THE FLORIDA STATE UNIVERSITY COLLEGE OF ENGINEERING DESIGN OF A TUNABLE STIFFNESS LEG FOR DYNAMIC RUNNING USING SHAPE MEMORY POLYMER By DUNCAN HALDANE A Thesis submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for graduation with Honors in the Major Degree Awarded: Spring Semester, 2011
The members of the committee approve the thesis of Duncan Haldane defended on April 19th, 2011. Dr. Jonathan Clark Professor Directing Thesis Dr. William Oates Committee Member Dr. Richard Liang Committee Member ii
TABLE OF CONTENTS List of Figures....................................... iv Abstract........................................... 1 Introduction 1 1.1 Background.................................... 1 1.1.1 Variable Stiffness Legs.......................... 2 1.1.2 Shape Memory Polymers........................ 4 1.1.3 Shape Memory Polymer Composite................... 4 2 Material Development and Testing 6 2.1 Shape Memory Polymer Synthesis....................... 6 2.1.1 Molecular Mechanism.......................... 8 2.1.2 Resin Composition............................ 8 2.1.3 Composite Design and Fabrication................... 10 2.1.4 Heating Elements............................. 11 2.2 Composite Fabrication Methods......................... 13 2.3 Material Testing................................. 14 2.3.1 D3039 Tensile Testing.......................... 14 2.3.2 D2344 Short Beam Shear Testing.................... 18 3 Shape Memory Polymer Composite Characterization 21 3.1 Temperature Control Circuit.......................... 21 3.1.1 Power Supply and Consumption.................... 21 3.2 Shape Memory Polymer Tensile Characterization............... 23 4 Variable Stiffness Leg Prototyping and Evaluation 25 4.1 Shape Memory Polymer Section Placement and Prototype Development.. 25 4.2 Leg Prototype Stiffness Characterization.................... 27 5 Conclusions 30 5.1 Future Work................................... 30 Bibliography........................................ 31 vi iii
LIST OF FIGURES 1.1 (a) A variable stiffness leg using a flexible slider [11] (b) A variable stiffness leg using a rigid slider[10]............................. 3 1.2 The Pseudo-Rigid Body model representation of a semi-circle leg...... 3 1.3 Schematic of shape memory properties during a thermodynamic cycle [13]. 4 1.4 Microbuckling in a highly strained shape memory polymer composite [8]... 5 2.1 A representation of the shape memory polymer used for this project..... 7 2.2 An illustration of the molecular mechanism for shape memory effect in a linear block co-polymer. The hard Polystyrene segments are represented by straight black lines. The Vinyl Neodecanoate switching sections are represented by the amorphous lines. From [14]............................ 8 2.3 The effect of Vinyl Neodecanoate on the transition temperature of a Styrene shape memory polymer. [19]........................... 9 2.4 Comparison of Specific Strength and Specific Modulus between several materials[9] 10 2.5 Comparison of Fracture Toughness and Young s Modulus between several materials[9].................................... 11 2.6 Experimental heating element patterns..................... 12 2.7 (Above) Surface view and a (below) Thermal profile of an A type heating element....................................... 13 2.8 Ultimate Tensile Strengths of Composites Fabricated with Resin Candidates 15 2.9 Strain at Failure for Composites Fabricated with Resin Candidates..... 16 2.10 Elastic Moduli of Composites Fabricated with Resin Candidates....... 17 2.11 Cross-sections of Short Beam Shear Specimens (1) Epoxy-SMP (2) SMP- Epoxy (3) Epoxy-SMP-Epoxy (4) SMP (5) Epoxy (6) Vinyl Ester...... 18 iv
2.12 Short Beam Shear Testing Jig [7]........................ 19 2.13 Relative Shear Strengths of Composites Fabricated with Resin Canidates and Bonding Methods................................. 20 3.1 The Baby Orangutan B-328 from Pololu.................... 22 3.2 Power Consumption During Stiffness Actuation................ 22 3.3 The Specific Modulus of Shape Memory Polymer Composite, normalized with the tensile modulus at room temperature.................... 24 4.1 Delamination failure in a prototype leg..................... 26 4.2 Shape memory polymer separation in a prototype leg............. 27 4.3 Stiffness values attained using the variable stiffness leg with the temperature control circuit................................... 28 v
ABSTRACT Recent research in dynamic legged locomotion has indicated that the running dynamics of the robot are largely determined by the passive compliance of the running limbs. Many walking robot have variable stiffness limbs, the stiffness of which is tuned using mechanical actuators. Due to dynamic constraints, running robots cannot use the bulky variable stiffness mechanisms that can be implemented of walking robots. Standard legs for dynamic running robots have a single compliance which is determined when they are fabricated. This limits the adaptability of the robot, and creates a small range of operating conditions in which the robot can operates effectively. The need for variable stiffness legs has led to the development of a mechanically variable stiffness leg capable of a 200% change in stiffness. We developed a materials based variable stiffness leg and control system. A shape memory polymer resin was synthesized, and methods for shape memory polymer composite fabrication were developed. The composite materials were characterized, and a temperature control circuit was designed and fabricated. We present a new design for a variable stiffness leg which uses a shape memory polymer segment to acheive a 350% change in stiffness without any moving parts. vi
CHAPTER 1 INTRODUCTION Running animals use their legs to run effectively over a diverse range of terrains. These animal running dynamics can be modeled using the Spring Loaded Inverted Pendulum or SLIP Model[4]. Blickan and Full have shown that the SLIP model captures the whole-body dynamics of a very diverse range of animals [2]. Additionally, this model has been used in the development of a number of dynamic running robots. One of the most successful of these is RHex, a biologically inspired hexapedal running robot that has been shown to run in a manner characterized by the SLIP model [1]. The RHex robot runs on six compliant C shaped legs using an alternating tripod gait. The standard legs for RHex are rugged, but their passive stiffness is fixed when the legs are fabricated. Recent studies in dynamic locomotion have found that modifying the leg stiffness is an effective way to tune running performance[12][2]. Based on these findings, several mechanically variable stiffness legs have been fabricated for the RHex robot [9], with the goal of experimentally characterizing the effect of a change in leg stiffness on the robot s locomotion dynamics. Early attempts used a rigid slider to alter the stiffness and displacement trajectory of the compliant leg [10]. Later work focused on a flexible, reinforcing slider that only altered the stiffness of the leg [11]. The goal of this research is to create an applied active-material based alternative to the mechanically variable stiffness legs. This design will allow for a greater degree of control over the stiffness of the legs and allow for stiffness adjustment during any point of the robot s operation. To integrate variable stiffness properties at the material level, a smart material called shape memory polymer forms part of the leg at the center of flexure. This material has an elastic modulus that varies greatly with temperature[17]. By simply heating the material in the leg, stiffness properties can be varied. The shape memory properties of the material allow for repeated stiffness adjustments without permanent deformation of the leg. While smart material science and dynamic legged locomotion are both rapidly expanding fields, the application of smart materials to modern dynamic robotics is largely unexplored. 1.1 Background Several areas of study are important to the creation of a smart material based variable stiffness leg. First, it is important to consider previous approaches to the design of variable stiffness legs. By assessing the successes and shortcomings of these designs, significant 1
leverage on the problem can be gained. Secondly, a fundamental understanding of shape memory polymers is critical. There are many classes of shape memory polymers, each with specific characteristics that may make them unsuitable for high deflection composites. The method for creating a shape memory composite also requires in depth experimentation. As well as having significant mechanical strength, this composite must be able to be remotely activated by a power source. The current state of the art in both of these areas is briefly summarized in the following sections. 1.1.1 Variable Stiffness Legs Legs with mechanically variable stiffness have been created for RHex. These legs utilize a small worm geared motor to drive a rigid or flexible slider along the leg [11][10]. Of these approaches, the flexible slider was found to be the more desirable [9]. The most successful mechanically variable stiffness leg was capable of achieving radial stiffnesses ranging from 1,100 N/m to 2,300 N/m [9]. A disadvantage of the mechanical approach was that it resulted in a bulky mechanism, weighing in at 85g. The multitude of parts required resulted in mechanical complexity and fragility. The main advantage of a mechanical adaptation is that the system maintains, if not improves the mechanical strength of the leg. However, accurate control of leg stiffness cannot be achieved while the robot is operating. The worm motor does not have an encoder and adding the requisite circuitry would further increase the complexity and size of the leg. A materials based approach has the potential to become a much more graceful solution than a bulky mechanism. The functionality of an 85g mechanism could be attained simply by using the leg itself as an active structure without increased complexity or weight. By setting the leg stiffness solely by temperature, a simple control circuit could be integrated on the leg. This system can control stiffness more accurately while the robot is operating, but it does have its disadvantages. The mechanical strength of the leg may be decreased while the resin is in the glass transition zone[17]. Additionally, if the leg needs to be constantly heated, this leg design will consume more power than its mechanical counterpart. A reduced order model known as the Pseudo-Rigid Body model has been shown to accurately match the large deformation behavior of RHex s C legs [10][11][9]. The Pseudo- Rigid Body model uses a combination of rigid beams and compliant joints to model large deformations of 2D beams. A representation of a C leg can be seen in Figure 1.2, the structure is modeled as two rigid beams of fixed length attached with a torsional spring at the characteristic pivot point. Most of the bending that occurs during deformation of the leg, happens at the characteristic pivot point. By reducing the stiffness of the composite at this point, the overall stiffness of the leg can be greatly reduced. This characteristic of the C legs suggests that the most effective use of a shape memory polymer segment would be at the characteristic pivot. 2
(a) (b) Figure 1.1: (a) A variable stiffness leg using a flexible slider [11] (b) A variable stiffness leg using a rigid slider[10] Figure 1.2: The Pseudo-Rigid Body model representation of a semi-circle leg 3
1.1.2 Shape Memory Polymers Shape memory polymers are a class of polymeric smart materials capable of recovering from a highly deformed state to their original shape when triggered by an external stimuli [14]. Upon transition to the glass temperature regime, shape memory polymers undergo a variation in elastic modulus of several orders of magnitude. As well has having a significant change in elastic modulus, shape memory polymers undergo a slight actuation pressure which allows shape recovery properties. Figure 1.3 details the deformation and recovery process of a shape memory polymer beam. The polymer is rigid below the glass transition temperature. When heated above this temperature the shape memory polymer undergoes a drop in elastic modulus in the range of several orders of magnitude. A distinguishing feature of shape memory polymers is that they maintain a level of toughness in this temperature zone uncommon to most polymers. When the shape memory polymer is deformed and cooled, it retains a deformed shape while below the glass transition temperature. Upon reheating, the shape memory polymer generates a recovery pressure which returns it to its original shape. By using shape memory polymers to form part of the running leg, the stiffness can be modified by varying the temperature of the leg. Shape memory polymers were selected for use in this research because of their ability to maintain shape after several heating cycles. They also have improved toughness over other polymers when above its glass transition temperature. Additionally, future research may investigate stiffness control schemes using the shape fixity properties of shape memory polymers in a composite spring. Figure 1.3: Schematic of shape memory properties during a thermodynamic cycle [13] 1.1.3 Shape Memory Polymer Composite By itself, shape memory polymer is not strong enough to use as a dynamic running leg. Research preformed by Kevin Galloway has shown that a composite, either fiberglass or carbon fiber, is a feasible option for creating a C shaped running leg. Standalone resins were shown to have mechanical properties inferior to composites by an order of magnitude [9]. To increase strength, the shape memory polymer resin is used with a reinforcing fiber to create a composite structure. A shape memory polymer composite should improve the mechanical properties of the shape memory polymer while maintaining the functionality of the shape memory polymer material. Creating a shape memory polymer composite, however, has unique difficulties associated with it. Delamination of the composite due to the high strains associated with shape transformation is common [13]. As shown in Figure 1.4, micro-buckling can occur at the surface of the composite when strained in the resin s glass transition zone [8]. Carbon fiber is used as the matrix in the shape memory polymer 4
composite because the resin bonds more readily with carbon fiber than fiberglass. This may be because of the sizing treatment carbon fiber undergoes to facilitate resin bonding. The successful creation of a shape memory polymer composite is essential for creating the running leg. In our design, only a small section of the variable stiffness leg uses shape memory polymer resin as the polymeric matrix, this reduces the power costs associated with heating the shape memory polymer. To minimize the area that needs to be heated, the shape memory polymer resin will be used at the effective center of flexure of the leg, shown in Figure 1.2. Figure 1.4: Microbuckling in a highly strained shape memory polymer composite [8] The remainder of this thesis will be organized as follows: Chapter Two describes the material development process for the composite leg, including resin formulation and mechanical testing. Chapter Three discusses the design of the temperature control circuit and the effect of temperature on the elastic modulus of the shape memory polymer composite. Chapter Four describes the prototype iteration process as well as the stiffness characterization of the variable stiffness leg. The contributions of this research and areas for future development are given in the conclusion, chapter Five. 5
CHAPTER 2 MATERIAL DEVELOPMENT AND TESTING 2.1 Shape Memory Polymer Synthesis A styrene based shape memory polymer resin was initially chosen to create the shape memory polymer composite because several research efforts [13][15][16][5] have already been made to functionalize this resin for remote electroactivation and composite fabrication. Unfortunately the resin utilized in these research projects has been discontinued by the manufacturer, CRG, and no other commercial alternatives exist for a thermoset shape memory polymer resin. Other shape memory polymer products, such as Composite Technology Development Inc. s TEMBO SMP Resin, or Mitsubishi Heavy Industry s MP-5510, are on the market, but only in unfeasible quantities or with stipulations precluding usage in research. In the face of these difficulties, we fabricated a custom polystyrene resin in-house. A custom synthesized resin offers the maximum capability for adaptability and tailoring for the specific purpose of a variable stiffness leg. The resin matrix used to create the shape memory composite was a styrene based linear block shape memory copolymer. A copolymer is a polymer derived from multiple distinct monomer subunits. A particular subset of copolymers, linear block copolymers, consist of a single main chain of two or more homopolymers that are linked with covalent bonds [14]. The shape memory polymer that was synthesized for this project consisted of two monomer segments, a stiff polystyrene block and a soft Vinyl Neodecanoate switching block. A physical crosslinking agent, Divinylbenzene was used to create physical links between the polystyrene chains. A representation of the shape memory polymer matrix is shown in Figure 2.1. 6
Figure 2.1: A representation of the shape memory polymer used for this project 7
2.1.1 Molecular Mechanism The mechanism of shape memory recovery is determined by the physical structure of the shape memory polymer. The molecular mechanism of a linear block co-polymer is illustrated in Figure 2.2. An elastomer will act as a shape memory polymer if it can be fixed in a deformed state in a given temperature range. This fixing is achieved by utilizing the temperature dependent flexibility of the polymer chains. Above the transition temperature Tg the switching chains, in this case Vinyl Neodecanoate, are flexible. Below the transition temperature, their flexibility is limited. When the polymer is deformed and then cooled, these polymer chains partially recrystallize which allows the shape memory polymer to have shape fixity. The permanent shape and shape memory properties of the polymer are determined by the covalently bonded hard block segments, in this case, polystyrene [14]. When reheated above Tg the polymer recovers to this permanent shape. The crosslinking agent, Divinylbenzene, is used to create physical links between the polystyrene chains. The cross-linking agent largely defines the tensile modulus of the polymer as well as shape memory performance in a styrene based shape memory polymer [6]. Figure 2.2: An illustration of the molecular mechanism for shape memory effect in a linear block co-polymer. The hard Polystyrene segments are represented by straight black lines. The Vinyl Neodecanoate switching sections are represented by the amorphous lines. From [14] 2.1.2 Resin Composition The composition of the resin described below was determined based on the results of several papers characterizing the effect of varying the monomer components in a styrene 8
shape memory polymer [6][18][19]. The optimum amount of the crosslinking agent in a styrene shape memory polymer was found to be 1% [6]. The amount of the switching polymer, Vinyl Neodecanoate largely controls the transition temperature of the shape memory polymer as shown in Figure 2.3 [19]. Figure 2.3: The effect of Vinyl Neodecanoate on the transition temperature of a Styrene shape memory polymer. [19] The target transition temperature for this shape memory polymer was designed to be 80 C to allow a large transition range for the polymer so 7% Vinyl Neodecanoate was used. In order to initiate the polymerization reaction, Benzoyl Peroxide was used as an activator as described in [18]. The Benzoyl Peroxide attacks a styrene monomer and initiates a free radical based polymerization reaction. The amount of initiator in the resin was chosen to be 2%. The final composition of the resin is shown in Table 2.1 Table 2.1: Shape Memory Polymer Resin Composition Component Function Amount (%mass) Styrene Base Material 90% Vinyl Neodecanoate Switching Polymer 7% Benzoyl Peroxide Initiator 2% Divinylbenzene Crosslinking Agent 1% The resin was created using the prepolymer process by incorporating the polymer components, Styrene, Vinyl Neodecanoate and Divinylbenzene in a beaker on a stirring plate. The Benzoyl Peroxide initiator is then incorporated and the resin is left to sit for at least fifteen minutes. After this step, the resin is ready for composite processing. 9
2.1.3 Composite Design and Fabrication By incorporating shape memory polymer resin in a composite, the yield strength, fracture toughness and elastic modulus of the material are increased while decreasing the loss coefficient of the flexural structure[9]. Several factors contribute to the properties of the final composite. The largest modifier of these properties is the choice of reinforcing fiber. There many types of reinforcing fibers; for example, carbon fiber, fiberglass, or aramid fibers (Kevlar). Of these, carbon fiber and fiberglass are the most common and the least expensive. These fibers also have the most choices of weight and weave. Figure 2.4 compares the relative specific modulus and specific strength of carbon fiber and fiberglass composites. Carbon fiber composites have a higher specific strength as well as a higher specific modulus than fiberglass composites. Figure 2.4: Comparison of Specific Strength and Specific Modulus between several materials[9] Fracture toughness describes a material s resistance to crack propagation. Large internal stresses in a compliant composite flexure create failure mainly by fiber delamination caused by an internal crack. This property of compliant composite mechanisms is the limiting factor for the fatigue life and maximum allowed deflection of the composite part. Figure 2.5 compares the relative fracture toughness of resin alone, and fiberglass and carbon fiber composites. The fracture toughness of a composite is largely dependent on the fracture toughness of the reinforcing matrix as well as the interfacial bonding strength between the matrix and the reinforcing fibers. Therefore one reinforcing fiber may be more suited to the shape memory polymer resin than another. As a shape memory polymer approaches the glass transition zone, the loss modulus of the material increases. Carbon fibers have much lower damping in a composite than glass fibers. So, to compensate for the increased 10
damping from the shape memory polymer, carbon fiber is selected the best option for a reinforcing fiber. Figure 2.5: Comparison of Fracture Toughness and Young s Modulus between several materials[9] To prevent the variable stiffness leg from collapsing in the case that the shape memory polymer section reaches its glass transition temperature, a secondary reinforcing matrix will be used in the composite variable stiffness leg. The bonding properties between the two matrices, the shape memory polymer and the secondary structural matrix must be evaluated. There are two main options for the secondary resin matrix: vinyl ester, a polymer resin, or an epoxy. Epoxy bonds well to carbon fiber and fiberglass and is generally more suited to flexural composites than vinyl ester resin as shown in Sections 2.3.1 and 2.3.2. Moreover, epoxy does not experience weakening with temperature like vinyl ester resin does [3]. However, a polymer resin such as vinyl ester may be capable of bonding more completely with the shape memory polymer resin due to similarity in bonding chemistry. Mechanical tests used to determine a suitable candidate can be found in Section 2.3. 2.1.4 Heating Elements Several activation modes can be used to articulate the stiffness of this shape memory polymer composite,the most promising of which fall into the category of resistive heating. There are several challenges associated with incorporating heating elements into the composite layup. When the shape memory polymer is highly deformed, surface strains of up to 2-5% cause local deformations and mirco-buckling [8] as shown in Figure 1.4. Any heating element needs to be able to accommodate these surface strains. Additionally, the low thermal conductivity of the shape memory polymer laminate ( 2.5 W/M-K [8]) 11
necessitates direct application of the heating elements to the area of the composite being activated. Mallick et al. enumerates and examines several methods of electroactivation including heating through the graphite fibers of the composite as well as externally bonded heating elements which are laminated on a polyimide film [8]. Graphite fiber heating was ruled out due to uneven heating, low resistance and the difficulty of creating a corrosion resistant, electrical connection to the fibers. The external polyimide heating elements delaminated from the composite due to an elastic modulus mismatch. Their final choice was a Nichrome heating element that had been stitched into a light fiberglass scrim which was sold by Watson Polymer Technologies. This material is no longer available but a similar method of activation was used in this research. To enable remote electroactivation, 0.0031 diameter Nichrome wire heating elements, resistivity 2.47Ω/cm, were embedded in the composite layup. The target resistance for the heating section of the leg is 15Ω to enable low power actuation at 7.2V. Conductive fillers were investigated as a means of remote activation, as described by [15][16], but free radical absorption during the polymerization reaction compromised the structural integrity of the custom resin used in this research. It was found that the majority of the heating element wire should run parallel to the axis about which the leg bends to preclude delamination resulting from the heating element. Mallick et al. found that the inclusion of a heating element of this type had no effect on the mechanical strength of the composite [8]. We evaluated several heating element patterns, as shown in Figure 2.6, for evenness of heating and for their effect on the mechanical strength of the composite. Figure 2.6: Experimental heating element patterns Heating elements C and D experienced shorting across the power leads, leading to a burnout of the composite. Heating elements A and B activated successfully at low voltage. The resistance of heating element B was too low, such that undue current would be consumed while operating the heating element. Therefore the option selected for this application is an A pattern heating element. Multiple layers of heating elements were included in the composite layup to ensure even heating through the thickness of the shape memory polymer composite. A thermal image of a shape memory polymer composite with A pattern heating elements can be seen in Figure 2.7. As can be seen from the thermal image qualitatively, heating element A provides relatively even heating. 12
Figure 2.7: (Above) Surface view and a (below) Thermal profile of an A type heating element 2.2 Composite Fabrication Methods The Vacuum Assisted Resin Transfer Molding (VARTM) process was used to create all of the composites evaluated in this research. The previous manufacturing method for RHex and Edubot legs used 6781 S-fiberglass that had been pre-impregnated (pre-preg) with a thermoset epoxy. Standard pre-preg techniques were then used to create a composite[9]. No commercial pre-preg exists for shape memory polymer composites so an alternate method was selected. When using the VARTM process, the resin and dry fibers are selected independently of each other and the user is not subject to the constrictions of the limited pre-preg family of products. All materials for the VARTM process can be stored at room temperature, and dry fibers are easier to orient and apply than pre-preg fibers. In addition to ease of processing, the VARTM process offers a lower void content and more complete control over the resin weight fraction of the composite, a major determinate of the strength of a shape memory polymer composite [8]. A methacrylate adhesive, sold under the brand name Devcon Plastic Bonder was used to bond the shape memory polymer composite section to the rest of the leg. Early prototypes of the leg failed by delamination when the shape memory polymer section approached the glass transition zone. This adhesive bonds at the fiber level, often creating a bond that is stronger than the surrounding composite, as shown in section 2.3.2. The inclusion of this adhesive prevented early delamination failure of the leg. 13
2.3 Material Testing In order to verify that the new leg design can function at least as well as current standard legs without any stiffness adaptation, the mechanical properties of all composite materials and adhesives considered for the leg were tested at room temperature to verify standard performance. Two testing standards were used: ASTM D3039 for tensile testing and ASTM D2344 for short beam shear testing. It should be noted that the ASTM no longer classifies the metric acquired from D2344 as shear strength due to the uneven stress distributions inherent to the test. However, the short beam shear strength can be used as a comparison between the multiple composites evaluated for the leg prototype. 2.3.1 D3039 Tensile Testing Tensile specimens were prepared using an identical layup and fabrication process for three resin matrices, shape memory polymer, vinyl ester and epoxy to evaluate a suitable pairing for the variable stiffness leg. These resin candidates were four layers of carbon fiber, alternating 0 and 45 layers, were applied flat to a glass plate and VARTM processed. All three panels were then post cured in a convection oven and cut into tensile specimens using a wet saw. Fiberglass end tabs were used to prevent failure at the clamp in accordance with D3039. Specimen failure in the gage length indicated successful sample preparation. Five of each specimen were tested on an MTS material testing machine with a 250 kn load cell, using an extensometer. All samples were tested at a temperature of 70.6 F, a reasonable temperature for nominal robot operation. The results from the tensile tests are shown in Figures 2.8, 2.9 and 2.10. 14
Ultimate Tensile Strength (MPa) Figure 2.8 shows the relative ultimate tensile strength (UTS) of several composites fabricated with identical fiber layups but varying reinforcing resin matrices. The average UTS of the epoxy composite was the highest at 350±20.7 MPa. The shape memory polymer composite had a similar UTS of 335±24.5 MPa. Both the epoxy and shape memory polymer composite failed by a sharp break directly across the composite, orthogonal to the loading direction. The similar ultimate tensile strengths and the dominant failure mode of these composites indicates that failure likely occurred as a result of fiber failure not resin failure. The vinyl ester samples had a mean UTS of 202±29.7 MPa, much lower than the other resins evaluated. The main failure mode in the vinyl ester samples was delamination followed by fracture indicating poor resin bonding. These results indicate that vinyl ester resin is not a good candidate for a secondary resin in the composite leg. 400 Ultimate Tensile Strength 350 300 250 200 150 Vinyl Ester Shape Memory Polymer Epoxy Figure 2.8: Ultimate Tensile Strengths of Composites Fabricated with Resin Candidates 15
Strain (mm/mm) In addition to tensile loading, composite legs for RHex and Edubot undergo significant amounts of strain during normal operation [9]. Figure 2.9 shows the strain at failure from the tensile specimens. The shape memory polymer and epoxy specimens had approximately identical strain at failures of (1.145±0.146) 10 2 mm/mm and (0.01126±0.078) 10 2 mm/mm respectively. This close correlation indicates failure was likely caused due to the reinforcing fibers, indicating good resin bonding. The vinyl ester samples had a lower allowable strain than either the epoxy or the shape memory polymer samples. As before, legs made with vinyl ester as a secondary resin would be expected to fail earlier, making it a poor choice. 0.014 Strain at Failure 0.012 0.01 0.008 0.006 0.004 0.002 0 Vinyl Ester Shape Memory Polymer Epoxy Figure 2.9: Strain at Failure for Composites Fabricated with Resin Candidates 16
Elastic Modulus (MPa) The elastic moduli for composites fabricated with all of the resin candidates are roughly equal, as shown in Figure 2.10. The epoxy composite had the highest elastic modulus with a mean value of 31.83 GPa, almost identical to the shape memory polymer composite which had a mean value of 31.75 GPa. The vinyl ester composite had the lowest elastic modulus of 29.86 GPa. The combination of similar UTS, strain at failure and elastic modulus for the epoxy and SMP, suggest that epoxy would be a good choice as a secondary resin. 35000 Elastic Modulus 34000 33000 32000 31000 30000 29000 28000 27000 26000 25000 Vinyl Ester Shape Memory Polymer Epoxy Figure 2.10: Elastic Moduli of Composites Fabricated with Resin Candidates 17
2.3.2 D2344 Short Beam Shear Testing To determine the effect of variable resin compositions in the composite leg, a short beam shear test was used to determine the strength of inter-laminar bonding in the composite. In total, six types of composite layup were evaluated, as shown in Figure 2.11. Five of each type of specimen was prepared and tested in accordance with ASTM standard D2344. Figure 2.11: Cross-sections of Short Beam Shear Specimens (1) Epoxy-SMP (2) SMP-Epoxy (3) Epoxy-SMP-Epoxy (4) SMP (5) Epoxy (6) Vinyl Ester The short beam shear samples were fabricated using twelve layers of carbon fiber applied in alternating 0 and 45 layers. The external dimensions, given in Table 2.2, are specified by the D2344 standard based on the thickness of the sample. Table 2.2: Short Beam Shear Sample Dimensions Dimension Specification Value Thickness t 3mm Width 2 t 6mm Length 6 t 18mm Loading Span 4 t 12mm An Aluminum jig was fabricated and utilized to cut the samples to the correct length and width on a diamond bandsaw. Once the specimens were fabricated, they were mounted in a short beam shear fixture, shown in Figure 2.12, and loaded until failure. Load and displacement data were collected using a MTS material testing machine and analyzed to find the peak load at failure. The short beam shear was then calculated using Equation 2.1. 18
F sbs = 0.75 Pm b h (2.1) F sbs : Short beam shear strength P m : Maximum load b: Specimen width h: Specimen thickness Figure 2.12: Short Beam Shear Testing Jig [7] The results of the short beam shear tests are shown in Figure 2.13. No significant difference was found when reversing the loading direction for sample sets one and two. The composites comprised of cohesive sections of the distinct resins had the highest short beam shear strength, in both orientations, of all the methacrylate bonded test samples. Sample set three had the greatest variability and lowest overall strength, possibly indicating fabrication inconsistencies from multiple methacrylate bonds. The pure shape memory polymer samples had the highest shear strength, indicating good interfacial bonding. Epoxy, case five, had a lower strength and vinyl ester, case six, had the lowest average short beam shear strength of all the individual composites. These results indicate that the addition of a single methacrylate bond in the composite does not significantly affect the shear strength of the composite. Therefore, the shape memory polymer section of the final leg will consist a cohesive section of shape memory polymer composite bonded to a cohesive section of epoxy composite using a methacrylate adhesive. 19
Short Beam Strength (MPa) 31 Short Beam Strength 29 27 25 23 21 19 17 15 1: Epoxy-SMP 2: SMP-Epoxy 3: Epoxy-SMP-Epoxy 4: SMP 5: Epoxy 6: Vinyl Ester Figure 2.13: Relative Shear Strengths of Composites Fabricated with Resin Canidates and Bonding Methods In this chapter, the mechanical properties of the shape memory polymer composite, operating at room temperature, were evaluated. Its mechanical attributes are shown to be comparable with a commercial epoxy which was selected as the secondary resin of choice for this application. Composites made with vinyl ester resin were initially considered because of chemical similarity to the shape memory polymer, but lacked the structural integrity to preform well in composite legs. The relative shear strength of the composite materials was also investigated. Early prototypes of the variable stiffness leg failed by delamination upon heating, so a new fabrication process using a methacrylate adhesive was developed. Short beam shear tests confirmed that the methacrylate adhesive did not negatively impact the shear strength of the composite. The optimum layup structure for the shape memory polymer composite section was determined using these shear tests to be either case one or case two, see Figure 2.11. 20
CHAPTER 3 SHAPE MEMORY POLYMER COMPOSITE CHARACTERIZATION This chapter describes the design of a small temperature control circuit intended to be mounted directly to the variable stiffness leg. This circuit was used to evaluate the effect of temperature on the stiffness of the shape memory polymer composite. 3.1 Temperature Control Circuit The elastic modulus of a shape memory polymer varies drastically with temperature. The stiffness of the leg can therefore be modulated by controlling the temperature of a shape memory polymer segment. To control the temperature of the leg a circuit was designed to read a thermocouple and then drive a resistive heating element using a simple proportional control law. The circuit is based on a Baby Orangutan B-328 Robot Controller from Pololu (See Figure 3.1). The Baby Orangutan has several features that make it desirable for this application: a fast ATmega328P AVR microcontroller running at 20 MHz, a dual H-bridge motor driver that can be used to drive resistive heating elements, an on board potentiometer for setting a desired temperature, and a UART for serial LCD debugging and future implementation of XBee communication. The small footprint of the Baby Orangutan allows it to be mounted directly to the variable stiffness leg. A K-type thermocouple was used to measure the temperature of the shape memory polymer section of the leg. The MAX6674 Cold-Junction-Compensated K-Thermocoupleto-Digital Converter (0C to +128C) provided a digital SPI interface to the K type thermocouple. A software SPI interface was created to interface the chip with the Baby Orangutan. The MAX6674 has a resolution of 0.125 C with an accuracy of ±2 C, and communicates at 500 kbps with the software SPI interface. The MAX6674 was polled every 50 milliseconds so that the control loop could be closed at 20Hz. A circuit diagram for the temperature control circuit can be found in the appendix. 3.1.1 Power Supply and Consumption To determine the size of power supply required to drive the stiffness control circuit, a leg with a 14Ω resistive heating element was heated to, and maintained at several temperatures. 21
Power Consumption (W) Figure 3.1: The Baby Orangutan B-328 from Pololu For several temperature settings, the current consumed and operating voltage was recorded. As shown in Figure 3.2, the maximum power consumed was 2.135 W for a temperature of 85 C. This maximum value is not expected to be reached during normal stiffness actuation. 2.5 Power Consumption 2 1.5 1 0.5 0 40 50 60 70 80 90 Temperature (C) Figure 3.2: Power Consumption During Stiffness Actuation 22
There are several options for powering the stiffness control circuit. A slip ring stator and rotor could be used for power transmission and communication, as described in [9]. For this project, however, a self contained circuit is mounted directly to the leg for simple evaluation of the shape memory polymer s effect on leg stiffness. The operating voltage range of the Baby Orangutan is 5V-13.5V. A 2-cell 7.4V 300mAh Lithium polymer battery was chosen as the power source. The capacity of this battery will allow the leg to operate at maximum power for over an hour. Stiffness actuation in the nominal range would extend this duration by a factor of two. 3.2 Shape Memory Polymer Tensile Characterization To determine the effect of the shape memory polymer section on the variable stiffness leg, the effect of temperature on the tensile modulus of the shape memory polymer composite was evaluated. The control circuit described in the previous section was used to control the temperature of a shape memory polymer composite beam loaded in an MTS Insight testing machine. The gage length of the specimen was 50 mm, a heating element of the same dimensions and pattern used in the variable stiffness leg prototype was applied to the middle of the beam. The data that resulted from these tests has not been calibrated to the other measurements, such as the tensile modulus at room temperature, taken from the shape memory polymer composite. Therefore, only the relative effect of temperature can be observed from this set of tests. While the magnitude of the stiffness change cannot be calculated, but the temperature at which the change occurs can be determined. The results from these tests can be seen in Figure 3.3. The modulus was measured every five degrees from 50 C to 90 C. The specific modulus remains relatively constant until 70 C. At this point, the specific modulus begins to drop and continues to decrease until the maximum temperature, 90 C. The magnitude of the change in specific modulus cannot be evaluated from this test. This data indicates that there is only a small drop in the tensile modulus at the maximum temperature attainable with the control circuit. As a result, several modifications were made to the layup design for the shape memory polymer section. The change in the tensile modulus was maximized by increasing the number of fiber layers applied at ±45. The resin stiffness becomes more dominant in determining the overall stiffness of the composite when layers oriented at ±45 reduce the fiber volume fraction in the bending direction of the composite. The final layup for the shape memory polymer section consisted of five layers of carbon fiber oriented at ±45. 23
Specific Modulus 1.03 Specific Modulus of the Shape Memory Polymer Composite 1.02 1.01 1 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Temperature ( C) Figure 3.3: The Specific Modulus of Shape Memory Polymer Composite, normalized with the tensile modulus at room temperature. 24
CHAPTER 4 VARIABLE STIFFNESS LEG PROTOTYPING AND EVALUATION 4.1 Shape Memory Polymer Section Placement and Prototype Development A successful variable stiffness leg must fulfill several criteria. It must maintain the mechanical properties of standard legs made for the RHex robot. The composite legs undergo repeated large deformations necessitating very high mechanical strength. Additionally, the variable stiffness leg must be able to attain the correct stiffnesses in a given range. The target range for this leg is 800-2,000 N/m, similar to the values attained by the mechanically variable stiffness leg in [9]. Several additional considerations must be made for a shape memory polymer based adaptation. To minimize the amount of energy required for stiffness actuation, the shape memory polymer section was made as small as possible. By placing the variable stiffness section at the effective center of flexure, as described by the pseudo-rigid body model, the greatest change in stiffness can be attained for a given change in stiffness of the shape memory polymer composite section. Due to the intrinsic nature of a shape memory polymer composite, i.e. the several order of magnitude drop in stiffness at glass transition temperature, some supporting structure is required to prevent the leg from collapsing entirely. Keeping in mind these constraints, numerous leg prototypes were developed and evaluated. The earliest prototypes used fiberglass as the reinforcing fiber for the shape memory polymer composite. This fiberglass composite delaminated easily and lacked mechanical strength and had very high damping. The low delamination strength indicated poor resin bonding between the fiberglass and the custom resin. The interfacial bonding strength was greatly increased by using carbon fiber as the reinforcing material. The proprietary sizing formulation that the carbon fiber is treated with during its manufacturing seems to greatly facilitate bonding with a styrene based resin. Consequently, carbon fiber was selected as the reinforcing material for use in futher variable stiffness prototypes variable stiffness leg prototypes. The next design challenge that needed to be surmounted was to determine the best way to incorporate a finite shape memory polymer section into the variable stiffness leg without creating stress concentrations or locations for early delamination. Early versions 25
of the legs were fabricated by creating standard legs and machining out a section of the leg using wet abrasive tooling. a shape memory polymer section was then glued in using a methacrylate adhesive. These prototypes failed at very small deflections by fracturing across the composite where it was cut. This remained true of any leg fabricated by a post-machining process. This indicated that the shape memory polymer composite section needed to be incorporated on a layer by layer basis, remaining cohesive across the width of the variable stiffness leg. The ideal option for including a shape memory polymer section in the leg is to cure the resin in a localized section of fibers that run the length of the leg. This would mitigate the effect of including a dissimilar material in the composite layup. Several attempts were made at fabricating a leg with this method. The complication in fabricating legs with this method resulted from the requirement for a closed mold during the resin curing process. A discrete section of the fibers could not be sealed off from the rest to allow the resin to cure. An alternative method was developed using a two part mold to cure a wet layup in a hot press. This method failed because the resin distribution in the composite was uneven, causing a stress concentration which led to delamination, as shown in Figure 4.1 when it was included in the rest of the leg layup. These results indicated that a discrete section of shape memory polymer had to be fabricated and then included in the leg layup separately. Figure 4.1: Delamination failure in a prototype leg Short beam shear tests, see Section 2.3.2, were preformed to determine the effect of the location of the shape memory polymer section on the strength of the overall composite. The tests indicated that the strength of the composite was greatest when the shape memory polymer and epoxy sections were included in cohesive layers, bonded with a layer of methacrylate adhesive. Omission of the methacrylate adhesive caused delamination of the shape memory polymer section when it was heated, as shown in Figure 4.2. When the shape memory polymer segment was included on the outside surface, the composite separated at 26
the intersection of the epoxy and shape memory polymer sections. The leg then fractured at this location before attaining significant deformation. When the shape memory polymer section was included on the inside surface, the intersection of the epoxy and shape memory polymer sections was in compression during bending, preventing separation. Another step taken to mitigate the effect of including a dissimilar material in the composite layup was to directly heat only a small section of the shape memory polymer composite, evening out the stiffness change of the section. The shape memory polymer section occupied 30 of the leg, centered on the center of flexure. The heating element was applied to the middle of this section, occupying 15 of the composite leg. This, final, iteration of the prototype leg has the highest mechanical strength during nominal operating conditions as well as during stiffness actuation of the shape memory polymer section. Figure 4.2: Shape memory polymer separation in a prototype leg 4.2 Leg Prototype Stiffness Characterization The final version of the variable stiffness leg is the only prototype to withstand the stiffness testing without experiencing mechanical failure. The shape memory polymer segment is comprised of five layers of carbon fiber, all applied at ±45, to maximize the effect of the change in stiffness of the shape memory polymer resin. This section is embedded on the inner surface of a leg fabricated from ten layers of carbon fiber, applied in alternating 45 layers, reinforced with epoxy. A single 15Ω heating element was applied to the inner 27
surface of the shape memory polymer on a light fiberglass scrim soaked with epoxy. The external leads of the heating element were reinforced with methacrylate adhesive. The effect of controlling the temperature via the circuit designed in Section 3.1 was tested. Stiffness measurements were made by using a MTS material testing machine to compress a variable stiffness leg on a linear guide rail, similar to methods previously used to evaluate the stiffness of Edubot legs [9]. The stiffness measurement was taken at 10% compression of the rest length of the spring, a standard value to use [11][10][9]. The leg was unloaded and reloaded for each measurement taken for a given temperature setting. The results of the leg characterization are shown in Figure 4.3. 2500 Leg Stiffness Vs. Temperature Effective Radial Stiffness (N/m) 2000 1500 1000 500 0 20 30 40 50 60 70 80 90 Temperature ( C) Figure 4.3: Stiffness values attained using the variable stiffness leg with the temperature control circuit The stiffness values ranged from 2,310 N/m, at room temperature, down to 650 N/m at 28