 kHz, 16-bit resolution Depew, NY, USA)  Integrated Blocking force 923 NGPIB, Free strain 1800 ppm  Capacitance 9.3 nF 2 rms) I/O  hard drive, serial, and other 2 pk) peripheral Active length 85 mm, active width 57 mm Broadband resolution: 0.00015 g rms (0.0015 m/srate Measurement range: ±50g pk (±490m/s Sensitivity: (±10%) 100 mV/g (10.2) Up(352C34, to eightPCB, analog output, independent update up to 1 MHz, 16-bit resolution  Sensor Depew, NY, USA) Blocking force 923 N8. Set-up FPGA Free strain 1800 ppm  NI controller (PXI-7853R, NI) Capacitance 9.3 nF 2experimental 2 pk) Frequency range: (±5%) 0.5 toof(10.2) 10,000 Hz Broadband resolution: 0.00015 g rms (0.0015 m/s rms)or counters Figure the milling process system. Measurement range: ±50g pk (±490m/s  Sensitivity: (±10%) 100 mV/g Up to 160 digital lines configurable as inputs, output at rate up to 40 MHz Blocking force 923 N8. Set-up User-defined triggering, timing, and decision making in hardware with 25 ns resolution  Free strain 1800 ppm 2experimental  (a) Piezoelectric patch (M-8557-P1, M + P) 2  Frequency range: (±5%) 0.5 to 10,000 Hz Broadband resolution: 0.00015 g rms (0.0015 m/s rms) Figure of the milling process system.  Measurement range: pk (±490m/s Direct memory access±50g channels for datapk) streaming Updetailed to eight analog inputs, independent sampling rates up to 750 kHz, 16-bit resolution Blocking force 923 N8.ofactive The information this hardware is: process Active length 85 mm, width 57Hz mm   Piezoelectric patch (M-8557-P1, M +10,000  Frequency range: (±5%) 0.5 to Broadband resolution: 0.00015 gP)rms (0.0015 m/s2experimental rms) Figure Set-up of the milling system. ‚  Power amplifier (HVA1500, M + P) Up to eight analog output, independent update rate up to 1 MHz, 16-bit resolution Capacitance 9.3 nF The detailed information of this hardware is:  Active length 85 mm, active width 57 mm  Piezoelectric patch (M-8557-P1, M + P)  Frequency range: (±5%) 0.5 to 10,000 Hz Sensor (352C34, PCB, Depew, NY, USA)  Updetailed to 160 digital lines configurable as inputs,  Free strain 1800 ppm Capacitance 9.3 nF The information ofactive this hardware is: output or counters at rate up to 40 MHz Active length 85 mm, width  Piezoelectric patch (M-8557-P1, M +USA) P) 57 mm  Sensitivity: (±10%) 100 mV/g (10.2) Up(352C34, to four independent channels Sensor PCB, Depew, NY,   Direct access channels for data streaming Blocking force 923 N8. Freememory strain 1800 ppm Capacitance 9.3 nF 2 pk)  Sensitivity: Active length 85 mm, active width 57 mm Figure Set-up the milling process experimental system. Measurement range: pkof (±490m/s  (±10%) 100 Voltage: up to 1500 V±50g Sensor (352C34, PCB, Depew, USA)   Power amplifier (HVA1500, MmV/g + NY, P) (10.2)  Capacitance Blocking force 923 N Free strain 1800 ppm  9.3 nF 2 pk) Broadband resolution: 0.00015 gsingle rms (0.0015 m/s2experimental rms)and MFC Figure 8.±50g Set-up the milling process system. Measurement range: pkof (±490m/s Sensitivity: (±10%) 100 mV/g (10.2) Designed for precise control of MFC actuators actuator arrays   Up to four independent channels Blocking force 923 N  Free strain 1800 ppm The detailed information of this hardware is: 2 2  Frequency range: (±5%) 0.5 to 10,000 Hz Broadband resolution: 0.00015 g rms (0.0015 m/s rms) Figure 8. Set-up of the milling process experimental system.  Measurement range: ±50g pk (±490m/s pk) Voltage: up device to 1500V ‚  Data acquisition CI, Santa is: Clara, CA, USA)  Blocking force 923(COCO-80, N8.ofSet-up The detailed information this hardware Piezoelectric patch (M-8557-P1, M +USA)  Frequency (±5%) 0.5 to 10,000 Hz Broadband resolution: 0.00015 gP)rms (0.0015 m/s2experimental rms) Figure ofsingle the milling process   Sensor (352C34, PCB, Depew, NY, Designed forrange: precise control of MFC actuators and MFCsystem. actuator arrays The detailed information of this hardware is:  Active length 85 mm, active width 57 mm  Piezoelectric patch (M-8557-P1, M + P) Frequency range: (±5%) 0.5 to 10,000 Hz  Sensitivity: (±10%) 100 mV/g (10.2) Inputs: Two to eight BNC connectors with voltage or IEPE  Sensor (352C34, PCB, Depew, NY, USA)  Data acquisition device (COCO-80, CI, Santa Clara, CA, USA) Capacitance 9.3 nF The detailed information of this hardware is: 2 pk)  Active length 85 mm, active width 57 mm Piezoelectric patch (M-8557-P1, M +USA) P) Measurement range: ±50g pk (±490m/s Sensitivity: (±10%) 100 mV/g (10.2) Outputs: 1toSMB connector, 100 dB dynamic range, Inputs: Two eight BNC connectors with voltage or 24-bit IEPE D/A converter    Sensor (352C34, PCB, Depew, NY,  Measurement Free strain 1800 ppm Capacitance 9.3 nF 2 pk) m/s2 rms)  Active length 85 mm, active width 57 mm Broadband resolution: 0.00015 g rms (0.0015 range: ±50g pk (±490m/s  Outputs: 1 SMB connector, 100 dB dynamic range, 24-bit D/A converter  Sensitivity: (±10%) 100 mV/g (10.2) Maximum sampling rate: 102.4 kHz simultaneously  Sensor (352C34, PCB, Depew, NY, USA)  Blocking force 923 N 0.00015 Free strain 1800 ppm Capacitance 9.3 nF 2 rms) 2  Frequency range: (±5%) 0.5 to 10,000 Hz Broadband resolution: g rms (0.0015 m/s   Maximum sampling rate: 102.4 kHz simultaneously Measurement range: ±50g pk (±490m/s pk)data storage Sensitivity: (±10%) 100 mV/g Flash memory: 4 GB used for(10.2) system and Blocking force 923 N 0.00015  Free strain 1800 ppm   Piezoelectric patch (M-8557-P1, M +10,000 2 data  Frequency range: (±5%) 0.5pk to(±490m/s Hz Flash memory: 4range: GB used for system and Broadband resolution: gP)rms (0.0015 m/s2 rms) Measurement ±50g pk) storage Blocking force 923 N active  Active length 85 mm, 57Hz mm m/s2 rms)  Piezoelectric patch (M-8557-P1, +10,000  Frequency range: (±5%) 0.5 M towidth Broadband resolution: 0.00015 gP)rms (0.0015  Capacitance 9.3 nF Active length 85 mm, active mm  Piezoelectric patch (M-8557-P1, +10,000 P) 57Hz  Frequency range: (±5%) 0.5 M towidth  Free strain 1800 ppm Capacitance 9.3 nF  Active length 85 mm, activeMwidth  Piezoelectric patch (M-8557-P1, + P) 57 mm Blocking force 923 N active width 57 mm  strain 1800 ppm Capacitance 9.3 nF  Free Active length 85 mm,  Capacitance Blocking force N Free strain 1800 ppm  9.3923 nF  Blocking force 923 N Free strain 1800 ppm  Blocking force 923 N

Figure Figure9.9.Data Dataflow flowof ofthe themilling millingprocess processexperiment. experiment.

In this experiment, the milling machine cuts two grooves on the aluminium plate with the following cutting parameters: speed 585 r/min; feed rate 60 mm/min and cut depth 2 mm. The experimental vibration responses are analyzed and compared in Figure 10 by frequency spectrum, energy histograms and time-frequency waterfall diagram. It can be seen from these plots or

Sensors 2016, 16, 68

10 of 12

In this experiment, the milling machine cuts two grooves on the aluminium plate with the following cutting parameters: speed 585 r/min; feed rate 60 mm/min and cut depth 2 mm. The experimental vibration responses are analyzed and compared in Figure 10 by frequency spectrum, energy histograms and time-frequency waterfall diagram. It can be seen from these plots or comparisons that the vibration amplitude or energy is reduced obviously when the constructed active control method is on, especially the low-frequency range energy histograms in which the the original value of the controlled vibration energy is reduced by more than 50%. The machining effect is shown in Figure 11. Aluminum plate is cut with two grooves, in which one is cut with the active control system on and one with the control system off. It can be seen that the second groove with the control system on is obviously better than the first one, whose surface is rougher. Therefore, the constructed active control algorithm is effective and useful in on-line manufacturing process, and it Sensors 2016, 16, 68 10 of 12 Sensors 2016, 16, 68 smoothness in manufacturing. 10 of 12 can improve surface 0.07

0.07

0.018

0.018

Control off Control off Controlon Controlon

0.06 0.06

Control off

Control off Control on Control on

0.016

0.016

0.014 0.014

0.05 0.05 Energy/g 2 Energy/g

Amplitude/g

2

Amplitude/g

0.012 0.012

0.04 0.04

0.03 0.03

0.01 0.01 0.008 0.008 0.006 0.006

0.02 0.02 0.004 0.004

0.01

0.01

0

0.002

0.002

0

0

0

100

100

200

200

300 400 300 400 Frequency/Hz

Frequency/Hz

(a)(a)

(c)

(c)

500

500

600

600

0

00 0

100

100

200

300

200 Frequency/Hz 300 Frequency/Hz

400

400

500

500

600

600

(b) (b)

(d)

(d)

Figure 10. Experimental results of active vibration suppression in a milling process: (a) frequency

Figure 10. Experimental results of active vibration suppression in a milling process: (a) frequency spectrum (b) energy histogram waterfall diagramin with control off (d) time-frequency Figure 10. Experimental results(c) oftime-frequency active vibration suppression a milling process: (a) frequency spectrum (b) energy histogram (c) on. time-frequency waterfall diagram with control off (d) time-frequency waterfall with control spectrum (b)diagram energy histogram (c) time-frequency waterfall diagram with control off (d) time-frequency waterfall diagram with control on. waterfall diagram with control on.

Figure 11. Machining effect of the aluminium plate with and without on-line vibration suppression.

4. Conclusions Figure 11. Machining effect of the aluminium plate with and without on-line vibration suppression. Figure 11. Machining effect of the aluminium plate with and without on-line vibration suppression. Based on the classical LMS, a frequency-domain active control method is constructed for on-line 4. Conclusions vibration suppression of milling processes to improve the surface smoothness of the workpiece. A hybrid criterion is constructed by combining the global frequency error and frequency Basederror on the classical LMS, a frequency-domain active control method is constructed for node on-line error together, thus the adaptability, anti-interference ability and efficiency of this method is A vibration suppression of milling processes to improve the surface smoothness of the workpiece. improved. Spindle-based simulation and milling machine-based experiments are introduced to hybrid error criterion is constructed by combining the global frequency error and frequency node verify the proposed method and control platform. In theability experiment, taking aluminium plate as is error together, thus the adaptability, anti-interference and efficiency of this method

Sensors 2016, 16, 68

11 of 12

4. Conclusions Based on the classical LMS, a frequency-domain active control method is constructed for on-line vibration suppression of milling processes to improve the surface smoothness of the workpiece. A hybrid error criterion is constructed by combining the global frequency error and frequency node error together, thus the adaptability, anti-interference ability and efficiency of this method is improved. Spindle-based simulation and milling machine-based experiments are introduced to verify the proposed method and control platform. In the experiment, taking aluminium plate as control object, two grooves are cut by a milling machine, one with the control on and one in the natural condition. Analysis of the results, including frequency spectrum, energy histograms and time-frequency waterfall diagram, indicates that the proposed hybrid error criterion-based frequency-domain active vibration suppression method can achieve satisfactory effects in on-line milling processes. The machining effect of the aluminium plate also proves this point again. Vibration is only one of the factors affects the machining quality of workpieces. Faults are another threat to machining quality, and may lead to unpredictable consequences. Therefore, in order to guarantee the reliability and machining effect, we plan to integrate together the condition monitoring, fault diagnosis and active vibration suppression units into machine tools to improve the performance of machine tools. Acknowledgments: This work was supported by the National Natural Science Foundation of China (Nos. 51405370 & 51225501), the National Key Basic Research Program of China (No. 2015CB057400), the project supported by Natural Science Basic Plan in Shaanxi Province of China (No. 2015JQ5184), and Shaanxi Province Postdoctoral Research Project. Author Contributions: Xingwu Zhang and Chenxi Wang developed the control algorithm. Xuefeng Chen and Xingwu Zhang conceived the experiment; The experiment and simulation of this work was conducted by Chenxi Wang, and Shibin Wang; Ruqiang Yan and Robert X. Gao performed the analysis of the work; All authors wrote and approved the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Novakov, T.; Jackson, M.J. Chatter problems in micro-and macrocutting operations, existing models, and influential parameters—A review. Int. J. Adv. Manuf. Tech. 2010, 47, 597–620. [CrossRef] Kayhan, M.; Budak, E. An experimental investigation of chatter effects on tool life. J. Eng. Manuf. 2009, 223, 1455–1463. [CrossRef] Abele, E.; Altintas, Y.; Brecher, C. Machine tool spindle units. CIRP Ann. Manuf. Technol. 2010, 59, 781–802. [CrossRef] Elliott, S. Signal Processing for Active Control; Academic Press: Lodon, UK, 2001. Kakinuma, Y.; Enomoto, K.; Hirano, T.; Ohnishi, K. Active chatter suppression in turning by band-limited force. CIRP Ann. Manuf. Technol. 2014, 63, 365–368. [CrossRef] Hesselbach, J.; Hoffmeister, H.W.; Schuller, B.C.; Loeis, K. Development of an active clamping system for noise and vibration reduction. CIRP Ann. Manuf. Technol. 2010, 59, 395–398. [CrossRef] Monnin, J.; Kuster, F.; Wegener, K. Optimal control for chatter mitigation in milling—Part 1: Modeling and control design. Control Eng. Pract. 2014, 24, 156–166. [CrossRef] Monnin, J.; Kuster, F.; Wegener, K. Optimal control for chatter mitigation in Millingpart 2: Experimental validation. Control Eng. Pract. 2014, 24, 167–175. [CrossRef] Long, X.; Jiang, H.; Meng, G. Active vibration control for peripheral milling processes. J. Mater. Process. Technol. 2013, 213, 660–670. [CrossRef] Xu, X.; Chen, S. Field balancing and harmonic vibration suppression in rigid AMB-rotor systems with rotor imbalances and sensor runout. Sensors 2015, 15, 21876–21897. [CrossRef] [PubMed] Kwak, M.K.; Lee, J.H.; Yang, D.H.; You, W.H. Hardware-in-the-loop simulation experiment for semi-active vibration control of lateral vibrations of railway vehicle by magneto-rheological fluid damper. Veh. Syst. Dyn. 2014, 52, 891–908. [CrossRef]

Sensors 2016, 16, 68

12.

13.

14. 15. 16. 17. 18. 19. 20.

21. 22. 23. 24.

25. 26. 27. 28.

12 of 12

Nguyen, S.D.; Nguyen, Q.H.; Choi, S.B. A hybrid clustering based fuzzy structure for vibration control—Part 1: A novel algorithm for building neuro-fuzzy system. Mech. Syst. Signal Process. 2015, 50–51, 510–525. [CrossRef] Nguyen, S.D.; Nguyen, Q.H.; Choi, S.B. A hybrid clustering based fuzzy structure for vibration control—Part 2: An application to semi-active vehicle seat-suspension system. Mech. Syst. Signal Process. 2015, 56–57, 288–301. [CrossRef] Sun, W.C.; Gao, H.J.; Yao, B. Adaptive robust vibration control of full-car active suspensions with electrohydraulic actuators. IEEE Trans. Control Syst. Technol. 2013, 21, 2417–2422. [CrossRef] Li, H.Y.; Yu, J.Y.; Hilton, C.; Liu, H.H. Adaptive sliding mode control for nonlinear active suspension vehicle systems using T–S fuzzy approach. IEEE Trans. Ind. Electron. 2013, 60, 3328–3338. [CrossRef] Daley, S.; Johnson, F.A.; Pearson, J.B.; Dixon, R. Active vibration control for marine applications. Control Eng. Pract. 2004, 12, 465–474. [CrossRef] Kim, H.S.; Sohn, J.W.; Jeon, J.J.; Choi, S.B. Reduction of the radiating sound of a submerged finite cylindrical shell structure by active control. Sensors 2013, 12, 2131–2147. [CrossRef] [PubMed] Zhang, X.W.; Chen, X.F.; You, S.Q.; He, Z.J.; Li, B. Simulation and experimental investigation of structural dynamic frequency characteristics control. Sensors 2012, 12, 4986–5004. [CrossRef] [PubMed] Zhang, X.W.; Chen, X.F.; You, S.Q.; He, Z.J. Active control of dynamic frequency responses for shell structures. J. Vib. Control 2015, 21, 2813–2824. [CrossRef] Chamroon, C.; Cole, M.O.T.; Wongratanaphisan, T. An active vibration control strategy to prevent nonlinearly coupled rotor-stator whirl responses in multimode rotor-dynamic systems. IEEE Trans. Control Syst. Technol. 2014, 22, 1122–1129. [CrossRef] Li, Y.L.; Wang, X.J.; Huang, R.; Qiu, Z.P. Active vibration and noise control of vibro-acoustic system by using PID controller. J. Sound Vib. 2015, 348, 57–70. [CrossRef] Lin, J.; Lian, R.J. Intelligent control of active suspension systems. IEEE Trans. Ind. Electron. 2011, 58, 618–628. [CrossRef] Ferrari, G.; Amabili, M. Active vibration control of a sandwich plate by non-collocated positive position feedback. J. Sound Vib. 2015, 342, 44–56. [CrossRef] Sun, X.; Jing, X.; Cheng, L.; Xu, J. A 3-D quasi-zero-stiffness-based sensor system for absolute motion measurement and application in active vibration control. IEEE ASME Trans. Mechatron. 2014, 20, 254–262. [CrossRef] Wu, Q.; Yue, H.; Liu, R.; Zhang, X.; Ding, L.; Liang, T.; Deng, Z. Measurement model and precision analysis of accelerometers for maglev vibration isolation platforms. Sensors 2015, 15, 20053–20068. [CrossRef] [PubMed] Her, S.C.; Lin, C.S. Vibration analysis of composite laminate plate excited by piezoelectric actuators. Sensors 2013, 13, 2997–3013. [CrossRef] [PubMed] Widrow, B.; Hoff, M.E. Adaptive Switching Circuits. In Proceedings of the IRE WESCON Convention Record: At the Western Electronic Show and Convention, Los Angeles, CA, USA, 23–26 August 1960. National Instruments Products: NI PXI-7853R. Available online: http://sine.ni.com/nips/cds/ view/ p/lang/en/nid/206323 (accessed on 30 December 2015). © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).