DESIGN PROJECT I: TIRE PRESSURE GAUGE

DESIGN PROJECT I: TIRE PRESSURE GAUGE Diana Nelson 09/26/2014 University of Florida EML 4501

1 P a g e Table of Contents Table of Contents... 1 Components of Gauge... 2 How the Gauge Works... 3 Physics... 2 Functional Design Requirements... 7 Pros and Cons of Design... 12 Component Materials... 13 Plastic and Elastomer Identification... 14 Assembly Process... 18 Assembly Time... 21 Appendix A: Assembly and Part Drawings... 22 Appendix B: Closure Analysis... 33 Assembly... 35 Barrel/Keeper... 36 Schrader Valve/Cap... 37 Keeper/Ruler... 38 Cap/Barrel... 39 Cap/Washer... 40 Plunger/Barrel... 41 Plunger/Spring... 42 Grip/Barrel... 43 Appendix C: Material Identification and Assembly Charts... 44 Plastic Identification Chart... 45 Elastomer Identification Chart... 46 Manual Handling Estimated Time Charts... 47 Manual Insertion Estimated Time Charts... 48 Process Tolerance Chart 1... 49 Process Tolerance Chart 2... 50 References... 51

Components of Gauge The labeled part names in the drawing below will be referred to throughout this report. 2 P a g e

How the Gauge Works Figure 1 Schematic of an example pressure gauge being applied to a tire Source: http://auto.howstuffworks.com/pressure-gauge3.htm Overview Figure 1 provides a visual representation of a pressure gauge very similar to the one being analyzed in this project. As shown, the cap of the gauge is lined up with the Schrader valve stem of an inflated tire. When pressure is applied from the gauge to the stem, the pin inside the cap of the gauge compresses the pin of the valve stem allowing for pressurized air in the tire to flow into the gauge. As air rushes into the barrel of the gauge, the plunger is moved to the right and the spring resists the motion of the plunger. The distance the plunger travels is relative to the pressure in the tire. The gauge is designed to measure a maximum pressure of approximately 50 psi and the spring is calibrated so that at the maximum pressure it will compress and move the plunger to the far end of the tube. There is a calibrated measuring stick (the ruler) inside of the spring that the plunger pushes on as pressure flows into the barrel. As pressure increases, the ruler is pushed out of the barrel and when the gauge is released from the valve stem the plunger and spring return to their default states while the ruler remains in its extruded state allowing the user to read the pressure measurement. 3 P a g e

Physics Once pressurized air enters the barrel, its corresponding force acts on the plunger as modeled in Figure 2 below. P F s Figure 2 Schematic of the forces acting on the plunger neglecting friction P = F/A F a = P A The spring applies an opposing force to the plunger and is represented as Fs where F s = kδ Where k is the spring constant and δ is the displacement of the spring. In an idealized situation, the force applied by the pressurized air can be equated to the spring force so that F s = P A = kδ With the spring constant and area known, the pressure can measured with respect to how far the ruler is pushed out of the barrel (δ), where δ = PA k This is how the distance between tick marks on the ruler is correlated with the pressure resolution of the gauge. The above analysis is an idealized situation which does not account for the friction of the plunger/barrel interface or the keeper/ruler interface which also oppose the motion of the plunger down the barrel. These forces were found experimentally as described below. 4 P a g e

Barrel/Plunger friction force Since the plunger and barrel are concentric with each other, the frictional force of the plunger occurs along the circumference of the widest edge of the plunger as shown in the figure below. F P Figure 3 Line of contact between plunger and barrel FP was found by placing the barrel vertically on a scale, ensuring the plunger was aligned concentrically inside of the barrel, and then pushing the plunger concentrically downwards with the ruler. This process was repeated a few times while the force on the scale was observed and measured. The maximum force seen on the scale was taken to be the initial frictional force that had to be overcome to start the plunger moving. The average value found in class was approximately 10 grams or 0.022 lbs. Ruler/Keeper friction force The keeper provides a frictional force that prevents the ruler from sliding out of the barrel when not taking measurements. The absolute minimum force required to keep the ruler from sliding out is equivalent to the weight of the ruler which was found in class to be about 1.18 g or about 0.0416 oz. To better estimate the friction force, a test very similar to the one described above with the barrel/plunger was performed. First, the ruler was weighed and then the scale was zeroed with the ruler on the scale. Next, the ruler was held vertically on top of the scaled while the keeper was slid down the ruler in the same orientation in which the gauge operates. The force on the scale was observed during the process and the maximum value seen on the scale was taken to be the friction force between the keeper and the ruler. The approximate average value found in class was 20 grams or 0.044 lbs. F K Figure 4 Source of friction between keeper and ruler 5 P a g e

Spring Constant, k The spring constant, k, was found experimentally in class by loading the spring in compression with known masses and recording the displacement of the spring at each load. Digital calipers were used to measure displacement in inches. Table 1 Displacement of compression spring with respect to applied mass Mass (g) Displacement, δ (in) 0 0 200 0.258 500 0.738 700 1.088 1000 1.522 1200 1.824 Next, the displacement was plotted with respect to the mass and a linear relationship was found. The slope of this line was taken to be the spring constant, k, and had a value of 0.0015 in/g 0.6818 in/lb. 6 P a g e

Functional Design Requirements Cap Requirements Depress the valve stem pin Allow pressurized air into the pin House the rubber washer Connect to the barrel How requirements are met The pin in the cap is dimensioned and toleranced to be able to depress any standard Schrader valve. Closure equations of the interface between the cap and the valve stem are in Appendix B. The inner diameter, d1, is dimensioned such that it can fit over the outer threaded portion of a Schrader valve and maintain an interference fit with the washer. Connection to the barrel is achieved with a press-fit which is further analyzed in Appendix B. The upper lip of the cap prevents over-straining of the barrel by stopping the barrel from being pressed too far onto the cap. Washer Requirements Support the pin inside the cap sphere Prevent air from leaking out of the valve stem when taking measurements How requirements are met The washer is made of a soft rubber which is what contacts the rim of the Schrader valve. The depressed rubber acts as a seal as pressurized air flows into the cap of the gauge. The washer fits tightly inside the cap with a strong interference fit (Appendix B) preventing it from moving around inside the cap or falling out. The washer must be able to deform a maximum of 0.027 inches in order to displace the valve enough in the worst case scenario (length of the cap pin minimized,depth of the valve is maximized, length of washer maximized). Details of this analysis are in Appendix B. The nature of the material that the washer is composed of allows it to deform a sufficient amount to maintain functionality in the worst case scenario. 7 P a g e

Barrel Requirements House and protect the plunger, ruler, spring, and keeper Securely connect to the cap Allow plunger to move laterally within its housing and ruler to extend out of its housing Maintain structural integrity when pressurized How requirements are met The barrel is made of aluminum which has a high modulus of elasticity making it able to maintain its structural integrity under pressure. Its modulus of elasticity also allows it to be strained by the cap press-fit while still maintaining an adequate seal and modularity. Details of the press-fit between the cap and the barrel are located in the closure analysis of the cap/barrel interface in Appendix B. Plunger Requirements Respond to pressurized air inside by moving down the length of the barrel Maintain enough friction and contact with the inner walls of the barrel to be able to stop when pressure is released and slide back up the barrel Connect to the spring and allow the spring to control its movement within the barrel Transfer kinetic energy to the ruler to allow the ruler to slide out of the barrel How Requirements are met There is an interference fit between the outermost diameter of the plunger and the inner diameter of the barrel. The closure analysis of this fit is detailed in Appendix B. The wall thickness of the outermost diameter of the top side of the plunger allows for its walls to be more flexible. These two properties allow more leeway in the tolerancing of the plunger. For example, when the plunger diameter is minimized and the barrel inner diameter is maximized, there is a clearance of 0.003 inches. Despite the clearance, friction is still maintained with the barrel under pressure because as pressure is applied to the plunger, the thin walls of the plunger spread radially outward and maintain contact with the barrel wall. The plunger is designed to that the spring can be concentrically pressed against one diameter step of the plunger, secured by the next lowest diameter step, and it s final diameter step serves to transfer it s kinetic energy to the ruler as displayed in the figure below. 8 P a g e

Spring Requirements Attach to the plunger Compress under pressure and return to relaxed state when pressure is released Be calibrated to push the plunger and ruler to their maximum positions under a predetermined pressure. How requirements are met The spring attaches to the plunger as explained above in the plunger functional analysis. The spring s diameter is dimensioned such that it can securely fit onto the middle diameter step of the plunger. The spring has a calibration constant of 0.0015 in/g so that can be correlated with the ruler since 40 psi is equal to 2.4 inches on the ruler. Ruler Requirements: Slide through the keeper Measure pressure How requirements are met The ruler was dimensioned and tolerances so that it could exit the bottom of the keeper with plenty of clearance. Detailed closure analysis of the keeper and ruler is provided in Appendix B. In order to measure the pressure, the ruler has tick marks that are calibrated with the pressure and the amount of displacement of the ruler. For example, when the gauge is exposed to 40 psi, the ruler displaced about 2.4 inches so then the resolution of the ruler was determined accordingly. Keeper Requirements: Prevent ruler from sliding out when not measuring pressure Allow ruler to slide out when measuring pressure How requirements are met The keeper is engineered to have an interference fit with the ruler. It is designed so that the pinchers can flex outward to allow the ruler to fit and when the pinchers return to their default state with the ruler inside of them, there is a resulting force on the ruler preventing it from sliding out of the keeper. The physics of the interaction between the keeper and the ruler is explained below. 9 P a g e

δ F N L R L K L Figure 5 Interference fit between the keeper and ruler. The purple dotted line represents the relaxed state of the pinchers. The interference is found using closure analysis. Details of the closure analysis of these two pieces are in Appendix B. Since the keeper is symmetric, interference = L R L K δ = interference 2 δ = F NL 3 3EI Where E is the modulus of elasticity of the keeper and I is the moment of inertia found using the parallel axis theorem below Figure 6 Moment of Inertia about a semi-circle Source: http://en.wikipedia.org/wiki/list_of_area_moments_of_inertia 10 P a g e

The normal force in this case is found to be (0.0035 in F N = 3δEI (3 ( 2 ) (30E3 lb in 2) (0.1908(0.071 in)4 )) L 3 = (0.21 in) 3 = 0.082 lb f = 37.22 g The total friction force is a product of the normal force and the coefficient of friction [7]. It is multiplied by two below to account for both sides of the keeper/ruler. F = 2(μF N ) = 2(0.2)(37.22 g) = 14.88 g 15 g This tells us that with an interference of 0.0035 in, the friction force between the ruler and the keeper is approximately 15 g. The weight of the ruler is 1.2 grams which would be the minimum frictional force to keep the ruler from sliding out. Since the frictional force is 15 grams, the requirement is met and exceeded so that the ruler cannot easily be shaken out of the keeper. Grip Requirements: Fit securely onto the barrel Serve as an ergonomic interface between the gauge and the user s hand How requirements are met The interference fit between the grip and the barrel is detailed in Appendix B. The closure analysis proved that an interference existed in the maximum material condition and least material condition. The flexibility of the rubber material of the grip allows it to be stretched over the barrel and the surface of the rubber is also smooth which facilitates it sliding up the barrel. The outer surface of the grip is curved to adapt to the user s grip. Its dimpled surface enhances the gripping surface. 11 P a g e

Pros and Cons of Design Pros Cost-effective material choice Meets functional requirements Simple design Assembly requires no tools Blue anodized aluminum is aesthetically pleasing The clip is designed for convenience Cons Measurable pressure range is limited; Gives inaccurate results when pressure is less than 4 psi. High assembly time for one part When the ruler is extended it can be torqued such that it could break and potentially damage other parts Difficult to disassemble (this is probably a positive design feature from the consumer side but it is a con if a part needed to be replaced or repaired) The clip could be easily broken or deformed if bent past its elastic limit 12 P a g e

Component Materials The materials of the gauge components were identified by running a series of tests. The plastic and elastomer identification flow chart located in Appendix C was used in determining the material of the plastic and rubber parts of the gauge. The plastic parts were first pressed with a soldering iron to determine if they were a thermoset or thermoplastic. All three parts softened when they came in contact with the soldering iron so they were determined to be thermoplastics. The parts were then dropped in water followed by being burned with a controlled flame. Observations of how the materials behaved during these tests were made to narrow down material type. Tables displaying the flow of tests performed on the plastics and elastomers are on the following pages. The first step in identifying the metal components (spring and barrel) was to use a magnet to determine if they were ferrous or not. To narrow it down further, density calculations were performed and compared with standard known material properties. The barrel had a density of 2.7 g/cm 3 and was not magnetic so it was determined to be aluminum. The spring was ferrous and was determined to steel. 13 P a g e

Part: Cap Material: Polyester Table 2 Physical observations of the cap under a series of tests Dropped into Water Sinks Yes Description of Burning Self Drips? Fast/Slow Flame Extinguishing Burn No No Fast Yellow with blue base Floats No Other Characteristics Black Smoke with Soot Odor Burning Rubber The cap was determined to be a thermoplastic polyester. Polyester is an ideal material for the cap because of its dimensional stability. The front face of the cap has to be able to come into contact with the metal surface of a Schrader valve numerous times in its life and polyester does not become brittle under repeated stress like this. Polyester is also fairly inexpensive. Part: Keeper Material: Polyethylene (PE) Table 3 Physical observations of the keeper under a series of tests Dropped into Water Sinks No Description of Burning self Drips? Fast/Slow Flame extinguishing Burn N/A Yes Fast Blue with yellow tip Floats Yes Other Characteristics N/A Odor Paraffin The keeper was determined to be Polyethylene (PE). PE is a suitable material for the keeper because of its lubricious properties. The low friction of the PE allows the ruler to slide smoothly through the keeper. PE also has high wear resistance and is inexpensive making it a good choice for this application. 14 P a g e

Part: Ruler Material: Polyester Table 4 Physical observations of the ruler under a series of tests Dropped into Water Sinks Floats Yes No Description of Burning self Drips Fast/Slow Burn Flame Other extinguishing? No No Fast Yellow with blue base Characteristics Black Smoke with Soot Odor Burning Rubber The ruler was determined to be polyester. The mobile functions of the ruler require it to have high stiffness properties as well as dimensional stability which are both found in polyester materials. The ruler must maintain its shape over time and under high stress in order for the gauge to continue to function properly. Part: Plunger Material: Inconclusive. Possible urethane polyester. Table 5 Physical observations of the plunger under a series of tests Self Extinguishing Sinks Yes Drips? Dropped into Water Floats No Description of Burning Fast/Slow Flame Other Burn Characteristics Black Smoke while flame on the part, grey smoke after flame extinguished. Did not turn white. Sputtered. No No Slow Yellow, Orange Flame Odor Burning Rubber but different than washer The specific material of the plunger was unable to be identified based on the elastomer identification chart in Appendix C. It is possible that it s a urethane polyester type based on its reaction to the performed tests. The rubber that it is made of has a rougher surfaces which provides friction for the spring to remain secure. The rubber is also able to flex which aids in the frictional forces required between the plunger and barrel. At the same time the rubber must be able to flex and also maintain its material properties and return to its original state. 15 P a g e

Part: Washer Material: Inconclusive. Possible urethane polyester or silicone Table 6 Physical observations of the washer under a series of tests Dropped into Water self extinguishing Sinks Yes Drips? Fast/Slow Burn Description of Burning Flame No No Slow Yellow, Orange Flame Floats No Other Characteristics Black Smoke while flame on the part, grey smoke after flame extinguished. Burned part turns white Odor Burning Rubber, kind of a minty smell The specific material of the plunger was unable to be identified based on the elastomer identification chart in Appendix C. It is possible that it s a urethane polyester type based on its reaction to the performed tests. The washer turned white after being burned which suggested that it could also be a silicone, however, it did not have white smoke which deterred me from labeling it as silicone. The washer has to be able to deform and flex to fit inside of the cap. The face of the washer also has to deform when pressure is applied to it by the Schrader valve and it must also maintain its strength at the same time. A tough, yet deformable rubber was chosen for the washer for this reason. Part: Grip Material: Inconclusive Table 7 Material observations of the grip under a series of tests Dropped into Water Sinks Floats Yes No Description of Burning Self Extinguishing Drips? Fast/Slow Burn Flame Other Characteristics Yes No Slow Yellow, Black Smoke while Orange flame on the part, Flame grey smoke after flame extinguished. Did not turn white. Odor Burning Rubber but different than other two 16 P a g e

Turns glossy color when being burned. The rubber material of the grip aids in keeping it secure to the metal barrel because of the high friction coefficient between metal and rubber. The elasticity of the rubber allows it to be able to stretch over the diameter of the barrel and then clamp back down on the barrel. The plushness of the rubber enhances the comfort of the grip. Part: Barrel Ferrous? No Density: 2.7 g/cm 3 Material: Aluminum Aluminum is a cost effective metal with good strength properties particularly in tension [4]. The barrel acts as a pressurized vessel so it must be made of a material that can maintain its structural integrity under pressure exceeding 50 psi. The modulus of elasticity of the aluminum also allows for the cap to be properly press-fitted into the barrel because the aluminum can be strained and retain its stiffness properties. Aluminum responds well to machining and manufacturing so it was a practical choice of metal from that stand-point as well. Aluminum is also highly rust resistant and the anodized aspect adds an aesthetic appeal. Part: Spring Ferrous? Yes Material: Steel/Stainless Steel Steel has excellent machining and manufacturing properties which makes it a good choice when manufacturing a spring. Steel wire responds well to bending which is essentially what the coiling process does to the steel. The coiled wire is stressed in torsion when a load is applied to it [5], so it must be made of a material with a high modulus of elasticity which steel has. Steel is also one of the cheapest metals which aids in the cost-effectiveness of the gauge. Although tests were not conducted to confirm the type of steel used, it can be hypothesized that the spring is made of stainless steel because of the rust and corrosion resistance of stainless steel. Stainless steel is also a very common material used for compression springs across many industries. 17 P a g e

Assembly Process 1. Pick up ruler with dominant hand by the end with the cylindrical knobs 2. Pick up keeper with non-dominant hand insert the ruler into the pinching end of the as shown below (due to the interference fit on the top face of the keeper, it helps to approach entry into the gap of the keeper from the side walls). Do not slide ruler all the way into the keeper. Slide it in so that the end of the ruler is only slightly exposed out of the keeper on your dominant side (Fig. 7) 2 1 Figure 7 Insertion of ruler into keeper 3. Holding the keeper/ruler assembly in your dominant hand, pick up the barrel with your non-dominant hand and slide the keeper/ruler into the barrel with the keeper leading. Figure 8 Insertion of ruler/keeper into barrel 4. While holding the barrel assembly in your non-dominant hand, pick-up the spring and slide it into the barrel. Leave about a half-inch of the spring exposed out of the barrel. Figure 9 Insertion of spring into barrel 18 P a g e

5. Slide your hand down the barrel in order to simultaneously hold the barrel and the spring in place Figure 10 Holding the exposed end of the spring in place 6. Pick up the plunger with your dominant hand and press its smaller diameter side into the first couple of coils of the spring as shown below. Slide the plunger and spring into the barrel. Figure 11 Assembling plunger onto spring 7. Pick up cap with dominant hand and press into the barrel so it is secure but not so it is a press fit. Figure 12 Pressing cap into barrel 19 P a g e

8. Holding the gauge assembly by the cap in your dominant hand, pick up the grip with your non-dominant hand and slightly press it onto the end of the barrel with the wide end of the grip going onto the barrel. Simultaneously press the cap and the grip into and onto the gauge until the barrel is pressed against the lip of the cap and the grip is flush against the cap as shown in the Figure 14 below. Figure 13 simultaneously press-fitting grip and cap to barrel Figure 14 Final placement of the grip and cap after being pressed onto the barrel 9. Insert washer into cap by squeezing it and manipulating it into the cap from an angle. Figure 15 Inserting rubber washer into the cap 20 P a g e

Assembly Time The assembly times in the table below were found using the handling and insertion charts located in Appendix C. Table 8 Assembly time of gauge in terms of handling and insertion Assembly Step α β α+β Handling time Insertion time Total time 1 360 180 540 1.8 0 1.8 2 360 180 540 2.1 2.5 4.6 3 360 0 360 1.5 2.5 4 4 180 0 180 1.13 1.5 2.63 5 slide hand down barrel 1.13 0 1.13 6 360 0 360 1.8 2.5 4.3 7 360 0 360 1.8 2.5 4.3 8 360 0 360 1.5 5 6.5 9 180 0 180 1.43 7.5 8.93 Completed pressure gauge assembly Assembly Time 38.19 s 21 P a g e

Appendix A Drawings 22 P a g e

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Appendix B: Closure Analysis 33 P a g e

Introduction to Closure Analyses Process tolerances used in the following analyses were estimated using the process tolerancing charts in Appendix C on pages 49 and 50. Actual tolerances were found by multiplying the process tolerance by the nominal dimension. After closure analysis was performed at each critical dimension, it was determined whether or not the tolerance needed to be adjusted to better meet the functional requirements of the gauge. 34 P a g e

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43 P a g e When the barrel diameter is minimized and the grip diameter is maximized, there is still an interference which makes the current tolerances okay. The interference is very small but the rubber/metal interface also aids in keeping the grip in place. When the barrel diameter is maximized and the grip diameter is minimized, the interference is 0.019 inches which is also okay because the material properties of the grip allow it to be stretched to fit onto the barrel.

Appendix C: Source Charts 44 P a g e

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References [1] http://auto.howstuffworks.com/pressure-gauge3.htm [2] http://www.engineersedge.com/spring_general.htm [3] http://springipedia.com/compression-general-design.asp [4]http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061t6 [5] http://www.leespring.com/int_learn_compression.asp [6] http://en.wikipedia.org/wiki/list_of_area_moments_of_inertia [7] http://www.dotmar.com.au/co-efficient-of-friction.html [8] http://www.consultekusa.com/pdf/tech%20resources/new%20id%20chart%20.pdf 51 P a g e