1

Abstract—Ultrasonic vibration assisted machining is known to

reduce friction forces for various processes and materials. In this paper, the friction forces between an asymmetrical cutting blade and sheet stack for different cutting velocities are investigated. Materials used for the sheets are plain label paper and polyethylene terephthalate. The cutting blade operates at a resonant longitudinal mode, resulting in a discontinuous relative movement between blade surface and stack. Along the normal vector of the cutting edge, the friction force reduction changes with the amplitude of the longitudinal mode of the blade. It is shown that for low cutting velocities no friction force is visible, and at higher cutting velocities friction increases.

Index Terms—ultrasonic, friction, sheet stack

I. INTRODUCTION In recent years, a substantial amount of research has been

done on ultrasonic vibration assisted machining. The hybrid process allows conventional manufacturing processes to be enhanced with high frequency vibrations, to reduce forces [1], increase workability of hard materials [2], improve surface quality, and increase tool life [3]. For the print and paper industry, the need for new technologies to lower production costs is of major interest. The cutting of paper sheet stacks is an essential process in the production line that calls for high speed and high precision. Presently, conventional guillotining of sheet stacks is used to bring paper coming from offset printing or gravure printing into the correct dimensions with a single translational guillotine or swivel guillotine. One key advantage of ultrasonic vibration assisted cutting as a hybrid process is allowing conventional cutting to be enhanced by creating an oscillating movement of the tool edge while cutting. It has been shown that ultrasonic vibration assisted cutting of food materials can reduce cutting forces [4] due to reduction in friction forces.

There are three basic vibration modes that can be used individually or in combination for ultrasonic vibration assisted

cutting: longitudinal, transversal, and lateral. At the cutting edge, a longitudinal mode has a maximum displacement in cutting direction, a transversal mode has a maximum displacement perpendicular to the cutting direction and cutting edge, and a lateral mode has a maximum displacement perpendicular to the cutting direction and parallel to the cutting edge.

Rozner et al. [5] showed that ultrasonic vibration effects the friction forces between metals in strip drawing. For the metal drawing process a reduction in drawing and die forces was observed. Static friction forces subject to vibrations are reduced and a change in elastoplastic deformation of the contact in a static friction joint is observed [5]. Another investigation in plastic forming showed that ultrasonic oscillations apply additional acoustic stress that affects friction resulting in lower drawing forces [6]. Dynamic friction forces are also reduced when under the influence of vibrations [7]. Littmann et al. [8] conducted thorough investigations on friction force reduction when applying longitudinal vibrations and developed an analytical model that matches the qualitative observations. Friction occurring during the ultrasonic vibration assisted process was used to study surface characteristics on microscopic devices [9]. While most applications use vibrations parallel to the process's primary direction of motion, longitudinal and transversal vibrations affect sliding friction. An increasing amplitude showed an increased reduction in friction forces for aluminum, brass, copper, and stainless steel [10]. Friction reduction in longitudinal vibration direction was larger than in transversal vibration direction. The above mentioned models mostly rely on the Coulomb friction model, where the discontinuous duty cycle [3] lowers the average measured friction force.

In this investigation, the friction forces between sheet stacks and asymmetrical steel tool are discussed for a range of cutting velocities at constant vibration frequency and amplitude.

Friction Effects between Ultrasonic Cutting Blade and Sheet Stack

Karl-Robert Deibel, Konrad Wegener Department of Mechanical and Process Engineering

Institute of Machine Tools and Manufacturing ETH Zurich

8092 Zurich, Switzerland E-Mail: deibel@iwf.mavt.ethz.ch

Telephone: +41446322414

Jens Boos inspire AG ETH Zurich

8092 Zurich, Switzerland

2663978-1-4673-4562-0/12/$31.00 ©2012 IEEE 2012 IEEE International Ultrasonics Symposium Proceedings

10.1109/ULTSYM.2012.0667

Fig(B)

betblavis20conforparthemapri0.0maave

desresthemobeccutconblatheof thicutamTorearegpre

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g. 1. Experimen). The stack juts

II. EXPER

In order to tween sheet sade, the experisible in Figure00 N and are ntact the metarce is thereforerallel to the noe cutting edge.aterial used is pinted via offs06 mm and anaterial, polyetherage thicknessThe cutting blsigned asymmsonance operate entire blade ode at the cutcause the meastting blade wntact surface fade, an ultrasoe M8 screw at tthe cutting ed

is amplitude, ttting velocity

mplitudes, and o avoid the efarrangement asgarding the friceceded with fivAll experimenntact occurs dth a three axis

ntal setup with cuout 2 mm.

RIMENTAL PROC

experimentallystacks and flatimental setup e 1, the sheets

aligned at thal surface of e parallel to theormal vector of

Total height oplain label papset printing w area density hylene terephts of 0.08 mm alade used for etrical cutting ion at 35 kHz was shown in

tting edge is surement data

was milled oufinished by grionic piezoelectthe top. The vi

dge is set at 1.the PET sheet

experiments no significant ffect of increas discussed in ction of the pave runs. nts use the sduring reset. As Kistler force

utting blade (A),

CEDURE AND My test the frit metal surfacshown in Figu

s are clamped he front to allthe cutting bl

e sheets, and thf the sheets andof the stack is per on which tywith an averaof 68 gm-2. Athalate (PET) are used. the experimenblade, which wwith a longitudFigure 2. The

neglected in is obtained 5 m

ut of X37CrMinding. For extric transduceribration amplit33 ms-1 for allts do not meltas was obserthermal effect

ased dry frict[11] and [12],

aper stack and

ame sliding dAll measuremee measurement

, and clamped st

MATERIALS ictional behavce of the cutture 1 is used.

with a force low all sheets ade. The norm

he friction forced perpendicular7 mm. The pap

ypical designs age thickness s the second t

sheets with

nts is a speciawas optimized dinal mode acre minor bendthe experimen

mm above it. TMoV5-1 with

citing the cuttr is connectedtude at the midl experiments. t during the lrved with higts were observion due to fib, the experimecutting blade

direction andents are recordt platform with

tack

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mal e is r to per are of

test an

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At low her

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with xvibratiovelocity

with vrultrasonCoulomUltrason

for vf <the Couforce realong thFigure 3positionnormal

FigurultrasonAt low

FEM modal anaexperiments. Shoashed area (C) inetween blade ament with maxim

crosstalk of ing of frictioned synchronous

Hz.

III. Ring the frictionper sheet stackvelocities betw

mpact of the uls on the frequesulting discement during v

being the dispon frequency, y during vibrat

rel being the nic vibration

mb friction mnic friction for

< ωx0, with FRulomb friction eduction is rehe surface of t3. Therefore, n between cuttforce applied ire 4 shows tnic vibration o

cutting veloci

alysis of the asyown is the long

ndicates the meaand stack. Colomum amplitude

approximatelyn force, normasly with LabV

RESULTS AND Dnal behavior bk and PET shetween 10 mm mltrasonic vibraency and ampontinuous re

vibration assistcplacement, vf t

and x0 the tion assistance

relative veloassisted frict

model presenterce is calculate2 sin

being the aven force. It was elated to the athe cutting blathe friction foting blade andis 9 N in all exthe friction ff the cutting bities, the fricti

ymmetrical cuttiitudinal mode asuring position f

ors show absoluat the cutting ed

y 1 %. Measual force, and pView at a samp

DISCUSSION between the ceet stack is domin-1 to 20’00ation on the frlitude of the v

elative movetance is calculacos

the cutting velvibration ampis calculated bsin

ocity. To undion forces, thed in [8] is d by

erage friction fobserved that

amplitude of tade (Figure 2) orces at the sad stack is conxperiments. forces with ablade for paperion force redu

2

ng blade used

at 35 kHz. The for the friction ute values of dge.

urement data position was pling rate of

cutting blade ne using the

00 mm min-1. friction force vibration and ement. The ated by

locity, ω the plitude. The

by

derstand the he modified

considered.

force, and FC t the friction the vibration as shown in ame relative sidered. The

and without r sheet stack. uction due to

2664 2012 IEEE International Ultrasonics Symposium Proceedings

Figthehigmebetfor(△)15’

theforforvibFigvibasspapdispapbacmitheranobdispoinc[14expRemolowdepof obneamosta70

g. 3. Friction foe blade. Here, nogher above the easurement positween vibration rce. Reduction i), 5000 mm min’000 mm min-1 (

e vibrations is rces. At higherrce can be bration assistedgure 5 for frictbration of thesisted friction per than for Psplacement at hper fibers. At ck and forth foinimal, but incre experiments nge stay consserved due to scussed in [lytetrafluoroethcrease in fricti4]. The increapected regardi

egarding the frodel cannot bewer relative pendency of boconventional

served at low car zero for boodel well. Regack, no friction00 mm min-1.

orce reduction bao friction force measuring posi

ition for the eassisted frictio

is shown for 10n-1 (♢), 7000 mm(x), and 20’000 m

very high, resr cutting velocobserved for d testing. Simion forces of P cutting bladeforce increase

PET can be exhigh relative vhigh relative

or one vibrationreases with lowwith PET, fritant while at the viscoelasti13], which hylene (PTFEion at higher vse in friction wing the modi

friction forces e applied herevelocity, bec

oth materials afriction force

cutting velocitoth materials agarding the fricn was observe

For PET, t

ased on positionreduction is obsition (Figure 2) xperiments. FVA

on force and co000 mm min-1 (

m min-1 (◯), 10mm min-1 (◃).

sulting in unmeities, an increa

conventionalmilar observatiPET without ane. The differee at lower relaxplained by thevelocity and th

velocity, the n cycle and thewer relative veiction forces ahigh velocity

ic behavior of is also obseE) and polyavelocities was with higher refied Coulombof paper and

e for high cuttcause the noas seen in the e. However, thies (= low relaand fit the moction between ed for cutting the friction

n of the stack aloserved 3.5 mm

with 0 being A/FCC is the ra

onventional frict□), 3000 mm m’000 mm min-1

easurable frictase in the frictl and ultrasoons are made

nd with ultrasoence in vibratative velocity e smaller relathe bending of

paper fibers fe actual slidinglocity. Regard

at a low velocy, an increase

polymers as iterved here. Famide (PA), also observed

elative velocityb friction mod

PET stacks, ting velocities onlinear velocexperimental dhe friction forative velocity) odified Couloblade and papvelocities bel

increased abo

ong and the

atio tion

min-1 (▿),

ion ion

onic in

onic ion for

tive the flip g is ing city e is t is For an

d in y is del. the or

city data ces are mb per low ove

Fig. 4. between 10 mm mcalculateCoulomb±0.3 N.

100 mmTo a

jutting 3.5 mm1000 mconductfriction forces astack bforce, boscillati

In coaffect tsurfacescutting choose friction friction that fomeasurehigher cVibratiothe clamapproprneed toneeds tovibratio

Conventional (n blade and papemin-1 to 20’000ed vibration ab model with F

m min-1. analyze the deof the stack,

m, 5.25 mm amm min-1, 300

ted. Figure 6 shforces withou

are higher at sbending stiffnebecause the indion of the cutti

onclusion, it hathe friction fos. When usinsheet materiala clearance anreduction of veffects betwee

or low cuttinged during ultcutting velociton assisted fricmped sheet stariate model foro be conductedo be conductedon assisted cutt

(◯) and vibratier sheet stack fmm min-1. The

assisted frictionFC = 1.5 N [8].

ependency of measurement

and 7 mm j00 mm min-1 hows that the j

ut vibration, busmall juts. At ess [15] has adividual sheetsing blade and t

IV. CONCLU

as been shownforces betweenng an asymml or any other ngle > 0 to prvibration assisen sheet materig velocities, trasonic vibraties, reduced frction forces alsack. Further inr the modified d. Thermal behd as well as weting.

ion assisted (♢) for cutting veloc

black dashed lin force from

Measurement u

the friction fs with 0.5 mmut at cuttingand 5000 mmjutting has no

ut vibration asslarger jutting, an impact on s can move alothereby no slidi

SION n that ultrasonn sheet stacks

metrical cuttingmaterial, it is operly utilize

sted cutting. Rial and blade, ino friction

ation assistancriction forces aso depend on tnvestigations invelocity depenhavior of fibroear of cutting b

3

friction force

cities between ine shows the the modified uncertainty is

force on the m, 1.75 mm, g velocities m min-1 are effect on the isted friction the reduced the friction

ong with the ing occurs.

nic vibrations s and metal g blade for important to the effect of

Regarding the it was shown forces were

ce, while at are observed. the jutting of n finding an

ndent friction ous materials blades during

2665 2012 IEEE International Ultrasonics Symposium Proceedings

Figbet10 calCo±0.

Fig100

forLitmo

g. 5. Conventiotween blade andmm min-1 to 20

lculated vibratioulomb model .3 N.

g. 6. Friction for00 mm min-1 (□)

The authors wr the input regttmann for soodel.

onal (◯) and vd PET sheet sta0’000 mm min-1.on assisted friwith FC = 2 N

rces with and w), 3000 mm min-

ACKNOWL

would like to sgarding the ex

ome help rega

vibration assistedack for cutting . The black dashiction force fr[8]. Measurem

ithout vibration -1 (△), 5000 mm

LEDGMENT specially thankxperimental searding the mo

d (♢) friction fovelocities betwhed line shows rom the modif

ment uncertainty

for different jutm min-1 (♢).

k Sascha Weiketup, and Walodified Coulo

orce

ween the

fied y is

ts at

kert lter mb

[1] V. A(vib96,

[2] E. ShardAnn444

[3] D. BPre

[4] Y. fooBiopBarSpr

[5] A. fricSoc

[6] R. Pon 196

[7] T. Sund1, p

[8] W. the long71,

[9] P. chaultr212

[10] V. Kmetvibr840

[11] A. “PaInte65,

[12] N. Gof p

[13] N. polyTrib

[14] B.-Bbehundno.

[15] D. “BaLeh

Astashev and Vbro-impact) proc1998.

Shamoto and T. dened steel by nals - Manufact4, 1999. Brehl and T. Doecision EngineerSchneider, S. Zds,” in Ultr

oprocessing, serrbosa-Canovas, ringer New YorkG. Rozner, “Ef

ction during striciety of America,Pohlman and Emetallic friction

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Littmann, H. Stpresence of

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0, 2004. Johansson, C.

aper friction -ernational Pape1997. Garoff, C. Fellepaper,” Wear, voMyshkin, M. Pymers: Adhesibology InternatiB. Jia, T.-S. Li

haviors of seveder dry friction a

11-12, pp. 1353Gross, W. H

alkenbiegung,” hrbuch. Springer

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2666 2012 IEEE International Ultrasonics Symposium Proceedings