Automatic Test Machine for Rebreather

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IN THE FIELD OF TECHNOLOGY DEGREE PROJECT

MATERIALS DESIGN AND ENGINEERING AND THE MAIN FIELD OF STUDY

MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2020,

Automatic Test Machine for Rebreather

Breathing patterns simulations of dosage regulators at depths down to 120m in water CARL BÜHLMANN

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

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Automatic Test Machine for Rebreather

Breathing patterns simulations of dosage regulators at depths down to

120m in water

Carl Bühlmann

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Abstract

Product performance and quality assurance are two critical steps in competitive product development. Especially important when developing life enabling products such as breathing equipment for smoke- and water diving as the company Interspiro. Specific tests of simulated scenarios have to be developed, designed and conducted in order to ensure the product intended functions. However, these tests can be complex and time consuming to perform. Therefore, there is a drive for developing dedicated test machines, especially for the more complex and time consuming tests.

This project contains the development and suggestion of a test machine prototype for Interspiro’s dosage regulators. The dosage regulator is a critical component of the mine clearance diving apparatus, IS-MIX. It regulates the pressure of the breathing gas to suit the diver during different diving depths, supplying the diver with the right amount of oxygen when breathing.

Due to the posing risks of working in high pressure environments, such as when diving, it is important that the diving equipment functions as intended, passes the safety regulations and quality tests. For instance, some factors that affect how the diving equipment adapts the gas distribution for the diver are human respiratory physiology, the movement of oxygen to the cells within the body, the effect of high pressures on humans and gas compositions for oxygen delivery amongst other factors.

Furthermore, IS-MIX regulates the breathing gas supply mechanically, it is a complex and robust system which has to be tuned in through settings to function as intended.

Consequently, Interspiro tests the dosage regulators in a large pressure chamber, a time consuming process which requires manual operations to set up. Hence, the main focus of this project is to provide a prototype for enhancing the test execution speed, accuracy and efficiency. Thus, a test machine capable of performing evaluation of the dosage regulators performance, how it adapts the gas flow and pressure at different depths, is a great asset to obtain.

As a result, a test machine prototype is developed, capable of simulating breathing patterns and pressure transmitters to log pressures in order to evaluate the dosage regulators. The concept features a programmable linear motor for simulating breathing and controlling the dosage regulator.

Furthermore, a main body housing and lock, specialized for fast and safe swapping of dosage regulators is suggested. The error analysis reveals that the tests can be performed with an error of

<0,005 bar and time saved is about 80% per test, from ~1h to 5min manual involvement. Some room of improvements are to minimize the size and weight in order to further enhance the mobility of the test machine.

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Sammanfattning

Produktprestanda och kvalitet är två viktiga aspekter i konkurrenskraftig produktutveckling. Speciellt vid utveckling av produkter för att upprätthålla liv, så som andningsutrustningar för rök- och vattendykning, vilket görs på företaget Interspiro. Specifika tester av scenarion måste utvecklas, designas och konstrueras för att säkerställa produktens funktion. Dessa tester kan vara komplexa och tidskrävande att genomföra. Det finns därför en drivkraft för utveckling av testmaskiner, speciellt för de komplexa och tidskrävande testerna.

Detta projekt inkluderar utvecklingen och förslaget av en testmaskin prototyp för interspiros dosering regulator. Dosering Regulatorn är en viktig komponent i minröjnings apparaten IS-MIX. Den reglerar trycket och andningsgaser så att den passar dykaren under olika dykdjup och tillförser dykaren med rätt mängd syre vid andning.

På grund av de medföljande riskerna vid dykning under höga tryck, är det avgörande att utrustningen fungerar felfritt, att den uppfyller säkerhetsföreskrifterna och kvalitetstesterna. Faktorer som påverkar hur dykutrustningen måste adaptera gas-distributionen är bland annat människors respiratorisk fysiologi, syrets transport i blodet till cellerna i kroppen, effekten av höga tryck på kroppen och andnings gasens sammansättning för att uppnå rätt syrenivå. IS-MIX dosering regulator reglerar andningsgas mekaniskt, ett komplex men robust system som behöver ställas in genom inställningar för att doserings regulatorn ska fungera som tänkt.

Interspiro testar dosering regulatorerna i en tryckkammare, vilken är både tidskrävande och kräver ett flertal manuella operationer att genomföra. Huvudmålet med projektet är därför att utveckla en prototyp för att förbättra test-utförande tiden, träffsäkerheten och effektiviteten i produktiuonen. En testmaskin kapabel att utföra dessa tester för att evaluera dosering regulatorer och hur de accepterar gasflödet samt trycket vid olika djup, är en stor tillgång att tillgodose.

Som resultat, utvecklas en test maskin prototyp, kapabel att simulera andningsmönster och avläsa tryck genom tryckgivare för att evaluera dosering regulatorerna. Konceptet inkluderar en programmerbar linjär motor för simulering av andnings kurvorna och kontrollering av dosering regulatorerna. Huset och ett lås utvecklas med fokus på snabbhet och säkerhet. Felanalysen visar att test kan genomföras med en felmarginal på <0,005 bar och att tiden för varje test reduceras med ca 80% per test, från ~1h till 5 min manuell inverkan. Några utvecklingsmöjligheter är att minimera storlek och vikt för att förbättra mobilitets möjligheterna.

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Acknowledgements

I would like to thank Interspiro for the opportunity to work for a company like them. This project has been a perfect balance between challenging tasks and rewarding experiences. Many thanks to my supervisor Bjarne Eriksson and all the people working at Interspiro, for providing a satisfactory work atmosphere and always willing to support throughout the project.

I would like to thank KTH, without the foundry of knowledge provided during my time at KTH, this master thesis would not have been possible. Especially the 3D modelling, mathematics and mechanics courses have been useful. I would like to thank my supervisor Per Johansson, for providing good input and support during the project.

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List of Abbreviation

ACSC DCSC ATPS BTPS STPD

Alternatively Closed Semi Closed Demand controlled semi-closed circuit

Ambient Temperature Pressure Saturated with H2O Body Temperature Pressure Saturated with H2O Standardized Temperature Pressure Dry (without H2O)

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1. Introduction

This master thesis, within the school of Production Engineering and Management, is conducted during the spring semester of 2020 at the company Interspiro in collaboration with the Royal Institute of Technology, KTH. It consults the development process of a test machine for dosage regulators in order to achieve a greater efficiency in production and quality testing. These specific dosage regulators are used in the diving equipment IS-MIX. Current solutions at the company have shown it possible to simulate breathing patterns through the use of servo and stepper motors. However, these solutions can be improved in order to achieve a greater efficiency. Consequently, solutions are evaluated and components for a new test machine are carefully selected in order to enhance the accuracy, speed and error margin of these tests.

1.1. Background

Due to the high pressure and catastrophic life danger risks of breathing equipment malfunctioning in high pressure environments, quality assurance through specific tests is a critical step in the production process. The strive for greater efficiency in production is always persistent. Interspiro develops multiple products requiring different quality assurance methods to ensure their intended function. Some of these methods are time consuming processes which require a high degree of manual operations to perform. Hence, this project is initiated in order to find a solution to one of these time consuming tests.

In short, the dosage regulator is positioned in the mine clearance diving equipment IS-MIX, a full semi closed rebreather diving equipment, specialized in mine clearance for diving depths down to 120m. Specially developed by Interspiro to examine and disarm modern-day sea mines, based on over 30 years of experience and the well-proven ACSC (Alternatively Closed Semi Closed) and DCSC (Demand controlled semi-closed circuit) systems diving equipment. [1]. The challenge is to find a suitable test machine for these dosage regulators, which can provide the efficiency, accuracy and automation desired. Furthermore, in order to design such a test machine, it is important to understand how the diving apparatus and the dosage regulator functions. Interspiro has developed a reliable and robust mechanical solution for their diving system IS-MIX which has to be tuned in through settings in order to distribute gas to the diver at the correct composition, flow, pressure and volume with alternating diving depths. Therefore, the test machine has to be able to simulate these environments, while at the same time, provide statistics for evaluation of the dosage regulators performance.

1.2. The Company Interspiro

“Keeps you breathing”, a quite fitting slogan for a company such as Interspiro. In fact, Interspiro develops breathing equipment for both smoke diving (for firefighters) and water diving (for divers).

Within this field of work, multiple aspects have to be taken into consideration, human respiratory physiology, movement of oxygen to the cells within the body, the effect of high pressures on humans, gas compositions for oxygen delivery and more, affects how the product has to adapt gas distribution and pressures at different depths.

Interspiro has its origin in 1904, under the company AGA. AGA started off developing “navigation aids and gas to a wide range of products”, one of which was the gas distributions in AGA’s

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lighthouses. They later began developing breathing equipment in the field of medicine, aircraft respiratory systems, smoke and water diving under the name Interspiro. Interspiro was first in the world in developing the now standardized method of positive pressure breathing systems. Today, Interspiro develops market competitive products within the field of diving and firefighting [2].

Furthermore, Interspiro has multiple patents amongst their products, a requirement when developing new competitive products.

1.3. Project Definition

The project can be defined as a development and suggestion for a test machine, capable of enhancing the test- execution speed, accuracy and efficiency for dosage regulators used in the diving equipment IS-MIX. Consequently, the aim of the project is to enhance the execution, quality assurance and time consumption of these tests. Moreover, in order to ensure efficiency and high quality standard of dosage regulators, the goal is to develop a prototype test machine, fulfilling the requirements presented in 1.5. Product Requirements.

Delimitations applied during the project are as follows; breathing curves are approximated as versions of sinus curves, with alternating amplification and frequency. This enables a simplified yet close adaptation of reality [3]. Furthermore, as the test machine suggested is a first prototype, the construction does not have to take mass production efficiency into account. In detail, the test machine prototype concerns the test machine itself, the housing, simulation motor, pressure transmitters, locking mechanism, adapter connections. Eventual dosage volumes, buffet volume, pressure-in-regulators and different hoses/valves for connection are created as dummies since Interspiro already has these parts in stock.

1.4. Driving Forces for the Project

The driving forces that initiated the need for this project are as follow:

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Minimize lead times by test automation and setup time reduction.

Minimize the need for manual operations.

Minimize the need for R&D’s involvement in complicated tests.

Minimize the need for transportation are generated from the specific and complex tests.

Simplify instructions for production.

Minimize costs.

Minimize human failure factors.

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1.5. Product Requirements

The requirements of the project and product is defined below:

● The top priority in developing this testing machine is to make it safe for the operator to handle. Preferably an implementation of a smart lock mechanic which will be kept locked if high pressures is present.

● The test machine should be able to simulate breathing at different diving depths from 0- 120m. As a result, the system must handle ~21bar as the dosage regulator is fed a Pin

equal to 9bar above ambient pressure. At 120m depth the ambient pressure is 12bar above surface. Therefore, Pin equals 21bar above surface pressure. As a result, material selection, housing design and construction needs to be carefully considered when designing a solution.

● The test machine solution should be easy to understand with focus on test execution speed reduction. Furthermore, ~10 dosage regulators tests per hour is desired.

● The Level of Automation of the test machine should require as little manual control as possible. Ideally the user should only have to put in the dosage regulator being tested and select which test to run.

● In order to test different variants of IS-MIX gases the dosage regulator requires a modular system where the dosage volume can change and the depth of the tests can be decided by the user.

● The Simulation Motor has to be durable, accurate, programmable as well as provide the speed and acceleration required for the force required. All of which need to be estimated by calculations in order to plan what motor to order.

● The cost shall be aimed to be kept as low as possible without compromising the function and efficiency of the test machine. Furthermore, this test machine will not be created in large quantities and mass production costs are therefore not a main concern.

1.6. Method

In order to obtain an understanding of which tests are suitable for the test machine to handle, a theory study of the current solutions and functionality of the product, is conducted. Previous work has shown it possible to simulate breathing patterns through the use of programmable motors, simulating bellow movement (breathing patterns) at different ambient pressures (depths). A concept generation is conducted and solutions are considered. Constructions are generated in 3D modelling for evaluations of functionality before concept specializations are made. As a result, a prototype is developed with suggested parts, drawings and technical solutions. Furthermore, through the use of a linear actuator, pressure transmitters and a time log, different breathing patterns and dosage regulator performances can be evaluated efficiently. The project is categorized into different phases in order to structure the work ahead, as seen in Table 1.

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Table 1: Project Procedure Overview

Phase: Description:

Problem definition A definition of the project's purpose.

Theory study An understanding of the origin to why the product is developed and areas related to pressure chambers and seals.

Analysis Current product functionality, construction and solution.

Furthermore, explanation of the current test machine.

Requirements Requirements are set up for a solution.

Concept generation Creating multiple solution suggestions in order to widen the view.

Concept specialization Selecting and specialization in one solution.

Prototype presentation Suggesting a solution.

1.7. Current Test Machine

In the company’s current solution, tests of IS-MIX’s dosage regulators is a time consuming process which requires a high degree of manual operations to perform. The old test machine consists of a pressure chamber where different depths can be simulated by manually adjusting the pressure. In detail, to test a dosage regulator the main components of the diving equipment are firstly placed inside the pressure chamber. Secondly, a stepper-motor is mounted to the IS-MIX apparatus.

Thirdly, an angle guide, for keeping the stepper-motor breathing angle in positions during tests, hooks into place. Lastly, the stepper-motor is mounted and connected to a computer, thereupon breathing patterns are simulated through a computer software. If simulations are successful at surface ambient pressure, the pressure chamber is closed and different depths can be simulated by alternating the pressure. Due to the large containment of the pressure chamber, it takes a while for the pressure to build up. Furthermore, in case the tests are not successful, the current solution requires the operator to reopen the pressure chamber and take apart the diving equipment in order to enable adjustment of the dosage regulator settings. In conclusion, it takes about 1-2 hours on average to test one dosage regulator. The current test machine with simulation motor, diving equipment and pressure chamber can be seen in Figure 1. With a test machine that can automatically execute accurate tests, a faster production, safer and higher degree of quality assurance can be achieved. The current solution utilizes the diving equipment, pressure transmitters, simulation program and a stepper motor, Figure 1 a). Figure 1 b) reveals the stepper simulation motor, capable of simulating breathing movement through the use of a simulation program. An angular guide for adjusting the stepper-motors starting position is shown in Figure 1 c).

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a)

b) c)

Figure 1: a) Current solution b) Stepper simulation motor c) Angular guide

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2. Respiratory Physiology

This chapter explains essential theories within respiratory physiology, necessary in understanding how a breathing equipment is designed.

2.1. Diving and Effects on Body

Working in water posts a series of increased levels of complexity for humans. Performing tasks is harder due to the higher inertia of water requiring extra workload and resulting in less efficiency.

Furthermore, because of the increased pressure from surrounding water, it is important that the diver is weighted correctly to not have to perform unnecessary work adjusting pitch or roll. Moreover, the cold environment of water also affects the body negatively. If the human body core temperature reaches around 30 degrees’ Celsius unconsciousness occurs. At 25 degrees Celsius the human heart stops functioning. Furthermore, visibility and hearing is affected negatively which in turn affect the balance system. Therefore, diving equipment often features some kind of protective layers, such as wetsuits, to keep the diver warm [4].

2.2. Breathing Gas and Pressure

In this project, Pascal (Pa) and bar is utilized. Below, useful conversions are presented between water pillars and bar, equation (2.2). Equation (2.1) describes the conversion between different pressure standards. [5]

100𝑘𝑘 𝑃𝑃𝑃𝑃 = 1 𝑏𝑏𝑃𝑃𝑏𝑏 =10 𝑁𝑁

𝑐𝑐𝑐𝑐² ≈ 1𝑘𝑘𝑘𝑘

𝑐𝑐𝑐𝑐² (2.1)

𝛥𝛥1𝑐𝑐𝑏𝑏𝑃𝑃𝑏𝑏 ≡ 𝛥𝛥1𝑐𝑐𝑐𝑐 𝑤𝑤𝑃𝑃𝑤𝑤𝑤𝑤𝑏𝑏𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑃𝑃𝑏𝑏 (2.2)

There are three types of pressure differences utilized in this project. Firstly, Absolute pressure, corresponding to the total pressure-difference to vacuum. Secondly, Ambient pressure, which corresponds to the pressure of the surrounding medium, is ~1bar absolute at sea level etc. Lastly, Relative pressure which corresponds to the pressure difference between two pressures. For example, (Absolute pressure) - (Ambient pressure) [6]. A pressure of an ideal gas can be described by the ideal gas law of thermodynamics. The pressure is a function of the volume, temperature, moles of gas molecules and the type of gas molecules. The Ideal gas law is demonstrated in (2.3).

𝑃𝑃𝑃𝑃 = 𝑛𝑛𝑛𝑛𝑛𝑛 (2.3)

Where P is the pressure in [Pa] or [bar], V, Volume in [m³], n, mole of gas [mole], R, gas constant and T, Temperature in kelvin [K]. In conclusion, an increase in pressure while the volume is kept constant brings an increase in temperature and vice versa. However, in reality the pressure deviates from the ideal gas law but it can still be used as an estimation [7]. The partial pressure of a specific gas describes the specific composition's pressure at the same volume as the mixture. For example, the normal air at earth's surface has 21% oxygen and the pressure is 1atm (~1bar). 21% oxygen of 1atm is 0,21 atm. Therefore, the partial pressure of oxygen is 0,21 atm. In detail, the air composition of air at earth's surface can be seen below in Table 2.

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Table 2: Normal air composition at earth surface

Pressure Composition Substance Partial pressure of substance

1 atm

21% O2 0,21 atm

78% N2 0,78 atm

1% Other 0,01 atm

2.3. Linear and Turbulent Critical Flow

In order for gas flow to pass through different constructions, requirement calculations for hole dimensions have to be conducted. In short, Interspiro has a flow calculation software utilized to calculate hole dimensions. The software calculates the output flow and notes if it is either a linear or turbulent flow. As a result, in order to reach a desired flow rate, a program such as this can be utilized to decide the hole dimensions.

2.4. Oxygen Consumption

Chapter 2.4 discusses oxygen consumption and breathing which the diving equipment has to adapt for. Oxygen consumption is dependent on the ventilation ratio, known as volume of air breathed per oxygen consumed. On the whole, ventilation ratio follows different standards and is different for each individual. For a person in good condition the ventilation ratio is between 17 and 23. Hence, ventilation of 10L of air, results in 10L/~20=0,5L oxygen consumed. In short, the amount of air ventilated is a good estimation of oxygen consumed. Thereupon, the ventilation ratio can be utilized as an input for deciding how much distributed gas that is required in the diving equipment. However, gas compositions volumes change with the temperature and pressure as discussed in 2.2. Thereby, there are different standardized measurement methods for these. Thus, it is important to always specify which pressure and temperature that is prevailing at a specific volume. the standard measurements of those are as follow [8,4,10]:

ATPS Ambient Temperature Pressure Saturated with H2O BTPS Body Temperature Pressure Saturated with H2O STPD Standardized Temperature Pressure Dry (without H2O)

Oxygen shortage, also known as hypoxic or anoxic, is a dangerous phenomenon where the respiratory system is unable to supply enough oxygen for the body to function. Furthermore, oxygen exchange requires an oxygen partial pressure above ~ 0,073bar, which is close to the partial pressure of oxygen at the top of mount Everest (~8000m). Revealing the reason why it is such a dangerous task walking there without oxygen cylinders. At ~ 0,073bar the oxygen saturation in the blood is about 85% in contrast to 97% at normal oxygen partial pressure, which can be seen in

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Figure 2. This drop in saturation is enough for the body to die of oxygen shortage [9].On the other hand, if the partial pressure of oxygen reaches a higher concentration it can have toxic effects on the body, also known as oxygen poisoning. Exposure of high partial pressures of oxygen results in lung damage which enables body fluids to enter the lungs. As a result, these block the alveoli from exchanging the oxygen, thereupon, the person dies from oxygen shortage. [9]

Figure 2: Illustrates the saturation of oxygen in the blood and oxygen partial pressure of the air breathed Since the exchange of oxygen can only occur in the lungs, the air being in the throat, nose and mouth will not exchange oxygen for carbon dioxide. Consequently, the last bit of air that exits the lungs is also the first air that enters the lungs. This is referred to as dead space. Additionally, breathing through a mouthpiece or breathing mask further increases this dead space. Thus, it is beneficial to keep the dead space as small as possible when constructing breathing equipment as the dead space will have a lower concentration of oxygen.

2.5. Risks of High Pressures on the Human Body

The human body requires gas pressures as close to the ambient pressure as possible of which the person is present. This is because of how our lungs are designed and function. At just about 3 m water depth, the pressure difference around the lungs is so high that it is impossible for a human to take a breath of air with surface pressure. As a result, it is impossible to breathe through a snorkel at ~ 3 m water depth or deeper due to the high pressure surrounding the lungs. Furthermore, the high pressure causes a number of serious health risks for humans. For example, if the diver is not able to equalize pressure in sinuses or ear canals etc. a phenomenon called squeeze can occur.

Due to the difference in pressure without equalization, blood vessel can burst and ear canals rupture.

In short, every area where there is gas is at risk of squeeze if not equalized in pressure. On the other hand, in case a diver holds his breath (without pressure equalizing the lungs) while ascending, lung rupture can occur because of the higher pressure in the lungs compared to the ambient pressure.

The decrease of ambient pressure around the lungs makes them expand and since lungs have no sense of pain, it is important to be aware of those risks and take action accordingly, while diving [4, 8].

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Another risk when ascending from high pressure environments is decompression sickness. A phenomenon where gas bubbles are being released in the body due to the decrease in pressure. It can occur when a diver has ascended too fast and depending on where those gas releases occur they can be more or less dangerous. To avoid decompression sickness, the human body requires time to decompress. Therefore, dive tables and calculated schematics are developed to avoid decompression sickness. The dive tables inform how long can the diver stay at a depth and how fast can the diver ascend. For example, if the diver stays at a depth of 90m for 1h they have to decompress their body for 11 h 31 m to avoid decompression sickness. In cases such of long decompression times, special pressure chambers can be used to store the diver in while gradually decompressing, at the surface [4, 8].

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3. Pressure Seals and Chambers

This chapter introduces the pressure seals and chambers commonly used in diving equipment. It is beneficial for the full construction of the test machine and peripherals.

Pressure seals are used to seal pressure chambers, allowing for pressure differentials. Hence, understanding how they function is a critical step in designing a pressure chamber such as the test machine. Seals can either be stationary or dynamic seals, for example, move or stay still. Stationary seals are used to seal two chambers from leakages between each other where dynamic seals can also be used for opening and closing different pressure chambers from each other. In this project, four different seals are studied. The first one being surface sealing which occurs when two surfaces are pressured together, causing a seal. Normal types of surface seals are plastics to plastic, plastic to metal or metal to metal. Secondly, O-ring Seals, of which there are two different types, Axial and Radial O-ring seals. Axial O-ring seals seal when they are pressured against a flat surface. They have the advantage of small accelerations if bursting pressures are reached, due to the short acceleration distance between sealing and not sealing. Radial O-rings seal in the radial direction of a cylinder. They have the advantage that they often can seal on smaller radiuses of holes which results in less stress on components. However, since they seal in the radial direction, they are also able to gain acceleration if bursting pressures are present. Lastly, membranes seals, illustrated in Figure 3, are seals which seals two areas though a membrane being squeezed between. As seen in Figure 3, they can sometimes pressure against a rod. In cases such as this, the active membrane area is represented by A1. For small horizontal movements of the rod with diameter A2, this area is approximately the same. However, if the rod moves to the right or the left this area changes which can result in problems if not kept in mind when designing a rod to membrane solution. The membrane satisfies the function to create a tight seal between the chambers. To calculate the active area of a membrane A1, the pressure difference pushes on the membrane which is held back by the connection points. This is represented by the red forces arrows and can be seen in Figure 3. The force equilibrium for Figure 3 is presented in equation (3.1).

Figure 3: Illustration of Membrane sealing against a rod.

𝐹𝐹1 + 𝑃𝑃2 ⋅ 𝐴𝐴2 − 𝑃𝑃1 ⋅ 𝐴𝐴1 = 0 (3.1)

In order to construct a high pressure compartment, the most commonly used shape is a cylinder with rounded edges. Ideally, the strongest pressure compartment is a sphere, however, a sphere as the disadvantage of being hard to stack and carry. On the other hand, a cylinder is much easier to stack while at the same time allowing for withstand of high pressures without causing a critical point of stress. However, not all stress directions are equal. In fact, the radial stress is greater than the axial

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stress. Hence, it is important to calculate the radial forces that the material has to withstand. Figure 4 represents the section views of a cylinder shape, the red + and -’s represent forces due to a pressurized compartment. The symbols r represents radius, L represents the length of the cylinder and P represents pressures.

Figure 4: Cylinder stress, Radial vs Axial Forces

This phenomenon can be explained as follows. The radial forces of the cylinder are defined by equation (3.2) and equation (3.3), where 𝐹𝐹𝑝𝑝𝑝𝑝is the radial force from pressure and 𝐹𝐹𝜎𝜎𝑝𝑝 is the radial force from stress within the material.

𝐹𝐹_{𝑝𝑝𝑝𝑝} = 𝛥𝛥𝑃𝑃 ⋅ 2𝑏𝑏₁⋅ 𝐿𝐿 (3.2)

𝐹𝐹_{𝜎𝜎𝑝𝑝}= 𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟⋅ 2 ⋅ (𝑏𝑏₂− 𝑏𝑏₁) ⋅ 𝐿𝐿 (3.3)

The axial forces of the cylinder are defined by equation (3.4) and equation (3.5), where 𝐹𝐹_{𝑝𝑝𝑟𝑟}is the axial force from pressure and 𝐹𝐹𝜎𝜎𝑟𝑟 is the axial force from stress within the material.

𝐹𝐹_{𝑝𝑝𝑟𝑟} = 𝛥𝛥𝑃𝑃 ⋅ 𝑏𝑏₁²⋅ 𝜋𝜋 (3.4)

𝐹𝐹𝜎𝜎𝑟𝑟 = 𝜎𝜎𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟⋅ (𝑏𝑏22− 𝑏𝑏12) ⋅ 𝜋𝜋 (3.5)

As the cylinder is in equilibrium, 𝐹𝐹𝑝𝑝𝑝𝑝=𝐹𝐹𝜎𝜎𝑝𝑝 and 𝐹𝐹𝑝𝑝𝑟𝑟=𝐹𝐹𝜎𝜎𝑟𝑟 (3.2) and (3.3) can be rewritten to (3.6) to present 𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟.(3.4) and (3.5) can be rewritten to (3.7) to present 𝜎𝜎𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟.

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𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟= 𝛥𝛥𝑃𝑃 ⋅ 𝑏𝑏₁

𝑏𝑏2− 𝑏𝑏1 (3.6)

𝜎𝜎𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟= 𝛥𝛥𝑃𝑃 ⋅ 𝑏𝑏₁²

(𝑏𝑏₂²− 𝑏𝑏₁²) (3.7)

Consequently, the ratio between 𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 and 𝜎𝜎_{𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟}can be determined as the limes function where 𝑏𝑏₁ approaches 𝑏𝑏2 (3.8) and (3.9). Derivation can be seen in appendix A. Figure 5 represents a 3D plot where if either 𝑏𝑏1or 𝑏𝑏2decreases or increases respectively, the 𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 / 𝜎𝜎𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟 increases

𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝜎𝜎𝐴𝐴𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑏𝑏₂²− 𝑏𝑏₁²

𝑏𝑏1⋅ (𝑏𝑏2− 𝑏𝑏1) (3.8)

𝑤𝑤𝑤𝑤𝑐𝑐

𝑝𝑝1→𝑝𝑝2

𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝜎𝜎_{𝐴𝐴𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟} = 2 (3.9)

Thus, the critical stress occurs in the radial directions of cylinders with uniform thickness. Even thicker walls results in an increase of the ratio between 𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟/ 𝜎𝜎𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟, as shown in figure 5. In conclusion, when designing a gas cylinder bottle, as long as the design can withstand the radial stress, the axial stress is within safe margin. Assuming that the material thickness is uniform.

Figure 5: Plot of 𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟/ 𝜎𝜎𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟where 𝑥𝑥 = 𝑏𝑏1, 𝑦𝑦 = 𝑏𝑏2, 𝑧𝑧 = 𝜎𝜎𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟/ 𝜎𝜎𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑟𝑟

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4. The Dosage Regulator of IS-MIX

This chapter introduces the functionality of the dosage regulator in order to understand why specific tests are required and how to construct the prototype test machine.

4.1. Functionality

The dosage regulator apparent in Interspiro’s IS-MIX diving equipment transforms the pressure and flow of gas to a specific amount, suitable for the diver at a given depth. Two springs are utilized together with different valves to achieve the correct pressure combinations.

When the diver breathes, each breath moves a bellow. This bellow is connected to a thrust arm which pushes on the dosage regulator. In turn, the dosage regulator distributes more air into the system from the high pressure gas cylinders. The dosage regulator is constructed in such a way that it automatically adjusts for the ambient pressure and delivers dosage pressures accordingly.

However, on exhalation some of the air is rebreathed and the rest is dumped. As a result, longer diving times can be achieved compared to open systems, where all breathed out gas is dumped. A schematic picture of the dosage regulators function can be seen in Figure 6. The blue colored surfaces represent moving parts. The red colored arrow represents the force of the thrust arm. P0

represents ambient pressure which depends on the depth. Pstear represents steering pressure which regulates how much Pdos differs from the P0. Pdos represents dosage pressure which is the pressure delivered to the diver. Pⁱⁿrepresents the incoming pressure which is 9 bar above ambient pressure.

Farm represents the force from the thrust arm pressuring against the dosage regulator

Figure 6: Illustration of full overview of the dosage regulator

Each chamber has a desired pressure at specific depth. Therefore, spring constants and areas between different chambers are designed to achieve desired pressures. A section view of the dosage regulator can be seen in Figure 7, where the thrust arm and trust arm cup is seen on the far left. F1 represents the force from spring 1 which can be adjusted by the pressure of the thrust arm.

Consequently, resulting in a change in Pstear which correlates to a pressure for Pdos. F2 represents the spring force from spring 2. A1-A5 represents the different sealing areas.

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Figure 7: Section view of Interspiro’s Dosage regulator for IS-MIX

The force equilibriums can thereby be set up as defined in equation (4.1), (4.2) and (4.3). In detail, the force equilibrium changes depending on if the dosage regulator is filling or emptying gas to the diver, as can be described in equation (4.2) and (4.3).

𝐹𝐹1 + 𝑃𝑃₀⋅ 𝐴𝐴1 − 𝑃𝑃₀⋅ 𝐴𝐴2 − 𝑃𝑃_{𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝}(𝐴𝐴1 − 𝐴𝐴2) = 0 (4.1) 𝐹𝐹2𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝐹𝐹𝐹𝐹+ 𝑃𝑃_{𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝}⋅ 𝐴𝐴4 − 𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑}⋅ 𝐴𝐴4 + 𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑}⋅ 𝐴𝐴5 − 𝑃𝑃_{𝑟𝑟𝐹𝐹}⋅ 𝐴𝐴5 = 0 (4.2)

𝐹𝐹2𝐸𝐸𝐸𝐸𝑝𝑝𝑆𝑆𝐸𝐸𝑟𝑟𝐹𝐹𝐹𝐹+ 𝑃𝑃_{𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝}⋅ (𝐴𝐴4 − 𝐴𝐴3) − 𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑}⋅ (𝐴𝐴4 − 𝐴𝐴3) = 0 (4.3)

When the dosage regulator is set up for filling breathing gas, the schematic illustration can be redrawn as in Figure 8. Thus, the blue moving parts allows the 𝑃𝑃𝑟𝑟𝐹𝐹to flow into 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 when 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 is dropping. Moreover, 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 is sealed off from 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝when filling occurs.

Figure 8: Illustration of filling the dosage regulator

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In the same way, the dosage regulator illustration can be redrawn for emptying, as seen in Figure 9.

In this case, 𝑃𝑃_{𝑟𝑟𝐹𝐹} is completely sealed off from the rest of the regulator and 𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑} can flow into 𝑃𝑃_{𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝} and 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝 to 𝑃𝑃0.

Figure 9: Illustration of emptying the dosage regulator

Furthermore, the different spring forces 𝐹𝐹1 and 𝐹𝐹2, as seen in figure 7, can be calculated from the deformation of spring 1 and 2. The spring force is a function of deformation 𝛥𝛥𝑥𝑥 and a spring constant 𝑐𝑐 which is 𝑐𝑐₁ and 𝑐𝑐2 for spring 1 and 2 respectively. 𝐹𝐹2 is represented in equation (4.4) and (4.5) for filling and emptying respectively. 𝐹𝐹1 is represented in equation (4.6) and is a function of the thrust arm’s pressing force, see figure 7.

𝐹𝐹2𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝐹𝐹𝐹𝐹 ≈ 𝑐𝑐₂⋅ 𝛥𝛥𝑥𝑥𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝐹𝐹𝐹𝐹 (4.4)

𝐹𝐹2𝐸𝐸𝐸𝐸𝑝𝑝𝑆𝑆𝐸𝐸𝑟𝑟𝐹𝐹𝐹𝐹≈ 𝑐𝑐₂⋅ 𝛥𝛥𝑥𝑥𝐸𝐸𝐸𝐸𝑝𝑝𝑆𝑆𝐸𝐸𝑟𝑟𝐹𝐹𝐹𝐹 (4.5)

𝐹𝐹1 ≈ 𝑐𝑐1⋅ 𝛥𝛥𝑥𝑥 (4.6)

In conclusion, through the reformulation of equation (4.1) 𝑃𝑃_{𝑑𝑑𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝} can be expressed as equation (4.7).

𝑃𝑃_{𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝}(𝑃𝑃₀) =𝐹𝐹1 + 𝑃𝑃0⋅ 𝐴𝐴1 − 𝑃𝑃0⋅ 𝐴𝐴2

𝐴𝐴1 − 𝐴𝐴2 =𝐹𝐹1 + 𝑃𝑃0⋅ (𝐴𝐴1 − 𝐴𝐴2)

𝐴𝐴1 − 𝐴𝐴2 = 𝐹𝐹1

𝐴𝐴1 − 𝐴𝐴2 + 𝑃𝑃⁰ (4.7)

Likewise, 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 can be reformulated from equation (4.2) and (4.3). Notice how 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 represents filling in equation (4.8) and emptying in equation (4.9) .

𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 𝑓𝑓𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝐹𝐹𝐹𝐹 =𝐹𝐹2𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝐹𝐹𝐹𝐹+ 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝⋅ 𝐴𝐴4 − 𝑃𝑃𝑟𝑟𝐹𝐹⋅ 𝐴𝐴5

𝐴𝐴3 − 𝐴𝐴1 (4.8)

𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 𝑆𝑆𝐸𝐸𝑝𝑝𝑆𝑆𝐸𝐸𝑟𝑟𝐹𝐹𝐹𝐹=𝐹𝐹2𝐸𝐸𝐸𝐸𝑝𝑝𝑆𝑆𝐸𝐸𝑟𝑟𝐹𝐹𝐹𝐹 + 𝑃𝑃_{𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝}⋅ (𝐴𝐴4 − 𝐴𝐴3)

𝐴𝐴4 − 𝐴𝐴3 =𝐹𝐹4𝐸𝐸𝐸𝐸𝑝𝑝𝑆𝑆𝐸𝐸𝑟𝑟𝐹𝐹𝐹𝐹

𝐴𝐴4 − 𝐴𝐴3 + 𝑃𝑃^{𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝} (4.9) In conclusion, 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝 is a function of 𝑃𝑃0 and F1, 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 is a function of 𝑃𝑃𝑑𝑑𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝 and 𝑃𝑃𝑟𝑟𝐹𝐹. If 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 𝑓𝑓𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝐹𝐹𝐹𝐹 and

𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 𝑆𝑆𝐸𝐸𝑝𝑝𝑆𝑆𝐸𝐸𝑟𝑟𝐹𝐹𝐹𝐹 are plotted as functions of 𝑃𝑃_{𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝}, the hysteresis can be seen as the difference between

the two lines, illustrated in Figure 10. The blue line represents 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 𝑆𝑆𝐸𝐸𝑝𝑝𝑆𝑆𝐸𝐸𝑟𝑟𝐹𝐹𝐹𝐹 and is always above the red line 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 𝑓𝑓𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝐹𝐹𝐹𝐹. Hysteresis is a phenomenon where there is a lag between the cause of an effect

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and the property actually changing [10]. In this case, there is a lag between Pdos filling and Pdos emptying. Consequently, the dosage regulator can be in a third state of neither filling or emptying. As a result, both the valve for filling and emptying are closed between the lines, a necessity for the dosage regulator to follow breaths of a diver. However, in order for the dosage regulator to open and close for filling and emptying at the correct pressures with the correct hysteresis it is important to have it set up correctly. In short, the pressure of 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 will start to fill from 𝑃𝑃𝑟𝑟𝐹𝐹 if it drops and empty out if it rises to 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝.

Figure 10: Hysteresis plot of 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 Filling and Emptying at different 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑝𝑝pressures

4.2. Dosage Regulator Control

The thrust arm assembly, figure 11, is built into the diving equipment and the housing of the dosage regulator assembly can be seen in figure 12. The function of the assembly is to regulate how much the thrust arm pressures on the dosage regulator according to the volume of air breathed. The thrust arm is held in place by a cup, the cup is held in position with a setting screw that can be loosened in order to adjust the height of the cup. This setting affects how the dosage regulator will perform. The cup is fastened to the red axis illustrated in Figure 12, that holds the bellows and will follow the breathing patterns of the diver. Consequently, the thrust arm is directly dependent on the bellow- movement, in other words, the volume of the breath taken. Furthermore, the geometry of the thrust arm cup enables the thrust arm to rotate, a necessity as the thrust arm is connected to a point, collinear with the dosage regulator.

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Figure 11: The thrust arm and thrust arm cup

The model of the thrust arm assembly is portrayed in a trigonometric geometry for a calculation of how rotational movement from the bellow translates to axial movement for the dosage regulator. By analyzing the trigonometric calculations of the thrust arm, the axial positions can be calculated. The maximum height of the thrust arm is 18 mm and the minimum height is 11,5 mm. Those settings correspond to different linear movements depending on the angle of the bellows position. The bellow can move from 0-24 degrees, which translates to 0-4,5L at surface pressure. In Figure 12 a), the bellow is empty, and thus the red arm (which is connected to the bellow) is in its lowest position. In Figure 12 b), the bellow is filled and thus the red arm is in its highest position. Consequently, the thrust arm is pushing at maximum in Figure 12 a) and minimum in Figure 12 b).

a) b)

Figure 12: Dosage regulator housing in IS-MIX. a) Emptied bellow, b) Filled Bellow.

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4.3. Steady State of Oxygen Concentration in Rebreathers

This chapter explains how a steady state of oxygen concentration can be achieved in rebreathers, a fascinating construction which allows longer diving times. In conclusion, this is one of the reasons the dosage regulator has to be tested.

When breathing in a semi-closed rebreather, such as IS-MIX, new gas is being distributed with each new breath. IS-MIX is constructed in such a way that the amount of new gas being distributed into the system corresponds to the amount of oxygen consumed. Since the human body can only consume around 5% of the oxygen in a normal breath, not much new gas is required to keep the oxygen levels stable [11]. Therefore, some of the gas that is already in the system reenters the lungs in a rebreather. This re-breathed air has a lower oxygen concentration than that of the new gas dosage. However, in the lungs, the new gas dosage and the old gas is mixed. Furthermore, after each breath taken, some of the breathed out air is dumped from the system. The remaining gas then passes through an absorber which absorbs the carbon dioxide exhaled. In conclusion, after some time, this leads to a steady state for the amount of oxygen in the breathing system. As a result, when the steady state of oxygen consumption is reached, the oxygen concentration in the system during breathing stabilizes [11].

A steady state is reached when equation (4.10) is satisfied. K is Respiratory Minute Volume per L Oxygen consumed, equation (4.11). The 𝐶𝐶𝐶𝐶2 exhaled is absorbed in an absorber and transformed to water and heat.

{𝐴𝐴𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝑛𝑛𝑤𝑤𝑤𝑤 𝐶𝐶2𝑤𝑤𝑛𝑛𝑤𝑤𝑤𝑤𝑏𝑏𝑤𝑤𝑒𝑒} = {𝐴𝐴𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝐶𝐶2 𝑤𝑤𝑛𝑛 𝑤𝑤ℎ𝑤𝑤 𝑠𝑠𝑦𝑦𝑠𝑠𝑤𝑤𝑤𝑤𝑐𝑐} + {𝐴𝐴𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝐶𝐶2𝑐𝑐𝐴𝐴𝑛𝑛𝑠𝑠𝐴𝐴𝑐𝑐𝑤𝑤𝑒𝑒} (4.10)

𝐾𝐾 = 𝑛𝑛𝑅𝑅𝑃𝑃/𝐿𝐿 (4.11)

This can be reformulated assuming that the temperature is held constant through the use of the ideal gas law as discussed in chapter 2.2. Equation (4.12), (4.13), (4.14) and (4.15) describes this reformulation, where: 𝑐𝑐_𝑂𝑂₂ 𝑑𝑑𝐸𝐸𝑑𝑑𝑆𝑆𝑆𝑆𝐸𝐸 is Oxygen concentration of the system gas [%], 𝑐𝑐_𝑂𝑂₂ 𝐹𝐹𝑆𝑆𝑛𝑛 𝐹𝐹𝑟𝑟𝑑𝑑 is Oxygen concentration of the new gas [%], 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 is the Dosage volume [L], 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 is the dosage pressure [Bar],

𝑃𝑃𝑑𝑑𝑠𝑠𝑝𝑝 is the Surrounding Pressure [Bar], 𝑛𝑛𝑅𝑅𝑃𝑃 is the Respiratory Minute Volume [L/min].

{𝐴𝐴𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝑛𝑛𝑤𝑤𝑤𝑤 𝐶𝐶2𝑤𝑤𝑛𝑛𝑤𝑤𝑤𝑤𝑏𝑏𝑤𝑤𝑒𝑒} = 𝑐𝑐𝑂𝑂₂ 𝐹𝐹𝑆𝑆𝑛𝑛 𝐹𝐹𝑟𝑟𝑑𝑑⋅ 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑⋅ 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑 (4.12)

{𝐴𝐴𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝐶𝐶2 𝑤𝑤𝑤𝑤𝑙𝑙𝑤𝑤 𝑤𝑤𝑛𝑛 𝑠𝑠𝑦𝑦𝑠𝑠𝑤𝑤𝑤𝑤𝑐𝑐} = 𝑐𝑐𝑂𝑂₂ 𝑑𝑑𝐸𝐸𝑑𝑑𝑆𝑆𝑆𝑆𝐸𝐸⋅ (𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑⋅ 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑−𝑛𝑛𝑅𝑅𝑃𝑃

𝐾𝐾 ⋅ 𝑃𝑃^{𝑑𝑑𝑠𝑠𝑝𝑝}) (4.13) {𝐴𝐴𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝐶𝐶₂𝑐𝑐𝐴𝐴𝑛𝑛𝑠𝑠𝐴𝐴𝑐𝑐𝑤𝑤𝑒𝑒} =𝑛𝑛𝑅𝑅𝑃𝑃

𝐾𝐾 ⋅ 𝑃𝑃^{𝑑𝑑𝑠𝑠𝑝𝑝} (4.14)

Thus, (4.12), (4.13) and (4.14) can be combined with (4.10) to formulate (4.15)

𝑐𝑐_𝑂𝑂₂ 𝐹𝐹𝑆𝑆𝑛𝑛 𝐹𝐹𝑟𝑟𝑑𝑑⋅ 𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑}⋅ 𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑}= 𝑐𝑐_𝑂𝑂₂ 𝑑𝑑𝐸𝐸𝑑𝑑𝑆𝑆𝑆𝑆𝐸𝐸⋅ (𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑}⋅ 𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑}−𝑛𝑛𝑅𝑅𝑃𝑃

𝐾𝐾 ⋅ 𝑃𝑃^{𝑑𝑑𝑠𝑠𝑝𝑝}) +𝑛𝑛𝑅𝑅𝑃𝑃

𝐾𝐾 ⋅ 𝑃𝑃^{𝑑𝑑𝑠𝑠𝑝𝑝} (4.15)

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This retraces to concentration of 𝐶𝐶2 in the system as described in equation (4.16).

{𝐶𝐶𝐴𝐴𝑛𝑛𝑐𝑐𝑤𝑤𝑛𝑛𝑤𝑤𝑏𝑏𝑃𝑃𝑤𝑤𝑤𝑤𝐴𝐴𝑛𝑛 𝐶𝐶₂ 𝑤𝑤𝑛𝑛 𝑤𝑤ℎ𝑤𝑤 𝑠𝑠𝑦𝑦𝑠𝑠𝑤𝑤𝑤𝑤𝑐𝑐} = {𝐴𝐴𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝐴𝐴𝑙𝑙 𝐶𝐶2 𝑤𝑤𝑛𝑛 𝑤𝑤ℎ𝑤𝑤 𝑠𝑠𝑦𝑦𝑠𝑠𝑤𝑤𝑤𝑤𝑐𝑐}

{𝑛𝑛𝐴𝐴𝑤𝑤𝑃𝑃𝑤𝑤 𝑃𝑃𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝑘𝑘𝑃𝑃𝑠𝑠 𝑤𝑤𝑛𝑛 𝑤𝑤ℎ𝑤𝑤 𝑠𝑠𝑦𝑦𝑠𝑠𝑤𝑤𝑤𝑤𝑐𝑐} =

={𝐴𝐴𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝑛𝑛𝑤𝑤𝑤𝑤 𝐶𝐶₂𝑤𝑤𝑛𝑛𝑤𝑤𝑤𝑤𝑏𝑏𝑤𝑤𝑒𝑒} − {𝐴𝐴𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝐶𝐶₂𝑐𝑐𝐴𝐴𝑛𝑛𝑠𝑠𝐴𝐴𝑐𝑐𝑤𝑤𝑒𝑒}

{𝑛𝑛𝐴𝐴𝑤𝑤𝑃𝑃𝑤𝑤 𝑃𝑃𝑐𝑐𝐴𝐴𝐴𝐴𝑛𝑛𝑤𝑤 𝐴𝐴𝑙𝑙 𝑘𝑘𝑃𝑃𝑠𝑠 𝑤𝑤𝑛𝑛 𝑤𝑤ℎ𝑤𝑤 𝑠𝑠𝑦𝑦𝑠𝑠𝑤𝑤𝑤𝑤𝑐𝑐}

(4.16)

Consequently, the steady state of the oxygen is calculated through equation (4.17).

𝑐𝑐_𝑂𝑂₂ 𝑑𝑑𝐸𝐸𝑑𝑑𝑆𝑆𝑆𝑆𝐸𝐸=𝑐𝑐𝑂𝑂₂ 𝐹𝐹𝑆𝑆𝑛𝑛 𝐹𝐹𝑟𝑟𝑑𝑑⋅ 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑⋅ 𝑃𝑃𝑟𝑟𝑑𝑑𝑑𝑑− 𝑛𝑛𝑅𝑅𝑃𝑃𝐾𝐾 ⋅ 𝑃𝑃^{𝑑𝑑𝑠𝑠𝑝𝑝} 𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑}⋅ 𝑃𝑃_{𝑟𝑟𝑑𝑑𝑑𝑑}− 𝑛𝑛𝑅𝑅𝑃𝑃𝐾𝐾 ⋅ 𝑃𝑃^{𝑑𝑑𝑠𝑠𝑝𝑝}

(4.17)

If the test machine prototype can provide an accurate evaluation of the dosage regulator, much time can be saved as setting changes consequently are more accurate.

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5. Concept Generation

This chapter describes different concept ideas. Creating multiple solution suggestions in order to widen the view.

5.1. Desired Test Features

First of all, the dosage regulator's ability to provide a static nominal pressure difference is desired.

Secondly, the dosage's ability to perform correct differential pressures during simulated breathing at different RMV (rated minute ventilation) should be evaluated. Lastly, an evaluation of how the dosage regulator performs the same tests at different ambient pressures (diving depths) is desired. In theory, all of which can be achieved by a motor, pressure chamber, pressure regulators and pressure transmitters.

5.2. Simulation Strategy

In order to simulate breathing in the test machine, some approximations have to be made. A commonly utilized simulation of breaths is a sinus curve with alternating frequency and amplitude.

This model describes the volume of air in the bellow as a function of time. In IS-MIX assembly the bellow is connected to the thrust arm which pushes on the dosage regulator according to the change of volume in the bellow. However, this pushing motion does not have to follow reality and can be altered in order to find a more optimized strategy. Two different concepts are thereby created. In short, the breathing simulation could either focus on simulating the bellow movement or the thrust arm movement.

By simulating the bellow movement, the test machine will have the advantage of being close to the diving equipment solution. The motor is connected to the rotational axis of the bellow and stimulates breathing by rotating it. However, a con of this solution is the amount of settings that has to be done between each run. Furthermore, a lock for the thrust arm to not fall out of the thrust arm holder would be required to create. In short, the dosage regulator and the thrust arm have one setting screw each.

The assembly of the current solution has to be taken apart and put together again before the next test can begin. Preferably an implementation of a quick and easy tool connection is beneficial as it would enable the user to change the settings from the outside of the test machine. However, implementing a solution such as this requires multiple extra parts and seals. An advantage of simulating the bellow movement is that it is possible to utilize a normal rotary motor which can alter between 0-30 degrees with fine accuracy. Furthermore, since the motor is simulating the bellow movement it can be approximated to the normal sinus curve movement of breaths. Many servo and stepper are available with programmable rotational options. In Figure 13, the bellow movement is illustrated.

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Figure 13: Illustration of bellow movement

By simulating the thrust arm movement, the main advantage is that settings can be altered in the control program. As a result, setup time can be greatly reduced. However, it increases the requirements on the motor and control program to be able to perform a linear movement with sufficient accuracy for adjustments of settings. It requires calculations as to how the bellow movement translates to thrust arm positions at different settings. An advantage is that the number of required parts is minimized. At the same time, it requires a high level of precision and repeatability when applying movement at the thrust arm directly. Figure 14 illustrates how the thrust arm is moving due to the bellow movement.

Figure 14: Illustration of thrust arm movement

In simulating the bellow movement, a rotational motor would be preferred. It can rotate the thrust arm holder axis back and forth, as if it is the bellow moving it. On the other hand, in simulating the thrust arm movement a linear motor would be preferred as the motion of the thrust arm is linear. In Figure 15, A and B represents settings that can be adjusted for the dosage regulator. C represents the thrust arm movement to control the regulator. B is the height adjustment of the thrust arm cup and A represents the offset distance of the dosage regulator. In the linear motor solution, both A and B are simulated as linear motions. Notice how B is much shorter for the linear motor. This is due to the fact that the height of the thrust arm cup does not affect the horizontal linear motion much. During the working process one of these motor types should be selected.

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a) b) Figure 15: a) Rotational motor b) Linear motors

5.3. Stepper vs Servo Motors

Two different types of electrical motors are taken into consideration, a servo or a stepper motor. In short, they are both reliable types of motors, relatively easy to control while providing good accuracy.

Stepper motors are often cheaper though not as strong as servo motors. However, they often lack position feedback, resulting in that the position has to be calibrated on startup. Servo motors on the other hand often include position feedback and therefore no need for calibration on startup is required [12].

5.4. Thrust Arm Embedded in Test Machine

The main aim for the thrust arm solution is to allow for quick and easy adjustment of settings while at the same time be a robust and durable construction. Furthermore, the thrust arm should feature a bit of flex in during movement as the collinearity of the dosage regulator central axis and the thrust arm is not always collinear. Lastly, the thrust arm should be integrated within the test machine as it would increase the test setup times.

Figure 16 illustrates a thrust arm concept. The thrust arm on the top can rotate around an axis and is balanced by the counterweight on the backside. The design is made with the mass centrum (yellow and black circle) in mind, it is located vertically beneath the centrum axis. Therefore, the arm returns to a horizontal neutral position when hanging free. Enabling it to align easily with the dosage regulator. Furthermore, the height of the thrust arm can be adjusted by a screw and a guide pin, resulting in the thrust arm always pointing in the correct direction. However, a downside of this solution is that the construction does not allow alignment in the horizontal plane. If the dosage regulator is not perfectly concentric to the thrust arm this might cause shear forces.

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Figure 16: Thrust Arm holder concepts to keep the thrust arm in place between setups.

5.5. Motor Placement

The advantages and downsides of integrating the motor inside versus outside of the pressure chamber is considered. The main advantage of placing the motor inside of the pressure chamber is that a linear motor will not have to overcome this pressure differences. The disadvantage is that the motor has to be electrically connected to the outside through a sealed connection from the pressure chamber. As a result, all the cables have to be sealed. Furthermore, there is a small risk that the motor might not be able to cope with the higher ambient pressure.

On the other hand, the motor can be placed outside of the pressure chamber. Resulting in the advantage that no sealed cables are required and the motor won't be affected by the ambient pressure. However, the axis into the pressure chamber has to be sealed. Furthermore, a linear motor will therefore be forced to pressure against different depth pressures. Resulting in a possible risk of errors in the simulated breathing curves at different depths. The comparison of breathing curves at different depths is one of the more important evaluation tests of the test machine.

5.6. Test Machine Housing

The housing concept generation is created while following the requirement factors for the test machine. Furthermore, factors such as ease of production, weight and price are valued. In conclusion, the shape and material depends on what is available from producers and can fulfill the requirements.

Two main body shapes are considered, cylindrical housing vs square housing. Creating the housing as a square shape has the advantage of enabling the test machine to stand on a flat table without the need of legs etc. It enables easy bore operations to reach into the dosage regulator or openings for a rotational motor axis etc. On the other hand, a circular house has the advantage of being favorable for tuning operations in production, beneficial for the interior design. Furthermore, it can be beneficial for a linear motor design since it allows for “easier” collinearities throughout the cylinder.

Both of the two shapes concepts feature a cutout for the dosage regulator to fit inside and canals for different pressures to be measured and or transported.

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Aluminum is suggested as the preferred material of choice for the housing. It has the advantages of being both easy to cut and relatively lightweight, compared to brass or steel. On another note, brass is also considered a possibility, however, it is denser than aluminum which would result in a heavier test machine. Lastly, Acetal Copolymer is considered, also known as POM-C. It is a lightweight engineered plastic, though not as strong as aluminum or brass which would result in a larger test machine construction.

5.7. Locking Mechanics

Different lock mechanisms for keeping the dosage regulator in place during tests are considered.

The lid of the test machine could be set up as a wide screw. This would enable an easy to understand solution. However, a screw lid could be undone even if the high pressure is on. Resulting in a potential risk. Therefore, a warning or a secondary lock function has to be implemented. On the other hand, an advantage of the screw lid is that it only requires one O-ring. In Figure 17 an illustration of a screw lock concept can be seen.

a) b)

Figure 17: Illustration of a screw lid a) open b) closed

Another strategy is to lock a plug with a pin, illustrated in Figure 18. This lock has the advantage of being easy to understand and fast to lock and unlock. However, just as the screw lock, it has the downside of being able to unlock even when the pressure is on. Furthermore, it requires more parts than the screw lock.

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a) b)

Figure 18: Illustration of a plug and pin lid a) open b) closed

The third lid considered is a lock which twists into a locked state, Figure 19. It achieves this either by grappling around knobs or running pins into slots and then twisting. This lid has the advantage of being easy and fast to lock and unlock. However, implementing a smart and easy way to stop operators from undoing the twist lock might require a more complex implementation.

a) b)

Figure 19: Illustration of a twist lid a) open b) closed

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5.8. Program for Control

The control program should allow programming of simulated breathing curves for either bellow or thrust arm movement, in order to fulfil the requirements of the test machine. Furthermore, it should have the ability to alter the RMV (rated minute ventilation), in other words, breathing frequency and amplitude of the simulation. Moreover, the ability to adjust the breathing curves depending on the diving depth. Optionally, the program should also feature the ability to store different amplitudes and frequencies to use as thrust arm settings and settings for dosage regulator position.

In current solutions, breathing simulators have been controlled by pulses through the program LabVIEW at Interspiro. LabVIEW is a program enabling creation of clear user interfaces and representations of inputs and outputs. Therefore, a motor controlled by pulses, which can be controlled through LabVIEW, would be preferred as no new simulation program is required.

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6. Concept Specialization

This chapter describes which concepts are developed and selected.

6.1. Orientation of Motor

Due to the advantage and ease of settings adjustments, execution speed and automation possibilities, simulating the thrust arm movement with a linear motor is selected as the concept specialization for the motor orientation. This concept enables the highest amount of automation as it can adjust for dosage regulator settings by adjusting start positions and movement patterns.

6.2. Motor Calculations

In order for the motor to be suitable for the application, estimated specification calculations are performed. Hence, an excel ark with the required stroke, position repeatability, incremental movement, lost motion, axial forces, speed and acceleration is calculated. In detail, this is presented in the Appendix B Motor Calculations and specifications. The thrust arms trigonometric geometry affects how the bellow movement translates to linear positions for the thrust arm. In detail, the height settings of the thrust arm cup can be adjusted which will result in requirements on the motor calculations.

Firstly, the thrust arm position at L (liter) breath is calculated from the thrust arm geometry and the height setting of the thrust arm cup (~11,5-18mm). During a breath size of 0-4L the bellow moves 0- 24 degrees (at surface pressure). Consequently, the position of the thrust arm per L breath is calculated, see Appendix B for greater detail. As seen in the graph of figure 20, the thrust arm step length is affected by the thrust arm cup height and the size of breath. In conclusion, these positions can be seen as a requirement for the motor to be able to simulate.

Figure 20: Thrust arm movement depending on different thrust arm heights

Automatic Test Machine for Rebreather

Automatic Test Machine for Rebreather

Breathing patterns simulations of dosage regulators at depths down to 120m in water CARL BÜHLMANN

Automatic Test Machine for Rebreather

Breathing patterns simulations of dosage regulators at depths down to

120m in water

Carl Bühlmann

Abstract

Sammanfattning

Acknowledgements

Table of Contents

List of Abbreviation

1. Introduction

1.1. Background

1.2. The Company Interspiro

1.3. Project Definition

1.4. Driving Forces for the Project

1.5. Product Requirements

1.6. Method

1.7. Current Test Machine

2. Respiratory Physiology

2.1. Diving and Effects on Body

2.2. Breathing Gas and Pressure

2.3. Linear and Turbulent Critical Flow

2.4. Oxygen Consumption

2.5. Risks of High Pressures on the Human Body

3. Pressure Seals and Chambers

4. The Dosage Regulator of IS-MIX

4.1. Functionality

4.2. Dosage Regulator Control

4.3. Steady State of Oxygen Concentration in Rebreathers

5. Concept Generation

5.1. Desired Test Features

5.2. Simulation Strategy

5.3. Stepper vs Servo Motors

5.4. Thrust Arm Embedded in Test Machine

5.5. Motor Placement

5.6. Test Machine Housing

5.7. Locking Mechanics

5.8. Program for Control

6. Concept Specialization

6.1. Orientation of Motor

6.2. Motor Calculations