Problem Definition/Statement:

 

What is the problem?

           

Currently, prophylactic elastic knee sleeve supports on the market do not adequately provide a correct compressive stress to cancel out other stresses acting on the knee.  The knee sleeve must be able respond to dynamic situations with a compressive stresses in the necessary areas to stabilize the knee.  Current supports provide only average assistance for knee ligaments.  More advanced knee braces, while providing more support than knee sleeves, have bulky hinges and stays that can add weight and interfere with performance.  Athletes need a better sleeve to allow them to compete at a high level while protecting their knees.  A better elastic knee sleeve would reduce the number of knee injuries while allowing people to wear unobtrusive knee protection.

 

What are the goals and objectives of the project?

           

The primary goal is to develop a novel knee sleeve system that will provide more stability to the user than any other knee sleeve currently available.  To reach this goal, a list of new ideas will need to be formulated and analyzed to select the best one.  Important material properties will need to be identified to create some sort of figure of merit to determine the best materials for the device.  Cost will always need to be kept in mind during the development of the product.  It is very important to demonstrate clearly that the new design is better than what is currently available.  The design team will have to figure out a way to best present the information about the product in order to “sell” the idea.

 

What’s out there now?

           

Most of the knee sleeves currently on the market offer the same general design.  The elastic nature of the sleeves allows them to be uniformly tight to provide compression on the knee.  The following are examples of what is currently out there:

 

 


This McDavid Open Patella Knee Support is made from neoprene and provides support and warmth for minor ligament problems.  This model is also available in a closed patella design for the same cost.  Cost: $14.99

 

This Elastic Knee Support by Mueller is made out of a lightweight elastic knit.  The manufacturer claims that it provides firm support and the user to maintain a full range of movement.  Cost: $12.00

This Wraparound Knee Support with Adjustable Straps by Mueller is supposed to provide firm, comfortable compression.  The adjustable straps are supposed to allow for “adjustable tension for controlled compression”.  Cost: $14.99

These previous three models represent what this design is out to improve upon.  These are both simple knee sleeves that can be pulled on.  They both provide a small amount of compressive support to the knee.  What follows are a few models (functional knee braces) with more features such as metal springs or side stays, large adjustable straps, hinges, and polymer support pads.  The goal of this design project is to try to approach the level of support found in these bulkier, more expensive knee braces while keeping the lightweight, easily portable sleeve design.

 

 

This Ligament Knee Support Brace by McDavid features a horseshoe buttress, springsteel stays, and four crossing straps.  Cost: $39.99

This Pro Stabilizer by McDavid features geared polycentric hinges and contoured rubber pads.  Cost: $79.99

This Protective Knee Guard by McDavid features and M-2 geared polycentric hinge, a polycarbonate resin construction, and aluminum inlays for impact management.  Cost: $64.99

donjoy playmaker knee brace

 

 

   

 

 

 

 

 

This Enhanced Drytex Playmaker Brace features a patented 4-point dynamic leverage system to control all major knee instabilities.  It is designed to be worn by people who have undergone major knee surgeries.

 

Armor by DonJoy

This Armor knee brace by DonJoy is a lightweight, performance brace that comes in different models for different ligament stabilities (ACL, PCL, MCL, and LCL).  The frame is made from 6061 T6 aircraft aluminum, and the brace also features an anti-migration Supra Condyle pad.  Cost: $500.00.  Similar braces are specifically made for one individual based on measurements taken of the said individual’s knee.  These braces tend to cost more than $1000.00.

Where are you planning to go?

The approach will involve different ways in which to apply more compressive stress in areas that need it most.  Most efforts will revolve around some sort of input to the sleeve that causes it to tighten in the right places to give more support.  Materials will be sought out that will contract upon application of heat, current, or some other input.  The standard knee sleeve design that is out there now will also be examined and improved upon.

Solution Constraints

  • This design will not attempt to substitute current functional knee braces that use supports and hinges to compensate for damaged ligaments.
  • The product will not cost more than thirty dollars.
  • The knee sleeve will not endanger the safety of the wearer.
  • The sleeve cannot be more uncomfortable than what is currently on the market.
  • The sleeve will not provide added features such as padding.
  • Materials will not be used that do not hold up to the wear and tear to which the sleeve is subjected.

              

 

 

 

Technical Term Definition

 

Functional Knee Brace- A functional knee brace is designed to substitute for damaged ligaments.  It is supposed to be able to compensate for the damage in the knee and support the knee as well as a ligament would.

Prophylactic Knee Sleeve- These devices are the focus of this design project.  They are used during physical activity where there is a high risk of damage to the ligaments in the knee joint.  It is designed to provide compressive stress that prevents excessive rotation, anterior translation, and posterior translation.

 

Engineering Characteristics:

 

            The primary goal of a knee brace is to support and stabilize the knee in place of injured ligaments.  To accomplish this, modern braces are designed to apply compressive force around the knee.  This force will alleviate the stress on the uninjured tendons and impede the motion of the knee, preventing further injury.  Our knee sleeve will accomplish this same goal.

There are two types of knee braces on the market.  The first type is either made of elastic or neoprene that stretches as they are placed on the knee.  The stretched knee sleeve then applies a compressive force to the knee as it tries to resume its original shape.  In engineering terms, this can be modeled by Hooke’s Law,

 

σ = εE,

 

where ε is the strain, E is the elastic modulus, and σ is the stress.  Hooke’s Law shows that as strain increases (smaller knee sleeve on a larger knee), it will produce more stress (compressive force on the knee).  To model this stress, consider the sleeve as a cylinder.  When the cylinder is stretched, a strain of ∆A/A is introduced, where A is the internal surface area of the unstretched cylinder.  This strain results in a stress σ according to Hooke’s Law.  For the purposes of our design, it is convenient to assume that stress is uniform throughout the sheet.  The stress that is generated is therefore uniform throughout the knee.  This key assumption helps in modeling the sleeve’s performance further.  A representation of this is shown in Fig. 1.

This type of model also lends itself to a hoop stress situation.  In this case, an internal pressure (stress) is exerted by the knee onto the brace, and the brace responds with a compressive stress.  A hoop stress is dependant on the radius of the cylinder, the internal pressure exerted, and the thickness of the cylinder wall according to

 

σ = Pr/t

 

This hoop stress modeling is a very rough approximation, but it is the best way to simplify the situation.

 

Compressive force from sleeve

 
 

Fig. 1.  Representation of forces acting on a knee sleeve

 

            The second property that is important to an elastic knee sleeve is the modulus of resilience, UR.  The modulus of resilience, the area under the elastic region of the stress-strain curve, represents the amount of energy that an elastically deformed material can absorb and release.  A good knee sleeve should have a high modulus of resilience to provide the best compressive support.  It is also important that the sleeve not plastically deform when it is stretched so that it can be used multiple times.

            The second type of knee brace uses metal supports or springs to stabilize the knee.  These braces are designed to support the knee after a serious injury or surgery.  The theory behind the braces are similar to an elastic sleeve, but to a much larger degree.  Metal bars hold the knee much more rigid than an elastic sleeve, effectively preventing lateral motion.  Other braces are designed to support the patella or another ligament of the knee.  Our sleeve will not attempt to replace this second type of brace.

            Thus, the main characteristics that we are concerned with are the modulus of elasticity, the modulus of rupture, the durability of the material, and its susceptibility to cyclic fatigue.  Other concerns are the geometry of the knee brace to improve comfort and the manufacturing cost.  Customers demand the knee sleeve provide support, be durable and comfortable, and be reasonable in cost.  These values will be explained in a House of Quality.

 

    

TRIZ Concept Development:

 

            The TRIZ method was used to generate possible resolutions to performance contradictions in our knee sleeve.  The contradictions and their TRIZ solutions are listed below.  Some possible devices using the TRIZ solutions are explained, as well.

 

Contradictions:   11 (Pressure) and 31 (Object-generated harmful)

Specifications:  The brace should provide adequate pressure to stabilize the knee, not so much that it risks injury.

Solutions:  2 (Taking out), 33 (Homogeneity), 27 (Cheap, short-lived objects), 18 (Mechanical vibration)

Possible devices:

27, Using one-time only sleeves.  The sleeves would stretch and plastically deform to fit the knee snugly, but would have to be discarded afterwards.  These would need to be inexpensive enough to merit the lack of durability.

33, Choose a material close to a ligament’s mechanical properties to not exceed the mechanical strength of the other components of the knee.

 

Contradictions:  11 (Pressure) and 15 (Durability – moving object)

Specifications:  The device must apply pressure, yet should be durable enough to be used multiple times.

Solutions:  19 (Periodic Action), 3 (Local Quality), 27 (Cheap, short-lived objects)

Possible Devices: 

3, Selectively strengthen part of the sleeve.  This one part would be designed for maximum protection, but the rest of the brace would be designed towards comfort or durability.

27, Use one-time only sleeves.  Durability becomes a moot point if the sleeves are inexpensive.

 

Contradictions:  12 (Shape) and 36 (Complexity)

Specifications:  Generating a better shape for support could make the brace too complex.

Solutions:  16 (Partial or Excessive Actions), 29 (Pneumatics and hydraulics), 1 (Segmentation), 28 (Mechanics substitution)

Possible Devices: 

1, Have individual tightening bands instead of one large sleeve.  This method would allow several simple components to be integrated instead of having one complex component.

28, Use some sort of magnetic particles woven into the brace to tighten it.  Applying an electric current would induce a magnetic field, attracting the particles and tightening the brace.

29, Fill a bladder with a dilatant fluid (ie cornstarch and water) that will flow when minor stresses are applied.  When a large stress is applied, the fluid’s viscosity increases drastically and prevents movement of the knee.

 

Contradictions:  33 (Ease of Operation) and 36 (Complexity)

Specifications:  If the brace becomes more complex, it could be harder to use.

Solutions:  32 (Color changes), 26 (Copying), 12 (Equipotentiality), 17 (Another dimension)

Possible Devices: 

17, Instead of trying to integrate all of the protection into one sleeve, have a secondary support system designed to be worn over the first sleeve.  The secondary system could provide more specific support, while the first is more general.

 

Contradictions:  29 (Manufacturing Precision) and 36 (Device Complexity)

Specifications:   As the complexity of a device increases, the difficulty in manufacturing it will increase.  This could lead to braces being produced incorrectly.

Solutions:  26 (copying), 2 (taking out), 18 (mechanical vibration)

Possible devices: 

2, Manufacture a sleeve and a tightening band separately (different bands for different types and levels of tightness.

 

Contradiction:  11 (Tension, Pressure) and 35 (Adaptability).

Specifications:  For pressure, the device must provide enough compressive stress to stabilize the knee.  For adaptability, the device must adaptable to various users.

Solution:  35, Transformation of physical and chemical states of object.

Possible Device:  Use a liquid filled sleeve.  The liquid needs to be dilatant and viscous under normal conditions.  Upon application of a large stress, the fluid will solidify.  An example of this type of behavior is the mixture of corn starch and water.

 

Contradiction:  11 (Tension, Pressure) and 2 (Weight of nonmoving object).

Specifications:  For pressure, the device must provide enough compressive stress to stabilize the knee.  For weight, the device cannot weigh more than an amount that would be cumbersome or bothersome to the user during activity.

Solutions:  13, Inversion.  29, Use of pneumatic or hydraulic construction.  10, Prior action.  18, Mechanical vibration.

Possible Devices:  13, Make a sleeve that can be molded to the individual user with heat.  The device would need to stay fixed in form but still be able to come on and off.  An example of a similar device is a mouth guard that is fit to an individual after it is placed in boiling water.

29, Use a sleeve with air bladders that can be inflated after the device is put on.  The level of support would be adjustable.

10, Create a device with sensors that can adjust the sleeve when an incident is imminent that will put dangerous stress on the knee.

 

Contradiction:  14 (Strength) and 35 (Adaptability).

Specifications:  For strength, the device must be strong enough to operate at all conditions of use.  For adaptability, the device must be adaptable to various users.

Solutions:  15, Dynamicity.  3, Local quality.  32, Change color.

Possible Devices:  15, Make a device which allows the user to selectively tighten parts of the sleeve for customizable support.  This could be done with various bands, clips, or clamps.

3, Design a knee sleeve that uses different material at points where the most support is needed, which is where the most stress is felt by the knee.

 

Contradiction:  14 (Strength) and 33 (Convenience of Use)

Specifications:  For strength, the device must be strong enough to operate at all conditions of use.  For convenience of use, the product must not be a large hassle for a user to apply and must be simple to use.

Solutions:  32, Change color.  40, Composite materials.  25, Self-service.  2, Extraction.

Possible Devices:  40, Use metal fibers to reinforce the sleeve to increase its strength.

2, Eliminate the parts of the sleeve that are not directly supporting the susceptible parts of the knee.  Attachment to knee would have to be through magnets or adhesive.

 

Contradiction:  11 (Tension, pressure) and 33 (Convenience of use)

Specifications:  For pressure, the device must provide enough compressive stress to stabilize the knee.  For convenience of use, the product must not be a large hassle for a user to apply and must be simple to use.

Solution:  11, Beforehand cushioning.

Possible Device:  11, Create a knee sleeve with backup support mechanisms.  The backup mechanisms would be layered on top of the primary mechanisms.  When a primary support is overcome, the secondary support kicks in to provide support.

 

Contradiction:  11 (Tension, Pressure) and 12 (Shape).

Specifications:  For pressure, the device must provide enough compressive stress to stabilize the knee.  For shape, the device must be able to operate based on the geometry of the knee.

Solutions:  35, Parameter changes.  4, Asymmetry.  15, Dynamicity.  10, Prior action.

Possible Device:  Design a knee sleeve that has geometry based upon knee geometry.  In this case, a sleeve would be available for both the right knee and the left knee.

 

Contradiction: 32 (Manufacturability) and 36 (Complexity of Device)

Specifications: As the complexity of a device increases, the difficulty in manufacturing will increase.  This could lead to braces being produced inefficiently or incorrectly.

Solutions:  27 (Cheap, short-lived objects), 26 (Copying), 1 (Segmentation)

Possible Devices:

27, Use one-time only sleeves.  The sleeves would stretch and plastically deform to fit the knee snugly, but would have to be discarded afterwards.  These would need to be inexpensive enough to merit the lack of durability.

1, Have individual tightening bands instead of one large sleeve.  This method would allow several simple components to be integrated instead of having one complex component.

 

Contradiction: 16 (Durability of non-moving object) and 34 (Repairability)

Specifications:  The device should be durable enough to be used multiple times, yet be easy to repair in case of damage to localized areas.

Solution: 1 (Segmentation)

Possible Device:

1, Have individual tightening bands instead of one large sleeve.  This method would allow for the brace to be easily disassembled for easy repair to localized areas of damage.

 

Contradiction:  30 (Harmful factors acting on object) and 34 (Repairability)

Specifications:  The brace should not have qualities that are harmful to the user or cause additional harm if user had previous knee injury.  Yet, the device should be easily repairable if it causes hindrance to the user.

Solutions:  35 (Parameter changes), 10 (Preliminary action), 2 (Taking out)

Possible Devices:

35, Use a liquid filled sleeve that is not chemically volatile to user in case of leakage.  The liquid needs to be dilatant and viscous under normal conditions.  The device’s degree of flexibility can also be changed if e.g. using a vulcanized rubber, which in turn may increase durability.

10, Create a device with sensors that can adjust the sleeve when an incident is imminent that will put harmful or dangerous stress on the knee.

2, Eliminate the parts of the sleeve that are interfering or not directly supporting the susceptible parts of the knee.  Manufacture a sleeve and a tightening band separately (different bands for different types and levels of tightness for user’s choice of comfort level).  Do not want the bands to constrict user’s blood circulation at the knee joint, therefore having different levels of tightness can repair any harmful knee constrictions.

 

Contradiction:  30 (Harmful factors acting on object) and 35 (Adaptability)

Specifications:  The brace should not have qualities that are harmful to the user.  For adaptability, the device must be adaptable to various users.

Solutions:  35 (Parameter changes), 11 (Beforehand cushioning), 22 (Blessing in Disguise), 31 (Porous material)

Possible Devices:

35, Use a liquid filled sleeve that is not chemically volatile to user in case of leakage.  The liquid needs to be dilatant and viscous under normal conditions.  The device’s degree of flexibility can also be changed which in turn may increase durability and adaptability for user.

11, Create a device with backup support mechanisms.  The backup mechanisms would be layered on top of the primary mechanisms.  When a primary support is overcome, the secondary support kicks in to provide support.

22, Amplify a harmful factor to such a degree that it is no longer harmful.  The device is to be very compressive so as to eliminate the need for side stabilizing hinges or heavy supports (from users who have weak or loose knee joints).

31, Introduce opened sections into the sleeve for breathability that will add comfort and user adaptability, relieving chances of harmful constriction to blood circulation.

 

Contradictions:  30 (Harmful factors acting on object) and 16 (Durability of non-moving object)

Specifications:  The brace should not have qualities that are harmful to the user, yet should be durable for multiple use.

Solutions:  17 (Another Dimension), 1 (Segmentation), 40 (Composite Materials), 33(Homogeneity)

Possible Devices:

17, Instead of trying to integrate all of the protection into one sleeve, have a secondary support system designed to be worn over the first sleeve.  The secondary system could provide more specific support, while the first is more general.  Having secondary support increases the durability of entire device in case of failure of primary system.

1, Have individual tightening bands instead of one large sleeve.  This method would allow several simple components to be integrated instead of having one complex component.

40, Use metal fibers to reinforce the sleeve without adding too much weight, to increase its strength, support level and durability.

33, Choose a durable material close to a ligament’s mechanical properties to not exceed the mechanical strength of the other components of the knee.

 

Concept Selection, A New Compressive Knee Sleeve:

           

Use of the TRIZ methodology generated numerous possible devices.  In order to eliminate concepts and select a winning concept, the importance of the various sleeve properties and customer needs were examined.  It was clear that the device has to be fairly simple, be able to exert good compressive stress on the knee, and be durable and strong.  Some of the more complicated concepts were eliminated.  Other concepts eliminated were those that seemed to be too similar to what is already on the market or those that did not seem feasible to manufacture.  For example we eliminated an idea that involved a corn starch type dilatant fluid that would solidify when stress was applied.  We discovered that these types of fluids tend to solidify through vibrations and would not respond as needed in a knee sleeve.  They would most likely harden an unacceptable amount due to vibrations while running or walking.  Another idea involved sets of sensors on the sleeve that could detect when an impending action was going to occur to put a dangerous stress on the knee and correspondingly adjust itself.  This idea would have been far too expensive and probably not feasible.  One idea that was eliminated involved the sleeve type design by using adhesive supports that would be placed on parts of the knee.  This concept was flawed in that it would not provide adequate support and it would be very difficult to find an adhesive that would be comfortable yet effective at staying on the skin.  

            Another factor that was examined was how many different contradictions a certain idea solved.  It was clear that a design concept that satisfied multiple sets of contradictions was superior to a concept that only solved one contradiction.  After using these elimination techniques and analysis methods, it was apparent that one design stood above the rest.  This concept employs a thin band that is pulled over the knee.  There are six small band attachment points on the knee with nubs.  Bands can then be placed on top of the primary sleeve and attached between different points to provide support to different areas of the knee.  This idea incorporates several of the solution types from the TRIZ analysis.  It is segmentation design because a good percentage of the support is coming from bands that can be attached on top of the main sleeve.  It is secondary cushioning because the top support bands can take over when the stress on the knee overcomes the base sleeve.  This design also incorporates layering, repairability, and homogeneity.

            The functionality of our knee brace is based on many factors.  According to customer demands, the brace should be durable, comfortable, and supportive.  Satisfying each of these demands and resolving the engineering conflicts through TRIZ methodology led us to our final design.  Our brace consists of two parts: a comfortable inner sleeve and supportive outer bands.  By relegating the bulk of the support aspect of the brace to the outer bands, many different types of support can be produced based on the arrangement of the tightening bands.


As seen in Figure 2, the design incorporates side stabilizers, preferably made of the same material as the base inner sleeve, to provide a firmer support to the medial and lateral sides of the knee.  Incorporated in the side stabilizers are attachment points with nubs, three on each side.  These nubs will protrude out of the base sleeve, but not excessively to deter the customer from wearing the sleeve underneath articles of clothing.  The base sleeve will have no apertures (circle drawn in figure to show relative locations of nubs to patellar region); the patella will be closed as to prevent any irritation that may arise with tightening bands that overlap the patella. 

 

Fig. 2.  Concept design of base knee sleeve with six attachment points

 

Representations of two differing tightening bands are seen in Figure 3.  Figure 3(a) displays a thin band with circular apertures along the entire length which allows the wearer to selectively choose tightness over portions of the knee joint for comfort.  Apertures need to be smaller than the size of the nubs so that the band can stay in place and have minimal loss of support from stretching during physical activity.  Figure 3(b) represents a tightening band that is used for tightening across the patella.  The second band (Fig. 3b) incorporates a design that provides greater comfort to the wearer while in motion; having a thin band over the knee (Fig. 3a) may irritate the wearer because the band may shift up and down across the patella during activity.  Our design also incorporates attachment sites at the back ends of the tightening bands, in which excess portions would attach to the base inner sleeve to prevent dangling.  One of the many customer demands is to wear the sleeve underneath clothing.  Using this additional concept keeps excess portions of the bands from dangling freely and allows the customer to wear the sleeve easily without excess bunching. 

 

(a)                                              (b)

Figure 3: Concept design of tightening bands

 

 

 

 

Developing Figures of Merit:

 

            For the material selection process, indices of merit had to be developed for each of the components of the knee sleeve system: the base sleeve, the support bands, and the attachment nubs for the bands.

 

The Base Knee Sleeve:

 

            The first indices developed were for the base knee sleeve.  The most important function of the sleeve is that it provide a greater amount of compressive stress to the knee than those sleeves currently on the market.  This function was modeled using the idea of hoop stress.  The knee will exert a force on the sleeve, and the sleeve must respond by exerting a compressive stress on the knee.  The objective function used to derive this figure of merit was to minimize the mass, which is based on a customer need of lightweight knee support.  The constraint equation was the hoop stress involved, and thickness was the free variable.  The result of this derivation was an index of merit of M1 = [σ/ρ], where σ is yield strength of the material and ρ is the density of the material.  A second figure of merit derived for the knee sleeve involved the modulus of resilience.  The objective was to maximize modulus of resilience per weight, and the constraint was the hoop stress.  The free variable was again taken as thickness.  The result of this derivation was an index of merit of M2 = [σ3/(Eρ)], where E is the elastic modulus of the material.  The derivations to these figures can be found in the Appendix to this report.  With these two figures of merit, classes of materials were compared to select the best material available.  A number of material classes were found that satisfied both of the figures of merit.  These materials and their indices can be seen in the following table.  All material properties were taken from Matweb and Materials Science and Engineering: an Introduction by Callister.

 

Performance Indices for the Base Knee Sleeve

 

 

 

 

 

M1

M2

 

Σ (MPa)

ρ (g/cc)

E (GPa)

σ/ρ

σ3/Eρ

Butyl Rubber

17

1.35

0.00425

12.59

856296.30

Silicone Elastomer

56.5

2.7

0.392

20.93

170410.17

Polyurethane elastomer

6

1.26

0.012

4.76

14285.71

EVA

2.5

0.956

0.14

2.62

116.74

SBR

12.4

0.94

0.01

13.19

202832.34

Nitrile

6.9

0.98

0.0034

7.04

98592.14

Neoprene

28

1.5

0.028

18.67

522666.67

 

A number of the materials, such as metals (not shown here) were disqualified from contention because they did not meet the customer need of being lightweight and because they had values that were far too different from the values for the actual human knee components.  One of the TRIZ solutions was based on the fact of trying to replicate the device you are supporting, and a material with far more strength than the body could cause injury and would not work well as an overall knee sleeve support.

The best material for the knee sleeve was determined to be neoprene (polychloroprene).  It performed well on the first index of merit and was far and away the best material based on the second index of merit.  This, along with its relatively low cost compared to other materials, is the reason it was selected as the material for the base sleeve.

After careful consideration, the side stabilizers were decided to not be included in the final design.  This is because they account for shear stresses on the knee, which were not a part of any of our models.

 

            Support Bands:

 

            The second component that needed a material selected was the support bands that provide extra support to certain parts of the knee.  The bands are connected at each end to a nub that is on the base sleeve.  They are designed to exert additional compressive stress on the knee.  These bands were modeled as cantilever beams fixed on both ends and with a uniform load across their length.  It was discussed that they should be modeled as portions of a cylinder undergoing hoop stress, but this was found to be too involved and a poor representation of the situation.  The first index of merit for the bands was based on a limited deflection of the band to prevent unwanted motion of the knee.  The objective for this derivation was once again to minimize mass, and the constraint was the limited deflection.  Thickness was the free variable.  The result of this derivation was a figure of merit of M1 = [E 1/3 / ρ].  The second figure of merit for the support band was based on surface stress.  The derivation was based on an objective function that minimized mass and a constraint that limited surface stress to the fracture stress of the material.  Once again, the thickness was selected as the free variable.  The result of this was a figure of merit of M2 = [σ ½ / ρ].  The derivations for these figures can be found in the Appendix of this report.  The material possibilities, taken from Ashby charts, are listed in the following table along with their values for the performance indices.

 

Performance Indices for the Support Bands

 

 

 

 

 

M1

M2

 

E (GPa)

Σ (MPa)

ρ (g/cc)

E 1/3 / ρ

σ ½ / ρ

EVA

0.04

2.5

0.956

0.3577

1.654

PTFE

0.4

9

2.3

0.3204

1.304

Polyurethane

0.44

4

1.3

0.5851

1.538

Silicone Elastomer

0.392

56.5

2.7

0.2711

2.784

Neoprene

0.0035

28

1.5

0.1012

3.528

W alloy

2.61

784

17.1

0.0805

1.637

Butyl rubber

0.002125

17

1.35

0.0952

3.054

Butadiene acrylonitrile

0.0034

6.9

0.98

0.1534

2.68

Styrene butadiene

0.002

12.4

0.94

0.134

3.746

 

Other metallic materials were quickly eliminated because they contradicted with customer needs and did not give very good indices, as can be seen in the tungsten alloy.  The final material selected for the support bands was a silicone elastomer because it performed well in both indices of merit.  There are several different grades of this polymer, but most are proprietary.  Most of the grades have the same mechanical properties; it is the thermal management properties that vary between different kinds.  The bands will be manufactured from the cheapest silicone elastomer available.

 

            Band Attachment Points (Nubs):

 

            The final component that required a performance index for material selection was the attachment nub that holds the support bands in place.  There are a total of six nub attachments on the base sleeve.  One figure of merit was developed for the nubs, and it was based modeling the nub as a cantilever beam with one fixed end and a concentrated load on the free end.  The objective function was to minimize deflection and the constraint was to not exceed the tensile stress of the material.  Length of the nub was treated as the free variable.  Using these guidelines, a figure of merit was developed of M = [E/σ3].  The derivation for this figure can be found in the Appendix of this report.  The following table shows candidate materials and their respective index values.

 

 

 

 

 

 

 

 

Performance Index for the Nubs

 

 

 

 

M

 

E (GPa)

σ (MPa)

E/σ3

1020 Low Carbon Steel

205

350

4.78E-06

302 Stainless Steel

193

240

1.39E-05

308 Stainless Steel

195

205

2.27E-05

Cast Iron

66

152

1.88E-05

Titanium Alloy

110

827

1.94E-07

Polyurethane elastomer

0.012

6

5.55E-05

Polyurethane

0.44

23

3.62E-05

 

            From these candidates, 308 Stainless Steel was chosen as the material for the manufacturing of the nubs.  It can be seen that both of the types of polyurethane listed here give better indices of merit, but both are also quite a bit more expensive that stainless steel.  It was decided by the company that the extra cost was not worth the increase in performance index.  The stainless steel nubs will be fairly easy to manufacture and will provide another desired property by resisting corrosion.

 

Dimensional Specifications:

 

Derivations for these dimensional specifications can be found in the Appendix at the end of this report.  The methods used in calculating them will be briefly discussed.  Starred values have been assumed and fixed.

 

·        Length of base sleeve*:  20 cm

·        Diameter of base sleeve*:  11.5 cm

·        Thickness of base sleeve:  5.6 mm

·        Length of stretched support band on knee*:  20 cm

·        Length of stretched support band on knee (1/1000000 failures)*:  35.6 cm

·        Length of unstretched support band:  17.5 cm

·        Length of unstretched support band (1/1000000 failures):  31.1 cm

·        Thickness of support band:  0.57 mm

·        Thickness of support band (1 in a million failures):  1.01 mm

·        Height of nubs:  1.1 mm

·        Diameter of nubs*:  2.5 mm

 

To determine these values, a methodical approach was taken.  First, the average circumference and standard deviation of the human knee must be found (39.4cm and 2.127cm, respectively)