arems,ors

twod alersthetro-The

by ofcesgesand

desionballedtriconseed

byign

heir Ononsred.ion

CIRP Annals - Manufacturing Technology 60 (2011) 779796

tool

are

heir

are

ping

and

IRP.

Contents lists available at ScienceDirect

CIRP Annals - ManufMachine tool feed drives

Y. Altintas (1)a,*, A. Verl (2)b, C. Brecher (2)c, L. Uriarte (3)d, G. Pritschow (1)b

aManufacturing Automation Laboratory, University of British Columbia, Vancouver, Canadab Institute for Control Engineering of Machine Tools and Manufacturing Units (ISW), Stuttgart, GermanycMachine Tool Laboratory (WZL), University of Aachen, GermanydMechatronics Dept. Tekniker-IK4, Eibar, Basque Country, Spain

1. Introduction

Feed drives are used to position the machine tool componentscarrying the cutting tool and workpiece to the desired location;hence their positioning accuracy and speed determine the qualityand productivity of machine tools. A general architecture of feeddrive hardware and its computer control structure are shown inFig. 1. Feed drives are either powered by linear motors directly, orby rotary motors via ball screw and nut assembly as shown inFig. 2. The drive train consists of a machine tool table resting on theguide, and moved linearly either by a ball screw drive-nut or by alinear motor system. The ball screw may be connected to therotary servo motor directly or via gear reduction for largemachines. The motor is powered by amplier electronicsconnected to a Computer Numerical Control (CNC) system asshown in Fig. 1a. The table is positioned by the servo drives byfollowing a trajectory generation and control algorithm as shownin Fig. 1b. An NC program generated in CAD/CAM system is loadedto the CNC unit of the machine tool. CNC parses the NC programinto tool path segments which may consist of linear, circular,spline or other geometric motions. The feedrate entered in the NCprogram is combined with the acceleration and jerk limits of thefeed drives, and time stamped discrete position commands aresent to each drive servo by the real time trajectory generationalgorithm. The trajectory generation algorithm considers thekinematics of the machine in decoupling the spatial tool motioninto each feed drive. Modern CNC units use jerk continuous, i.e.fth order polynomials, to generate position commands at eachdiscrete time interval [3]. The discrete position commands areprocessed by real time control laws of each servo drive, and thecorresponding digital velocity commands are converted intoelectrical signals which are fed to the amplier and motor of the

drive. The speed and accuracy of positioning the machine toolaffected by the trajectory generation and control algorithmechanical drives and guides, ampliers, motors and sensused in each feed drive.

By considering the importance of the topic, CIRP published key note articles on feed drive systems. Koren et al. presentesurvey of feedback, feedforward, and cross-coupled controlapplied on feed drives [62,63]. Pritschow et al. compared performance of linear drives against the conventional elecmechanical ball screw drives Electromechanical Drives [83]. latest CNC design architecture has also been surveyedPritschow et al. [84]. This keynote paper presents a reviewrecent technological developments and academic advanachieved in feed drive systems. Ongoing research challenare also discussed in order to push the feed drive accuracy performance to higher levels.

The paper is organized as follows. The machine tool guibased on friction, roller bearing, hydrostatic and levitatprinciples are presented in Section 2. The rack-pinion, screw and linear drive structures are given in Section 3, followby their structural dynamic models in Section 4. Elecmotors and sensors used in feed drives are discussed in Secti5 and 6, respectively. The control of rigid and exible fdrives is presented in Section 7. The paper is concludedhighlighting the current research challenges in feed drive desand control.

2. Machine tool guides

The roller-based guides have gained popularity due to thigh performance and modular integration to machine tools.the other hand, hydrostatic guides are preferred in the applicatiwhere higher accuracy, stiffness and damping are requiAerostatic, magnetic or vacuum guides are used in the precispositioning applications where the external load is small.

A R T I C L E I N F O

Keywords:

Feed

Drive

Machine tool

A B S T R A C T

This paper reviews the design and control of feed drive systems used in machine tools. Machine

guides designed using friction, rolling element, hydrostatic and magnetic levitation principles

reviewed. Mechanical drives based on ball-screw and linear motors are presented along with t

compliance models. The electrical motors and sensors used in powering and measuring the motion

discussed. The control of both rigid and exible drive systems is presented along with active dam

strategies. Virtual modeling of feed drives is discussed. The paper presents the engineering principles

current challenges in the design, analysis and control of feed drives.

2011 C

* Corresponding author.

0007-8506/$ see front matter 2011 CIRP.doi:10.1016/j.cirp.2011.05.010journal homepage: http: / /ees.acturing Technology

elsevier.com/cirp/default .asp

Tfollo

Ge Stfo

Wph

To

2.1.

Floadprimminscraslideon twithVari

Dguidslidismopheis hiof

Fig. 1drive

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796780he required functional r for the longitudinal guides are thewing:

ometric accuracy since it is translated to the part directly.iffness to withstand the machining process and the inertialrces with minimum deformation.ear resistance and low friction to avoid gripping, stickslipenomena and aging of the surfaces.ughness to withstand impacts from the machining process.

Friction guides

riction guides have good damping, strength against impacts and high load capacity with up to 140 MPa. They arearily used in speeds under 0.5 m/s. Uniform contact withimum adhesion between the bed and slide is obtained byping and leaving uniform marks on the contact surfaces. The-ways are lubricated by 1 mm deep lubrication slots openedhe moving part of the guides. The guides can also be coated

few mm thick polymers in order to reduce the friction.ous congurations of friction guides are shown in Fig. 3.ifferent pairs of materials are used to manufacture frictiones. Casting, steel, bronze and certain polymers are used asng materials. A key factor to ensure the controllability andoth operation of the guide is to avoid the stickslipnomenon which appears when the static friction coefcientgher than the dynamic friction coefcient. The developmentpolymer based materials with additives which favour

lubrication, for example, TurciteTM, SKC1 or Moglice1, hasallowed to a great extent the reduction of the stickslipphenomenon (see Figs. 4 and 5).

2.2. Rolling guides

Recirculating and stationary roller-based guides are mostwidely used in present machine tool applications (see Fig. 6).The stationary rolling bearings tend to be used when the stroke ofthe slide is relatively short. The rolling elements can be steel balls,rollers or needles, which are preloaded between two cagesattached to stationary and moving parts of the guides. They have

. Architecture of a feed drive control system. (a) Physical components of a feed (WZL). (b) Feed drive control algorithms (UBC).

Fig. 2. Linear and ball-screw drive mechanisms.

Fig. 3. Congurations of friction guides (by Busak Shamban1).

Fig. 5. Coated slideways in a table of a gantry milling machine (by SKC1).

Fig. 4. Comparative diagram of frictional behaviour (SKC1).

ells arethence

oilnce,ide.eric, pc.

(1)

andTheo be

the theted

(2)

N)

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796 781low friction, high load capacity and stiffness, but with lowstructural damping. The recirculating rolling guides are manu-factured with different size and load capacity by the manufacturersas listed in Table 1. They can be supplied with integrated positionsensors or racks to expedite the design and assembly of machinetool drives.

Fig. 7 shows the clamping systems for linear guide technologies.To release the clamping action by safety clamps (see Fig. 7 top), thechamber between the two spring diaphragms is lled withcompressed air. The diaphragms deect outwards, allowing theclamping body to return to its original relaxed position. The brakeblocks lift off the rail. When the chamber is not inated, thediaphragms move back pushing apart the upper clamp body. Withthe horizontal strut acting as fulcrum point, the brake blocks areforced against the linear rail, thus clamping the carriage. Theoperating pressure amounts to 56 bar. To activate the clampingaction by clamps with air (see Fig. 7 bottom), the chamber underthe spring diaphragm is lled with compressed air. The springsheet is pushed upwards and stretched. With the horizontal strutacting as fulcrum point, the brake blocks are forced against thelinear rail, thus clamping the carriage. When the chamber is notinated, the diaphragm moves back into the bended position andthe upper clamp body goes back in its relaxed position. The brakeblocks lift off the rail. By clamps with air the operating pressureamounts to 46 bar.

2.3. Hydrostatic guides

The sliding surfaces of the components are separated by cpressurized with thin oil, hence stick slip and static frictionavoided in hydrostatic guides [55,81,96]. Oil is released to surrounding land as it loses pressure (see Fig. 8). The distabetween the land and the surface which slides over it is thegap, h, which is about 1040 mm. The oil gap generates resistaRc against the ow of the uid, Q, from the oil cell to the outsThe pressure difference between the cavity and the atmosphpressure which acts on the outside is known as cell pressure

The oil ow resistance along the gap can be estimated as:

Rc D pQ

12hLbh3

where h is the dynamic viscosity coefcient of the oil, L is the llength and b is the total width of the land along its perimeter. pressure gradient along the length of the land can be assumed tlinear, and the pressure acts on up to one half of the length ofland for initial force prediction. The complete pressure acts oneffective area (Aeff). The hydraulic suspension force, F, is calculaas follows:

F PcAe f f

Table 1Load capacity of guiding systems.

Size no. Outer dimensions Basic load rating, Radial, reverse radial and side

Height, M (mm) Width, W (mm) Length, L (mm) Dynamic rating, C (kN) Static rating, C0 (k

15 24 34 64.4 14.2 24.2

20 30 44 79 22.3 38.4

25 36 48 92 31.7 52.4

30 42 60 106 44.8 66.6

35 48 70 122 62.3 96.6

45 60 86 140 82.8 126

55 70 100 171 128 197

65 90 126 221 205 320

Fig. 6. Linear guides with rolling bearings. (a) Guides with linear, stationary rollingbearings (INA1). (b) Recirculating rolling guide model (THK1). (c) Linear rolling

guides by Schneeberger1.

Fig. 7. Clamping systems for linear guides (HEMA1).

Fig. 8. Hydrostatic V-at and wrap-around guides (by Hydrostatic1).

Ttheysuppvaryrestpres

pc

wheresisthe resis

Rk

wherespdiamlimithe cdesion diamspir

Tand (Eq.almthe equicapipres

K

whedeperetaaddidire

Tthancell.lamthe

Tthe be eforc

Wp

wheis thstre

tr

wheover

Wr

wheT

due thro

Tguid

the manufacturing accuracy, elastic deformations of the slides, theloss of oil viscosity due to temperature rise, and poor regulation ofoil ow and pressure from a central pump may diminish the gapbetween the sliding surfaces. Especially, the oil viscosity andtemperature rise are highly coupled; hence the mathematicalmodeling of the interaction between the two needs to be iterativein order to predict the equilibrium of their states. A comprehensivemathematical model of the hydrostatic guide design, whichpredicts oil circuit dynamics (i.e. pressure, ow velocity, normaland friction force distribution), ow energy, temperature, oil

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796782tance. The restrictors are built in the form of capillaries whereresistance depends on the viscosity of the oil in the cells. Thetance to the oil ow of a capillary is estimated as:

8hLkpr4k

(4)

re Lk and rk are the length and radius of the capillary,ectively. The short restrictors should have a very smalleter to provide the necessary resistance. This diameter isted by the size of suspended particles in the oil which can blockapillary. The use of short capillaries is also limited because thegn is very sensitive to their diameter; the resistance dependsthe fourth power of the diameter. Capillaries with largereters and a longer length are also used, which tend to be in

al form.he restrictor automatically increases the cell pressure (Eq. (3))tends to decrease the oil gap and increase the ow resistance

(1)) when external forces are applied. The oil gap is keptost stable near the equilibrium gap height, h0. The stiffness ofsystem is formed from the pump, restrictor and cell at thelibrium state of the gap. In case of a cell supplied through allary by means of a pump which operates at a constantsure, the resulting stiffness is,

3F0h0

RkRk Rc0

(5)

re F0 is the suspension force at equilibrium. As the stiffnessnds on the load supported by the cell, hydrostatic guides withining plate are used in order to apply high preloads. Intion to gaining stiffness, the guide can absorb loads in bothctions.he hydrostatic guides provide much higher damping values

the roller-based guides against motions perpendicular to the The source of the damping is the friction force that the oilina presents on sliding. In case of motions parallel to the cell,damping is reduced because there is no displacement of uid.he temperature changes in the oil affect the viscosity, hencedamping and lifting force of the system. The temperature canstimated from the total work done by the pump and frictiones. The work carried out by the pump is:

Q ppe (6)

re e is the pump efciency. The source of the friction work (Wr)e translational motion of the table on the guides. The shearss of the oil is:

hv

h(7)

re v is the translational velocity. The work carried out tocome the hydrodynamic friction can be determined as

trArv Arh v2

h(8)

re Ar is the land area.he dimensioning of a hydrostatic guide is relatively complexto the strong dependency on the temperature rise of the oilughout the hydraulic circuit.here are several challenges in optimal design of hydrostatices. It is desired to have as small oil gaps as possible. However,

viscosity, elastic deformation of sliding surfaces, and prediction ofdynamic oil cell gap and its stiffness could be highly useful tool formachine tool designer.

Most machine builders opt for proled linear rail guides, whichprovide a good combination of performance and ease of installa-tion. Hydrostatic guides are relatively expensive, time-consumingto mount and require a larger design envelope compared toproled rail guides. Paepenmuller have combined the positiveproperties of both rolling element and hydrostatic guideways toform a new hydrostatic compact linear guide [127]. This newguideway system is based on the standardized dimensions ofrolling element guideways. The new hydrostatic linear guides arenow a cost-effective option, as they offer both high precision andbetter damping characteristics for high dynamic rigidity and muchgreater design freedom (see Fig. 9).

2.4. Guides for ultraprecision applications

The use of cylindrical non-circulating roller bearings iscommonly used in the linear carriages of ultra precision machines.The conguration should be kinematic [104] with the rollerscontacting the minimum degrees of freedom needed (see Fig. 10).The preload force is estimated to t the application and the relatedloads that the carriage is expected to experience during operation.When high precision is the primary objective, a constant preload

Fig. 9. Hydrostatic compact linear guide (Schaefer1).

Fig. 10. Ultraprecision rolling guides in a semi-kinematic conguration.he hydrostatic guides are designed with several cells, such that can support off-centre forces and moments. Each cell islied at a different pressure, in order to withstand forces ating operating conditions. Usually a single pump is used withrictors to supply each cell at the appropriate pressure. Thesure in a cell is estimated as:

ppRc

Rk Rc(3)

re pp is the supply pressure and Rk is the restrictor ow

ent

e ofan-ials.om

areoadsmsned

intionface

bytra-heirDMingsm.

asare

Y):3, Kv:

near

).

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796 783case of aerostatic guides, where load is supported over a thin lmof air, the low viscosity and compressibility of air require highmanufacturing and assembly tolerances. The aerostatic guidespresent low losses due to low friction [35,98,109] and the lowviscosity of air, even at high speeds. The air viscosity isapproximately three orders of magnitude less than those of theoils used in hydrostatic guides at the ambient temperature. Inaddition, it is not necessary to return the uid. The viscosity of air isvery low and does not vary in a wide range of temperature. Theaerostatic guides are the best option for applications with a widerange of temperature variation. The compressibility and poordamping of the air make the dimensioning of aerostatic guidesmore difcult than hydrostatic guides. They may exhibit self-excitation, known as air hammering, which may degrade theoperation of the guides. This vibration can be mitigated throughthe use of a high number of cells, each with its own restrictor.Recent developments in modeling have allowed the improvementof their stability and their active compensation [1,2].

Presently, the guides are manufactured from porous materials[80,99], and the porosity emulates the operation of multiplerestrictors. Aerostatic guides are seldom used in machine toolapplications, mainly due to the difculty in attaining sufcientload capacities at a reasonable cost [105]. It is necessary tomachine the sliding surfaces to a very high degree of accuracy, suchthat the gap can be extremely small. Typical gap values can be inthe order of 510 mm for a standard air pressure supply of 6 barowing in a continuous way to the atmosphere. Howeveraerostatic guides are widely used in high speed, precisionpositioning steppers for electronics manufacturing and micro/nano-machining machine tools. In particular, the vacuum pre-loading of air bearings offers an excellent method of achieving acompact aerostatic guideway designed, for planar motion, whichprovides both vertical and angular pitching stiffness [40,98]. Theycan meet precision positioning demands [8,9]. The lack of dampingof aerostatic guides is overcome by additional damping elements,as electro-rheological uid dampers [100]. A new principle of uidbearing, which utilizes travelling waves produced by piezoelectricactuators, is proposed in [97]. Denkena et al. presented anaerostatic linear guide for microsystems with dimensions of8.4 mm 1 mm and the air is supplied from capillaries with0.15 mm diameter [29]. The application of various aerostatic andelectro-magnetic guide design concepts can be found in [24].

2.5. Magnetic levitation guides

Magnetic levitation guides are mainly used in precisionpositioning applications. They have the advantage of zero frictionwith its associated benecial effects of wear free operation withoutany lubrication. In combination with linear motors, they avoidmechanical contact between the moving slide and the xed part.There are few cases of application in machine tools [28], andlimited to one linear axis [129]. The disturbances caused byperiodic milling forces are attenuated by linear guides which areused as both sensors and actuators in [25]. Their main drawbacksare the lack of damping and the complexity of the control systemwhich tries to control ve degrees of freedom motion. Fig. 11presents a two dimensional magnetic drive [41], where the movingpart of the system is free of any contact and wires. Whenmechanically well designed, the dynamic behaviour and overallprecision of such magnetic drives can be increased as they allow

the integration of the measuring system in the centre of movemlocation.

There are other ultraprecision guiding systems for low rangmovement based on compliant mechanisms. Compliant mechisms base their performance in the elastic properties of materTheir main advantages as guiding solution are freedom frfriction, backlash and stickslip effects. Their main limitationsthe short stroke (micrometers or few millimeters) and low lcapacity. Although the basic principles of compliant mechaniare well known, design methods and applications have remaifragmented without a detailed methodology. The advanceprecision machining by wire-EDM allows currently the producof complex monolithic structures with good accuracy and surroughness. Recently, the growing number of applicationscompliant mechanisms (space, scientic instruments, and ulprecision machines) has produced a systematic approach to tdesign. Fig. 12 shows a 3D positioning device for a micro-Emachine with a travel range of 6 6 6 mm, and a positionaccuracy of 0.1 mm by means of a parallel kinematic mechani

3. Mechanical drives

The ball-screw and linear drives are most commonly usedmachine tool feed drives, and their fundamental principles

Fig. 11. Planar motor magnetically levitated (by Tekniker1). Stroke (X and100 mm, max velocity: 60 m/min, max acceleration: 20 m/s2, jerk: 1000 m/s

10 m/mm min, linear resolution: 60 nm, angular resolution: 0.046 arcsec, li

accuracy: 0.2 mm, workpiece weight: 120 kg, linear force: 2000 N.

Fig. 12. 3D compliant mechanism for a Micro-EDM Machine (by of Agie1method is advantageous over constant displacement solutions,due to its ability to hold the imperfections of the rolling elements.Constant force preload can be achieved in different ways, e.g.created by the weight of the system itself in the case of horizontalcarriages, by means of counterbalancing masses in verticalcarriages or by spring-based locking systems.

Hydrostatic and aerostatic guides are also widely used inprecision positioning of tables due to reduced friction and wear[69,70]. They are insensitive to small random irregularities in theways and pads, producing the so-called averaging effect. In the

hightool

3.1.

RBy arealindedomwelltrantorqbe dfeedcoulshowwithmovwhirack

Apinitwohighto re

3.2.

Tdrivhigh

Fi

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796784lighted rst followed by a review of recent advances. Machines with long working paths use rack-pinion-drive.

Rack-pinion-drive

ack-pinion-drives are recommended for long travel distances.dding several racks together, very long feed travel can beized. The resulting total stiffness of rack-pinion-drive is alwayspendent of the length of travel distance. The total stiffness isinated by the torsional stiffness of gear and pinion shaft as

as contact stiffness of rack-pinion-combination. The powersfer on the pinion is characterized by low revolutions and highue. It needs additional gear steps. The whole drive line shouldesigned with high torsional stiffness and free of clearance. A

transfer with clearance freedom in both movement directionsd be achieved through the separation of the pinion. Fig. 13s a feed drive with clearance elimination through pinions

helical gearing that combine with a rack. The lower pinion ised axially through spring force on a spline-shaft shoulder,ch allows both pinions bearing against opposite ank of the

and compensating the gearing error.nother possibility to realize clearance freedom in the rack-on-drive is the application of tension by driving the pinion with motors in opposite directions. While the main motor applies

torque to deliver the motion, the second delivers less torquemove the clearance. Fig. 14 shows the torque lines.

Ball screw drives

he ball-screw is currently the most frequently used in feedes of the machine tools. Ball screw drives are characterized by

efciency (h = 9598%) and thus by low heating, low wear and

high service life without a stickslip effect [73]. The ball-screwdrive consists of a screw supported by thrust bearings at the twoends, and a nut with recirculating balls (Fig. 15) [57]. The nut isconnected to the table. One end of the ball-screw is either attachedto a rotary motor directly or through gear/belt speed reductionmechanisms. The nuts are preloaded [42] to avoid backlash byadjusting the spacer, creating offset between the leads or usingoversized balls as shown in Fig. 16. It is rather difcult to grind thepitch at uniform intervals, and the pitch errors are transmitted asposition errors unless they are compensated [43,57,78].

The design, calculation and acceptance terms of ball screw drivesare described in DIN standards [31,32] and [33]. Ball screw driveswith a length of approximately 12 m may be used in machine toolswith long travel strokes. Depending on the application, the screwdiameter and pitch may vary between 16 and 160 mm, and 5 and40 mm, respectively. The current ball-screw drives can deliver up to100 m/min travel speed with 2 g acceleration. Optimizations of theball screw drive design [47], the coating of balls to reduce the frictionand wear, deection and nut preload control [107], led to signicantincreases in the speed and accuracy performance of ball screwdrives. The balls roll between the guide slots of the screw and nutbased on either the internal or external recirculation designprinciple shown in Fig. 17. External ball recirculation is achievedby a recirculation tube or channel. An adapted design of the tube

g. 14. Clearance-free rack-pinion-system with electric generated preload.

Fig. 15. Structure of ball screw system.HIWIN.

Fig. 13. Clearance-free rack-pinion-system with split pinion.

Fig. 17. Ball recirculation systems [Hiwin, WZL].

Fig. 16. Ball-screw and nut mechanism.

rew theearighandighnes,e tonut.ner].

aryible

isnut,recttor.pidivessely

15)

r. Aithear

N)ightaindueeatlingrivemnay

37].ersand

ings.

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796 785even rolling and noise development.The design of feed motors and the mechanical components is

initially carried out by considering only the rigid body dynamicsand static stiffness of the system. From the application require-ments, a suitable combination of the design parameters of ballscrew, nut, bearings, motor torque, nominal motor speed, spindlepitch and transmission ratio are determined.

The total feed force (Ffeed) acting on the drive consists of cuttingand friction loads

F feed Fcut F friction (9)The force is transmitted to the motor as an external disturbance

torque tfeed

t feed hs2p

1

hertF feed (10)

where hs, he, rt are the pitch length of the screw, mechanicalefciency of the overall system and transmission ratio if the motoris connected to the screw via pinion-gear system (rt > 1),respectively. The mass of the table/work is transmitted to themotor as an equivalent rotary inertia (Je)

Je 1

r2t

ml2r2l

hs2p

2mt

" #mm

2r2m (11)

where ml, mt, mm are the mass of the screw, table and motor,respectively. rl and rm are the pitch radius of the screw and motor,respectively. The motor must deliver torque larger than the totalload torque at speeds and loads to be experienced by the drive,

t > Jed2u

dt2 Bdu

dt t feed (12)

where u [rad] and B [N m/(rad/s)] are the angular rotation of themotor shaft and equivalent viscous damping in the drive train,respectively. The feed force and torque cause axial and torsionaldeformation of the ball screw drives. The deformations arecoupled, and distort the positioning accuracy of the table. Whilestatic deformations occur during constant travel speeds underconstant loads, the drive may experience vibrations duringdynamic positioning and under interrupted cutting operations.

The static stiffness is determined primarily by the equivalentaxial stiffness of the ball screwnut contact as outlined in [DIN69051-6]. The ball screw drive system with bearings and theintermediate transmission or clutch, has a nite stiffness thatassists in determining the static displacement of the table underload during high speed positioning of the table. The ball screw issupported by thrust bearings at two ends. Bearings provide radialguidance to the screw and absorb the feed forces in the axialdirection. If the bearings at both ends are xed, the equivalent axialstiffness of the ball screw system is given by (see Fig. 18),

keq 1ki kii

1kM

1(13)

where the stiffness terms contributed by the left (ki) and right (kii)bearings are dened as,

ki 1

k1 1k

1; kii

1

k2 1k

1(14)

The axial stiffness is reduced when the right bearing is preloadfree (kii = 0). As the table position changes, the axial stiffness of the

drive varies which leads to time varying dynamics of ball scdrives. It must also be noted that the motion delivery betweenball screw and the nut exhibits a hysteresis type of nonlinbehavior [22]. In feed drives of large milling machines with hmachining forces, highly preloaded stiff bearings are used resulting friction loads are disregarded. However, when hpositioning accuracy is required such as in grinding machilow friction is required. The ball screw system also expands duthermal loads produced by friction on the guides, bearings and Thermal simulation of the ball screw system may assist the desigto predict the changes in the stiffness of the overall system [45

3.3. Linear direct drives

The table is moved by the magnetic force between the primand secondary parts of the linear motor, hence there is no exmotion transmission element in linear drives. The guide systemthe same as ball screw drives. While the exibilities of screw, coupling, motor shaft and thrust bearings are avoided in didrives, the cutting load and mass are directly transmitted to moLinear drives allow higher acceleration, feed speed and rapositioning with high servo bandwidths over ball screw dr[86]. The acceleration capacity of linear motor is inverproportional to total moving mass (mtotal).

Acceleration Fshearmtotal

(

where Fshear is the magnetic force capacity of the linear motocomparison of accelerations between the ball screw system wtwo different pitches (h1 = 40 mm, h2 = 20 mm) and the lindirect drive with two different maximum forces (8000 N, 2000is shown in Fig. 19. While the linear motor can reach to haccelerations for light payloads, the ball screw drive can mainits acceleration capacity for a larger variation of payload mass to reduction of inertia reected to the rotary motor. The hgenerated by the motor needs to be dissipated through coostrategies in order to minimize thermal distortion of the dsystem and machine tool. Heavy machine tool table and columasses carried by high speed, high acceleration linear drives mexcite low frequency modes of machine tool structures [136,1The resulting inertial vibrations are picked up by linear encodplaced on the table, which may destabilize the controller produce poor surface nish.

Fig. 18. Axial stiffness of the ball screw with single and double sided thrust bearWZL.allows the balls to exit the bearing nut area and to enter it moretangentially, allowing a more even and smooth ow as well as higherspeeds. A signicant drawback of this design is the slight damagethat may occur to the recirculation tube, which hinders the balltransport and leads to damage of the nut system. Recirculationchannel based systems may be subdivided into various types, suchas end cap recirculation or front end recirculation. The internalrecirculation system guides the balls via channels at the end of eachthread. While this design has the advantage of requiring less space,the unfavorable ball entry and exit angles have adverse effects on

4. S

Bshafaxiaexiapplinteasseservnising, tablsee paraThe mot

Ball

Line

Fig. 2UBC.

Fig. 1WZL.

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796786tructural dynamic model of drives

all screw drives exhibit torsional exibilities at the motortscrew coupling, screw itself, and nut as shown in Fig. 20. Thel displacement of the screw is coupled with its torsionalbility, and the screw may experience lateral exibilities whichy tension and compression loads on the tableguidewayrface. The structural vibrations caused by the ball screwmbly occur typically above the bandwidth frequency of theo drive, i.e. above 100 Hz. However they affect the surfaceh quality and precision positioning accuracy during machin-hence they need to be avoided. The linear cutting force (F1) ande mass (mt) are transmitted to motor as a reduced torque (t),Fig. 20. The bandwidth and speed are increased by using twollel ball screw drives in most recent, high speed machine tools.mechanical drive system Gm(s) is represented by its rigid bodyion when the structural dynamic exibilities are neglected.

screw Gms u2t2 1

Jes bKes

ar drive Gms x2F2

1mes b

Kes

(16)

where x1, x2 are the linear positions of the table and motor; F1, F2are the forces acting on the table and motor, respectively. In thecase of ball screw drives, the angular position (u) and torque (t) aregiven by,

u xrg

; t rgF (18)

Transfer functions Gpq(s) determine the relationship betweenthe forces and positions of the table and motor due to the exibilityof the mechanical drives, and they replace the rigid body basedtransfer functions Gm(s). A simple structural dynamic model of theball screw drive system can be approximated by the reectedinertias at the motor (Jm) and lead screw Jl connected by a torsionalspring (kt) and damping ct elements as shown in Fig. 20. Theconnection can be considered at the motorscrew coupling orscrewnut coupling junctions for simplicity. By neglecting viscousfriction, the structural dynamics of the ball-screw system can beexpressed by:

s2Jm 00 Jl

s ct ctct ct

kt ktkt kt

umul

tmtl

(19)

which leads to the following transfer function of the system:

Gs Jls

2 cts kt cts ktcts kt Jms2 cts kt

s2JlJms2 ctJl Jms ktJl Jm

(20)

The ball screw system has the torsional natural frequency:

v0

ktJlJm=Jl Jm

s(21)

The inertias (Jm, Jl) can be replaced by equivalent masses (mm,mt) at the motor and table for the linear drives, respectively. Thenatural frequency will remain the same. Methods of estimatingmodel parameters can be found in [23].

The system may have more natural modes depending on thestructural conguration of the drive train. The parameters areexperimentally identied by exerting impulse load on the table(F1) and measuring the displacement x1 with vibration sensor orlinear encoder, and u2 with the angular encoder of the motor.Motor torque (t2) can be used as an excitation load by injecting awhite noise or harmonic signal to the current amplier of themotor. The modal parameters are estimated through least squaresbased identication algorithms [77].

Research efforts have been primarily concentrated on thedynamic modeling of the screw, nut, bearings, coupling, motorshaft, table and guide [67,128]. Generally, computer models of ballscrew drives are obtained using hybrid nite element methods(FEM). Relatively rigid components of the drive are modeled aslumped masses connected by springs while components withdistributed mass and stiffness, like the ball screw, are modeledusing nite element structures. The method is able to capture theessential dynamics of the drive while maintaining computationallyadvantageous low-order models, which is an important require-ment for virtual prototyping. Varanasi et al. [121] and Whalleyet al. [130] modeled the ball screw using EulerBernoulli beamformulations, which capture the axial and torsional dynamics ofthe ball screw drive. However, neither model considers the lateral

0. Ball-screw drive mechanism.

9. Acceleration capacity comparison between linear and ball screw drives.where K is the encoder gain, b is the viscous damping, and Je, me arethe equivalent inertia and mass as seen by the motor, respectively.

However, it may be important to damp the structural vibrationsof the machine which are excited by the cutting and inertial forcesduring high speed motions. The general mechanical transferfunction between the loads and table/motor position can berepresented as

x2sx1s

G11s G12s

G21s G22s

F2sF1s

(17)

deformations of the ball screw, which could affect the positioningaccuracy and performance of the machine tool. Similarly, theresearchers in [57] modeled the ball screw using nite-elementbeam formulations. With the exception of Zaeh et al.s model [131],the past models include only the axial and torsional dynamics ofthe ball screw while neglecting its lateral dynamics. Zaehconsidered the lateral deformations of the ball screw but themodel used for the screwnut interface stiffness matrix fails tocapture the coupling between the lateral, axial and torsionaldynamics of ball screw drives. Okwudire et al. [77] modeled the

from the manufacturers catalogs. Screwnut interface model isdeveloped to capture the dynamic interaction between the axial,torsional and lateral dynamics of ball screw drives. The simulatedand experimentally measured natural frequencies and modeshapes are shown in Fig. 21. The most dominant mode (218 Hz)that affects the axial positioning accuracy of the table is due tocoupled torsional, axial and lateral deformation of the ball screwwhich varies as the table moves from one extreme towards themotor side. The second and third modes are due to twisting of thescrew and yaw motion of the table, and they do not affect the table

andtactver,eful

ast actorsivesheiruseThe70s.recticalewivestedeaspm

rs

ostors,the byoreithoremicherave

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796 787ball screw using Timoshenko beam elements, while representingrelatively more rigid components of the drive (nut, table andguideway) as lumped masses/inertias connected by multi-direc-tional springs at exible joint interfaces. The ball-nut stiffness ismodeled by considering the Hertzian contact of each re-circulatingball and projecting their stiffness at the nut node of the FE model.Stiffness values of the guideway and thrust bearings are obtained

position signicantly. The discrepancy between the simulation measurements are mainly due to analytically estimated constiffness of nut and assumed bearing stiffness values. Howevirtual design and analysis model of the ball-screw drive is usduring prototyping of the machine tool and controller [106].

5. Electrical drives

5.1. Introduction

A variety of electrical motors are used in machine toolssummarized in Fig. 22. Usually synchronous permanent magneservo drives are used in feed drives, while asynchronous moare typically employed in spindles. At rst, asynchronous drbecame widely accepted for spindle drives because of toverload capacity and synchronous drives for feed drives becaof their degree of efciency and the related lower heating. synchronous motors became dominant for feed drives in 19Ball-nut screw drives for large traveling length and linear didrives were developed in 1980s. The latter made the mechantransformation from rotary to translatory motion redundant. Nelectrical drive concepts like transversal or axial ux [49] drhave not been commonly used yet. Typical feed drives have a rapower up to 20 kW and a speed range up to 8000 rpm, wherspindle drives can go up to 100 kW power and 2060,000 rangular speed.

5.2. Permanent magnet AC synchronous and AC induction moto

Permanent magnet synchronous motors (PMSM) are mwidely used in machine tool drives. Similar to brushless DC motthe PMSM has a permanent magnet rotor and windings on stator. The PMSM is driven with sinusoidal current generatedField Oriented Control (FOC). High-torque motors can deliver m30,000 N m torque [122]. Some manufacturers offer motors whigher inertia than standard designs in order to have mfavorable motor/load inertia ratios for achieving a better dynaperformance in feed drives with varying inertia. The furtdevelopments of rotary synchronous motors in recent years h

Fig. 21. Mode shapes and frequency variation of ball screw drive as table travels360 mm. M: Measured, S: Simulated with FE model.

UBC [77].

Fig. 22. Common feed drive motors with applications and characteristics.ISW.

lead to power improvement and reduction of the cogging effects byrare earth magnets embedded in the rotor. In well-designedmotors the cogging effect is less than 1% of the operational torque.

The AC induction motor consists of a cage-like rotor and a statorwith three brushless windings. Control methods of AC Inductionmotor can be divided into four major groups, namely the constantVoltage/frequency, sensor-less vector, eld-oriented and the directcontrol method [10,113].

5.3. Linear drives

Acut powinersimipermtimesecoguidcogg

distuwhithusdesidirehighsecothersecoa sythe

5.4.

Aprevbe psamthe masbackfor travredustanlineaThe cont

Sacceforcof cosam

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796788 linear motor [83] can be viewed as a rotary motor that has beento its axis, rolled out and stretched in length. The direct drivesered by linear motors have high mechanical stiffness, lowtia and zero backlash. The primary part of the linear motor islar to the stator of a PMSM. The secondary part consists ofanent magnets. There is a high attraction force (about threes more than the driving force) between primary (with iron) andndary part (with magnets) which has to be supported by thee ways. This leads to the position dependent disturbance oring forces. Force ripple occurs due to an electromagneticrbance resulting in periodic variations of the motors constant,

ch depend on the instantaneous motor force. The iron cores and the attraction forces can be omitted when the secondary part isgned as a comb with magnets on both sides. The ironless linearct drives have much lower electrical time constants and thus

bandwidth. For applications where permanent magnets in thendary part are prohibited or too costly for large travel lengths,e are new linear direct drives with permanent magnet-lessndary part (e.g. Siemens 1FN6 drive series). The basic principle isnchronous linear motor where the magnets are integrated intoprimary part with its windings for each phase.

Hybrid feed drive concepts

combination of two drives is used in some applications, i.e. toent the tilting of gantry bridges. The resulting force vector canlaced at the center of gravity with double drives. Feeding thee reference position commands simultaneously may distortmechanically coupled drives. It is more common to use ater-slave setup, which compares the torque values and feed

to each drive. Since linear motors need permanent magnetsthe entire traverse, their application to machines with longel lengths can be complex and costly. Instead, the concept ofndant axes may be used for long strokes as shown Fig. 23. Adard ball-screw drive is used for the entire traverse, and a shortr direct drive is used to enhance the dynamic performance.motions of both drives are kinematically combined androlled to position the tool at the required location.ince linear drives are capable of delivering more than 10 gleration, the excitation of the machine bed caused by reactiones of the table motions can be quite signicant. One possibilitympensating these forces is to accelerate a second slide on thee guide but in the opposite direction [46,73]. Another solution

6. Sensors

Feed drives use position, velocity, acceleration and load sensorsto improve their positioning accuracy and response bandwidth.The most widely used sensors are briey reviewed here along withtheir associated performances.

6.1. Position measurement

The absolute position of the feed drive needs to be measured forprecision positioning of the tool on the workpiece. The tableposition is directly measured using optical encoders in machinetools. Laser interferometer methods are used in precision machinesdesigned for manufacturing of optics, electronic circuits or inmachines. Rotary encoders or syncro-resolvers are measuring tothe rotary servo motor shafts for indirect measurement of the tableposition from the angular position of the motor shafts.

Optical encoders are based on the principle of transmitting orreecting light by a glass or metal grating. A light source and photodetector array are used to sense the position of moving encoder diskor scale containing equally spaced reective grating. The absoluteencoders have binary (gray or pseudo-random) coded absolutepositions. Incremental encoders have an additional reference markwhich allows the controller to track the absolute position bycounting the equally spaced marks relatively to the reference mark.In case of a rotary or linear encoders with equivalent pitch spaces (i.e.around 10 mm), the scanning unit moving in the direction of motionilluminates the scale at the measurement point. Motion between thescale and the scanning unit is evaluated through a scanning grid bymeans of photo elements. The received modulated signal has anearly sinusoidal shape per scanned increment. The alignment oftwo receiving elements is used to detect the direction of the motion.The resolution of the encoders is improved by a factor of 1000 ormore by interpolating the sinusoidal pattern of the encoder readings.Interferometric measurement principle is used for encoders withhigher resolution.

Recent developments improve the non-ideal sinusoidal signaloutput of incremental sensors by reducing the harmonics oferror frequencies, hence a position-signal is taken with at veryhigh sampling rates, which allows to process harmonics of theerror-frequencies.

6.2. Speed measurement

The velocity of the feed drive is needed by the servo controllerfor tracking and damping of the table motion. Rotary tacho-generators, which provide DC voltage proportional to the angularspeed, are integrated to the motor shaft. Its operation principle isequivalent to that of a DC machine with a stationary exciting eldand rotary sensor winding unit. The brush contacts of DCtachogenerators limit their service life. AC tachogenerators havea permanent-eld rotor with a stationary winding system, whichgives longer service life. AC tachogenerators produce trapezoidalAC voltage with an amplitude and frequency proportional to thespeed. However, both tachogenerators have low signal to noiseratio at low speeds, which negatively affect the velocity control offeed drives. Recently, speed sensors based on eddy-currentprinciple have been investigated by researchers [59,115].

It is most common to estimate the velocity by digitallydifferentiating the position measurements obtained from theFig. 23. A concept for redundant axes test bench.would be to damp the peak forces. Instead of stiff mounting of thefeed drive to the frame, it can be stacked on a second guide to avoidthe transmission of acceleration forces to the machine frame. Thesecond guide moves in the opposite direction to the feed drive, andabsorbs the acceleration load [13,79]. The dynamic stroke of thesecond table is limited and damped by a spring-damper-system,and its counter-motion is measured and included in the controlloop. This concept also works for ball screw and rack and pinionfeed drives [61].

encoders [16]. The accuracy of the velocity estimation depends onthe resolution of encoders, quantization [12,15], speeds andharmonic error-frequencies [59]. When the change in the velocityis too small in a very short digital integration interval, i.e. controlinterval of the servo, the velocity prediction becomes highlyinaccurate and noisy. Low pass and FIR lters are employed tosmooth the velocity estimation, which adds undesired phase delayto the drive controller. There are research attempts in treating thesystem at low and high frequency zones separately in order toimprove estimation of the velocity from discrete position samples.

the

lersawsjerkarence,

osts atheC tots aas atroltionandtatesfer areely.r in

of 4hann iss istheoopiththetrolncecedand

al.ting

theers.e asrsttedtrolow-andighg ofcanbleces,hisherthe

s.

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796 7896.3. Acceleration measurement

Acceleration feedback is used in control laws for damping thestructural dynamics and inspecting the actual trajectory of the feeddrive. The acceleration can be measured directly, or from thesecond digital derivative of the position measurements[44,66,135]. Standard, piezoceramic-based accelerometers provideabsolute acceleration of the drive; hence both rigid body andstructural vibrations are mixed in the signal. Pritschow et al. [85]introduced electro-magnetic based Ferraris sensor which mea-sures the relative acceleration between the moving drive (i.e. table)and stationary base (i.e. guide), which is advantageous for activedamping of structural vibrations. The bandwidth of the systemwith a stationary exciting eld is up to 1500 Hz.

6.4. Current measurement

The current of a servo motor is used in the rst loop of a cascadecontroller, where the given value for the force or moment in formof the current is controlled via a PI controller. The current is alsoused to compensate friction and cutting force disturbances. Therehave been several research attempts to in predict the cutting forcesfrom the motor current as well [4,26]. The current is measuredfrom the shunt resistors, inductive transformers or utilizingmagnetic effects. Shunt resistors are placed in series to the load.A voltage drop across the shunt-resistor is proportional to thecurrent through the resistor. This method has its key benet in awide frequency-range. Inductive transformers operate by trans-forming the current of a motor phase through magnetic coupling,leading to AC signals proportional to the current. Hall-sensors aremost commonly used in measuring the current-induced magneticeld, which has a drawback of limited bandwidth. Recentdevelopments replace the Hall-sensor by GMR (giant magnetore-sistance) semiconductor-elements, which have magneto-resistivedetecting elements with about 1 MHz bandwidth.

7. Control of feed drives

The general architecture of most feed drive controllers isillustrated in Fig. 24. The mechanical structure of the drive isrepresented by Gmwhich is either considered to be rigid or exible.Amplier (GA) and electrical winding of the motor (GE) have fastdynamics, and are usually modeled as gains. However, they may beconsidered as rst order lags or with higher order dynamics insome advanced controllers. The digital control law tries tominimize the position error e(k) at each control interval (k):

ek xrk xk (22)

where xr(k) and x(k) are the reference and actual position oftable, respectively.

There have been a signicant number of advanced controlreported in the literature. In addition to position, the control lmay use velocity (xrk; xk), acceleration (xrk; xk) and (x _rk). Feedforward (GFF) and feedback (GFB) compensators used to minimize the effects of friction, cutting force disturbaand unmodeled or varying dynamics of the drive.

The cascaded control structure shown in Fig. 25 is mcommonly used in industrial feed drives; hence it is used areference controller against new algorithms published in literature. The position commands are transmitted from the CNthe drive via eld bus. The block diagram (Fig. 25) represendirect drive system with rigid mass (mg), and the controller hcurrent loop inside, surrounded by velocity and position conloops. Cascaded controllers use a proportional gain (Kv) on posierror (e), proportional gain (Kp) on the velocity error (xr x), integral action with time constant (Tn) to minimize the steady serror caused by the disturbance (Fd) and lag caused by the tranfunction of the system. The inertia and viscous damping forcescompensated by the feedforward and feedback terms, respectivThe current controller is in general designed as a PI controlleseries with the power converter. It usually has a bandwidth1 kHz with a PWM (Pulse Width Modulation) converter of20 kHz. The maximum bandwidth of the velocity loop is less t10% of the current loop (i.e. 100 Hz) when the velocity gaituned around Kp = 600 s

1 for linear drives [89,93]. The mascompensated by a gain factor of mg because it affects proportional velocity control gain Kp. The position control lusually has 30% less bandwidth than the velocity loop, i.e. wKv = 200 s

1 the bandwidth is about 30 Hz. However, bandwidth can be increased by three fold with modern conand compensation methods [87]. If the external disturbasources are well known, such as friction and pitch error induball screw loads, they can be compensated using feedforward set point variations in the controller [57,76,82]. Tonshoff etpresented the challenges and possible solutions in compensafriction and cogging forces in linear drives [112].

7.1. Rigid body controllers

The structural exibility of the machine tool reected to drive is not explicitly considered in rigid body based controllThe objective is to widen the positioning bandwidth of the drivmuch as possible. However, to avoid interfering with the vibration mode, these types of designs are frequently implemenalongside notch or low-pass lters that avoid the con(actuation) signal from exciting the machine structure. A lpass lter provides good high frequency gain attenuation, therefore a robust solution against unknown or varying hfrequency structural dynamics. If the frequency and dampinthe mode(s) are well-known and do not change over time (or be accurately predicted), notch lters provide a more favorameans of attenuating the amplitude due to mechanical resonanwithout inducing as much phase lag as low-pass lters. Tprovides better stability margins and the ability to achieve higcontrol bandwidths. When implementing the control laws, Fig. 24. General structure of a feed drive control system.

Fig. 25. Equivalent block diagram of the cascade controller for linear drive

saturation limits of the feed drive motor and amplier [125] mustbe avoided as shown in Fig. 25.

Although cascaded control system parameters are tuned toaccomplish rigid drive control, several modern algorithms are alsoproposed as alternative methods. Tomizuka et al. [111] developeda zero phase error-tracking controller (ZPETC) by canceling thestable dynamics of the servo drive in a feedforward fashion. Thebandwidth of the overall system, hence the tracking accuracy ofthe drives increases dramatically with ZPETC provided that thedrive model is accurate and does not vary with time. Weck and Ye[124richtoolcontpropcontperfin hthe smoaddrobse

Tis thBraeit is inudynOthefeed[87]predfeeddesifrictinercontcomand Cholineamodcontcurrbandagaiuse mea

7.2.

TpiecVibroverthe vunst

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796790] noted that ZPETC generates feedforward commands with frequency content, leading to distorted motions at high speed paths with sharp corners. They removed the high frequencyent by pre-ltering the position commands. Dumur et al.osed several predictive control methods [34] which generaterol commands by predicting the behavior of the driveormance few sampling periods ahead. The contouring accuracyigh speed machining depends on the tracking bandwidth anddisturbance rejection of the axis control system, as well as theothness of the reference trajectory. Van Brussel et al. [117]essed the disturbance compensation problem by adding anrver to the control law.he main drawback of the classical controller design techniquese sensitivity to modeling errors, as addressed by Van denmbussche [120]. Especially when feedforward control is used,vital to establish a robust feedback loop that will mitigate theence of changes in the inertia, friction as well as otheramics which may be dependent on the drives position [132].rwise, as the open or closed loop dynamics change, theforward controller would try to cancel the incorrect model. In addition, process forces, which in most cases are difcult toict and compensate in real-time, have to be rejected by theback loop. Hence, recent research articles focused on thegn of controllers which are capable of coping with changingion and external disturbances, and uncertainties in the drivetia. Jamaluddin et al. compared the performances of cascadedrollers against sliding mode controller with disturbancepensation [52,53]. They showed improved dynamic stiffnessbetter tracking accuracy in comparison to cascaded controller.i et al. considered the effect of cutting force disturbances on ther drive stiffness [20]. Altintas et al. [6] presented a slidinge controller with disturbance compensation (Fig. 26). Theroller was implemented on ball-screw and linear drives inent control mode, and demonstrated to have as highwidth as ZPETC in command following while being robustnst inertia changes up to 30%. The control command needs toreference position, velocity, acceleration commands, andsured position and velocity of the drive.

Control algorithms with exible drive structure

he relative structural vibrations between the tool and work-e degrade the surface quality and tolerance of the parts.ations accelerate the wear of the power train components, andload the drives and machine tool structure. Furthermore, whenibrations are felt by the servo system, the controller can becomeable which leads to unsafe operation of the machine tool.

The source of vibrations reected on the feed drives includescutting forces, unbalanced spindle loads, friction and backlash inthe drives as listed in Fig. 27. The discontinuities in the motiontrajectory algorithms, which generate position, velocity, accelera-tion and jerk command proles for each drive, also excite thenatural frequencies of the machine tool structure. More impor-tantly, interaction between the drives mechanical response, thecurrent loop, and the digital servo controller can be one of the maincauses of vibrations. If the controller is not designed properly, thiscan lead to stability and robustness problems.

The vibrations of mechanical structures can be rst reduced atthe design stage by changing the topological structure, using stiffercomponents connected with materials having higher dampingratios. However, stiffer designs usually lead to larger movingmasses, which reduce the high speed positioning performance ofthe drives. If the dominant natural modes of the structure cannotbe avoided during the design stage, damping elements, which aretuned to damp specic natural frequencies, can be used betweenexternal force and vibrating structure [18]. Alternatively, theeffects of oscillating forces can be countered with active dampersactuated by electromagnetic, piezoelectric or hydraulic actuators[11,50,72,74,133]. While these measures typically lead to goodresults, it can be difcult and more costly to incorporate them intothe machine tool design. Fundamental real time algorithms, whichare used to avoid and damp vibrations, are discussed in thefollowing sections.

7.2.1. Trajectory generation

The motion commands to feed drives constitute a major sourcefor excitation of the machine tool vibrations. If the referencetrajectory motion, e.g. position, velocity, acceleration and jerkcommands at discrete control intervals, have discontinuities, theywill have wide frequency content. Drives with high speeds andacceleration create high reactive forces between the moving massand the stationary bodies of the machine. Inertial forces for highfrequency content excite the machine tool structure causingundesired transient vibrations, which are suppressed by smoothtrajectory motion proles, passive dampers, or active controlmethods are used.

The present CNC systems use jerk limited-trapezoidal accel-eration motion proles (i.e displacement commands are at least acubic function of time) while avoiding the saturation of drivemotors [3]. When three trajectory generation algorithms arecompared in Fig. 28, cubic acceleration with a second ordercontinuous jerk has the least amount of acceleration amplitude athigh frequencies. That is translated as having smaller inertialforces at the high frequencies, hence the excitation of structuralFig. 26. Sliding mode controller for a rigid feed drive [6].

Fig. 27. The source of feed drive vibrations and their compensation method.

red

23)

antodeble

24)

tion

ctive

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796 791modes at those frequencies are reduced. In addition, thefrequencies which excite the natural modes can be removed fromthe motion commands by pre-ltering before injecting them to theservo system. Such pre-ltering techniques are covered broadly inthe literature, including low pass and notch lters [31,32,33],moving average lters [48,54,95,114], and input-shaping usingimpulse sequences and form functions [36,56,101]. The notch lterprevents the excitation of the problematic modes by the trajectorycommand signals, but cannot stop the table disturbance forcesfrom exciting them. Furthermore, the bandwidth of the drivebecomes less than the structural resonance of the drive. Thisconservative approach reduces the productivity of the machines,and they are especially not suitable for high speed machines withlight structures. The lters have to be applied with care as theymay alter the path geometry or cause overshoot. As thesetrajectory proles are smooth, they introduce relatively lowexcitation compared to acceleration limited motion proles.Nevertheless, low acceleration and jerk settings may be requiredfor machines with prominent resonances. More advanced trajec-tory generation techniques include spline based path and velocityproles, and smoothing of jerk proles [19,51,65,71]. Oneinteresting idea that has been proposed by ISW researchers isthe optimization of axis jerk durations to avoid excitation offrequency content around certain resonances [30]. A sampleapplication of smooth trajectory generation avoids excitation oframs natural frequency as shown in Fig. 29. In addition to smoothtrajectory generation at CNC, passive damping systems can be usedto absorb the energy created by the inertial vibrations. Denkenaet al. presented a novel, energy efcient guide system whichdecouples the jerk from the stationary base through a tuned mass,spring and damper system [27].

7.2.2. Active damping of drive vibrations

Independent of the individual techniques, only vibration modesthat are controllable by the actuators and that are observablethrough the sensors available on the machine can be damped.Various closed loop control techniques have been demonstratedto damp the vibrations with the feed drive motor by usingposition, velocity, acceleration, current and force feedback[14,17,21,75,102]. The algorithms are designed assuming constantor time varying and position dependent structural dynamics of thedrive.

An easy to apply damping method is illustrated here usingcascade control structure applied to a ball-screw drive. Thevelocity loop is modied by considering the structural vibrations ofthe drives and adding an acceleration feedback at the dominantnatural frequency as shown in Fig. 30. The current control loop isneglected, and the velocity is controlled by a PI controller. The

transfer function between the motor torque and velocity measuat the motor shaft can be obtained from Eqs. (17)(20):

Gmots vmott2 sG11s

rg Jls2 cts kt

sJlJms2 ctJl Jms ktJl Jm(

with natural frequency v0 as given in Eq. (19). The less dominmode v01 and the bandpass lter is neglected for a single mdamping. The transfer function between the velocities at the taand motor shaft is given as:

Gmecs vvmot

sG12ssG11s

cts ktrgJls2 cts kt

(

Fig. 29. Reduction of transient vibrations through smooth trajectory genera(ISW).

Fig. 30. Velocity loop of ball screw drives with multi-resonance modes and adamping [64,90].

Fig. 28. Frequency content of trajectory generation algorithms with innite,constant and continuous jerk proles.

UBC MAL.

Tmeashafis mmeationto bbe uwithv01The bandattetwomacattethan15 sband

Wdomsuftunedam

Fig. 3v0 =

Fig. band

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796792he indirect velocity loop uses the motors angular velocitysured from a tachogenerator or encoder mounted on the motort (vmot), whereas the tables velocity (vma) or acceleration (svma)easured in the direct velocity loop. When the tables position issured from linear encoders, its second derivative (accelera-) is used in the feedback but normalized at the vibration modee damped (v0). Alternatively a Ferraris acceleration sensor cansed directly [85]. A sample application to a milling machine

a dominant vibration mode at v0 and a less exible mode atis illustrated (see Fig. 30). First, only the mode (v0) is damped.feedback s/v0 raises the phase by 908. The closed loopwidth is practically not affected due to the open feedbacknuation below resonance frequency (v0), see Fig. 31, where coupled rotational and translational modes of a turninghine is shown. The magnitude peak at the resonance (v0) isnuated, and the effective phase of the open loop becomes less

1808. The position control loop gain (Kv) can be increased from1 to 150 s1 with active damping, hence improving thewidth close to the resonance frequency v0 [90].hen additional natural frequency (i.e. v01) exists ahead ofinant mode (v0), the acceleration feedback (s/v0) may not becient to widen the bandwidth. In such cases, a bandpass lterd to (v01) is used in the direct velocity loop. While (s/v0)ps mode (v0), the bandpass lter attenuates all amplitudes

around v01 which is also damped [64], see Fig. 32. The effect of thisactive damping strategy can be seen in the closed loop response ofthe position loop (Fig. 33), where the position gain Kv can bedoubled from 50 to 100 [s1]. The effect of active damping strategyon the transient vibrations measured at the table is shown inFig. 34.

There are various versions of active damping with accelerationfeedback. When the active damping strategy is incorporated to thevirtual simulation of entire machine tool, it is possible to optimizethe masses and design conguration of feed drives [107].

7.2.3. Advances in active damping of feed drive vibrations

Considering the drawbacks of the classical approaches, recentefforts are directed towards improving the bandwidth of thedrives using robust controllers with disturbance compensation.Zatarain et al. attached an accelerometer at the tool center point toestimate the relative position between the tool and slide tocompensate the deformations [134]. Dumur et al. used anadaptive generalized predictive control to compensate thestructural modes in the presence of variations of drive inertia[34] but it does not take into account the effects of externaldisturbance forces. The general sliding mode controller (SMC) wasrst introduced by Utkin [116] which required switching aroundthe sliding surface resulting in a discontinuous control law, andconsidered to be more robust than linear controllers. To alleviatethis problem, Slotine and Li [103] proposed an adaptive slidingmode controller (ASMC) to estimate and cancel various uncer-tainties (including disturbance forces) which do not necessarily

1. Frequency response of direct velocity loop with active damping of mode65 Hz (ISW).

32. Velocity control loops with a multi-resonances at v01 and v0 with apass lter at v01 and phase lead at v0.

Fig. 33. Closed loop response of the position control with active damping. Bandpasslter is set at v01.

Fig. 34. Experimentally measured effect of active damping network.

canoryuraltemthe

entd to

inlledl ofed,andinenitel ist todelineughC atowsl inivesl ofoopd in

Fig. 35. Adaptive sliding mode control with notch ltering and ripple compensation

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796 793vanish at the equilibrium point. A mode-compensating version ofASMC was proposed by Kamalzadeh and Erkorkmaz [39,57] foractive control of ball-screw drives. Okwudire et al. [78] applieddiscrete time sliding mode controller (DADSC) to compensatevibration modes of a ball screw driven table and linear drives [7].Symens et al. proposed a gain scheduling and robust algorithms tocontrol feed drives which have position dependent dynamics[108,119].

The approaches based on closed loop control presented so farhave the advantage that they can react to any vibrationindependent of its cause. At the same time, they have thedisadvantage that they only react once a vibration is present,which will be too late for some cases. It is desirable to use thecombination of feedforward blocks to compensate friction, back-lash and measurable disturbance forces, active damping ofvibration modes using various control laws, and notch lters toeliminate frequencies from the control signal [68,76,91,110]. Anadaptive sliding mode controller being used in conjunction withripple and friction compensation is shown in Fig. 35 [58].

7.2.4. Coupled exible multi-body and feed drive simulation of

machine tools

Machine tool feed drives are currently designed in virtualenvironment using Computer Aided Control Engineering Program[92]. MATLAB/SimulinkTM and ADAMSTM software systems allowintegration of control, kinematics and structural models of themachine tool and feed drives [60,118,126,127]. Virtual analysis ofinteraction between the feed drive control and machine tool isillustrated in Fig. 36. To simulate the machine tool a exible multi-body simulation model is used that describes its structural andkinematic behavior in one position. Large displacements in themachine axes can be described by a movable exible multi-bodysimulation model [5].

The control models of all drives are created either in MATLAB/Simulink environment or the real CNC is connected to thestructural dynamic model of the drives as in Fig. 36 [88]. Thetorque/force created by inertial motion as well as external friction/cutting loads are simulated and steady state results are applied atcontrol loop intervals onto the machine tool structure at feed driveand cutting points [37,38]. The resulting structural vibrations areprojected to the drive positions and fed back to the controller. The

time varying and machine tool position dependent dynamics be simulated along the tool path, and the inuence of trajectgeneration and controller parameters on the overall structdynamics of the machine tool can be analyzed [92]. The sysalso allows tuning of control parameters for damping structural dynamic modes.

7.2.5. Hardware in the loop simulation

Instead of simulating the entire system in virtual environm(Fig. 36), the virtual dynamic model of the machine is connectethe physical, actual CNC for real time simulation as shownFig. 37. The real time simulation of virtual machine tools is caHardware in the Loop Simulation. The mathematical modethe machine tool, which consists of structural model of bcolumn, spindle, feed drives as well as the servo motors sensors are assembled to achieve virtual model of the machtool. The structure can either be represented by rigid body or FiElement models [88,94]. The virtual model of the machine tooconnected to the real CNC, hence the control commands are senthe mathematical model in real time. The mathematical mopredicts the vibrations and rigid body motion of the machreected at each drive. The machine positions are passed throthe models of the sensors which are sampled by the real CNcontrol intervals as outlined in Fig. 38. The system also allvisualisation of the machine tool motion and material removareal time [88]. The method allows realistic testing of feed drduring the design stage, well ahead of costly physical triaprototypes. A more detailed description of hardware in the lsystem used in practice under the name virtuous can be foun[123].

[58].

Fig. 36. Coupled exible multi-body simulation of machine tools.WZL.

Fig. 37. Design of a hardware in the loop simulator.ISW.

Fig. 38. Hardware in the Loop architecture.

8. C

Rcomthe Therfeedrate5 are posi

Tcomthrocontcomof daccu

Tdesitatiomactest matcomwaydyn

Ack

TtionAlexWZLtheiBruskind

Refe

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796794tioning demands from industry.he reduction of friction in the drives and their real timepensation by the CNC systems, avoidance of vibrationsugh adaptronic devices, advanced trajectory generation androl algorithms; energy efcient design of linear drives,pensation of backlash, thermal and geometric deformationrives require more research in order to push the speed andracy boundaries of present systems further.he physical prototypes and trials are costly and slow down thegn and development of new machine tool concepts. Compu-nally efcient, accurate and reliable mathematical models ofhine tools with feed drives need to be developed in order todesign concepts in the virtual environment realistically. Thehematical assembly of models representing each machine toolponent and drive in a modular but computationally affordable

still requires major research efforts, especially in multi-bodyamic modelling of machine tool and feed drive structures.

nowledgements

he authors thank all CIRP members who sent their contribu-s to this article. Special thanks are extended to Dipl. Ing.ander Haer of ISW Stuttgart; Dipl. Ing. Turker Yagmur of

Aachen; Prof. K. Erkorkmaz of University of Waterloo forr contributions to various sections in the paper. Prof. H. Vansel of KLU Leuven and Dr. H.C. Mohring of IFW Hannoverly reviewed the draft paper and suggested improvements.

rences

Aguirre G, Al-Bender F, Van Brussel H (2010) A Multiphysics Model forOptimizing the Design of Active Aerostatic Thrust Bearings. Precision Engi-neering 34(3):507515.

Al-Bender F (2009) On the Modelling of the Dynamic Characteristics ofAerostatic Bearings Films: From Stability Analysis to Active Compensation.Precision Engineering 33(2):117126.

Altintas Y (2000) Manufacturing Automation. Cambridge University Press,Cambridge, UK.

Altintas Y (1992) Prediction of Cutting Forces and Tool Breakage in Millingfrom Feed Drive Current Measurements. Transactions of ASME Journal ofEngineering for Industry 114:386392.

Altintas Y, Brecher C, Weck M, Witt S (2005) Virtual Machine Tool. Annals ofthe CIRP 54(2):651674.

Altintas Y, Erkorkmaz K, Zhu W-H (2000) Sliding Mode Controller Design forHigh Speed Feed Drives. Annals of CIRP 49(1):265270.

Altintas Y, Okwudire C (2009) Dynamic Stiffness Enhancement of Direct-Driven Machine Tools using Sliding Mode Control with True DisturbanceRecovery. Annals of CIRP 58(1):335338.

Aoyama T, Koizumi K, Kakinuma Y, Kobayashi Y (2009) Numerical andExperimental Analysis of Transient State Micro-bounce of Aerostatic Guide-ways Caused by Small Pores. Annals of the CIRP 58(1):367370.

Aoyama T, Kakinuma Y, Kobayashi Y (2006) Numerical and ExperimentalAnalysis for Small Vibration of Aerostatic Guideways. Annals of the CIRP55(1):419422.

Arias A, Romeral L, Aldabas E, Jayne M (2005) Stator Flux Optimised DirectTorque Control System for Induction Motors. Electric Power Systems Research73(3):257265.

Ast A, Braun S, Eberhard P, Heisel U (2007) Adaptronic Vibration Damping forMachine Tools. Annals of the CIRP 56(1):379382.

Baehr A, Mutschler P (2006) Comparisonof Speed AcquisitionMethods based onSinusoidal Encoder Signals. Journal of Electrical Engineering Edition 4 15824594.

Berkemer J, Altenburger R, Koch T, Lehner W-D (2004) Effektive Nutzung desLeistungspotenzials von Direktantrieben. wt Werkstattstechnik, Springer,Berlin. online Jahrgang 94 H. 5.

Brecher C, Schulz A, Weck M (2005) Electrohydraulic Active Damping System.Annals of the CIRP 54(1):389392.

Bunte A, Beineke S (2004) High-Performance Speed Measurement by Sup-pression of Systematic Resolver and Encoder Errors. IEEE Transactions onIndustrial Electronics 5(1):4953.

End Milling: Robust MIMO Approach. Mechatronics 15:12071224.[21] Chung B, Smith S, Tlusty J (1997) Active Damping of Structural Modes in

High-Speed Machine Tools. Journal of Vibration and Control 3:279295.[22] Cuttino JF, Dow TA, Knight BF (1997) Analytical and Experimental Identica-

tion of Nonlinearities in a Single-Nut, Preloaded Ball Screw. ASME Journal ofMechanical Design 119(1):1519.

[23] Dadalau A, Mottahedi M, Groh G, Verl A (2010) Parametric Modeling of BallScrew Spindles. Production Engineering 4(6):625631.

[24] Denkena B, Brehmeier S, Mohring H-C (2008) Active Linear Guidances forMicro Actuators: Alternative Concepts and First Prototypes. Journal of Micro-system Technologies 14(12):19611973.

[25] Denkena B, Hackeloeer F, Neuber C-C (2009) 5-DOF Harmonic FrequencyControl Using Contactless Magnetic Guides. CIRP Journal of ManufacturingScience and Technology 2(1):2128.

[26] Denkena B, Tonshoff HK, Li X, Imiela J, Lapp C (2004) Analysis and Control/Monitoring of the Direct Linear Drive in End Milling. International Journal ofProduction Research 42(24):51495166.

[27] Denkena B, Hesse P, Gummer O (2009) Energy Optimized Jerk-decouplingTechnology for Translatory Feed Axes. Annals of CIRP 58(1):339342.

[28] Denkena B, Kallage F, Ruskowski M, Popp K, Tonshoffr HK (2004) MachineTool with Active Magnetic Guides. Annals of the CIRP 53(1):333336.

[29] Denkena B, Li J, Kopp D (2004) An Aerostatic Linear Guidance for Micro-systems. Annals of the German Academic Society for Production EngineeringXI(2):203208.

[30] Dietmair A, Verl A (2009) Drive Based Vibration Reduction for ProductionMachines. Modern Machinery Science Journal 3(4). Prague, Czech Republic.

[31] N.N., DIN 69051-3: Werkzeugmaschinen; Kugelgewindetriebe; Abnahmebe-dingungen und Abnahmeprufungen, Mai 1998.

[32] N.N., DIN69051-4: KugelgewindetriebeBerechnung der statischen unddynamischen Tragzahl sowie der Lebensdauer, Entwurf April 1989.

[33] N.N., DIN69051-5: Werkzeugmaschinen; Kugelgewindetriebe; Anschlussmaefur Kugelgewindemuttern, September 1992.

[34] Dumur D, Boucher P, Ramond G (2000) Direct Adaptive Generalized Pre-dictive Control. Application to Motor Drives with Flexible Modes. Annals ofthe CIRP 49(1):271274.

[35] Ekinci TO, Mayer JRR, Cloutier GM (2009) Investigation of Accuracy ofAerostatic Guideways. International Journal of Machine Tools & Manufacturing49(6):478487.

[36] Eloundou RF, Singhose WE (2003) Command Generation Combining InputShaping and Smooth Base-line Functions, US Patent Application PublicationUS0218440A1, US Patent Ofce.

[37] Erkorkmaz K, Altintas Y (2001) High Speed CNC System Design. Part II.Modeling and Identication of Feed Drives. International Journal of MachineTools and Manufacture 41(10):14871509.

[38] Erkorkmaz K, Altintas Y, Yeung CH (2006) Virtual Computer NumericalControl System. Annals of CIRP 55(1):399402.

[39] Erkorkmaz K, Kamalzadeh A (2006) High Bandwidth Control of Ball ScrewDrives. Annals of the CIRP 55(1):393398.

[40] Erkorkmaz K, Gorniak JM, Gordon DJ (2010) Precision Machine Tool XYStage Utilizing a Planar Air Bearing Arrangement. Annals of CIRP 59(1):425428.

[41] Etxaniz I, Izpizua A, San Martin M, Arana J (2006) Magnetic Levitated 2D FastDrive. IEEJ Transactions on Industry Applications 126(12):16781681.

[42] Verl A, Frey S (2010) Correlation between Feed Velocity and Preloading in BallScrew Drives. CIRP Annals 59(1):429432.

[43] Frey S, Walther M, Verl A (2010) Periodic Variation of Preloading in BallScrews. Production Engineering 4(2):261267.

[44] Gianchandani YB, Tabata O, Zappe H (2008) Comprehensive Microsystems, vol.2. Elsevier, Amsterdam/Heidelberg. ISBN 978-0-444-52192-7.

[45] Gleich S (2007) Approach for Simulating Ball Screws in Thermal FiniteElement Simulation, Workshop on Supervising and Diagnostics of MachiningSystems. Journal of Machine Engineering 7(1):101107.

[46] Gromann K, Muller J (2009) Untersuchungsergebnisse zur Wirksamkeit derImpulskompensation von Lineardirektantrieben. ZWF Zeitschrift furwirtschaftlichen Fabrikbetrieb 104(9):S761S767.

[47] Golz HU, Weule H (1990) Vorspannungsregelung im Kugelgewindetrieb einneuer Ansatz fur den Werkzeugmaschinenbau? Wt Werkstattstechnik 80,Springer. 366368.

[48] Hara R (1989) Apparatus for Controlling Acceleration and Deceleration forServo Control, European Patent EP 0378708 A1, Paris.

[49] Huang S, Luo S, Leonardi F, Lipo TA (1999) A Comparison of Power Density forAxial Flux Machines Based on the General Purpose Sizing Equation. IEEETransactions on Energy Conversion 14(2):185192.

[50] Hwang CL, Chen YM (2004) Discrete Sliding-mode Tracking Control of High-displacement Piezoelectric Actuator Systems. ASME Journal of Dynamic Sys-tems Measurement and Control 126:721725.

[51] Heng M, Erkorkmaz K (2010) Design of a NURBS Interpolator with MinimalFeed Fluctuation and Continuous Feed Modulation Capability. InternationalJournal of Machine Tools & Manufacturing 50:281293.onclusion

ecent advances in electrical motors, power electronics,puters, actuators and sensors technology have been pushingspeed limits of spindle and feed drives upward continuously.e are already spindles which reach over 105 rpm which require

drives travelling over 5 104 mm/min with 10 g accelerations. Micro-machining applications use air spindles up to105 rpm, which require fast and precision feed drives. Thereresearch challenges in meeting such high speed accurate[16] Brown R, Schneider S, und Mulligan M (1992) Analysis of Algorithms forVelocity Estimation from Discrete Position Versus Time Data. IEEE Transac-tions on Industrial Electronics 39(1):1119.

[17] Chen Y, Tlusty J (1995) Effect of Low-Friction Guideways and Lead-ScrewFlexibility on Dynamics of High-Speed Machines. Annals of the CIRP44(1):353356.

[18] Chen Y-D, Fuh C-C, Tung P-C (2005) Application of Voice Coil Motors inActive Dynamic Vibration Absorbers. IEEE Transactions on Magnetics 41:11491154.

[19] Cheng C-W, Tsai M-C (2004) Real-time Variable Feed Rate NURBS CurveInterpolator for CNC Machining. International Journal of Advanced Manufac-turing Technology 23(1112):865873.

[20] Choi C, Tsao T-C (2005) Control of Linear Motor Machine Tool Feed Drives for

usselsent

y for

Tool

ard

hine

Path

derark

hineure-cture

ningTool.148.rivesan-

withn ofment

tent

tion

izing

otor-ning.

) X CIRP

neargical

mizeches

ayed

IEEE

412

adedering

008) MM

stics CIRP

ol ofCIRP

ntrolction

forional

trol..Newciety

, San

tion IEEE005,

ide-ns on

rans-

signrver.

Y. Altintas et al. / CIRP Annals - Manufacturing Technology 60 (2011) 779796 795[56] Jones SD, Ulsoy AG (1999) An Approach to Control Input Shaping withApplication to Coordinate Measuring Machines. ASME Journal of DynamicSystems Measurement Control 21(2):242247.

[57] Kamalzadeh A, Erkorkmaz K (2007) Compensation of Axial Vibrations in BallScrew Drives. Annals of the CIRP 56(1):373378.

[58] Kamalzadeh A, Erkorkmaz K (2007) Accurate Tracking Controller Design forHigh Speed Drives. International Journal of Machine Tools & Manufacturing47:13931400.

[59] Kavanagh RC (2000) Improved Digital Tachometer With Reduced Sensitiv-ity to Sensor Nonideality. IEEE Transactions on Industrial Electronics47(4):890897.

[60] Kim M-S, Chung S-C (2006) Integrated Design Methodology of Ball-ScrewDriven Servomechanisms with Discrete Controllers. Part I. Modelling andPerformance Analysis. Mechatronics 16:491502.

[61] Knorr M (2001) Impulsgekoppelter TransmissionsantriebEuropean Patentand Trademark Ofce, Patent Specication EP 1 247 613 B1 (date of ling06.04.2001).

[62] Koren Y, Lo CC (1992) Advanced Controllers for Feed Drives. Annals of the CIRP41(2):689698.

[63] Koren Y (1997) Control of Machine Tools. Transactions of ASME Journal ofManufacturing Science and Engineering 110:749755.

[64] Kunzel S, et al. (2002) Verfahren zur Dampfung mechanischer Schwingungenvon Achsen von Werkzeugmaschine. German Patent and Trademark Ofce,Patent specication DE 102 46 093C 1, Siemens AG, Munchen (date of ling02.10.2002).

[65] Ladra U, Schafers E, Schur T (2007) Operating Method for an AssemblyHaving a Mechanically Movable Element, Patent Application WO 2007/115874 A1.

[66] Lee SH, Song JB (2001) Acceleration Estimator for Low-velocity and Low-acceleration Regions Based on Encoder Position Data. IEEE/ASME Transactionon Mechatronics 6(1):5864.

[67] Lin MC, Ravani B, Velinsky SA (1994) Kinematics of the Ball Screw Mechan-ism. ASME Journal of Mechanical Design 116:849855.

[68] Marton L, Lantos B (2009) Control of Mechanical Systems with StribeckFriction and Backlash. Systems & Control Letters 58(2):141147.

[69] Mekid S (2000) High Precision Linear Slide. Part I. Design and Construction.International Journal of Machine Tools & Manufacturing 40(7):10391050.

[70] Mekid S, Olejniczak O (2000) High Precision Linear Slide. Part II. Control andMeasurements. International Journal of Machine Tools & Manufacturing40(7):10511064.

[71] Nam S-H, Yang M-Y (2004) A Study on a Generalized Parametric Inter-polator with Real-time Jerk-limited Acceleration. Computer-Aided Design36(1):2736.

[72] Neugebauer R, Denkena B, Wegener K (2007) Mechatronic Systems forMachine Tools. Annals of the CIRP 56(2):657686.

[73] Neugebauer R, Drossel W-G, Ihlenfeldt S, Harzbecker C (2009) DesignMethod for Machine Tools with Bionic Inspired Kinematics. CIRP Annals59(1):371374.

[74] Neugebauer R, Wittstock V, Illgen A, Naumann G (2006) Piezo-basedActuator-Sensor-Units for Uni-axial Vibration Reduction in Machine Tools.Annals of the German Academic Society for Production Engineering WGPXIII(2):211216.

[75] Novotny L, Strakos P, Vesely J, Dietmair A (2009) Potential of State-feedbackControl for Machine Tool Drives, Modern Machinery Science Journal2009(2):98112, Paper No. 4, Prague.

[76] Nordin M, Gutman P-O (2002) Controlling Mechanical Systems with Backlash A Survey. Automatica 38(10):16331649.

[77] Okwudire C, Altintas Y (2009) Hybrid Modeling of Ball Screw Drives withCoupled Axial, Torsional and Lateral Dynamics. Transactions of ASME Journalof Machine Design 131(071002):19. 10.1115/1.3125887.

[78] Okwudire C, Altintas Y (2009) Minimum Tracking Error Control of FlexibleBall Screw Drives using a Discrete-time Sliding Mode Controller. Transactionsof ASME Journal of Dynamic Systems Measurement and Control 131(5,051006):112. 10.1115/1.3155005.

[79] Ostermann T, Weck M (2003) Lineardirektantriebe mit Impulsentkopplung.Antriebstechnik 42(11):6164. ISSN 0722-8546.

[80] Park CH, Chung JH, Lee H, Kim ST (2004) Motion Error Analysis of the PorousAir Bearing Stages Using the Transfer Function. Journal of Korean Society ofPrecision Engineering 21(7):185194.

[81] Park CH, Oh YJ, Shamoto E, Lee DW (2006) Compensation for Five DOF MotionErrors of Hydrostatic Feed Table by Utilizing Actively Contro