A Morphing Extrusion Die for Manufacturing of Thermoplastic Hoses THESIS

Transcription

1 A Morphing Extruion Die for Manufacturing of Thermoplatic Hoe THESIS Preented in Partial Fulfillment of the Requirement for the Degree Mater of Science in the raduate School of The Ohio State Univerity By Paul Anthony ilmore, B.S. raduate Program in Mechanical Engineering The Ohio State Univerity 2015 Mater' Examination Committee: Vihnu Baba Sundarean, Advior Amo ilat

2 Copyright by Paul Anthony ilmore 2015

3 Abtract Thermoplatic hoe are manufactured in an indutrial proce where molten platic come out of an extruder a an unhaped tube, and then goe through a preciely machined izing die that form it outer diameter. The hoe then enter a vacuum chamber which maintain a et thickne and hape while it cool and olidifie to it finihed ize. The final diameter mut atify a tight tolerance, and the line operator can regulate the vacuum preure, extruder peed, and puller peed to tay within thee limit. However, during tartup and before teady tate operation i reached, thee control variable are often inadequate for maintaining the required diameter. Thi reult in crap generation, which i an unwanted and potentially preventable cot for the manufacturer. Therefore, the goal of thi thei i to develop a morphing die with a programmable inner diameter that can be et by the operator to regulate the ize of the finihed tube during tranient extruion condition. It i expected that thi direct control of the die diameter will ignificantly reduce crap and be a cot aving for the manufacturer. The work here include the reearch, analyi, and deign neceary for evaluating the feaibility of a morphing die for ue in a thermoplatic extruion line. From qualitative and quantitative analyi performed in thi thei, different combination of die material, die deign, and actuation mechanim are identified. The candidate that bet meet the hop floor requirement i identified to be a combination of a uperelatic alloy, elf-centering ii

4 actuation mechanim and an electric motor. The pecification for a complete morphing die are recommended for ubequent development. iii

5 Dedication Thi document i dedicated to all the family and friend who have contributed to my interet in cience and engineering iv

6 Acknowledgment I would like to acknowledgement Parker Hannifin Corporation Parflex Diviion in Ravenna, Ohio for ponoring the project. In particular, I would like to thank Scott Burrowbridge and Steven Powell for providing valuable guidance, feedback, and information on variou technical and non-technical apect of the project. Their tranparency ha kept the project tak and objective clear. I would alo like to acknowledge my advior, Dr. Vihnu Sundarean, for the opportunity to work on the project and for the intruction he ha given. I am thankful for all the knowledge and experience I have gained a a reult of thi work. I would alo like to thank Dr. Amo ilat who i a member of my Mater examination committee. v

7 Vita B.S. Mechanical Engineering, The Ohio State Univerity 2014 to preent...raduate Reearch Aociate, Department of Mechanical Engineering, The Ohio State Univerity Field of Study Major Field: Mechanical Engineering vi

8 Table of Content Abtract... ii Dedication... iv Acknowledgment... v Vita... vi Table of Content... vii Lit of Table... x Lit of Figure... xi Chapter 1: Introduction to Relevant Technology... 1 Decription of Overall Manufacturing Proce... 2 Decription of Sizing Die... 4 Chapter 2: Problem Formulation... 7 Fundamental Requirement... 7 Additional Requirement... 8 Technical Approach... 9 Organization of thi thei vii

9 Chapter 3: Material Selection and Die Deign Introduction to Material Selection Stre-Strain Analyi Die Deign Option 1: Solid Metal Die Solid Metal Die Uing Superelatic Alloy Summary of Nitinol and Solid Metal Die Introduction to Platic-baed Die Deign Die Deign Option 3: Metal-filled Polymer Die Die Deign Option 4: Platic Die with Metal Liner Summary of Die Deign Chapter 4: Actuator Deign Actuator Deign Criteria and Actuation Strategy Method 1: Tangential Actuation Method 2: Radial Actuation Method 3: Collet-baed Actuation A Radial Compreion Mechanim Detailed Actuator Deign and Analyi Chapter 5: Concluion Reference viii

10 Appendix A: Derivation of Equation Appendix B: Propertie of Nitinol Appendix C: Actuator Detail Drawing ix

11 Lit of Table Table 1: Project pecification given by indutrial ponor... 8 Table 2: Relevant material propertie of potential metal Table 3: Weight percentage of metal-filled polymer prototype Table 4: Parameter value ued to determine required pring force Table 5: Spring with a maximum load of at leat 255 pound Table 6: Potential troke for different land diameter uing Nitinol, auming 4% maximum recoverable train Table 7: Propertie of Nitinol Table 8: Bill of material x

12 Lit of Figure Figure 1: Extruion of a thermoplatic tube on the left and entry into a bra izing die on the right... 3 Figure 2: Side view of the vacuum chamber... 4 Figure 3: Cloe view of a bra izing die a; izing die with face plate removed to how water port b... 5 Figure 4: Detailed drawing of the izing die howing a front view and ide cro-ection view... 6 Figure 5: Schematic howing input and output to the PLC Figure 6: Feedback control trategy for morphing die Figure 7: Tranfer function repreentation of control ytem with a diturbance Figure 8: Morphing extruion die project phae with the current phae indicated in bold Figure 9: eometry and variable aociated with radial compreion calculation Figure 10: Stree in the die a a function of radial poition due to radial compreion a; direction of tre in the die b Figure 11: Ahby chart for the metal in Tab. 2 elatic modulu veru train at yield 20 Figure 12: Comparion between a regular izing die and propoed all-metal morphing die xi

13 Figure 13: Baic crytal tructure preent in Nitinol Figure 14: Temperature-dependent phae tranformation diagram for Nitinol Figure 15: Superelatic effect in Nitinol for tenile loading Figure 16: Infrared meaurement of operating temperature Figure 17: Accumulation of reidual train in Nitinol with cycling Figure 18: Concept deign for a bra die with a Nitinol morphing mechanim Figure 19: Ahby chart for potential platic material elatic modulu veru train at yield [4], [8] Figure 20: Metal-filled elatomer prototype right and aluminum mold left Figure 21: Electrical reitance of a metal film bonded to an elatomer a a function of train Figure 22: Summary of Die Deign Option Figure 23: Equivalent mechanical ytem for actuator-die combination Figure 24: raphical explanation of actuation trategy howing preload and operating region Figure 25: Different Nitinol uperelatic repone for different type of loading Figure 26: Schematic of tangential actuation concept and correponding mechanical model Figure 27: CAD model howing load applied in FEA imulation and collar angle a; diplacement reult hown by dahed red line b; tre contour in pi c Figure 28: Simulation of tangential collar with die: force applied cloe to die a; force ditributed over a larger area b xii

14 Figure 29: Concept deign for radial actuation method Figure 30: 3D model and load ued in imulation a; alternate die profile b Figure 31: Die diplacement from imulation caled by a factor of 10 for alternate die profile Figure 32: 3D model of collet deign option Figure 33: FEM imulation reult - tree in collet Figure 34: Radial compreion mechanim patented by off [11] Figure 35: Propoed actuator with minimum allowable gap width and 10 wedge Figure 36: Mechanical model of 10-jaw mechanim Figure 37: Required radially compreive force a a function of die outer diameter Figure 38: Summary of Actuator Deign Option Figure 39: Block diagram with a +1 and -1 added to the feedback ignal Figure 40: Block diagram of Fig. 34 with and -1 combined into one block Figure 41: Block diagram with D equal to zero Figure 42: Equivalent block diagram with cloed loop tranfer function Figure 43: Actuation mechanim aembly drawing xiii

15 Chapter 1: Introduction to Relevant Technology Thi chapter introduce the manufacturing proce of extruion of thermoplatic hoe and dicue the function of the izing die in that proce that are relevant to thi thei. Ue of Thermoplatic Hoe and Tubing Thermoplatic tubing i prevalent in a wide range of indutrie and application. In the medical indutry, it i ued a catheter component, in endocopic intrument, for fluid tranport and more. It i alo ued in heavy-duty operation a the inner layer of hydraulic hoe for fluid power delivery to all type of hydraulic machine. Refinerie, pharmaceutical companie, and biological laboratorie are ome other ector that rely on thermoplatic tubing. Thee are jut a few example to demontrate the importance of thi product in many different procee [1]. Thee tube mut be deigned and manufactured to meet the demand of a particular application. For example, in medical application they mut be reitant to contamination. In chemical proceing application, tube mut be chemically inert, and in natural ga tranport, they mut have a certain mechanical trength and withtand fatigue loading. In addition to required phyical propertie, the accuracy of their geometric dimenion i critical. The tube or hoe mut fit preciely with other component in a ytem. For example, if a hydraulic hoe i being connected to a 1

16 coupler, the hoe diameter mut be within a certain range for a perfect eal. A a reult, typical diameter tolerance are +/-.003 inche or le, and a preciely controlled extruion proce i ued for manufacturing the hoe. Decription of Overall Manufacturing Proce In the manufacturing proce, the thermoplatic material i initially in the form of mall olid pellet that are loaded into a hopper above an extruder. The extruder conit of a barrel and a heated crew. The rotation of the crew draw pellet into the barrel from the hopper and puhe them forward toward the front of the extruder. Simultaneouly, the applied heat convert the pellet into a homogenou polymer melt. Additional heater in the extruion path can alo be ued for maintaining the temperature of the polymer met within a et window [2]. The high preure polymer melt i puhed through a die at the front of the extruder. Thi tep i hown on the left ide of Fig. 1. The extruder die i haped uch that the extruded polymer melt form a tube. The tube travel freely over a certain ditance and then enter a bra izing die on the right ide of Fig. 1. It i the inner diameter of thi izing die that determine the final ize of the tube. Die are interchangeable o that tube of multiple ize can be made on the ame production line. 2

17 Figure 1: Extruion of a thermoplatic tube on the left and entry into a bra izing die on the right Directly after exiting the vacuum die, the tube enter a vacuum chamber which i filled with water, hown in Fig. 2. The vacuum preure prevent the tube from collaping, and hold it hape while it cool and harden. Multiple proximity enor located near the front of the tank meaure the hoe diameter and wall thickne, and thi information i fed back to the PLC controller. After exiting the tank, the tube pae through either a flame or chemical treatment that allow the product information to be printed on it. Before the product i wound on a pool, a high reolution enor meaure the outer diameter to check that it meet the required pecification. A puller device near the end of the line pull the product down tream at a contant rate through all of thee 3

18 tep. The thermoplatic extruion proce i automated by a PLC which can be ued to monitor and control different variable. Figure 2: Side view of the vacuum chamber Decription of Sizing Die Although each apect of the manufacturing proce i important, a more detailed undertanding of the izing die i neceary. Figure 3 and 4 how an image and a detailed drawing of the izing die repectively. The circular bolt pattern in Fig. 3a faten a bra face plate to the vacuum die. Referring to Fig.4, there i a 0.02 inch gap running between the face place and the die, which function a a channel for water to flow from an external ource to the urface of the hot thermoplatic. Figure 3b how the vacuum die with the face plate removed in order to ee the hole through which water enter the 4

19 gap. The proximity of thee hole caue the water to coalece in the gap, and then form a thin film around the tube. The purpoe of thi film i to create a mall eparation between the hot platic and the vacuum die, enuring that the tube and die do not come into contact and tick together due to the temperature gradient. Maintaining the water film i crucial to the operation becaue it prevent hot pot from forming on the tube, which ruin the product. Figure 3: Cloe view of a bra izing die a; izing die with face plate removed to how water port b 5

20 Figure 4: Detailed drawing of the izing die howing a front view and ide cro-ection view Another important feature of the vacuum die i land, the part that actually hape the outer diameter of the tube. Referring to the cro ection view in Fig. 4, the land i the final quarter inch of the die inner urface that i not tapered. The drawing aign it dimenion A which i predetermined by the ize of the tube to be fabricated. In general, the land diameter i about 0.03 inche larger than the final diameter of the tube to account for thermal expanion. The tube i till hot when i pae through the land and hrink lightly a it cool. The detail of the manufacturing proce decribed above are important to the undertanding of the project objective and will be referred to throughout thi thei. 6

21 Chapter 2: Problem Formulation Thi chapter introduce the problem definition and project objective. It alo outline the propoed olution, the tep to be taken toward the olution and the integration of the morphing die with the current ytem. Fundamental Requirement During the production proce, an external diturbance may caue the tube diameter to go out of tolerance, and the enor will indicate the fault. The operator ha three variable to control for reolving the iue. Thee control variable are: the vacuum tank preure the extruder peed the puller peed Increaing the vacuum preure would tend to increae the tube diameter, while decreaing the preure would do the oppoite. Thi i generally the firt variable that the operator would adjut in thi ituation. The extruder peed and puller peed alo influence the diameter, and can alo be controlled. Increaing the extruder peed would increae the material flow rate and put lack in the line, while increaing the puller peed would put tenion in the line. Both influence the tube diameter. In ome intance, even thee three variable do not offer enough controllability and a ignificant amount of crap i generated. Thi i often the cae during tartup, 7

22 when the production line i in a tranient operation. Therefore, a need exit for reducing thi crap,. The propoed olution i to change the land diameter of the izing die upon command, creating one additional degree of freedom and control variable in the ytem. It i anticipated that thi will allow for control of the tube diameter in a very direct manner at any time over the coure of the run, but will primarily be ued during tartup of the extruion line. The pecification for changing the die diameter during extruion were developed by our collaboration with Parflex Parker diviion in Ravenna, Ohio. Thee pecification were precribed for the izing die ued in the extruion line of a hoe 0.5 inche in external diameter. The nominal land diameter of the izing die for thi hoe, along with the required change in diameter, i pecified in Tab. 1. Objective: Change inner diameter upon command by 0.02 inche from to in tep of inche Table 1: Project pecification given by indutrial ponor Property nominal inner diameter, d 1 new inner diameter, d 2 diametral troke, d 1 -d 2 allowable tolerance Specification inche inche 0.02 inche inche Additional Requirement There are everal qualitative project requirement that are equally important to the pecification lited in Tab 1: 8

23 A mentioned in the previou chapter, the thin water film i critical in preventing the hot platic to come into contact directly with the die. If thi film i interrupted or broken by a urface defect, it performance i compromied and the product may become crap. Therefore, the morphing die hould allow for water to be introduced in the proce and maintain a mooth urface finih o that the water film i not broken until the tube enter the vacuum chamber. The die itelf hould alo have good heat tranfer characteritic. If it thermal conductivity i too low, the temperature on the inner urface will be too high, and hot pot may develop on the tube. While the required heat tranfer coefficient i unknown, it i known that the etablihed bra die ha ufficient thermal propertie. The new material hould have a imilar heat tranfer qualitie to that of bra. The third additional requirement i that the inner urface of the die hould be eamle. Thi retrict the ue of any origami-type tructure to achieve morphing. Any uch eam or boundarie may be reproduced on the material flowing over it, cauing a non-uniform outer diameter. Technical Approach The pecific die requirement have been defined, but it i alo important to develop a trategy for approaching the problem. The chematic in Fig. 5 outline the propoed olution and how it will integrate with the exiting machine. The current input to the PLC are the wall thickne and OD meaurement 1,2, and the output are the extruder peed and vacuum preure 3,4. The morphine die ytem will add one input 9

24 and one output: the die diameter 5 and the control ignal to a morphing mechanim 6 repectively. The new hardware i expected to conit of an amplifier, a motor or linear actuator, a mechanim which grip and compree the die, and the die itelf. The amplifier can be located remotely, but the die, morphing mechanim and actuator mut be integrated with the die block een in Fig. 1 and 5. Figure 5: Schematic howing input and output to the PLC The cloed loop control ytem for the morphing die i hown in Fig. 6 a a block diagram. The et point, which i a value between and 0.525, will be entered on the PLC. Thi reference value will be compared with the current die diameter to calculate an error ignal, et. iven the error ignal, the morphing controller calculate the control input neceary to change the diameter of the die to the deired value. A feedback enor meaure the new diameter and return it to the PLC to complete the baic tructure of the control ytem. 10

25 The propoed control cheme for tracking the reference value i to alway approach the deired diameter from a maller diameter. The actuator will firt compre the die to the mallet diameter, and then move backward to the commanded diameter. With thi trategy, the die will elatically expand to follow the poition of the actuator in a very controlled manner. Approaching the et point from thi direction will reult in the high reolution tep ize that i required in the project pecification. During implementation of the controller, the control gain be deigned tarting with evaluation of the ytem requirement and characteritic. Conidering that the dynamic of the manufacturing proce are relatively low, the ettling time of the cloed loop ytem in Fig. 6 i not critical. However, the controller hould have good diturbance rejection. For example, a change in the vacuum tank preure preent itelf a an unwanted diturbance that hould not influence the die diameter. Alo, the teady tate error hould be le than the allowable tolerance given in Tab. 1. The cloed loop pole can be elected to meet thee requirement. The control loop ha been modified in Fig. 7 to include an external diturbance, D, and the block have now been identified by tranfer function in the Laplace domain. By uing the final value theorem and reducing the block diagram, an expreion can be written for the teady tate error. Thi i given by Eqn. 1 in term of the block tranfer function. Once a working prototype ha been built, a parameter identification procedure can be ued to etimate the tranfer function and choe the controller gain. 11

26 12 Figure 6: Feedback control trategy for morphing die Figure 7: Tranfer function repreentation of control ytem with a diturbance lim 0 D R e d c d d c d c 1 Organization of thi thei The olution to the problem ha been broken down according to the chart in Fig. 8. The initial phae are the die deign/material election and actuator deign, which are completed in parallel. The ubequent tage are prototyping/teting and control. Thi thei contain the die deign/material election and actuation deign phae, which are eparated into Chapter 3 and 4 repectively. They involve evaluating the feaibility of the morphing die concept and invetigation of different die deign and actuator deign.

27 A future project phae will involve prototyping, teting, and development of the control ytem. Figure 8: Morphing extruion die project phae with the current phae indicated in bold 13

28 Chapter 3: Material Selection and Die Deign Thi chapter develop the criteria for potential die material and introduce everal die deign uing the material that meet thoe criteria. At the end, the bet die deign/material combination i identified. Introduction to Material Selection There were a few main criteria that were conidered when determining an appropriate material for the die. The mot important wa that the die hould remain in the elatic region throughout the troke length. If any platic deformation occur in the material, the die will not return to it nominal diameter. Stre-Strain Analyi To keep the problem imple, the firt material conidered wa bra. The vacuum die are routinely made from thi material, o a bra morphing die would add minimal complexity to the ytem. A mentioned, the die hould remain in the elatic region o that all the diplacement i recoverable. For linear elatic material, thi limit occur at the yield tre. Therefore, the tree in bra need to be etimated uing the required diplacement in the project pecification. It wa aumed that the die wa a uniform cylinder a hown in Fig. 9, with inner radiu r i and outer radiu r o. A uniform preure, P o, i applied to the outer urface, while a preure P i i applied to the inner urface. For thi application, the outer preure P o would be applied by an actuator, and the inner 14

29 preure i aumed to be zero. The tre-train derivation for thi geometry can be found in [3]. The material geometry and mechanical propertie of bra ued in the calculation are pecified in Fig. 9. The dimenion are thoe of the current izing die and were provided by Parker. Figure 9: eometry and variable aociated with radial compreion calculation The reult of the calculation wa that an external preure of 162 ki i needed to achieve the required radial troke of 0.01 inche. Thi preure i well beyond the yield trength of bra. Before concluding that bra i unatifactory, a cloer look wa taken at the equation, known a the Lamè equation, and the tree in the die. The radial and tangential train in a cylindrical member are given by Eqn. 2-3 where u i the radial diplacement variable. 15

30 du r dr 2 u t r 3 Hooke law can be written for both the radial and tangential direction uing Poion ratio and the train. r du E v t 4 dr u t E v r 5 r Equation 6 i obtained from a radial force equilibrium. If Eqn. 4-5 are ubtituted into Eqn. 6, the reulting expreion i a differential equation for the radial diplacement Eqn. 7. d r dr r t r d u 1 2 dr r du dr u 2 r 0 7 The olution to thi equation i below, which give the radial diplacement a a function of the applied preure and geometry. The radial and tangential tree can alo be found at any point in the die uing thi olution along with Eqn v ri Pi r P o o 1 v ro ri Pi Po u r E r r E o i ro ri r The aumption of thi derivation are that the geometry i a uniform cylindrical tube and that there i no tre in the axial direction. The die will likely have boundary condition 16

31 and tre concentration which violate thee aumption, but the equation till give a good etimate of the tree and train. The firt conequence of thee equation i that they can be ued to find the required train. iven the pecified radial troke of 0.01 inche and inner diameter of inche, the required tangential train i 3.67%, uing Eqn. 3. The radial train can alo be found by differentiating Eqn. 8 and plugging into Eqn. 2, giving 1.21%. Due to ymmetry, the hear train ε rθ i zero, and the maximum principal train i jut the tangential train. Therefore, the die material hould have a recoverable train equal to the tangential train of 3.67%. The econd ue of the equation i to analyze the tree in the die. Figure 10 how the radial and tangential tree a a function of radial poition reulting from the external preure that wa applied to achieve 0.01 inche diplacement. Becaue of ymmetry, the hear tre component, σ rθ, i zero, and only the radial and tangential tree contribute to the principal tre. When the internal preure P i equal zero, the maximum principal tre i the tangential tre at the inner radiu. Thi tre i -650 ki, which i much higher than the applied preure, indicated in the plot. If the applied preure i reduced until the maximum principal tre i below the yield tre of bra, the diplacement drop to approximately inche, a mall fraction of the required troke. Depending on the hear trength of bra, the die may fail in hear firt. The maximum hear tre i one half the difference between the principal train, and for thi die the maximum hear tre i 1/2σ t ince σ r = 0 at the inner radiu. Bra can be ruled out a a potential material option due to both failure in compreion and hear. 17

32 Figure 10: Stree in the die a a function of radial poition due to radial compreion a; direction of tre in the die b Die Deign Option 1: Solid Metal Die Although bra doe not meet the pecification, it i till deirable to ue a metal die becaue of it high thermal conductivity. Therefore, the olid metal die contitute the firt of three die deign option. From the previou ection, it i clear that the limiting factor for metal will be the elatic train. Conequently, an extenive earch wa conducted to find metal alloy capable of 3.67% elatic train. During the earch, the train at yield data wa recorded whenever it wa available. However in mot cae, manufacturer and online databae did not provide information on train at yield. In other intance, even the yield trength wa not available, in which cae ome material with relatively low elatic moduli were recorded. 18

33 The finding of the earch have been ummarized in Tab. 2 and Fig. 11 a an Ahby chart. enerally it i preferable to have a low elatic modulu o that low actuation force are needed. Thi would eliminate ome of the material in Fig. 11 uch a tainle teel. While the elatic modulu value are reaonable, many of the value for elongation at yield eem unreaonable. Indeed, no vendor were found who could confirm thi train at yield data for their product. For comparion, the train at yield were alo calculated uing Hooke law, Eqn. 9. In general, the material hould have a high yield trength and low elatic modulu for a high elatic train. The reult of thi calculation howed that none of the metal atified the train requirement, and in fact, mot have le than 1% recoverable train. y y 9 E Table 2: Relevant material propertie of potential metal Metal Elongation at Break, % Elongation at Yield, % 19 Elatic Modulu, Pa Thermal Conductivity, W/m-K 260 Bra Bra Copper Tin > Platic Mold Steel MoldMax Copper Alloy UIMA 303 Stainle Steel Aluminum Alloy Copper Alloy Nickel Alloy Silver, CP rade Superplatic Zinc Titanium Alloy [4]

34 Figure 11: Ahby chart for the metal in Tab. 2 elatic modulu veru train at yield The mot promiing metal from the lit wa tin, which had a reaonable value for elatic train, a low elatic modulu and i commercially available. Therefore, tin i the recommended material for a olid metal die prototype. It ha ome relevant propertie in the context of thi application. It ha good corroion reitance to water, but may be uceptible to other material. Alo, although tin may have up to 3.67% recoverable train, it ha the potential to ditort over time. Thee characteritic hould be invetigated while evaluating a tin die. The propoed deign of the all metal die i explained by Fig. 12 along with the conventional bra die for comparion. The new die deign i imilar except for the addition of an extended morphing feature that can be radially compreed. The major difference between the two deign i that the inner 20

35 tapered ection of the tin die extend farther before reaching the land. Thi mean that the water film will need to be maintained over a longer ditance. Otherwie, the all metal die keep the baic deign of the current die intact. Figure 12: Comparion between a regular izing die and propoed all-metal morphing die Solid Metal Die Uing Superelatic Alloy A ubcategory of the olid metal die option i the uperelatic alloy, nickeltitanium. It i mot commonly known a a hape memory alloy and by the trade name Nitinol. Nitinol can typically achieve 9-10% elatic train in one cycle and a repeatable 4-5% over multiple cycle due to a crytallographic phae tranformation. It i popular in medical application and i uually old a foil, wire or tubing. Nitinol can be ued in either hape memory mode or uperelatic mode, but will be ueful in uperelatic mode for thi application. To ue Nitinol in an engineering application, an undertanding of the material cience i eential. Nickel-titanium exhibit hape memory and uperelatic propertie becaue it can undergo a phae tranformation between autenite and martenite crytal 21

36 tructure. Thee crytal tructure are illutrated in Fig. 13. While autenite ha jut one form, martenite can exit in either the twinned or detwinned tate. Twinned martenite ha boundarie that form line of ymmetry between adjacent crytal. If a material tranform from autenite to a twinned martenite tructure, there will be negligible train in the material becaue of thi twinning. However, if a hape memory alloy tranform from autenite into detwinned martenite, or the oppoite, large train will be produced. Change from one tructure to another can be induced by either temperature or tre [5]. Figure 13: Baic crytal tructure preent in Nitinol Figure 14 explain the temperature induced phae tranformation. The four temperature indicated in the plot A f, A, M f, and M are material propertie and depend on the particular material compoition, amount of cold-work and heat treatment. Suppoe that the material begin at a temperature above A f and i cooled to a temperature below M f. From temperature A f until temperature M, the material will tay in the autenite tructure. Continued cooling from M to M f will reult in a tranformation from autenite to martenite, reaching 100% martenite at temperature M f. Thi will form twinned martenite, which i more energetically favorable than detwinned martenite, and 22

37 o negligible train will be produced. Now, if the temperature rie, the material will remain 100% martenite until temperature A. From thi point, the material will tart developing autenite until it reache 100% autenite at temperature A f. The y-axi in thi figure i percent martenite, o a value of zero on the y-axi repreent 100% autenite [5]. Figure 14: Temperature-dependent phae tranformation diagram for Nitinol In the previou explanation, autenite tranformed to twinned martenite and back again due to change in temperature. It i alo poible to obtain detwinned martenite by applying a load to the material. Thi i the mechanim behind uperelatic effect, diplayed in the tre-train diagram of Fig. 15. Suppoe that the material i in the autenite phae and i under no load at a temperature above A f. Now if a load i applied, it will be behave linear elatically up to a certain plateau tre. Once it reache thi 23

38 critical tre level, detwinned martenite will be induced and a correponding large train will occur in the material. If the load continue to increae, the material will tart to behave linear elatically again but will eventually undergo platic deformation. When the load tart to decreae, a hyterei effect occur becaue of friction between the crytal. A the decreaing load reache the lower plateau level, autenite form again and the material return to it tarting point. Thi tranformation allow nickel-titanium to achieve up to 8-10% recoverable train. Figure 15: Superelatic effect in Nitinol for tenile loading The temperature and tre induced phae tranformation have been dicued eparately. Now, they will be conidered together uing two cenario to complete the introduction to Nitinol. Scenario 1: It wa noted that martenite i table at lower temperature while autenite i table at higher temperature. Suppoe that the temperature i held below the martenite finih temperature o that the material i in a twinned martenite tructure. A load i then 24

39 applied until detwinned martenite form. When the load i removed, the material will remain in the detwinned tate becaue martenite i table at the preent temperature. Thi reult in a reidual train after the load i removed. Scenario 2: Alternatively, uppoed that the temperature i held above A f o that the autenite tructure i table. Now, if detwinned martenite i tre-induced, and then the load i removed, the material will return to the table autenite tructure and there will be no reidual train. The propertie of nickel-titanium decribed above are important in aeing it potential ue a a morphing izing die. Three important deign conideration are outlined below: When the die i compreed, it hould return to it original form upon unloading, with no reidual train. Therefore, the operating temperature mut be above the autenite finih temperature, a decribed in Scenario 2. There i alo an upper temperature limit above which it i impoible to tre-induce martenite. Thi bound the ueful temperature range for uperelaticity, which i generally a 90 or 100 F window. The autenite finih temperature can be tuned through heat treatment and varying weight percentage of nickel and titanium. The teady tate operating temperature of the izing die wa meaured with an infrared camera a hown in Fig. 16. The average temperature at two different point on the urface of the die are 120 and 140 F repectively. Auming that the land ha a imilar temperature, the minimum allowable A f temperature would be approximately F. More detailed thermal analyi will be neceary in a future phae of the project. 25

40 Figure 16: Infrared meaurement of operating temperature Nitinol mut go through a training proce before it can be ued in thi application. The need for training i explained by Fig. 17, which i a recreated plot from a paper by [6]. The plot how tre-train curve of a Nitinol wire at different loading cycle. In the firt cycle, N=1, the wire tart at zero train and return cloe to zero train after it i unloaded. However, a the cycle continue, a reidual train tart to accumulate, and by the 250 th cycle there i a reidual train of >2%. Thi reidual train build up becaue the material will tart to develop more preferable martenitic variant a it i cycled. Martenite can exit in 24 different variation, and the crytal will develop more of thee variation during the cycling proce. The purpoe of the training proce i to mechanically cycle the material until it reache a teady behavior and there i no further accumulation of train. The die hould be mechanically cycled o that thi table behavior i achieved before it i put into operation. 26

41 Figure 17: Accumulation of reidual train in Nitinol with cycling A olid Nitinol die, uch a the deign in Fig. 12, i unrealitic and undeirable. Nitinol i not available in tock ize thi large, and it high cot would preclude thi deign regardle. The concept deign in Fig. 18 conit of a bra die which can be imilar to the current deign, plu the addition of a morphing feature made from a Nitinol tube. Thi minimize the amount of Nitinol needed and alo keep the traditional deign of the die intact. A eam between the morphing feature and the bra die can be avoided by having the two material meet at the gap dicued in Chapter 1. The gap can now be ueful both a a water channel and a way for the two piece to be aembled without an interface on the inner urface. The Nitinol tube can be either pre fit or heat hrunk for aembly with the bra die. 27

42 Figure 18: Concept deign for a bra die with a Nitinol morphing mechanim Although Nitinol i the mot popular uperelatic alloy, it i not the only one. Scientit recently developed a ferrou uperelatic alloy capable of train of up to 13% [7]. Previou ferrou alloy were not ueful becaue they could not obtain uperelaticity at room temperature. A ferrou alloy i appealing over Nitinol becaue of it lower cot and higher train. However, Nitinol i much more commercially available than any other uperelatic metal. Summary of Nitinol and Solid Metal Die In ummary, the olid metal die i an attractive option, but i implauible becaue of the inability of metal to meet the elatic troke requirement. A bra die with a Nitinol-baed morphing mechanim i a trong poibility, with repeatable elatic train of 4-5%. A dicued, Nitinol will require ome extra deign conideration, but can provide both the thermal conductivity of a metal and the train of a non-metal. 28

43 Introduction to Platic-baed Die Deign Due to the train limitation of metal, ome platic-baed die deign option were invetigated. Although it i noted that thee option begin to diverge ignificantly from the conventional die deign, they do have ome advantage. The firt advantage i that platic can utain higher elatic train than metal, and many type of platic meet the troke pecification. The econd advantage i that platic have a low elatic modulu, which mean they will be eaier to actuate than metal. The Ahby chart in Fig. 19 plot the elatic modulu veru recoverable train for ome common platic that are potential candidate for thi application. The primary diadvantage i that platic have low thermal conductivitie. Special attention mut be devoted to the heat tranfer propertie of the die. A econd diadvantage i that platic will wear fater than metal, requiring replacement more frequently. However, thi might be acceptable for a low cot die. The following ection introduce two die deign concept and dicu their advantage, diadvantage and uggeted next tep. 29

44 Figure 19: Ahby chart for potential platic material elatic modulu veru recoverable train [4], [8] Die Deign Option 3: Metal-filled Polymer Die In thi option, the die i made from a polymer that ha metal powder dipered in it matrix. The concept i to ue the deirable propertie of both the metal and polymer to imultaneouly achieve high train and high thermal conductivity. To invetigate the concept, prototype coniting of a ilicone elatomer PDMS and copper powder were fabricated uing the aluminum mold in Fig. 20. The copper powder, PDMS rein, and a curing agent were mixed together, poured into the mold, and then heated to 150 C to cure. Prototype were made with three different weight percentage lited in Tab. 3. Baed on qualitative obervation, it wa hown that the tiffne of the prototype could 30

45 be controlled by varying the weight percentage of copper. The concluion from thi experiment were that a much tiffer die would be needed in the real application. Therefore, the next tep would be to make prototype with a tiffer polymer than PDMS and meaure the effective thermal conductivity. The thermal conductivity of thee ample wa not meaured, but it i expected to be between that of bra and PDMS. The advantage of a metal-filled polymer die i the quick and inexpenive fabrication of new die once a mold i made. Thi can offet the diadvantage of having to replace die often due to high wear rate. However, by uing other polymer, the die tiffne can be ignificantly increaed to minimize the amount of wear. The metal-filled polymer i a realitic deign option with plenty of room for further invetigation and improvement. Figure 20: Metal-filled elatomer prototype right and aluminum mold left Table 3: Weight percentage of metal-filled polymer prototype Part PDMS, % by weight Copper powder, % by weight

46 Die Deign Option 4: Platic Die with Metal Liner The concept of the die with the metal liner i to ue a platic die capable of the required train, but have a thin metal liner on the taper and land to obtain the deirable propertie of a metallic urface. The metal liner will help to reduce wear, maintain the water film, and promote heat tranfer. The ueful thickne range for the metal film i nm, and a thin film depoition proce uch a putter-coating can be ued to fabricate a prototype. Thi deign option depend on the phenomenon demontrated by [9] that metal film bonded to an elatomeric ubtrate can be tretched to higher train than a freetanding thin film or bulk material. When a crack develop in a freetanding film, any further deformation will take place at that location and the film will rupture quickly. However, when the film i bonded to a ubtrate, the propagation of an initial crack will be uppreed by the ubtrate, preventing a rupture. Thi phenomenon can be ued to obtain 3.67% train in a metal that would not be poible with a olid metal die. Figure 21 i a recreation of a graph from [9] plotting the electrical reitance veru applied train. The electrical reitance can be ued a a meaure of crack propagation. For thi particular elatomer, 3% train wa achieved before cracking. The reult in [9] indicated that if an elatomer with a higher elatic modulu i ued, the train can be increaed. The metal liner can be applied by a thin film depoition proce uch a putter coating. 32

47 Figure 21: Electrical reitance of a metal film bonded to an elatomer a a function of train Like the metal-filled polymer, thi i a feaible option that can be further invetigated. The mot important requirement for high train potential i the bond between the thin film and the ubtrate. If the bond break down locally, the film will be effectively freetanding in that location and a crack can propagate through the thickne. Alo, heat may travel eaily through the metal film but get trapped when it reache the platic die. Careful conideration of the effective heat tranfer coefficient will be important in thi deign. Summary of Die Deign The hierarchy chart for the die deign option can be een in Fig. 22. In general, the metal die will have good heat tranfer propertie but be difficult to actuate and will platically deform. The platic deformation that metal would experience 5-10 time the elatic limit concluively exclude them from the lit of potential material, with the 33

48 exception of uperelatic alloy. The platic-baed option are capable of large train and require low actuation force, but are primarily limited by their thermal conductivitie. Although platic die deign deviate from the accutomed die, they offer ome new advantage. With additional reearch on an intelligent thermal deign and election of material, a platic die option ha the potential for ucce. Becaue Nitinol ha proven repeatable elatic train of 4-5%, ha a high thermal conductivity, it i the bet option for a potential morphing die. Therefore, the analyi and deign of the actuator in the next chapter will aume the goal i to radially compre a Nitinol tube. If the reult of the prototyping phae warrant another look at the platic deign option, it will be done at that time. Figure 22: Summary of Die Deign Option 34

49 Chapter 4: Actuator Deign Thi chapter i on the deign and analyi of mechanim that can radially compreive the die. The actuation criteria and trategy are dicued firt followed by development of potential actuator deign. Actuator Deign Criteria and Actuation Strategy The actuator deign i another important apect in the analyi of the propoed morphing die. It mut be able to impoe the radial diplacement of 0.01 inche with a ufficient force and a repeatability. Another neceity i that it hould compre the die uniformly, keeping it circularity throughout the troke o that the thermoplatic hoe doe not go out of tolerance. There are two poible actuation trategie for thi application, which will be explained through the chematic in Fig. 23. A pring i initially at it free length in the neutral poition, and the actuator mut move the pring to the target poition. In the firt trategy, the actuator approache the target poition from a lower poition. In the econd trategy, the actuator overhoot the target in order to approach it from a higher poition. Now, intead of doing work againt the pring, the actuator i etting a moving boundary condition for the pring a it move backward. Thi will reult in much more precie poition control than the firt trategy. In context of the morphing die, the actuator will firt compre the die to the mallet diameter and then move backward, allowing the die 35

50 to elatically expand with it. Thi trategy will be adopted for each of the three actuator deign dicued later in thi chapter. Figure 23: Equivalent mechanical ytem for actuator-die combination The actuator will be upplemented by a et of pring which will preload the die Nitinol morphing feature to it plateau tre. Thi will greatly reduce the force required by the actuator becaue the plateau tre i often very high >300 MPa. Now the actuator can operate with low force in the deired uperelatic region uing the trategy jut dicued. The uperelatic repone from Fig. 15 i hown again in Fig. 24 with hade to indicate the preload and operating region. Thi plot i for a tenile loading in the axial direction, and the uperelatic region i nearly a flat line at contant tre. Other type of loading may not have thi intantaneou tranition and well-defined plateau tre. Figure 25 how tre-train curve for axial compreion of a bar [10] and compreion of a pipe between two parallel plate [11]. For thee example, the actuator would till have to do ome ignificant work becaue the uperelatic region i not flat. There have been no tudie on radial compreion of a Nitinol tube, o the hape 36

51 of the tre-train curve for the current application i unknown. However, it i expected to reemble the plot in Fig. 25. The preload can be et to the point where the lope of the curve begin to decreae, or up to a certain value of train. If too much train i produced by the preload, there will be inufficient elatic train remaining for the full troke. Depending on the deign configuration, either a compreion or tenion pring can preload the die. In the following ection, three different actuator deign are developed, and their ability to meet the criteria i analyzed. Figure 24: raphical explanation of actuation trategy howing preload and operating region 37

52 38 Figure 25: Different Nitinol uperelatic repone for different type of loading For the actuator analyi, equivalent mechanical model will be ued to do ome calculation. The equivalent tiffne of a Nitinol tube i derived here in preparation for that analyi. It i aumed that the internal preure, P i, from Eqn. 8 i equal to zero, and the equation reduce to: r r r P r r E v r r r P r E v u i o o i o i o o o Eqn. 10 can be olved for P o /u, reulting in Eqn. 11 which repreent the equivalent tiffne for radial compreion a a reult of an applied preure. To find the tiffne in term of the applied force, Eqn. 11 can be multiplied by the urface area over which the preure act. Thi will be ueful in the ubequent calculation for etimating required pring force r r r r v r r r r r r r E u P o o i o i o i o o 11

53 Method 1: Tangential Actuation The tangential actuation option i explained by Fig. 26 in which a collar urrounding the die i queezed by a linear actuator to apply compreion. A tenion pring attached to the collar applie the deired preload. The equivalent mechanical model conit of three pring in parallel: the die equivalent tiffne, the bending tiffne of the collar and the tenion pring. The die and collar will be in compreion, while the preload pring will be in tenion. The primary advantage of thi method i that it require jut application of force at jut one location. Figure 26: Schematic of tangential actuation concept and correponding mechanical model To invetigate the tree and diplacement in the collar due to the applied force, a finite element analyi wa performed on a realitic collar model uing Autodek Natran-in-CAD. The model i diplayed in Fig. 27a. The collar gap angle of 13 wa determined baed on the pecified troke. The final diameter of the collar hould be 0.02 inche le than the initial diameter of the collar, under the contraint that arc length remain contant. The following equation are olved for the gap angle, θ. 39

54 r2 12 i i r f i method with a collar doe not meet the actuator deign criteria. 40 i f 14 In the imulation, a force wa applied to each arm of the collar a hown in Fig. 27a. A trial and error method wa ued to determine the force required to cloe the gap. The reulting diplacement i indicated in Fig. 27b, with the dahed red line repreenting the un-deformed object. It wa oberved that the neceary radial diplacement wa achieved near the gap but that there wa no radial diplacement near the bottom of the collar. Thi i evident in the figure by the model edge aligning with the dahed red line toward the bottom. Thee reult ugget that the collet deign option will not reult it atifactory uniform compreion. The tree in the collar were alo analyzed and can be een in the contour plot of Fig. 27c. The maximum tre occur near the bottom and wa 40,000 pi for a wall thickne of inche, which i greater than the yield tre for many common metal. Therefore, a econd concluion wa reached that the wall thickne needed to keep the collar below it yield point would be too thin to appreciably compre the die. To ubtantiate the claim that the collar deign i unatifactory, the imulation wa performed again but now with a die inerted into the collar. The imulation diplacement reult are hown in Fig. 28 for two different loading condition. The diplacement profile are lightly different than that of Fig. 27b, but till have ignificant non-uniformity. The die become flattened near the top and ha minimal diplacement at the bottom. Thee two imulation reveal that the tangential actuation

55 Figure 27: CAD model howing load applied in FEA imulation and collar angle a; diplacement reult hown by dahed red line b; tre contour in pi c Figure 28: Simulation of tangential collar with die: force applied cloe to die a; force ditributed over a larger area b 41

56 Method 2: Radial Actuation The radial actuation method i explained by Fig. 29 in which four wedge move radially to compre the die. The wedge cover a much of the die urface area a poible, but a mall gap between them i till needed in order for them to move cloer together. In thi cae, the required gap angle of 13 degree can be plit by 4 to give an angle of 3.25 degree for each gap. The reduced gap width i one advantage that thi method ha over the tangential method. The die will be le likely to flow into the maller gap when it i compreed. The diadvantage of thi method i that it ha wore mechanical advantage and reolution than the tangential method. Figure 29: Concept deign for radial actuation method A finite element imulation wa performed to tudy the diplacement in the die, the etup of which i hown in Fig. 30a. A force i applied to each of the four wedge urrounding the die. In thi cae the die i cylindrical, but other die profile uch a the one in Fig. 30b were alo imulated. Matlab image proceing toolbox wa ued to find the diplacement profile of the inner urface of the die from the FEA reult. Figure 31 42

57 contain four of thee profile in which the diplacement are caled up by a factor of 10. The imilarity between them indicate that the reult i independent of the outer profile of the die. Additionally, diamond-haped diplacement profile indicate that none of the die profile reult in uniform compreion, and the propoed four-wedge radial actuation doe not atify the actuator requirement. Figure 30: 3D model and load ued in imulation a; alternate die profile b Figure 31: Die diplacement from imulation caled by a factor of 10 for alternate die profile 43

58 Method 3: Collet-baed Actuation The third actuation concept i to ue a collet to grip the die and actuate a tapered leeve moving over the collet. The collet grip the die in a imilar manner to the radial actuator with four jaw eparated by four gap, een in Fig. 32. ood reolution and mechanical advantage are achieved, but there are alo ome uncertaintie that exit for thi method. In a machine hop, a collet-type chuck i meant to grip a work piece but not deform it. Here, the goal i deformation, and the die diplacement profile i not obviou. A potential deign alternative i to eliminate the collet and move a tapered leeve directly over the die. Thi will reult in uniform radial compreion with no gap, but will create high urface contact tree. For either alternative, a lubrication ytem will be neceary to allow the leeve to move moothly over either the collet or the die. Figure 32: 3D model of collet deign option 44

59 A finite element imulation wa done to determine the bending tree in the collet and chooe a collet length that would keep thee tree below the yield point. The collet i fixed at the bae a hown in Fig. 33, and a radial force i applied to the oppoite end. The imulation how that the maximum tree occur near the bae of the collet, which i expected. However, in reality, there will be a leeve moving over the end of the collet which may caue high bending and contact tree in thi region. In ummary, thi deign ha the bet reolution, bet mechanical advantage and the bet poibility for uniform radial compreion. However, it may not be deirable to have a lubrication ytem with oil or greae in the manufacturing environment. Figure 33: FEM imulation reult - tree in collet A Radial Compreion Mechanim Invetigation of the three actuation method ha etablihed that none of the option meet all the requirement. One of the primary concern in each of the method dicued i the gap between the jaw or wedge gripping the die. A literature review 45

60 wa conducted to earch for radial compreion mechanim that overcame thi iue and other previouly dicued. The latet technology for radial compreion mechanim i patented by off [12]. The baic contruction i hown in Fig. 34 and conit of multiple wedge that form an approximately cylindrical cavity. The wedge have two joint each that allow the gap between them to be kept at zero throughout the entire range of motion. Thi mechanim i ued in low force application in which the approximately cylindrical cavity i ufficient. In thi high force application, it may not work well, but can be ued a a model for building a high force device. Figure 34: Radial compreion mechanim patented by off [11] Detailed Actuator Deign and Analyi Baed on the reearch and literature review, it i demontrated that a perfectly uniform radial compreion mechanim with a non-zero troke, no liding contact, and 46

61 ufficient force and reolution i only poible with an infinite number of wedge. Therefore, the deign trategy i to approximate thi uing a high number of wedge that reult in acceptable uniformity and gap width. The propoed mechanim, een in Fig. 35, ue 10 wedge that have the minimum allowable gap width between them. The wedge are attached to rod which are preloaded with compreion pring. An equivalent mechanical model for the ytem i hown in Fig. 36. During application of the preload, the compreion pring are in parallel with each other and in erie with the die. A preload i et by enforcing a diplacement x, a hown in the figure. Afterward, x i fixed, and an actuator applie the force F to caue the radial diplacement, u. The equivalent die tiffne, k D, i given by Eqn. 11. Figure 35: Propoed actuator with minimum allowable gap width and 10 wedge 47

62 Figure 36: Mechanical model of 10-jaw mechanim The mechanical model can be ued to determine the required force in each pring. The aumed die geometry along with propertie of Nitinol and the aumed Nitinol plateau tre are lited in Tab. 4. The plateau tre depend on the particular Nitinol product but i typically greater than 40 ki. The lat parameter needed for the calculation i the applied external preure. In Chapter 3, it wa hown that an externally applied radial preure P o reult in a much higher tangential preure Fig. 10. Therefore, in order to preload the die to the plateau tre, the required applied preure will be le than the plateau tre. Equation 2-8 were ued to find that thi preure i about 10 ki. Next, the model wa ued to find that the force required in each pring wa 255 pound. Table 5 lit ome pring meeting thi pecification. Another apect of the deign i the method with which the rod are radially actuated. Uing a elf-centering mechanim, thi can be achieved uing a ingle actuator. There are everal uch mechanim available, and one can be choen baed on it compatibility with the deign layout, it reolution and it mechanical advantage. 48

63 Table 4: Parameter value ued to determine required pring force Elatic modulu of Length of die to Property N r autenite [13] o in r i in Plateau tre be compreed Value Pa 10,877 ki.65/2.545/2 320 MPa 46 ki in Table 5: Spring with a maximum load of at leat 255 pound Part Number LHL 750D 02 LHP 170K 02S CV Rate lb/in Required Initial Deflection in Stroke Length in Outide Diameter in Max Load lb Vendor Lee Spring Lee Spring Raymond Another important deign conideration i the wall thickne of the die. A thin die i deirable to minimize actuation force, but buckling may occur if the wall i too thin. The outer diameter in the previou calculation ha been aumed to be 0.65 inche, but thi may change depending upon thee criteria. The force required by the actuator will be difficult to ae without firt meauring the tre train repone for radial loading of Nitinol. However, the required preload force can be etimated a a function of the die outer diameter, becaue the preload will remain in the linear elatic region. The aumed plateau tre for Nitinol i again 67 ki. Figure 37 plot the required force to achieve thi pre-tre a a function of the die outer diameter. The preload will alo caue a diplacement which need to be accounting for in the manufacturing of the die. If the nominal diameter of the die i inche, the die hould be machined to a lightly larger diameter o that it ettle to upon application of the preload. 49

64 Figure 37: Required radially compreive force a a function of die outer diameter Summary of Actuator Deign Analyi of the actuator deign revealed that the mot important criteria were uniform radial compreion and minimizing gap width to prevent the die from filling into the gap during compreion. Previou radial compreion mechanim have been hown to have zero gap width but are only ueful in low force application. The three baic actuation option, Fig. 38, each had ome limitation but were helpful in the path to a olution. A firt tage deign of a mechanim for radial compreion uing 10 wedge wa preented. If a prototype of thi device prove to be ineffective, there are two option available. The number of wedge can be further increaed, or a hydraulic apparatu can be invetigated. A oppoed to a mechanical device, hydraulic preure could apply more uniform preure. There i one previou known deign of a hydraulic method for radial compreion [14]. Alternatively, if a lubrication ytem i acceptable 50

65 in the manufacturing environment, a tapered leeve moving over the die decribed the Collet-baed actuation ection meet the actuation criteria. In addition to the phyical deign, two actuation trategie were dicued. The econd trategy, which achieve much higher preciion, i the preferred method for actuation in any deign configuration. Figure 38: Summary of Actuator Deign Option 51

66 Chapter 5: Concluion The firt phae of a project to determine the feaibility of a morphing extruion die wa preented in two part: die deign and actuator deign. Multiple option for each of thee were conidered. The option mot likely to ucceed were identified, and their important deign conideration were dicued. Nitinol ability a a metal to achieve 4-5% recoverable train make it the bet candidate for a die material while a mechanim with large number of wedge i the recommended actuator deign. In the cenario that the die material and actuator fail to meet expectation, alternative and next tep were propoed. Contribution from thi Thei In particular, the following contribution have been made toward the overall project goal: Formulation of propoed olution and integration with current proce Determination of 3.67% elatic train requirement and tre ditribution in the die and correponding identification of potential die material Identification and dicuion of key deign conideration for uperelatic alloy including: o Required autenite finih temperature of at leat C, if not higher, baed on die urface temperature o Development of a training chedule for a Nitinol die 52

67 o Deign of a morphing feature baed on availability of Nitinol tube, limited to diameter of 0.75 inche or le for tock ize Identification and dicuion of key actuator deign conideration including: o Method for achieving uniform radial compreion o Force and preure calculation required to compre a die a a function of die outer diameter. Preure are in the range of 5,000-15,000 pi, and force are in the range of pound. Although all the analyi ha aumed a land diameter of inche, the concept will eventually be extended to other izing die. Table 6 lit ome common die ize and the theoretical maximum diametral troke that can be achieved uing Nitinol. Baed on the work done here, it i concluded that the implementation of a morphing izing die into the production line i a realitic goal. Table 6: Potential troke for different land diameter uing Nitinol, auming 4% maximum recoverable train Land Diameter Stroke, inche

68 Reference 1. Parflex Diviion. n.d.. Retrieved April 3, 2015, from 237ad1ca/?vgnextoid=faededff4675e210VgnVCM dacRCRD&vgnextf mt=en 2. roover, M Shaping Procee for Platic. In Fundamental of modern manufacturing : Material, procee, and ytem 5th ed., pp John Wiley & Son. 3. Cae, J., Chilver, L., & Ro, C.T.F Thick Circular Cylinder, Dic and Sphere. In Strength of Material and Structure 4th ed., pp Elevier. 4. Online Material Information Reource - MatWeb. n.d.. Retrieved November 5, 2015, from 5. Smith, R Model Development for Shape Memory Alloy. In Smart Material Sytem: Model Development Vol. 32, pp Siam. 6. Nemat-Naer, S., & uo, W Superelatic and cyclic repone of NiTi SMA at variou train rate and temperature. Mechanic of material,385, Tanaka, Y., Himuro, Y., Kainuma, R., Sutou, Y., Omori, T., & Ihida, K Ferrou polycrytalline hape-memory alloy howing huge uperelaticity. Science, , PDMS. n.d.. Retrieved April 5, 2015, from 9. Li, T., Huang, Z., Suo, Z., Lacour, S. P., & Wagner, S Stretchability of thin metal film on elatomer ubtrate. Applied Phyic Letter, 8516,

69 10. Chen, W. W., Wu, Q., Kang, J. H., & Winfree, N. A Compreive uperelatic behavior of a NiTi hape memory alloy at train rate of International Journal of Solid and Structure, 3850, Machado,., Louche, H., Alono, T., & Favier, D Superelatic cellular NiTi tube-baed material: Fabrication, experiment and modeling. Material & Deign, 65, off, E., Warriner, J. J., & Knight, J U.S. Patent No. 7,886,661. Wahington, DC: U.S. Patent and Trademark Office. 13. Phyical Propertie of Nitinol. n.d.. Retrieved April 3, 2015, from Solar, R. J U.S. Patent No. 5,810,838. Wahington, DC: U.S. Patent and Trademark Office. 15. Superelatic Nitinol Alloy. n.d.. Retrieved April 8, 2015, from Superelatic.pdf 55

70 Appendix A: Derivation of Equation 1 According to the final value theorem in the Laplace domain, the teady tate error can be written a: e lim E 15 0 where E i the error. The error i defined a the difference between the reference input and the output, or R Y. The E in Fig. 7 i equal to Y R, which i not the actual error unle = 1. To find the error, the block diagram mut be manipulated to have unity feedback. The firt tep i to add feedback element of +1 and -1 to the block diagram and then combine and -1: Figure 39: Block diagram with a +1 and -1 added to the feedback ignal 56

71 Figure 40: Block diagram of Fig. 34 with and -1 combined into one block Next, the diturbance i et to zero to find the error a a function of the input. Figure 41: Block diagram with D equal to zero Now, the inner loop i conolidated into the equivalent cloed loop tranfer function uing block diagram reduction rule, hown in Fig

72 58 Figure 42: Equivalent block diagram with cloed loop tranfer function Now, the block diagram ha unity feedback o the error can be derived uing the relationhip in Eqn ] [ 1 E Y d c d c 16 E Y R 17 Next, ubtitute Eqn. 16 into Eqn. 17 and olve for E. Thi i the error due to R. A imilar procedure can be done to find the error due to D by etting R equal to zero in the block diagram of Fig ] [ 1 E E R d c d c 18 1] [ 1 1 E R d c d c 19 1] [ 1 1 E R d c d c E R d c d c d c 21

73 R E d c d c d c R R E d c d c d c d c d c 23

74 Appendix B: Propertie of Nitinol Table 7: Propertie of Nitinol Property Value Elatic modulu, autenite 75 Pa Elatic modulu, martenite 40 Pa Thermal conductivity 18 W/m- C Thermal expanion 6.6*10-6 / C Martenite; 11*10-6 / C Autenite Loading plateau % 380 MPa Autenite finih temperature, A f -25 to 30 C [13], [15] 60

75 Appendix C: Actuator Detail Drawing Figure 43: Actuation mechanim aembly drawing Table 8: Bill of material Number Part Quantity 1 houing 1 2 compreion pring 10 3 rod 10 4 wedge 10 61