University of Florida

EML 4501

DESIGN PROJECT I:

TIRE PRESSURE GAUGE Diana Nelson

09/26/2014

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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

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Components of Gauge

The labeled part names in the drawing below will be referred to throughout this report.

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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.

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Physics

Once pressurized air enters the barrel, its corresponding force acts on the plunger as modeled in

Figure 2 below.

Figure 2 Schematic of the forces acting on the plunger neglecting friction

𝑷 = 𝑭/𝑨

𝑭𝒂 = 𝑷 × 𝑨

The spring applies an opposing force to the plunger and is represented as Fs where

𝐹𝑠 = 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

𝐹𝑠 = 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.

P Fs

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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.

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.

Figure 4 Source of friction between keeper and ruler

FP

FK

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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.

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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.

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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.

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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 pre-

determined 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.

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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.

interference = LR − 𝐿𝐾

Since the keeper is symmetric,

δ =interference

2

δ =FNL3

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

δ FN

L

LR LK

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The normal force in this case is found to be

𝐹𝑁 =3𝛿𝐸𝐼

𝐿3=

(3 ((0.0035 𝑖𝑛

2 ) (30𝐸3𝑙𝑏

𝑖𝑛2) (0.1908(0.071 𝑖𝑛)4))

(0.21 𝑖𝑛)3= 0.082 𝑙𝑏𝑓 = 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(𝜇𝐹𝑁) = 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.

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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

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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/cm3 and was not magnetic so it was determined to be aluminum. The spring was ferrous

and was determined to steel.

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Part: Cap

Material: Polyester

Table 2 Physical observations of the cap under a series of tests

Dropped into Water

Sinks Floats

Yes No

Description of Burning

Self

Extinguishing

Drips? Fast/Slow

Burn

Flame Other

Characteristics

Odor

No No Fast Yellow

with blue

base

Black Smoke with

Soot

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 Floats

No Yes

Description of Burning

self extinguishing

Drips? Fast/Slow

Burn

Flame Other

Characteristics

Odor

N/A Yes Fast Blue with

yellow tip

N/A 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.

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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

extinguishing

Drips

?

Fast/Slow Burn Flame Other

Characteristics

Odor

No No Fast Yellow with

blue base

Black Smoke with

Soot

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

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.

Dropped into Water

Sinks Floats

Yes No

Description of Burning

Self

Extinguishing

Drips? Fast/Slow

Burn

Flame Other

Characteristics

Odor

No No Slow Yellow,

Orange

Flame

Black Smoke

while flame on the

part, grey smoke

after flame

extinguished. Did

not turn white.

Sputtered.

Burning

Rubber but

different than

washer

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Part: Washer

Material: Inconclusive. Possible urethane polyester or silicone

Table 6 Physical observations of the washer under a series of tests

Dropped into Water

Sinks Floats

Yes No

Description of Burning

self

extinguishing

Drips? Fast/Slow

Burn

Flame Other

Characteristics

Odor

No No Slow Yellow,

Orange Flame

Black Smoke while

flame on the part,

grey smoke after

flame extinguished.

Burned part turns

white

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

Odor

Yes No Slow Yellow,

Orange

Flame

Black Smoke while

flame on the part,

grey smoke after

flame extinguished.

Did not turn white.

Burning Rubber but

different than other

two

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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/cm3

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.

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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)

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

1 2

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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

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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

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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

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Appendix A

Drawings

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Appendix B:

Closure Analysis

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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.

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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.

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Appendix C:

Source Charts

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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