ORIGINAL ARTICLE

Application of time delay resonator to machine tools

Alireza Akbarzadeh Tootoonchi &Mohammad Sadegh Gholami

Received: 27 January 2010 /Accepted: 7 February 2011 /Published online: 9 March 2011# Springer-Verlag London Limited 2011

Abstract Undesirable vibration can negatively affect theperformance of machineries. In case of a machine tool, itnegatively affects machining accuracy and tool life.Performance may be improved at the design stage byincreasing machine stiffness. However, this is difficult toaccomplish with existing machines. This paper implementsa delay resonator (DR) on model of a typical machine toolto minimize relative vibration between the cutting tool andworkpiece during machining process. The DR is a tunablevibration absorber which converts a conventional passiveabsorber into a marginally stable resonator. This structureabsorbs all the vibratory energy at its point of attachment. Astrategy called “Stability charts” is used not only to resolvethe stability question but also to find out gain and timedelay of the absorption. Results show that relative motionbetween cutting tool and workpiece is reduced significantly.

Keywords Delay resonator . Machine tool . Cutting tool .

Vibration . Stability charts . MATLAB Simulink

1 Introduction

Today’s machines are required to take smaller foot print,weight less, more durable while having higher accuracy andoperation speed. One way to achieve some of these require-ments is by reducing undesirable vibrations. A great deal ofengineering efforts is placed to minimize undesirable vibration

of machineries. There are many solutions that may be usedsuch as changing electrical and mechanical stiffness. Theseparametersmay be altered at the design stage for newmachinesthat are not built yet. However, making any fundamentalchanges to existing machines is usually difficult to implement.Therefore, a method to improve the performance of an existingmachine, with a given mechanical and electrical stiffness, ishighly desirable. Among manufacturing equipment, machinetools and robots usually require higher accuracies. Forexample, in machining procedure, the cutting forces generatedduring the cutting process as well as external excitations willcreate undesirable vibratory motions of various structuralcomponents [1] that must be minimized. In particular, therelative motion between the cutting tool and the workpiececreates undulation on the machined surface, and hence,adversely affects the surface accuracy. Furthermore, if theamplitude of the vibration grows significantly, this undulationbecomes the source of oscillatory force in the following pass,which again excites the cutting tool more and eventuallyleads to an unstable situation. This type of vibration is called“regenerative mechanism” and occurs due to the closed loopnature of machining operations [1]. One of the majorconcerns in designing a machine tool structure is, therefore,reducing the relative amplitude of vibration between the tooland the workpiece. If a machine tool is extremely rigid or theexcitation frequency is below its first resonance frequency,the entire system will undergo a rigid body motion with norelative vibration between the tool and the workpiece. Thus,efforts are made to maximize the stiffness of a machine toolstructure during design and construction. However, severalfunctional requirements need to be satisfied within a limitedspace. The cost involved in building a very rigid systemlimits the achievable stiffness of the system, especially that ofthe cutting tool. Therefore, a certain amount of vibration isunavoidable during operation [2]. In the previous studies,optimization of passive vibration absorbers was effectively

A. A. TootoonchiME Department, Ferdowsi University of Mashhad,Mashhad, Irane-mail: ali_akbarzadeh_t@yahoo.com

M. S. Gholami (*)M.Sc. Ferdowsi University of Mashhad,Mashhad, Irane-mail: gholami.m.s@gmail.com

Int J Adv Manuf Technol (2011) 56:879–891DOI 10.1007/s00170-011-3225-6

used to remove undesirable oscillations from mechanicalstructures by Y.C. Shin and K.W. Wang [2]. Other commonpassive approach, modification to the tool holder wasconsidered by Rivin and Kang [3], and in other studies,adding a tuned mass vibration absorber was considered byHopkins and Kosker [3]. In more recent studies, activevibration absorber was used by adding damping to a singleaxis of the structure. In this manner, Matsubara, Yamamoto,and Mizumoto used piezoelectric actuators to apply controlmoments to the boring bar. Their system uses time delay tophase shift an accelerometer signal and achieve narrowbandvelocity feedback control [3]. Subsequently, Tewani, Rouch,and Walcott mounted a piezoelectric reaction mass actuator inthe bar itself and created what they termed an active dynamicabsorber [3]. To eliminate undesirable torsional oscillations inrotating mechanical structures, an active vibration absorptiondevice called centrifugal delayed resonator was introduced byHosek et al. [4]. This device was forced to mimic an idealreal-time tunable absorber utilizing a control torque in theform of proportional angular position feedback with variablegain and time delay. In another study, a DR absorber wasimplemented on a flexible beam, and the dynamic features of

its structure were studied by Olgac and Jalili [5]. In particular,the stability features obtained through analytical and exper-imental studies were compared. Results obtained concur withthe experimental findings better than the earlier dynamicmodels which use the finite difference method and idealclamped-clamped BCs. In other researches, many experimen-tal methods were developed for the optimization of themachine tool structural response. These approaches,however, were mainly dealt with the structural motionof a machine tool itself, not the relative vibrationbetween a cutting tool and a workpiece. Since thecutting tool or workpiece often is the most flexible part

Concept of DR

Selecting a representave machine tool

Modeling

Identifying state variables

State-space representation of the system dynamics

Show advantageous of using DR

Comparing results

DR attached to Tool holderDR attached to workpiece

MATLAB SIMULATION model for 2 case studies

Select g and Identify stability zoneIdentify time delay and gain

Stability analysis of the combinedsystem (Machine + DR)

Select location for DR

Cutting Tool Workpiece

Fig. 1 A detailed flow chartdepicting major steps carried outin this paper

Ma

Ka Ca

Ma

Ka Ca

a) b)

Fig. 2 a Passive absorber. b DR absorber with acceleration feedback

880 Int J Adv Manuf Technol (2011) 56:879–891

of an entire machine tool system, optimizing the rigidityof other structural components might have little effects onreducing the relative vibration at the cutting point [6, 7].Robustness of the control strategy against fluctuations in thestructural parameters of the controlled system was addressedby Martin Hosek and Olgac [8]. A new example waspresented by Olgac and Sipahi for assessing the stabilityposture of a general class of linear time invariant–neutraltime delayed systems. The ensuing method, which is namedthe direct method, offers several unique features: It returnsthe number of unstable characteristic roots of the system in

an explicit and non-sequentially evaluated function of timedelay, τ. Consequently, the direct method creates exclusivelyall possible stability intervals of τ [9].

The DR vibration absorber has some attractivefeatures in eliminating tonal vibrations from the system[10]. Some of them are ability of real-time tune, perfecttonal suppression, wide range of frequencies, simplicity ofthe control implementation, and robust design [11].Additionally this single-degree-of-freedom absorber canalso be tuned to handle multiple frequencies of vibration[12]. Z. H. Wang and H. Y. Hu presented a systematic

Table 1 Lumped spring-mass models

Modeled asWorkpiece

M2

K3 C3

K2 C2

K1 C1

Modeled M1

K2 C2

K4 C4

Modeled asM3

Ka Ca

K4 C4K3 C3

Modeled asDelay resonator Ma

Ka Ca

Cutting tool

f0 sin( t)

DR system

Primary system

C3K3

K4

M3

M2

Ma

Ka Ca

K2 C2

C1

M1

K1

C4

a) b) Fig. 3 a Spring-mass model ofthe machine tool—DR attachedto the m3. b Machine tool,cutting tool, and workpiece

Int J Adv Manuf Technol (2011) 56:879–891 881

method of stability analysis for high-dimensional dynamicsystems involving a time delay and some unknownparameters [13]. The term “unknown” means that theparameters are constants but yet to be determined. Theanalysis focuses on the stability switches of those systemswith increase of the time delay from zero to infinity. Onthe basis of the generalized Sturm criterion, the parameterspace of concern is divided into several regions deter-mined by a discrimination sequence and the Routh–Hurwitz conditions. It is found that as the time delayincreases, the system undergoes none, exactly one, ormore than one stability switches when the parameters arechosen from different regions [13].

Takagi–Sugeno fuzzy model was extended by Chen-YuanChen to analyze the stability of interconnected systems withtime delays in their subsystems [14]. They present a stabilitycriterion in terms of Lyapunov’s theory for fuzzyinterconnected models [14]. The stabilization problem wasconsidered by F. H. Hsiao for a nonlinear multiple time-delay large-scale system [15]. They employed a neural-network (NN) model to approximate each subsystem of thelarge-scale system [15]. They established a linear differentialinclusion state space representation for the dynamics of eachNN model. Finally, a delay-dependent stability criterion wasderived to guarantee the asymptotic stability of the nonlinearmultiple time-delay large-scale systems.

0 0.005 0.01 0.015 0.02 0.025 0.030

0.005

0.01

0.015

0.02

τ (s)

Gai

n (K

g)

0 0.005 0.01 0.015 0.02 0.025 0.030

500

1000

τ (s)

ω (R

ad/s

)

a)

Zoom in

DR alone

Stable zone

Combined system

l = 1 l = 2 l =3

DR alone

Combinedsystem

b)

c)

d)

Fig. 4 Stability charts. a Plot ofgain versus time delay forcombined system and DR alone.b Plot of excitation frequencyversus time delay for DR alone.c A zoom of selected zoneshown in a. d A zoom ofselected zone shown in b

m1 m2 m3 m4 k1 k2 k3 k4 ka C1 C2 C3 C4 Ca(kg) (N/m) (Nm/s)

100 10 8 0.3 100e4 80e4 10e4 80e4 1e4 50 60 7 60 0.5

Table 2 System parameters value

882 Int J Adv Manuf Technol (2011) 56:879–891

In this study, our goal is to demonstrate that theundesirable vibration of a machine tool with specificworking frequency can be minimized by utilizing a DRand without altering the existing control system ormechanical structure of the machine. Therefore, a machinetool and a delay resonator are chosen to minimize therelative vibration between the cutting tool and workpiece.The DR is first attached to the cutting tool and next to theworkpiece. In both cases, the relative vibration during

machining process are studied and reported in this paper. Adetailed flow chart depicting major steps carried out in thispaper is shown in Fig. 1.

2 The delay resonator concept

A brief overview of DR is presented here. DR has anunconventional control logic which is implemented on a

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1x 10-3

x 10-3

x 3 (

m)

x 3 (

m)

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1

Time (s)

a)

b)

Fig. 5 a Displacement of m3while g=0. b Displacement ofm3 while g≠0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.015

-0.01

-0.005

0

0.005

0.01

0.015

x a (

m)

x a (

m)

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Time (s)

a)

b)

Fig. 6 a Displacement absorberwhile g=0. b Displacement ofabsorber while g≠0

Int J Adv Manuf Technol (2011) 56:879–891 883

passive absorber. See Fig. 2a. It consists of a proportionalposition feedback with time delay. The position feedback canbe based on absolute or relative displacements of the absorber.These displacement measurements are prohibitively difficult

for high frequency-low amplitude applications. Accelerationfeedback is much more feasible for such cases. See Fig. 2b.

Naturally, the effects of substituting displacement mea-surements with acceleration should be carefully analyzed.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-3

-2

-1

0

1

2

3x 10 -4

x 10 -3

x 1 (

m)

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2.5

-2-1.5

-1-0.5

00.5

11.5

22.5

x 2 (

m)

Time (s)

a)

b)

Fig. 7 a Displacement of m1,while g≠0. b Displacement ofm2, while g≠0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-3

-2

-1

0

1

2

3

x 1 (

s)

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10-3

x 10-4

x 2 (

m)

Time (s)

a)

b)

Fig. 8 a Displacement of m1,while g=0. b Displacement ofm2,while g=0

884 Int J Adv Manuf Technol (2011) 56:879–891

Using this feedback control converts the dissipative passiveabsorber structure into a marginally stable one, i.e., aresonator with a specified resonance frequency, ωc [12].

Control goal is to place the dominant poles at ±ωj, wherej ¼ ffiffiffiffiffiffiffi�1p . Recommended force to achieve pole position isg � x��a t � tð Þ ð1Þwhere g is gain and τ is time delay. The corresponding newsystem dynamics is

max��a þ cax� a þ kaxa � gx��a t � tð Þ ¼ 0 ð2ÞThe Laplace domain representation leads to the transcen-

dental characteristic equation

mas2 þ casþ ka � gs2e�ts ¼ 0 ð3ÞThis equation possesses infinitely many finite roots for g≠0

and τ≠0. Their distribution can be sketched following the

root locus analysis [13]. To achieve ideal resonator behavior,two dominant roots of Eq. 2 should be placed on theimaginary axis at the desired crossing frequency ωc whilethe others remain in the left half of the complex plane.Substituting S=±ωj into Eq. 3 and solving for the controlparameters gc and τc, one obtains

gc ¼ 1wc

2

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficawcð Þ2 þ maw2c � ka

� �2q ð4Þ

tc ¼ 1wc

� �tan�1

cawcmaw2c � ka

� �þ 2 L� 1ð Þp

; L¼ 1; 2; . . .

ð5ÞThe variable parameter L refers to the branch of root loci

that happens to cross the imaginary axis at ωc. Extensivestudies on stability analysis have been done previously [7–10].

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1.5

-1

-0.5

0

0.5

1

1.5x 10-4

X3

(m)

Fig. 9 Control parameters areselected from unstable zone

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-3

-2

-1

0

1

2

3

4x 10-3

x 1 (

m)

x 1 (

m)

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-8

-6

-4

-2

0

2

4

6

8x 10-4

Time (s)

a)

b)

Fig. 10 a Displacement of m1without DR. b Displacement ofm1 with DR and gain ≠0

Int J Adv Manuf Technol (2011) 56:879–891 885

3 DR application on machine tool

A mechanical system can be described by a lumped spring-mass model. Since an actual machine tool structure cannot beregarded as a system with proportional damping, generalviscous damping must be used to describe the behavior of the

system. A typical machine tool, workpiece, cutting tool, andtime delay resonator with their lumped spring-mass models areexplained in Table 1. Equivalent masses of the machine tool,workpiece, and the cutting tool are represented by m1, m2,and m3, respectively. The delay resonator mass, ma, isattached to the cutting tool through a spring and a damper.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-3

-2

-1

0

1

2

3

4x 10-3

x 2 (

m)

x 2 (

m)

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-8

-6

-4

-2

0

2

4

6

8x 10-4

Time (s)

a)

b)

Fig. 11 a Displacement of m2without DR. b Displacement ofm2 with DR and gain

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4x 10-3

x3 (

m)

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1x 10-3

x3 (

m)

Time (s)

a)

b)

Fig. 12 a Displacement of m3without DR. b Displacement ofm3 with DR and gain

886 Int J Adv Manuf Technol (2011) 56:879–891

The stiffness and damping of the machine tool, workpiece,cutting tool, and delay resonator are represented by k1, C1, k2,C2, k3, C3, and ka, Ca, respectively. Additional relationbetween the cutting tool and the machine tool can be modeledby using an additional set of spring and damper, as k4, C4.Four basic coordinates, x1, x2, x3, and xa are defined torepresent the 4-degree-of-freedom of the system.

In milling process, an exciting force is generated betweencutting tool and workpiece. This force leads to additionalvibration in cutting tool, workpiece, andmachine tool. The goalof this study is to improve the quality of the milling process byreducing the vibration between cutting tool and the workpiece.

Assembled model is shown in Fig. 3.The state space representation of the system dynamics is

written in the form:

y� ðtÞ ¼ A0yðtÞ þ gAt y� ðt � tÞ þ f ðtÞ ð6Þ

Where, yðtÞ ¼fx1; x� 1; x2; x� 2; x3; x� 3; xa; x� ag and f ðtÞ ¼0; 0; 0� f ; 0; f ; 0; 0f g are state space variables and excitation

force, respectively. Furthermore, the amplitude deflection of theprimary structure and absorber are denoted by xi, where i=1, 2,3, a. The parameters A0 and Aτ represent correspondingsystem matrices. These matrices are shown in Appendix.Finally, g and τ are gain and time delay, respectively. TheLaplace transform of Eq. 6 is

sI � A0 � gse�tsAtð ÞY ðsÞ ¼ FðsÞ ð7ÞThe characteristic equation can be written as

Qðs;g;tÞ ¼ sI � A0 � gse�tsAtj j ¼ 0 ð8ÞPoles of the system are those (complex) values of s for

which sI � A0 � gse�tsAtj j is zero. For non-delay systems,these poles are the eigenvalues of the system matrix, A0.

4 Stability analysis of the combined system

The stability is an important property of any feedbackcontrol system. The sufficient and necessary condition forasymptotic stability is that the roots of the transcendentalcharacteristic Eq. 8 have negative real parts. The verifica-tion of the root locations, however, is not a trivial task. Thecharacteristic Eq. 8 can be written in a simplified form as

X1k¼0

HkðsÞgke�kts ¼ 0 ð9Þ

One can obtain its most general form as

Mðg;sÞþNðg;sÞge�ts ¼ 0; ð10Þwhere M and N are polynomials of s. When the combined(machine tools with DR on cutting tool) system is marginally

stable, there are at least two roots on the imaginary axis.Enforcing S=±ωj into Eq. 10 and solving for the controlparameters gcs and τcs yields the delay and feedback valuesthat make the combined system marginally stable as

gcs ¼ Mðg;sÞNðg;sÞ����

���� ð11Þ

tcs ¼ ð 1wcsÞ 2ðl � 1Þp þ tan�1ðMðg;sÞ

Nðg;sÞ Þ

ð12Þ

As shown in Fig. 4a and b, plots of gc versus τc and gcsversus τcs illustrate the stability points. Zoomed sections for aninterval containing operating frequency are shown in Fig. 4cand d. The ratio of the combined system gain and DR gain(gcs/gc) can be defined as the “stability margin” of the controlsystem, at the particular delay value τ. That is, for a given τc,the system is stable if gc

that for ideal suppression, the control must maintain the DRwithin the stability zone. As shown in Fig. 4c, this zone isbelow dotted lines and where gain of the DR is less than gainof the combined system (meshed zone).

Clearly, the desirable values of the combined systemgain and time delay should be in the stable operating zones.Figure 4b shows the relation between the delay, τc, and thefrequency, ωc. For instance, the stable interval of τ given inexample above corresponds to 575

is based on the time-delay resonator, which is a tonalvibration absorber. Unlike previous studies which try toreduce the total machine tool structure vibration, thisresearch is concentrated on minimizing the cutting tooland the workpiece vibrations under simple sinusoidalexcitations. This approach is thus more realistic andaddresses the metal cutting excitation problem directlywith minimal computation efforts. What makes thismethod more advantages is its additive nature. Thismeans that its control logic is independent of thecontroller used in the machine tool. Furthermore, the

additional mechanical components, DR, are added tothe system without altering the existing mechanicalstructure. Simulink model of the system is alsopresented. Results of this research indicate that theuse of DR technique for minimizing the vibrationsystem is highly efficient and effective. Results alsoshow that optimum location of DR is on the cuttingtool. This method can be expanded to more complexsystems with large DOF and multiple DRs. Theprocedure outlined can also be used as a design toolfor selecting the DR optimum parameters.

Appendix

x1

TransportDelay1

TransportDelay

x2

To Workspace3

x1

To Workspace2

xa

To Workspace1

x3

To Workspace

Sine Wave

Scope7

Scope5

Scope4

Scope3

Scope2

Scope1

Scope

1s

Integrator7

1s

Integrator6

1s

Integrator5

1s

Integrator4

1s

Integrator3

1s

Integrator2

1s

Integrator1

1s

Integrator

-K-

Gain9

-K-

Gain8

-K-

Gain7

-K-

Gain6

-K-

Gain5

-K-

Gain4

-K-

Gain3

-K-

Gain27

-K-

Gain26

-K-

Gain25

-K-

Gain24

-K-

Gain23

-K-

Gain22

-K-

Gain21

-K-

Gain20

-K-

Gain2

-K-

Gain19

-K-

Gain18

-K-

Gain17

-K-

Gain16

-1Gain15

-K-

Gain14

-K-

Gain13

-K-

Gain12

-K-

Gain11

-K-

Gain10

-K-

Gain1

-K-

Gain

x1dotdot

x1dot

x1dot

x1dot

x1dot

x1dot

x1

x1

x1

x1

x2dotdot

x2dot

x2dot

x2dotx2dot

x2

x2

x2x2

xdot3

xdot3

xdot3

xdot3

xdot3

x3

x3

x3

x3

xadotdot

xadot

xadot

xa

xa

x3dotdot

Fig. 13 MATLAB Simulink model—DR attached on m3

Int J Adv Manuf Technol (2011) 56:879–891 889

A0 ¼

� k1 þ k2 þ k4ð Þ=m1 � c1 þ c2 þ c4ð Þ=m1 k2=m1 c2=m1 k4=m1 c4=m1 0 00 1 0 0 0 0 0 0k2=m2 c2=m2 � k2 þ k3ð Þ=m2 � c2 þ c3ð Þ k3=m2 c3=m2 0 00 0 0 1 0 0 0 0k4=m3 c4=m3 k3=m3 c3=m3 � k3 þ k4 þ kað Þ=m3 � c3 þ c4 þ cað Þ=m3 ka=m3 ca=m30 0 0 0 0 1 0 00 0 0 0 ka=ma Ca=ma �ka=ma �ca=ma0 0 0 0 0 0 0 1

0BBBBBBBBBB@

1CCCCCCCCCCA

x1

TransportDelay1

TransportDelay

x2

To Workspace3

x1

To Workspace2

xa

To Workspace1

x3

To Workspace

Sine Wave

Scope7

Scope5

Scope3

Scope1

Scope

1s

Integrator7

1s

Integrator6

1s

Integrator51s

Integrator4

1s

Integrator3

1s

Integrator2

1s

Integrator1

1s

Integrator

-K-

Gain9

-K-

Gain8

-K-

Gain7

-K- Gain6

-K-

Gain5

-K-

Gain4

-K-

Gain3

-K-

Gain27

-K-

Gain26

-K-

Gain25

-K-

Gain24

-K-

Gain23

-K-

Gain22

-K-

Gain21

-K-

Gain20

-K-

Gain2

-K-

Gain19

-K-

Gain18

-K-

Gain17

-K-

Gain16

-1Gain15

-K-

Gain14

-K-

Gain13

-K-

Gain12

-K-

Gain11

-K-

Gain10

-K-

Gain1

-K-

Gain

x1dotdot

x1dot

x1dot

x1dot

x1

x1

x2dotdot

x2dotx2dot

x2

xdot3xdot3

x3

xadotdot

xadotxadot

xaxa

x3dotdot

Fig. 14 MATLAB Simulink model—DR attached on m2

890 Int J Adv Manuf Technol (2011) 56:879–891

At ¼

0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 g=m3 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 g=ma

0BBBBBBBBBB@

1CCCCCCCCCCA

References

1. Tlusty G (2000) Manufacturing processes and equipment. PrenticeHall

2. Shin YC, Wang KW (1991) Design of an optimal damper tominimize the vibration of machine tool structures subject torandom excitation. J Eng Comput 9:199–208

3. Pratt JR (1997) Vibration control for chatter suppression withapplication to boring bars. PhD. Dissertation, pp 40–83

4. Hosek M, Elmali H, Olgac N (1997) A tunable torsional vibrationabsorber: the centrifugal delayed resonator. J Sound Vib 205:151–165

5. Olgac N, Jalili N (1998) Modal analysis of flexible beams withdelayed resonator vibration absorber: theory and experiments. JSound Vib 218:307–331

6. Åkesson H (2007) Active control of vibration and analysis ofdynamic properties concerning machine tools. PhD. Dissertation,Blekinge Institute of Technology, pp 27–91

7. Rojas J, Liang C, Geng Z (1996) Experimental investigation ofactive machine tool vibration control. Proc SPIE Smart StructMater 2721:373–384

8. Hosek M, Olgac N (2002) A single-step automatic tuning algorithmfor the delayed resonator vibration absorber. IEEE J TransMechatron7:245–255

9. Sipahi R, Olgac N (2006) A unique methodology for the stabilityrobustness of multiple time delay systems. Syst Control Lett55:819–825

10. Olgac N, Holm-hansen B (1994) A novel active vibrationabsorption technique: delayed resonator. J Sound Vib 176:93–104

11. Jalili N, Olgac N (1999) Multiple delayed resonator vibrationabsorbers for multi degree of freedommechanical structures. J SoundVib 223:567–585

12. Olgac N, Hosek M (1996) Active vibration absorption usingdelayed resonator with relative position measurement. ASME JVib Acoust 119:131–136

13. Wang ZH, Hu H (2000) Stability switches of time-delayeddynamic systems with unknown parameters. J Sound Vib 233(2):215–233

14. Chen CY (2005) Fuzzy logic derivation of neural network modelswith time delays in subsystems. Int J Artif Intell Tools 14:967

15. Hsiao FH, Chen CW, Liang YW, Xu SD, Chiang WL (2005) T-Sfuzzy controllers for nonlinear interconnected systems with multipletime delays. IEEETrans Circuits Syst-I: Regular Pap 52(9):1883–1893

Int J Adv Manuf Technol (2011) 56:879–891 891

Application of time delay resonator to machine toolsAbstractIntroductionThe delay resonator conceptDR application on machine toolStability analysis of the combined systemDynamic simulations and resultCase study—ICase study—II

ConclusionAppendixReferences