Development and experimental verification of a numerical model for optimizing te cleaning performance of te doctor blade press roll tribosystem M. Rodríguez Ripoll, B. Sceicl,, D. Bianci, B. Jakab, F. Franek, A²T Researc Gmb, Austrian Excellence entre for Tribology, Viktor Kaplan Strasse, 700 Wiener Neustadt, Austria Vienna University of Tecnology, Institute of Fluid Mecanics and eat Transfer, Resselgasse /E, 040 Vienna, Austria Vienna University of Tecnology, Institute of Sensor and Actuator Systems, Floragasse 7/, 040 Vienna, Austria Email: ripoll@act.at Abstract: In te paper production, doctor (scraping) blades are placed in contact wit press rolls during wet pressing so as to purge te surface of te rolls from processing water, contamination, and stickies. Te contact is acieved by mounting te blade on a older, wic is tilted around a rotation axis until te blade tip contacts wit te roll. Te contact force is determined by te supply pressure of te air forced troug te tube tat is placed at te bottom of te older. Due to contact, te blade wears off and needs to be replaced periodically. Our aim is to optimize te cleaning performance of te system by modelling te tribological contact between doctor blade and press roll, in order to acieve an optimum cleaning performance, tus increasing te blade lifetime and reducing energy consumption. Te model is susceptible to an inextensive numerical evaluation. A first comparison wit experimental findings is encouraging. Key words: Paper industry, doctor blade, ydrodynamic lubrication, wear. INTRODUTION Modern papermaking factories are divided in four main sections, namely te forming section, te press section, te drying section and te calender section. Troug tese sections, te paper pulp is processed until a omogeneous paper seet is produced []. In te present paper, we focus on te wet pressing section, were te paper pulp gradually reduces its water content by passing between series of rolls and by being pressed against tem. As te paper pulp passes over te press roll and moves to te next one (Figure ), a certain amount of water containing contamination particles remains on te roll s surface. In order to keep its surface clean from particles and avoid contamination of te continuously flowing pulp, a scraping blade known as doctor blade is pressed against te roll s surface. Te blade contact force against te roll is determined by te air pressure applied to a polymer ose. A large pressure flow causes a
iger contact pressure at te blade tip, wic improves te cleaning performance at expenses of iger energy consumption and an increased wear rate of te blade. Figure. Press section of a paper macine. Te doctor blade keeps te press roll surface clean from contaminations and splas water. Due to te interest of te industry to save energy costs and an increasing pressure of lawmakers to reduce te immense energy consumption at paper mills, tere is great potential for energy saving if a more efficient cleaning strategy could be acieved. Te large number of subsequent rolls used in te press section and teir large dimensions provide room for improvement in order to reduce energy costs, avoid pollution and increase profit. Nowadays te optimum process parameters set at te doctor blade press roll tribosystem are based on te accumulated experience during years. Te aim of tis work is to develop a compreensive model of te tribosystem in order to optimise te cleaning performance of doctor blades troug a systematic and scientific approac.. NOTATION In wat follows, a list of te symbols and variables used in te paper is provided (see also Figure ). R F : Reaction force acting on te blade tip F : Force perpendicular to te blade tip F : Force parallel to te blade tip F µ : Friction force F N : Normal force v M : Roll speed vector at te contact point, wose components are v and v R FA : Reaction force acting on te rotating axis M : Momentum of te blade older r : Vector tat links te end of te older wit te blade tip r 0 : Initial position of r c0 before rotation F : Force per unit lengt of te pressurized ose r : Vector tat links te rotation axis wit te center of te ose p : Pressure of te ose E : Young s Modulus of te ose L : Lengt (perimeter) of te relaxed ose d : eigt of te compressed ose r: Vector tat links te rotation axis wit te blade tip x: Displacement of te blade due to bending R x : Displacement of te ose arm due to pressure canges γ : Rotation angle of te older due to bending of te blade β: Angle between te tangent to te mill and te blade µ: oefficient of friction E: Young s Modulus of te doctor blade I: Second moment of inertia of te doctor blade d: Tickness of te doctor blade l: Free lengt of te doctor blade l r U: Sliding speed at te surface of te press roll δ: Opening angle at te blade tip due to bending η: Viscosity of te lubricating fluid L: ontact lengt of te doctor blade 0 : Gap eigt at fluid intake : Gap eigt at fluid outtake So: Sommerfeld number K: onvergence ratio W: Blade widt in te out of plane direction α: Angle of te blade tip : ardness of te doctor blade k: Arcard wear coefficient k D : Arcard dimension wear coefficient V: Removed wear volume
guarantied as long as te film tickness between te doctor blade and te press roll is kept small. (a) (b) In a recently model proposed by te autors [], te doctor blade is considered as a pad bearing sliding over te roll surface. Assuming equilibrium conditions between ydrodynamic and contact forces, a non-dimensional group involving te key parameters was obtained. Its optimum value can be calculated by imposing te onset of ydrodynamic sliding conditions. In te present work, a mecanical model governing te deflection of te blade yields a relationsip between te linear contact force at its tip and te imposed air pressure. Te cange of te blade tip due to wear is taken into account by applying a geometrical wear model. Under tese assumptions, te influence of te process parameters on te cleaning performance can be systematically analysed... ydrodynamic Model A toroug description of te ydrodynamic model is found in []. In wat follows, only te most salient features are described for te sake of completeness. Te doctor blade is considered as a one dimensional beam, wose deflection is governed by te Euler-Bernoulli elastic beam teory Figure. (a) Scematic representation of te doctor blade and its older. (b) Detail of te doctor blade tip. (c) Detail of te pressurized ose.. MODELLING.. Modelling Approac Te modelling approac is based on te assumption tat an optimum cleaning performance can be acieved by forcing te doctor blade to operate under weak ydrodynamic conditions. In tis case, friction and wear are minimised, wile an optimum cleaning performance is (c) F Ed δ, () 6l were E is te Young s Modulus of te blade, l and d are te blade lengt and tickness and δ is te opening angle, 0 L sinδ ~ δ. () Imposing equilibrium conditions at te blade tip between ydrodynamic and contact forces, te following relationsip is obtained F cos β, () F N were β is te positioning angle of te blade (blade angle).
Te normal load F N : can be calculated analytically for a pad bearing using te Reynolds equation [] 6UηL So, (4) F N were U denotes te sliding velocity, η te viscosity, L te contact lengt and te minimum film tickness, i.e. te gap eigt at fluid discarge. So is te Sommerfeld number for te lubricated wedge flow and ence a function of te convergence ratio K 0 (5) solely: So So(K). Upon substituting eq. () and eq. (4) into eq. (), a linear furter relationsip between So and K is establised: So Ed. (6) 6UηL l cos β ( K ) K From tis relationsip one determines a unique value of K (Figure ). Figure. Relationsip between te Sommerfeld Number So and te convergence ratio K, for two different contact lengts L. An optimum cleaning performance is acieved for a small gap and small converging ratios ( 0 ~ ), i.e. wen K 0 in eq. (6). By tis means, te following condition for a non-dimensional group involving te key parameter is obtained: 6UηL Ed l cos β. (7).. Geometrical canges due to wear During te paper production, doctor blades need to be replaced periodically due to wear. During te wear process, te geometry of te blade canges, wic modifies te contact conditions at te tip. Based on purely geometrical relations, te actual blade lengt l and its contact lengt L (i.e. at a certain point of time) can be calculated for a given wear volume V [] V sinα L, (8) W sin β sin ( π α β ) ( cotα cot β ) V + l, (9) W were W is te blade widt in te out of plane direction. Te removed wear volume at every differential increment dv can be simply imposed or derived from te operational parameters by using a wear law, suc as te one proposed by Arcard [4]: FN U dv k dt kdfnudt, (0) were k D is a dimension wear coefficient to be fitted to experimental results, F N is te normal load, U is te sliding speed, te material ardness, and dt is te differential time increment..4. Mecanical Model Te ydrodynamic model and te relationsip between te geometrical key quantities at te blade tip, wic were recalled in te previous sections, rely in te fact tat te contact force at te blade tip is known. owever, in a paper mill, te only parameter readily available to te operator is te air pressure applied to te polymer ose. In tis section, a simple mecanical model aims to link bot pysical quantities. Te doctor blade is assumed to be a noncompressible one dimensional beam connected to a fixed older. Te older is free to rotate around
an axis in order to contact te press roll. Te contact force depends on te air pressure flowing troug a ose placed below te older. Te reaction force at te blade tip can be decomposed in two components, one component perpendicular F and one component parallel F to te blade tip contact line: F ( F F ) R +. () Te friction force F µ between te blade and te roll is given as v M FN Fµ µ FN µfn ˆv, () v F M N were v is a unit vector tangent to te roll at te contact point and F N and F µ are given by F F F, () + N F +. (4) µ FB F Te momentum at te blade older M is given by: M r R. (5) F We assume tat te forces and torques acting on te blade older are equal in magnitude and wit opposite sign to tose acting on te blade. Tereby, te following balance applies R F R 0. (6) FA + F By imposing conservation of momentum at te rotation axis M r F r R M 0 (7) so tat A F r F r R + M. (8) F We aim to relate te contact force at te blade tip wit te force imparted by te pressure ose. Based on te follow relation F + F F + F (9) N µ and substituting and combining eq. () and () we obtain tat te reaction force at te blade tip is R ( F vˆ + v ) ˆ F N µfn (0) and te related momentum ( F vˆ + v ) ˆ N M rc N µf. () Substituting te latter two equations in te balance of momentum (eq. 8) we finally obtain a relation between te force imparted by te pressure ose F and te normal load at te blade tip F N ( r + r ) ( F vˆ + v ) ˆ N r F c N µf. () So far, bending of te doctor blade upon contact wit te roll as been neglected in te mecanical model. In te conventional leading-order approximation, te deflection angle at te blade tip is given by F l α arctan. () EI According to tis angle, te displacement of te blade is r r 0 + x (4) wit x F l Fˆ. (5) EI Given a rotation γ, te relation between F N and F becomes: ( r Rx( γ )) F (( r + r 0 + x) R x( γ )) ( FN v ( γ ) + µfn v ( γ )), (6) wic according to eq. (9) can be updated for any wear rate. In a refined mecanical model, te elasticity of te pressure ose can be included readily. Tus, te pressure can be calculated from te required force component F according to p π 4F d L E W + + L d EW ( ) d π L (7)
4. RESULTS Te proposed model is applied in order to calculate te film tickness, wen typical operational parameters are applied (Table ). Table. Reference case parameters Parameter l d E F N Value 40 mm.5 mm 5 MPa 00 N/m Te results sow te gap eigt at fluid intake and at fluid outtake for tree different contact lengts L, namely 0.,.0 and.0 mm (Figure 4). For a rater new doctor blade (L 0. mm), te value of 0 and is small and a satisfactory cleaning performance can be expected. As te blade tip wears off, te cleaning performance degrades and for a severely worn doctor blade tip, te water film bot at flow intake and outtake becomes ticker. Figure 5. Gap eigt at fluid intake 0 and at fluid outtake for a doctor blade wit a free lengt of 0 mm. Instead of sortening te blade lengt, an even better cleaning performance can be acieved by increasing te blade tickness d up to 4.5 mm. Figure 6. Gap eigt at fluid intake 0 and at fluid outtake for a doctor blade wit a tickness of 4.5 mm. Figure 4. Gap eigt at fluid intake 0 and at fluid outtake for te parameters sown in Table. If te free lengt of te doctor blade l is sortened up to 0 mm, te model predicts an improvement of te cleaning performance for all values of L. 5. EXPERIMENTAL Dry and water-lubricated tribological model tests were performed on a pin-on-disc tribometer. Te pin was replaced by doctor blade samples wit a widt of 8 mm. During te tests, te blade was pressed against a 00r6 steel disc wit a constant normal load F N of 5 N, a blade angle β of 8 and a sliding velocity of 6 m/s. During te tests, wear was measured as te vertical displacement of te blade. After te test, te Arcard wear coefficient k d was calculated from te measured wear rate. Te results sow iger wear rates for glass fiber reinforced plastic blades wen compared to carbon fiber reinforced
polymer blades (Figure 7). In bot cases, wear was more severe under dry contact conditions. to predict te contact lengt as a function of time, provided tat te Arcard wear coefficient is obtained using independent experiments under similar wear conditions. 6. ONLUSIONS A matematical model for describing te cleaning performance and te lifetime of te doctor blade press roll tribosystem was presented. Figure 7. Arcard wear coefficient for different doctor blade materials An additional test was performed using a scale paper mill component test, wic was designed to performed tests on doctor blades wit a widt of 90 mm. Dry contact conditions were selected in order to accelerate wear and keep te duration of te component test witin a reasonable time. Te blades slid against a mill wit 0.7 m radius wit a sliding velocity of 0 m/s and a contact force of 95 N. Te latter value was set in order to ave te same contact force per unit lengt as in te pin-ondisc tests. Te blade angle was set in tis case to 0. Te test was interrupted regularly in order to measure te contact lengt of te doctor blade. Te results obtained are sown in Figure 8. Figure 8. Evolution of te contact lengt L as a function of time. Te dots are measured via a component test and te line is te prediction of te model. Te dots are te measurements obtained in te component test, wereas te line is te prediction of te geometrical wear model using te Arcard wear coefficient measured wit te pin-on-disc test. Tis result sows te feasibility of te model Te approac relied on a recently developed ydrodynamic model, wic links in a nondimensional group te most relevant operational parameters during wet pressing. anges of te blade tip due to wear were taken into account by a simple wear model based on Arcard. A mecanical model linked te contact force at te blade tip wit te force of te pressure ose, wic is te actual parameter controlled by operators. Te model allows a systematic analysis of te cleaning performance of te doctor blade as a function of te process parameters. Ticker and sorter blades reduce te gap eigt between te blade tip and te press roll, consequently improving te cleaning performance. Te building blocks of te model can be used independently in order to focus on particular penomena. For instance, te geometrical wear model was successfully applied to predict te result of a component test, by fitting te Arcard wear coefficient using model tests. 7. AKNOWLEDGEMENTS Te autors express teir tanks to te Austrian Researc Promotion Agency (FFG) for financial support. 8. REFERENES [] Papiermacer Tascenbuc. Auflage, Dr. Kurt aefner-verlag, eidelberg, 999, (in German). [] Rodríguez Ripoll, M., Sceicl, Jakab, B., Franek, F., Modelling te doctor blade-roller
tribosystem for improving te cleaning performance during paper production, Trib. Letters, 0, (under review). [] ameron, A., Basic Lubrication Teory ( nd Ed.). Jon Wiley & Sons, 976. [4] Arcard, J.F., irst, W.: Te wear of metals under unlubricated conditions, Royal Soc. of London Proc. Series A 6, 956, 97 40.