Cutting, by Pressing and Slicing, Applied to the Robotic Cut of Bio-materials, Part II: Force during Slicing and Pressing Cuts

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1 Ctting, b Pressing and Slicing, Applied to the Robotic Ct of Bio-materials, Part II: Force dring Slicing and Pressing Cts Debao Zho *, Mark R. Claffee +, Kok-Meng Lee + and Gar V. McMrra * * Food Processing Technolog Division, HES Laborator, Georgia Tech Research Institte, Atlanta, GA George W. Woodrff School of Mechanical Engineering, Georgia Institte of Technolog, Atlanta, GA {debao.zho, gar.mcmrra}@gtri.gatech.ed, m.claffee@gatech.ed, kokmeng.lee@me.gatech.ed Abstract The applications of robotics are becoming more and more common in non-traditional indstries sch as the medical indstr inclding robotic srger and sample microtoming as well as food indstr that inclde the processing of meats, frits and vegetables. In this paper, the inflence of the blade edgeshape and its slicing angle on the ctting of biomaterials are formlated and discssed based on the stress analsis that has been presented in Part I. Throgh modeling the ctting force, an optimal slicing angle can be formlated to maximize the feed rate while minimizing the ctting forces. Moreover, the method offers a means to predict ctting forces between the blade and the biomaterials, and a basis for design of robst force control algorithms for atomating the ctting of biomaterials. Ke words : robotics, blade ctting, slicing angle, sharpness. 1. Introdction Ctting is normall an oneros operation in the food indstr, which is reqired in the processing of meats, frits, and vegetables. In order to develop atomated machines to perform these ctting operations on non-engineering materials, this std attempts to establish a thorogh nderstanding of the science behind ctting of biomaterials. The initial test bed for or development is the wing-sholder ctting operation in a tpical poltr processing plant. This ct is not onl difficlt for the hman operator and ver labor intensive, bt it is also one that directl affects the ield of the breast meat; the most profitable margin item on a bird. Ctting line workers are at high risk of developing mscloskeletal disorders (MSDs) which are often attribted to the forces, postres and repetition of the processing tasks [1]. Dring ctting, the formation of the chips (or offcts) plas a major role in the amont of energ reqired to reslt in ctting. Metal ctting creates plasticall deformed offcts which permanentl store energ while the elasticall deformed food offcts (in materials sch as cheese, frit, etc) permanentl store almost no energ. Ths man researchers have formlated the food ctting problems sing the energ method throgh the application of the fractre toghness concept [2]; among them, Mahvash and Haward [3] formlated the relationship between the ctting force and ct depth dring deformation, ctting, and rptre and Atkins et al. [4] explained wh there is smaller ctting force reqirement when pressing and slicing compared to pressing onl. Atkins and Mai provided experimentall determined vales for fractre toghness of several bio-materials [5]. Starting from the energ perspective, Kamab et al. [6] formlated the stress and force distribtion in cheese ctting. An alternative method based on internal stress has also been sed to explain the ctting process. For example, Yoshihara and Matsmoto [7] stdied the shearing properties of wood sing the stress analsis method, where mainl average shear stress was considered. Throgh an in-plane shear test of a thin specimen, some of the material properties (sch as shear modls and shear strength) were obtained in [7]. Blade sharpness is also one of the important factors, which affects the reqired ctting forces. Contact between the ctting object and the blade is an area, which can be shown from the microstrctre of a knife. Tech Edge [8] has docmented the microstrctre of their knife prodcts. Kamab et al. [6] stdied the force per nit length of a wire cheese-ctter with varios wire diameters and ctting speeds. Blade sharpness also directl inflences the ctting moments and the grip forces applied b an operator. McGorr et al. [9] stdied the magnitde of the grip force and moment sing three kinds of blades with different sharpness; namel polished, smooth and coarse knife. The fond that a finel polished knife significantl redced mean grip force and ctting moment dring the ctting operation. Szabo et al. [10] developed a procedre to establish knife steeling schedles based on increased force de to knife dllness from repetitive se to minimize operator exertions and phsical stress associated with work-related mscloskeletal disorders. The ctting area when the blade ct to a carrageenan target is sed to qantif the absolte sharpness. Unlike the above methods that stdied the blade sharpness in terms of gripping force, this research ses internal stress to describe the ctting mechanics and the sharpness of a set of blades. Part I of this paper [11] has explicitl developed a stress distribtion model, which serves as a basis to explain the ctting principles in this paper. Reference [12] has defined a relative sharpness factor to describe the relationship between the applied force and the knife dllness. This paper provides the analtical expression for the relative sharpness factor. Additionall, other inflencing factors (sch as edge width and shape) are sstematicall analzed. Nmerical, simlation and experimental reslts are sed to verif the formlation. 2. Ctting Parameter Analsis Fig. 1 shows a simplified ctting model and the parameter notations sed in this paper. As shown in Fig. 1(a), the ctting force P acts on the srface of a semi-infinite bod, where the x plane is on the bondar of the semi-infinite bod; and P v and P h are the force components along the z and x directions respectivel. The slicing angle α is defined as the angle of P from the positive z direction.

2 Figre 1(b) illstrates the parameters that characterizes the knife. It is assmed that the knife exerts a constant ctting force along the direction parallel to the x-axis and has a ctting force distribtion in the z plane shown in Fig. 1(b). The force of the knife has a maximm intensit q at [-s, s] and is linearl redced to zero at -a,and a. In the following discssion, the parameters a and s are referred to as the blade edge-width and blade shape respectivel, and the position coordinates (x,,z) are normalized with respect to a. P P h α P v (a) Ctting model, (b) Force distribtion in oz plane, Fig. 1 Ctting force acting on a semi-infinite bod. The assmptions in this part are the same as those in Part I [11] where the ctting stresses are obtained b sperimposing the varios combinations of the stresses. The ctting stresses are a fnction of the total force P, the contact length l, and the knife parameters (a, s) as σ x τ x τ xz f1 cosα f5 sinα f6 sin α P [ σ ] = τ x σ τ z = ( + ) f 5 sin α f2 cosα f4 cos α (1) l a w τ τ σ f sin α cosα cosα xz z z 6 f4 f3 where f i (i = 1,, 6) are fnctions of the ltimate stress τ of the material being ct and the knife parameters (a, l, w). When α = 90 (onl tangential force acts on the bondar of the semiinfinite bod), onl τ x and τ xz are involved. On the other hand, when α = 0 (i.e. onl normal force), τ x and τ xz are zero. The principle stresses (σ 1, σ 2, σ 3 ) can be obtained b solving the following eigen-vale problem: s x = λx (2) The principle stresses σ 1, σ 2 and σ 3 and their directions x correspond to the eigen-vales and eigenvectors respectivel. The maximm shear stress can then be obtained as τ mn = ½(σ m - σ n ) (3) where m and n are 1, 2 or Fractre Initialization o z x Tresca s fractre criterion [14] is sed to identif the fractre initialization, which can be expressed as τ = Maxabs [ ( τ ), abs( τ ), abs( τ )] τ / K (4) max where τ and K s are the ltimate shear strength, and the notch stress concentration factor respectivel. For a given material, τ, is assmed to be constant. Two ctting states, pre- and postfractres, are of interest, dring the ctting of the material: Pre-fractre: As all of the stresses in the material are de to deformation, the notch stress concentration factor, K s = 1. Post-fractre: Once the stress reaches the failre criterion given in (4). the criterion K s = 1 is no longer valid and the stress concentration factor is determined b K = τ τ = F F, (5) s o Fractre Ctting -a q -w o w z s a where τ, and τ o are the ltimate stresses of the pre- and postfractres respectivel. From (1~3), we have the form: P τ = f (, z, a, w,α ), (6) mn 7mn l a + s ( ) p where the fnction f 7mn ( ) can be explicitl expressed sing f 1 to f 6. Consider the fractre that initiates at the location (, z ), the reqired force is obtained b sbstitting (6) into (5), τ l( a + w) P =, (7) K f, z, a,, α ( ) s 8 w where fnction f 8 ( ) can be explicitl expressed sing (6). If the relative position between the knife and the material remains nchanged, the position where τ max occrs does not changed. In this case, the relationship between P and α can be established. This will be discssed in detail in Section Effect of Relative Blade Sharpness Factor In general, the sharpness of a blade is an approximate measre of the applied force P for a given condition (or a specified set of parameters τ, l, w, α). Althogh it is possible to explicitl express the relationship between these parameters and the external force sing (7), it is often impractical to get the exact vale of these parameters. A relative sharpness factor η is defined (in the case of the same slicing angle α c ) as ( a + w) η = (8) K f, z, a, w, α s 8 ( ) Hence, P = lτ η = K η (9) The relative sharpness factor defined in (8) is the extension of the definition that we made earlier in [12], where the sharpness is defined onl for ctting b pressing or the case α = 0. Using the concept in [12], the relative sharpness factor can be measred as follows: First, a nominal blade is selected and its ctting force on a specified material is recorded as P. 0 Next, the corresponding blade sharpness is calclated: η 0 = P K 0 Then, the relative sharpness of other blades sed to ct the same material at a similar condition can be expressed as η = η P 0 P0 Given the maximm allowable force P f that can be applied to reslt in ctting, the dllest sharpness can be defined as η = η P P. f 0 f 0 For convenience, a second parameter, the knife relative sharpness level κ, is defined as ( n 1)( η η ) 0 κ = int + 1, η η f 0 where n is a ser-defined integer to distingish the sharpness level of a blade; and int(#) which ronds # to the nearest integer expresses the knife sharpness level. Ths a knife can be categorized into n-level of sharpness; level 1 is the relative sharpness level corresponds to η 0 = 1. c

3 3. Simlation Reslts The fractre of the material, which is a reslt of the interaction between the blade edge and the material, depends both on the knife geometr and the material properties. In Section 2, the smbolic expressions of the fractre criteria are given as general rles. The following analsis illstrates the exact mechanism. 3.1 Fractre Force via Slicing Angle Simlation is performed to examine the effect of the slicing angle. For this simlation, the following parameters are sed a = 1, w = 0.85, and P/l = 1. The simlation reslts for α = 0 and 90 are illstrated in Fig. 2. (a) a = 1; w = -w = 0.85a at z = 0; (b) a = 1; w = -w = 0.85a at z = 0.37; Fig. 2 Stress distribtion along at different z (normalized with P/l). From Fig. 2, it is fond that the maximm stresses occr at for locations which are expressed in (/a, z/a) and shown in Table 1 as (i) to (iv). Note that the position coordinates (x/a, /a, z/a) in this paper are normalized to a, half the width of the blade edge (Fig. 1). Table 1, Locations and vales of the possible maximm stresses. Location (/a, z/a) σ x σ σ z τ x τ z τ xz (i) ( 0.00, 0.00) (ii) (-0.85, 0.00) (iii) (-0.93, 0.00) (iv) (-0.93, 0.37) The changes of the maximm stresses, principle stress and maximm shear stress with the slicing angle are shown in Fig. 3(a), (b) and (c), respectivel. For clarit, onl the stresses at location (ii) are shown in Fig. 3. Other cases have similar trends. As the slicing angle α changes from 0 to 90 at the location (/a = -0.85, z/a = 0.00), τ x and τ xz change from 0 to its maximm magnitde, τ x remains at zero and s x, s and s z change from their maximm magnitde to 0. The principle stresses change from (-0.32, -0.54, -0.54) to (0.81, 0, -0.81). The maximm shear stresses change from (0.11, 0, 0.11) to (0.81, 0.4, 0.4). Using Tresca s fractre criterion [14] and (9) with K s = 1, (τ 31 ) max = τ and l =1, the simlated external force P is shown in Fig. 3(d). Similar reslts for the other three locations are given in Table 1. Fig. 3 Stresses and external forces change with slicing angle. In Fig. 4(a), (i) (iv) show the location of the maximm shear stress and the corresponding fractre external force, which is the same expression as shown in Fig. 3(d). Note that the maximm shear stresses and the corresponding external force P are shown in the same line stle in Fig. 4(a). Since the external force P is obtained sing the same ltimate shear stress τ, the smallest one among all the P at the for locations (i) to (iv) will initialize the fractre. It can be observed that when α is from 0 to abot 10, location (iv) will initialize fractre and when α is from abot 10 to abot 90, location (ii) will initialize fractre. For clarit, the largest maximm shear stress and its reqired smallest external force are redrawn in Fig. 4(b). From Fig. 4(b), it can be seen that as the slicing angle changes the reqired external force will change along the solid black line marked as P.

4 (a) 3.2 Fractre Force via Blade Shape The knife shape can be defined sing the parameters l, a, w and w. The inflence of l (contact length) and a (edge width) can be directl measred. If l and a increase, the distribted force intensit will decrease. In order to realize the ct, larger force mst be applied as shown in the experimental reslts in [12]. The inflence of the edge shape can be roghl expressed sing w. Using (2), the stress distribtion for the different vale of the knife shape parameter w on the srface is shown in Fig. 7. From Fig. 7, it is observed that b keeping the external force nchanged, when the force distribtion changes from constant intensit to linear intensit, the maximm magnitde of all the indced stresses increases. This leads to an increase in the magnitde of the maximm indced shear stress (b sing the same external force). Ths, b assming τ is constant, the external force to realize ctting fractre is redced, i.e. the knife sharpness is increased. (b) Fig. 4 Maximm shear stresses and reqired minimm ctting force. The total force and its components in the x and z direction are shown in Fig. 5. It can be seen that the fractre from 0 to abot 10 is de to τ z which is jst beneath the srface (z 0). It is the mode II fractre, edge-sliding fractre as shown in Fig. 6(a). The fractre from 10 to 90 is de to τ x and τ xz which is jst on the srface (z = 0). It is the mode III fractre, ot-of-plane tearing, as shown in Fig. 6(b). From the external force profile shown in Fig. 5, the inflence of the slicing angle can be clearl seen. The reqired force to ct b compression onl is far larger than the force reqired b both compression and slicing. Note also that force P h does not change greatl in mode III fractre and its vale is eqal to the total force. (a) Shearing mode (K II), 4. Model Validation Fig. 7 Stress changes with w. In the following, the stress distribtion trend is verified sing both FEM method and experimental reslts. Using the reslts in simlation and the ctting force with slicing angle (α 90 ), the theoretical ctting force is predicted and compared with the experimental reslts. 4.1 FEM Verification ANSYS finite element software was sed to provide nmerical versification. The properties of the selected material are E = psi and Poisson s ratio ν = A large cbic box was sed to simlate a half semi-infinite bod fixed in the space from its base. A distribted force was added over and area to the middle of the pper srface as shown in Fig. 1. w w Fig. 5 Total force and the force components in x and z direction, respectivel. (b) Tearing mode (K III). Fig. 6 Fractre modes dring ctting. The stresses for two cases: α = 0 and 90 are shown in Figs. 8 and 9 respectivel. Figres 8(a -d) show that when onl normal force is applied, τ x and τ xz are alwas zero and onl σ x, σ, σ z and τ z are non-zero as shown in Fig. 2. The distribtion of τ z in the z plane is shown in Fig. 8(e). On the other hand, when the force is applied in x direction onl Fig. 9 shows that τ x and τ xz have non-zero vales as also shown in Fig. 2.

5 atomating robotic bio-material ctting operations sing robotic tpe devices. (a) σ (b) σ (c) σ z x Fig. 11 Force changes with contact length. (d) Top view τ (e) Section view τ z z Fig. 8 Nmerical reslts of the stress distribtion with P v onl. Fig. 12 Force and displacement dring chicken meat ctting. (a) τ x (b) τ xz (c) σ z Fig. 9 Nmerical reslts of the stress distribtion with P h onl. 4.2 Experimental Verification The experimental setp is shown in Fig. 10, which consists of an ABB robot IRB 140 [15] for motion generation, speed control and distance measrement and an ATI Force/Torqe sensor [16] for force measrement. The robot is commanded to move at a ver low speed (0.5mm/s) for ctting. The force data is saved on a central compter. For the experiments, a baking potato and a chicken breast were selected as test materials. The force trajector obtained from compression ctting of the potato and chicken breast are shown in Figs. 11 and 12, respectivel. The data from different slicing angle cts on potatoes are smmarized in Fig. 13. Robot Connect to compter Force/torqe sensor Potato Razor Blade Potato holder Fig. 10 Experimental setp. According to the maximm external force when α 90, the ltimate shear stresses at other slicing angle are estimated according to Fig. 5. The experimental data and the theoretical data are shown in Fig. 13. A good match is observed in both force direction. The theoretical forces can then be sed as the desired force in the force control loop as shown in Fig. 14 for Fig. 13 Experimental data and theoretical estimation of the ctting forces in pressing and slicing ct on potatoes. Desired force Actal force + Force - controller Fig. 14 Illstration of a force control diagram for possible bio-material ctting operation control. 5. Conclsions Desired position Actal position Plant Position controller Based on the ctting mechanics presented in Part I [11], we investigate the principles of ctting biomaterials. The relationships between slicing angle, blade edge geometr, contact length, the fractre force, and material properties and the applied force are discssed. Experiments are carried ot to validate the formlation. The following conclsions are drawn: 1) the relationship between the ctting force and internal stress is established. 2) At -

6 the initialization of the ctting fractre, the ctting force P is proportional to the contact length l. 3) At the initialization of fractre, the ctting force P is not simpl proportional to the width of the blade edge a. Edge shape and edge width have the combined inflence on fractre force. For the same edge width, the external force is proportional to the maximm force intensit which the edge shape can generate. 4) For smaller slicing angles, the ctting fractre is de to shear force τ z (Mode II). For larger slicing angles, the ctting fractre is de to shear force τ x andτ xz (Mode III). Tpe III fractre reqires considerable less force than Tpe II fractre. 5) B sing the relative sharpness factor concept, blade sharpness can be qantified at certain slicing angles. 6) Based on the material properties, the knife sharpness properties and the interaction between the blade and the material, the reqired force to realize ctting can be predicted. This observation provides the principle to optimize the ctting mechanism design and the force control algorithm design for the atomation of bio-material ctting operations. In the ftre, the stress intensit factors K II and K III will be analzed and qantified. The inflence of the knife relative velocit to the material will also be investigated. This work is to provide the fondation for the development of a control sstem for robotic ctting of natral prodct. References [1] P. G. Dempse and R. W. McGorr, Investigation of a pork sholder deboning operation, Jornal of Occpational and Environmental Hgiene, vol 1, pp , of the 2005 ISTED International Conference on Robotics and Application, paper# , Hilton Hotel@MIT, Boston MA, Oct, [13] M. Sadd, Elasticit: theor, applications, and nmerics, Elsevier Btterworth-Heinemann, Brlington, MA, [14] L. Charlles and J. Robert, Handbook of stress and strength: Design and material applications, The Macmillan Compan, New York, [15] Prodct Manal IRB 140, ABB Robotics Prodcts AB pblication, article nmber: 3HAC isse: M2000, [16] Installation and Operations Manal for ISA F/T-16, ATI Indstr Atomation Inc. pblication, Manal PN , [2] K. Hellan, Introdction to Fractre Mechanics, McGraw-Hill Book Compan, New York, [3] M. Mahvash and V. Haward, Haptic Rendering of ctting: A fractre Mechnics Approach, Haptics-e, vol. 2, no. 3, pp. 1-12, [4] A. G. Atkins, X. X and G. Jeronimidis, Ctting, b pressing and slicing, of thin flopp slices of materials illstrated b experiments on cheddar cheese and salami, Jornal of Materials Science, Springer Science + Bsiness Media B.V., Formerl Klwer Academic Pblishers, vol. 39, pp , [5] A. G. Atkins and Y. W. Mai, Elastic and Plastic Fractre: Metals, Polmers, Ceramics, Composites, Biological Materials, Chichester: Ellis Horwood; New York: Halsted Press, [6] I. Kamab, S. Chalranarti and J.G. Williams, Ctting cheese with wire, Jornal of Materials Science, vol. 33, pp , [7] H. Yoshihara and A. Matsmoto, Measrement of the shearing properties of wood b in -plane shear test sing a thin specimen, Jornal of International Academ of Wood Science, Springer-Verlag, London, UK, pp. 1-14, [8] ge%20angles.htm, [9] R. W. McGorr, P. C. Dowd and P. G. Dempse, The effect of blade finish and blade edge angle on forces sed in meat ctting operations, Applied Ergonomics, Elsevier pblications, vol. 35, pp , [10] R. L. Szabo, R. G. Radwin and C. J. Henderson, The inflence of knife dllness on poltr processing operator exertions and the effectiveness of periodic knife steeling, American Indstrial Hgiene Association Jornal, Talor & Francis pblications, vol. 62, no. 4, pp , [11] D. Zho, M. Claffee, K.-M. Lee and G. McMrra, Ctting, b Pressing and Slicing, Applied to the Robotic Ct of Bio-materials, Part I: Modeling of Stress Distribtion, in the Proceedings of the IEEE International Conference on Robotics and Atomation (ICRA06), Ma [12] D. Zho, M. Claffee, K.-M. Lee and G. McMrra, Modeling Compression Ctting of Biomaterial for Robot Control, in the Proceedings