Sliding bearings in heavy duty engines
- A bearing wear comparative study
Mathias Anslin
Alexander Bölke
Master of Science Thesis Stockholm, Sweden 2017
Sliding bearings in heavy duty engines
- A bearing wear comparative study
Mathias Anslin
Alexander Bölke
Master of Science Thesis MMK 2017:88 MKN 190 KTH Industrial Engineering and Management
Machine Design SE-100 44 STOCKHOLM
Examensarbete MMK 2017:88 MKN 190
Glidlager i tunga motorer – En jämförande studie om lagernötning
Mathias Anslin Alexander Bölke Godkänt 2017-06-09 Examinator Ulf Sellgren Handledare Stefan Björklund Uppdragsgivare Scania CV AB Kontaktperson Christoffer Rindeström Petter Kylefors
Sammanfattning
Start-stoppsystem används idag i stor utsträckning inom bilindustrin men har ännu inte blivit implementerat fullt ut i den tunga fordonsindustrin. De större belastningarna som uppstår i motorn leder till överdrivet slitage på de hydrodynamiska glidlagren under start och stopp och har en tydlig inverkan på maskinens livslängd och pålitlighet.
Detta examensarbete har innefattat en jämförande studie om hur olika axelytor påverkar nötningen av hydrodynamiska glidlager vid start och stoppförhållanden. Målet var att se ifall man kan lyckas förlänga lagrets livslängd genom att genomföra mindre förändringar av axelytan. Detta har utförts genom att omkonstruera en befintlig start-stopprigg, ökat oljesystemets driftstemperatur till 90°C för att ge en mer exakt beskrivning av den riktiga lagermiljön, för att sedan ha utfört en serie start och stopp experiment. Resultaten från experimenten visade tydligt att en mer polerad axelyta minskar lagerslitningen avsevärt under start och stopp. Det noterades också att en mer polerad axelyta ger fullfilmssörjning vid en lägre axelrotationshastighet, varvid axeln och lagerytorna separeras.
Master of Science Thesis MMK 2017:88 MKN 190
Sliding bearings in heavy duty engines - A bearing wear comparative study
Mathias Anslin Alexander Bölke Approved 2017-06-09 Examiner Ulf Sellgren Supervisor Stefan Björklund Commissioner Scania CV AB Contact person Christoffer Rindeström Petter Kylefors
Abstract
Start-stop systems are widely used in the car industry today but have not yet been fully implemented in the heavy-duty vehicle industry. The greater loads arising in the engines leads to excessive wear of the hydrodynamic bearings during starts and stops which has a distinct impact on the machine´s lifetime performance and reliability.
This master thesis involves a comparative study of how different surface topographies of a shaft affects hydrodynamic bearing wear during start and stop conditions. The objective was to see if one can extend the bearing lifetime by doing minor changes to the shaft surface. This has been done by redesigning an existing start-stop test rig, increasing its operating system oil temperature to 90°C to provide a more accurate description of the bearing environment, to be able to conduct a series of start-stop cycling experiments. Upon examination of the experiment results, it becomes clear that a more polished surface of the shaft does reduce bearing wear significantly during starts and stops. It was also noticed that a more polished shaft surface does reach full-film lubrication at a lower rotational speed of the shaft, separating the shaft and the bearing surfaces.
Foreword
This part acknowledges people that helped to make this master thesis possible.
We would like to start this report by giving a big thanks to our great supervisors Christoffer Rindeström and Petter Kylefors at Scania, who have been guiding and assisting us at any time during the project. We also want to thank our supervisor Stefan Björklund at KTH who always inspires and guides in the right direction.
We want to give a great thanks to all the other people at Scania who showed their interest and supported us during the project, especially Lars Hammerström, Hubert Herbst, Henrik Mårtensson and Anna Andersson.
Finally, would we like to thank our examiner Ulf Sellgren for helping us with guidance of the structure in the project and the report.
Mathias Anslin Alexander Bölke Stockholm, June 2017
Nomenclature
This part describes the designations and abbreviations used in the report.
Designations
𝐴 Area [m2] 𝐸 Correction factor [-] 𝜌 Density [kg/m3] 𝑑 Diameter [m] 𝐷 Diameter [m] 𝜀 Emissivity coefficient [-] 𝐸 Energy [J] 𝑄 Heat [J] 𝐶 Heat capacity [J/K]𝑞 Heat per unit time [W]
𝐿 Length [m]
𝑚 Mass [kg]
𝑚̇ Mass flow rate [kg/s]
𝑠 Safety factor [-]
𝑐 Specific heat capacity [J/kgK]
𝜎 Stefan-Boltzmann constant [W/m2K4] 𝑇 Temperature [C or K] 𝑘 Thermal conductivity [W/mK] 𝑡 Thickness [m] 𝑆 Thickness of insulation [m] 𝑡 Time [s] n Vector length [-] 𝑣 Velocity [m/s]
𝑉̇ Volumetric flow rate [m3/s]
Abbreviations
3D Three dimensional
CMM Coordinate measuring machine
KTH “Kungliga tekniska högskolan”- Royal Institute of Technology
DC Direct current
e.g. For example
i.g. Namely
PID Proportional-integral-derivative
IGES Initial graphics exchange specification
Rpm Revolutions per minute
ISF Isotropic super finishing
3CD Controlled current chemical deburring
lr Sampling length
ln Evaluation length
Ra Arithmetic average roughness
Rq Root mean-square
Rp Maximum height of peak
Rv Maximum depth of valley
Rt Maximum peak-to-valley distance
Rz Mean value of the five highest points
Rk Core roughness depth
Rpk Reduced peak height
Rvk Reduced valley depth
MR1 Material ratio 1
Table of contents
Contents
1. Introduction ... 1 1.1. Background ... 1 1.2. Purpose ... 2 1.3. Specification of objectives ... 2 1.4. Delimitations ... 2 1.5. Method ... 2 2. Requirements ... 5 2.1. Expected results ... 6 Design Phase ... 6 3. Frame of reference ... 7 3.1. Bearings ... 7 3.1.1. Hydrodynamic bearing ... 7 3.1.2. Lubrication regimes ... 83.1.3. Scania bearings used at start-stop test rig ... 8
3.2. Two-body wear mechanisms ... 10
3.3. Surface parameters ... 12
3.4. Surface treatment ... 15
3.4.1. Isotropic Super Finishing- ISF ... 15
3.4.2. 3CD ... 15
3.5. Acquiring surface parameters and measuring wear ... 17
3.6. Thermodynamics ... 19
3.6.1. Thermodynamic system ... 19
3.6.2. Incompressible steady state flow ... 19
3.6.3. Steady state and thermal equilibrium ... 20
3.6.4. Energy of a system ... 20
3.6.5. Specific heat capacity ... 21
3.6.6. Conduction ... 21
3.6.7. Thermal radiation ... 21
3.6.8. Radiation losses for insulated objects ... 22
3.7. Heating element ... 23
3.7.2. Self-regulating heating cables ... 24
3.7.3. Heating Tape ... 24
3.8. Temperature regulation ... 25
3.8.1. Proportional-integral-derivative controller ... 25
3.8.2. On-off regulation ... 25
3.9. Start-stop journal bearing test rig ... 26
4. Implementation ... 29
4.1. Estimation of needed heat ... 29
4.1.1. Test rig before redesign ... 29
4.1.2. Defining the system ... 30
4.1.3. Estimating heat needed ... 31
4.1.4. Estimating losses in the system ... 32
4.1.5. Estimating heating time ... 34
4.1.6. Heating pipe flow ... 36
4.2. Concept development ... 38
4.2.1. Extended pipe concept ... 39
4.2.2. Chamber Concept ... 40
4.3. Concept evaluation ... 42
4.4. Further development of chosen concept ... 43
4.5. Manufacturing ... 45 4.6. Design of sleeves ... 49 4.6.1. Reference ... 49 4.6.2. ISF ... 49 4.6.3. ISF + 3CD ... 50 4.7. Tests planning ... 52 4.7.1. The model ... 52 4.7.2. Controllable factors ... 53
4.7.3. Experiment structure, settings and test matrix ... 54
4.7.4. Experiment pre- and post-process ... 57
5. Results ... 59
5.1. Test rig ... 59
5.1.1. Design ... 59
5.2.1. Full-film rpm test result ... 61
5.2.2. Runtime test result ... 62
5.2.3. Comparative wear test result ... 67
5.2.4. Comparative full-film test result ... 67
6. Discussion ... 71
6.1. Design phase ... 71
6.2. Experiment phase ... 73
6.2.1. Full-film rpm test ... 73
6.2.2. Runtime test ... 74
6.2.3. Comparative full-film test ... 74
6.2.4. Comparative wear test ... 75
7. Conclusion ... 77
8. Recommendation and further work ... 79
9. References ... 81 Appendix A ... i Appendix B ... i Appendix C ... i Appendix D ... i Appendix E ... i
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1. Introduction
This chapter describes the background, purpose, specification of objectives, limitations and methods used in the presented project.
1.1. Background
The demand of cost-effective and environmental friendly transportation is a constant promoter of finding new solutions and to improve existing solutions within the vehicle industry. This demand has contributed to an increased interest of using start-stop systems in hybrid vehicles and to reduce excess emissions and fuel consumption of traditional vehicles during times the combustion engine spends idling.
Start-stop systems are widely used in the car industry today, where loads arising in the load bearing components of the combustion engine are of an insignificant magnitude regarding to stress and wear. The start-stop technology has not yet been fully implemented in the heavy duty vehicle industry but is a trend on the rise. Why this is not yet implemented is because of the much greater loads acting on some of the load bearing components, specifically hydrodynamic bearings, which leads to excessive wear when starting and stopping the engine. During the start and stop phases the hydrodynamic bearings do not have a fully developed oil film carrying the loads, which is a cause of this excessive wear. Furthermore, the development of engine lubricants is moving towards more energy efficient oils with lower viscosity and more environmental friendly additives. This means that future bearing materials must not only be able to withstand more starts and stops, it must also be able to handle worse lubrication conditions.
As a step to implement the start-stop technology in the heavy duty vehicle industry, it is important to gather valuable information to see if one by smaller means can prolong the life of the bearings without a more extensive redesign of the engine components. An interesting aspect to examine is how the surface topography of a shaft correlates with the wear of a bearing and is what this master thesis investigates. This report compares the impact of different surface topographies on hydrodynamic bearing wear during starts and stops.
Previous thesis students have constructed a start-stop test rig for journal bearings which has been the basis for this project. The experiments executed in this report have been carried out with this specific test rig after a redesign of the oil heating system. An increase of the operating oil temperature had to be made to more properly represent the scenario of a hydrodynamic bearing positioned in the balance shaft module of a running truck engine. This project has been performed by the initiative of Scania CV AB and is the product of a MSc thesis within the Engineering Design program, track: Machine Design, at the KTH Department of Machine Design. The project is mainly executed at Scania NMDC department and partly executed at KTH Machine Department.
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1.2. Purpose
The objective of this work is to further develop and refine an existing hydrodynamic bearing wear test rig and use this to investigate if the surface topography of a shaft correlates with the wear of a hydrodynamic bearing during start-stop cycling simulations. The purpose of this work is to collect valuable information of how different shaft surface types affect the wear of the hydrodynamic bearings during the critical start and stop stages. This information can later be used as a basis to improve shaft design and increase the life expectancy of bearings to be used in start-stop systems.
1.3. Specification of objectives
Redesign the test rig to provide an oil temperature of 90 degree Celsius during operation.
Test a specified amount of shaft samples based on a well-defined test matrix. Analyse and document the results from the testing.
1.4. Delimitations
Delimitations have been made to be able to produce valuable results during the limited time of 20 weeks and to keep costs at a reasonable level. Since the hydrodynamic bearings and the shafts used in the engines already are designed and in production, one wants to see if minor changes of the shafts surface topography can make a significant difference instead of a major redesign of the components.
Delimitations regarding the shaft and bearings are listed below.
Different sizes, materials or geometries of the shaft have not been considered.
Only one type of bearing is used in the experiments, a standard type bearing used in the balance shaft module of the engine.
Only three different surface topographies were tested and analysed during the project. No respect regarding manufacturing methods for a future manufacturing line was
taken into consideration when deciding the surface topographies of the shafts tested. Delimitations regarding the test rig are listed below.
The test rig is designed as it was originally except for the new oil heating construction designed during the project.
The electrical oil pump was set to a constant volumetric flow and no dynamic regulation of the oil pressure occurred during testing.
1.5. Method
Through the whole project, continuous meetings with people involved in the project occurred. The project was divided into four phases; a planning phase, an information collection phase, an implementation and execution phase and lastly a discussion and evaluation phase. Even
3 though a whole phase was dedicated to collect information, continuous literature study and information gathering occurred during the entire project.
The project started with the planning phase. In this phase discussions the project goals occurred to acquire a good understanding of what to achieve with the project. A Gantt chart visible in Appendix A was produced to obtain a good overlook of the project where milestones were put out and a risk analysis was made, see Appendix B. At this phase the base of the background study started by defining the frame of reference.
The next step was to start collecting relevant information by reading various literature and talk to people at Scania and KTH having knowledge within the field. Discussions of the layout of experiments occurred to properly be able to set up a plan of how to execute the experiments and be able to test what needed to be tested.
The third phase, the implementation and execution phase, was initiated by concept generation for the new design of the test rigs oil heating system. Several concepts were generated, evaluated and discussed to find the most suitable approach of the problem. The chosen concept was then further developed and refined. This phase also included the experiments of the shafts and the bearings, executed with the start-stop test rig stationed at KTH. Each bearing was inspected before each test by a CMM, tested with the test rigs start-stop cycling program and afterwards evaluated with the CMM and a Matlab-script provided by Scania for bearing wear evaluation. Important data and results from the experiment were documented, discussed and analysed.
The final phase of the project included further discussions of the experiment results, evaluation of the entire project and finalizing the report.
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2. Requirements
This chapter presents the requirement specification for the oil heating system and expected results of the project.
In the beginning of the project was a requirement specification determined for the new design of the oil heating system at the test rig. The requirements were determined via a discussion with relevant personals from both Scania and KTH. The decided requirements can be seen in
Table 1 below.
Table 1: The table below shows the stated requirement specification Content # Requirement Target Validation Comment
Performance
1 Target operation temperature Ambient - 90°C Measure/sensor Measured at the temperature sensor
2
Oil heating time, ambient temperature to max operation temperature
1h timekeeping Measure/ Amount of time to heat the oil
3 deviation at fixed Oil temperature location
+/-
5°C Measure/ sensor Measured at the temperature sensor
4 Local maximum temperature of oil system surfaces, i.e. not temperature of oil Goal: 130°C Max: 150°C Regulation of the heating component. Validate with other device
To avoid excessive heating of the oil
5
Regulation of temperature from
outside the test cell.
Test
Be able to control the set value of temperature from
the computer that are connected to the test rig
Placement and size
6
No modification of parts not included
in the oil system Visualize
Do not want to interfere with components/ systems already proven to work
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Oil heating system shall fit/
be placed on current test rig
Visualize Do not want a stand-alone system excluded from the test rig
Safety
8 Connected to an emergency stop Technical sheet emergency stop outside test Should be able to use cell
9 Cover the heated parts Visualize Hot hazard areas should be covered
10 connected pipes Securely and hoses
Industry standards
The pipes and hoses of the oil system should not be able
to detach by accident
Maintenance
11 Access to the oil Visualize, test Should be able to withdraw oil for analysis
12 Replacement of oil Visualize, test
The oil used during operation shall be possible
to replace
13 removal of parts Access and Visualize, test investigate and replace parts Shall be possible to
Budget 14 heating system Total cost of oil redesign
ongoing Excel costs of all components, see A document including the Appendix D
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2.1. Expected results
The master thesis project was divided into two main implementation phases, a design and experiment phase. In the first phase were including the design and development of achieving correct temperature of the motor oil, it also included manufacturing and installation on the test rig. The second phase was the experiment phase where different surface topographies were tested and studied in order to analyse the wear produced in the start stop motion that are created by the test rig. In the list below are the main tasks that were stated in the beginning of the project of what was expected to be achieved.
Design Phase
A concept that was designed after the stated requirement specification. Finished and functional product, installed on the test rig.
Fulfilled requirement specification with confirmation and validation. Documentation and manual for further usage.
Report.
Experiment Phase
Three different types of surface topographies where to be studied. Sufficiently amounts of tests to give credible interpretable results.
Analysing and interpret results by the use of CMM, interferometric microscope and Matlab.
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3. Frame of reference
This chapter presents relevant information used during the project.
To be able to solve the new design for the test rig and to perform reliable experiments a literature study was conducted. The literature study was made to give a better understanding of what was needed to be considerate under the project. The study does involve market analysis and already existing facts that where relevant for design and experiments.
3.1. Bearings
A primitive type of bearing is a shaft (journal) that is placed in a hole which will only allow rotating motion of the shaft e.g. hinges on a door. To reduce the friction that will occur can lubrication be introduced between the shaft and housing. This type of bearings works well when low forces and speeds are used. But to be able to handle high speeds and loads may it be considerate to use rolling-element bearings, hydrodynamic bearings or bearings types with similar characteristics.
3.1.1. Hydrodynamic bearing
When a gas or fluid are present between two sliding and/or rolling surfaces, may the surfaces motion by themselves build up a pressure in the fluid film. Under some specific condition can the pressure be enough to separate the surfaces, this phenomena of self-supply full film lubrication is called hydrodynamic to indicate that motion is needed to maintain the oil film (Jacobson,Hogmark,1996).
The pressure in the fluid film can be built up by wedge gap effect or pressing action. If the surfaces contact are conformal will the contact pressure be lower due to the larger contact area, compared if the surfaces contact are non-conformal according to Hertz will result in very high pressure and in contact geometry that will change by elastic deformation (Jacobson,Hogmark,1996).
Hydrodynamic journal bearings can allow very low friction down to μ = 0.001-0.01 with the main origin from the shearing of the lubricant (Beek, 2015, p.272).
Hydrodynamic bearings shaft will change its position inside the bearing depending on what stage it’s in. At rest, will the shaft be positioned in the centre of the bearing with an offset in the loading direction. When the shaft is starting to rotate will it be pushed to one side to then when it reaches steady state move to opposite side (Beek, 2015, p.293), this is showed is
Figure 1 below.
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3.1.2. Lubrication regimes
In rolling or sliding contact may different regimes of lubrication occur. They are specified as Boundary Lubrication (BL), Mixed Lubrication (ML) and Hydrodynamic Lubrication (HL). To reach the often wanted regime of Hydrodynamic lubrication must the two other regimes be passed through due to that the pressure has to be built up, or another type of bearing would be needed for example hydrostatic bearing where the pressure are created externally.
Boundary lubrication regime: The load is mainly transferred by mechanical contact between
the surfaces asperities. This regime is typical active when the velocity is low and no hydrodynamic pressure has been built up. The lubricant main function is to reduce wear and friction between the contacting surfaces.
Mixed lubrication regime: The load is partially transferred by hydrodynamic pressure and
mechanical contact between the contacting surfaces asperities. Due to the higher hydrodynamic pressure and therefor greater separation between the contact surfaces will the friction be smaller with increasing velocity.
Hydrodynamic lubrication regime: In this regime has a full fluid film separated the contact
surface completely and almost all friction is created by the shearing of the lubricant. In Figure 2 below are the different regimes in typical Stribeck curve illustrated.
Figure 2: Different lubrications regimes in a typical Stribeck curve
3.1.3. Scania bearings used at start-stop test rig
In the start-stop test rig that was used in this project as previous mentioned in chapter 1 and 2 are sliding bearings used that are installed in the Scania DL5 engine on the balance shaft module. The bearing shells consists of two metals namely a steel back and an aluminium bearing material on top. The reasons for using a steel back are to ensure that the strength that is needed to provide a good fit to the housing is enough. The softer aluminium top layer is providing good characteristics for reduce the wear.
9 In the test rig are two identically shells as seen in Figure 3 used to form a journal bearing. The hole which is placed in the middle of a bearing shell is to provide the groove and bearing with oil from the bearing housing.
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3.2. Two-body wear mechanisms
Wear of hydrodynamic bearings is one of the limiting factors for implementing the start-stop technique in the heavy-duty vehicle industry. The excess wear that arises during starts and stops reduces the bearings service length vastly and therefore also the machines lifetime performance and reliability. Since the purpose of a journal bearing is to allow sliding between two surfaces, it is completely normal that wear occurs and is commonly a two-body wear mechanism. There are fundamentally four types of two-body wear mechanisms, which are divided as follows: abrasive, adhesive, corrosion and surface fatigue. The first three of the four mentioned two-body wear mechanisms mainly occur between sliding surfaces and are briefly explained in this chapter (Beek, 2015, pp.180-183).
Running in - Machine elements that tend to be subject to wear sometimes have a running-in
period. At first, before the different machine elements have conformed to each other, the wear can be severe, a high wear rate, and after this period the wear rate usually stabilizes at a more mildly pace and may remain constant for the rest of the elements service life (Beek, 2015, pp.190-191).
Abrasive wear - There are two types of abrasive wear, two-body abrasive wear and three-body
abrasive wear. Two-body abrasive wear is when hard asperity peaks of one surface ploughs another softer surface and results in elastic-plastic, plastic deformation or cutting of the softer surface, i.e. moving material or removing material. Three-body abrasive wear is when there are hard loose particles positioned between the two surfaces in motion and, just like the case of two-body abrasive wear, ploughs one of the surfaces resulting in moved or removed material (Beek, 2015, pp.180-182). Two-body and three-body abrasive wear are shown illustratively in Figure 4.
Figure 4: Two- and three-body abrasive wear
Adhesive wear - When material transfer occurs from one surface to another due to
micro-welding it is called adhesive wear and is caused by strong adhesive bonds that arise between the interacting surfaces. This material transfer can be permanent or temporary and the latter can give rise to free wear particles (Beek, 2015, pp.182-183). Figure 5 shows an illustration of adhesive wear.
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Figure 5: Adhesive wear
Corrosive wear - When a material is subject to a corrosive environment it can react with
molecules in its surrounding and reaction products can be produced on the material surface. These reaction products change the properties of the surface and can sometimes be easily abraded, resulting in removed surface material and loose particles which often are easily penetrated or removed by asperity summits or hard particles. Oxidation is the most common form of corrosion (Beek, 2015, pp.182-183).
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3.3. Surface parameters
There exist several surface parameters which describe the finish and texture of a surface. One parameter alone cannot always explain the surface but when combined these can often properly explain the surface characteristics. The surface finish of a product mainly depends on the manufacturing methods used and the post-processing techniques applied to it. Some common surface parameters are briefly explained below.
Sampling length - The sampling length is a specific length for a subject surface made to
evaluate the surface profile and extract different roughness profile parameters from it. The sampling length corresponds to the wavelength used to separate the roughness and the waviness of the surface (“Surface Roughness Terminology and Parameters”, 2017). In Figure 6
the sampling length is denoted lr.
Evaluation length - The evaluation length is the length over which the surface profile is
evaluated. The evaluation length must contain at least one sampling length but is commonly set to five sampling lengths (“Surface Roughness Terminology and Parameters”, 2017). In
Figure 8 the sampling length is denoted ln.
Mean line – The mean line is the reference line when measuring deviations of the surface
profile and extracting surface parameters. This line is usually created by using digital or analogue filters (“Surface Roughness Terminology and Parameters”, 2017). See Figure 6 to for
an illustration of a mean line.
Ra - The most common surface roughness parameter is the arithmetic average roughness, Ra,
also called centre line average or CLA. Ra is given by the arithmetic average of the surface profile deviations, i.e. the peaks and valleys, with respect to the mean line within the sampling length. Figure 6 presents a good overlook of what the arithmetic average roughness is.
Figure 6: Different surface parameters
Even if Ra is the most commonly used parameter it is not always the best. Since Ra is only a mean value it does not explain how the surface really looks, therefore two surfaces with very different properties can have the same Ra value. Nevertheless, it gives a first good general description of a surface profile. Figure 7 shows how two surfaces with very different properties
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Figure 7: Two different surface profiles both with Ra=0.2
Acquiring Ra is described in equation 1 below where 𝑙𝑟 is the sampling length and 𝑧(𝑥) is the distance to the local rough summit at place 𝑥 with respect to the mean line (Beek, 2015, p.145). 𝑅𝑎 = 1 𝑙𝑟∫|𝑧(𝑥)| 𝑙𝑟 0 𝑑𝑥 (1)
Rq - Sometimes called root-mean-square, RMS, is a good complement to Ra since the impact
of the peaks and valleys are more significant. Acquiring Rq is very similar to acquiring Ra with the difference that the peaks and valleys are amplified, thus giving the increased impact of the high and low readings (Beek, 2015, p.145). To see the difference between Ra and Rq, compare equation 2 below with equation 1.
𝑅𝑞 = (1 𝑙𝑟∫ 𝑧(𝑥)2 𝑙𝑟 0 𝑑𝑥) 1/2 (2)
Rp - The maximum height of a peak with respect to the mean line within a sampling length
(Blateyron, 2006).
Rv - The maximum depth of a valley with respect to the mean line within a sampling length
(Blateyron, 2006).
Rt - The maximum peak-to-valley distance, i.e. the distance between the highest peak and the
lowest valley, within the evaluation length (Blateyron, 2006 ). Rt is shown in Figure 8.
Rz - The mean value of the five highest points, each point in their own sampling length, over
the entire evaluation length. This parameter is good, as a complement to Ra, to get a better understanding about the peak profile of the surface. (Blateyron, 2006) See Figure 8 for
description.
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Rk - The core roughness depth, often only called core roughness, explains the core height of
the profile. The Rk value is derived from the Abbot-Firestone curve, a cumulative probability density function of the surface profile, and explains where most of the profiles surface material is. This core of the surface profile is delimited by the material ratio parameters Mr1 and Mr2. Rk together with Rpk and Rvk are good parameters for technical descriptions and characterisation of a surface. Figure 9 shows what the Rk value is and how to acquire it (Trelleborg, 2011, p. 30). A Firestone-Abbot curve is shown in Figure 10.
Figure 9: Brief explanation of the core roughness depth, Rk
Mr1 - A material ratio parameter. It delimits the core roughness of the surface profile from its
protruding peaks (Trelleborg, 2011, p. 30). See Figure 9.
Mr2 - A material ratio parameter. It delimits the core roughness of the surface profile from its
valleys (Trelleborg, 2011, p. 30). See Figure 9.
Rpk - The reduced peak height, Rpk, is the average height of protruding peaks that rises above
the core roughness of the profile (Trelleborg, 2011, p. 30). It characterizes peaks that might wear down during sliding contact. Rpk is described in Figure 9 and Figure 10.
Rvk - The reduced valley depth, Rvk, is the average depth of valleys that drops below the core
roughness of the profile (Trelleborg, 2011, p. 30). The Rvk characterizes the oil carrying capabilities of the surface and valleys that may retain particles from worn out material. Rvk is described in Figure 9 and Figure 10.
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3.4. Surface treatment
Since one of the targets in the project was to test different surfaces to analyse if it can achieve less wear under start stop conditions where different surface treatment studied. It is commonly known that smoother surfaces create smaller amount of wear, so a method for achieving that was decided to be further looked in to. One other method that was considered in surface treatment that is not as common, is to create a texture in the surface to gain properties that might benefit in start stop conditions.
3.4.1. Isotropic Super Finishing- ISF
ISF is a method that removes the surface asperities while preserving the integrity of the remaining compressive layer. The process maintains some valleys to allow oil to be preserved to improve the lubrication aspects. The surface treatment will improve the coherence of the oil film and thereby reduce the friction. The technique used to create an ISF surface is to use oxalic acids and non-abrasive finishing stones to remove the surface asperities and supposed to leave a mirror like finish when done. Figure 11 below is showing an illustration how the
surface would look like after processing.
Figure 11: Illustration of surface after ISF process
The isotropic super finish is performed by the company Curtiss-Wright Surface Technologies AB that are located in Arboga in Sweden.
3.4.2. 3CD
3CD is a controlled current chemical deburring method performed by the company AH Automation that are located in Smögen in Sweden. The foundation of the 3CD method is a process that works by using an electrolyte, a DC electric circuit and cooling equipment to control temperature. The process will remove different amount of material depending on how electrically charged different details are in direct proportion to the electrical voltage. The main area of usage is usually to improve surfaces, polishing of stainless materials and micro deburring sharp edges. The process will give a different structure comparing with mechanical machined surface which can be useful in some applications. Figure 12 below shows a detail that
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Figure 12: Before and after 3CD treatment
Because of the different structure between martensite and perlite and other crystalline structures in a metal detail will give divisions between the crystalline structures. The divisions will be affected different in the 3CD method and thereby create indentations in the surface. This texture of indentations is the purpose for using the 3CD method in this project case to test how it performs under start stop conditions.
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3.5. Acquiring surface parameters and measuring wear
A commonly used technique to collect different surface parameters of an object or to acquire its geometry is by probing the objects surface using a contact scanner. Why contact scanners are such a commonly used technique is because of the great precision this method can provide. The precision can be in the lower region of microns when scanning longer distances and the uncertainty can even be as low as sub-microns for shorter distances. A drawback for using this method is the limited object size this method usually can scan but it suits the parts used in this project. The contact scanner is usually a computer numerical control-mill, a CNC-mill, with a probe-unit mounted on it or a coordinate measuring machine, a CMM, which is designed to scan and collect information of surfaces. A typical CMM is shown in Figure 13.
Figure 13: A typical coordinate measuring machine
To acquire the surface parameters of an object the machine, CMM or probe-mounted CNC, scans a small distance of the surface with a stylus at the location where one wants to collect the surface parameters. The data from the scanning are then collected and processed by software to generate the surface parameters. The wear of an object can be measured in a similar way as how surface parameters are acquired. In this case the CMM traces the cross-section of an object and stores the coordinates of the tracing. The tracing of the object is done before and after the object is subjected to wear and a software processes these traces and calculates the wear from the two different shapes arisen by the wear process. Scania uses such technique with an in-house Matlab-script for evaluating bearing wear. An illustration of how a trace of a journal bearing could look like is shown in Figure 14.
18 Another technique to collect surface parameters and to acquire a good understanding and overlook of a surface is by scanning the surface with a non-contact scanner, such as a confocal microscope or an interferometric microscope, and using a software. Those scanners are computer numerical controlled and can provide a 3D-image of the surface, using filters to remove distortions and measuring errors and compute several surface parameters.
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3.6. Thermodynamics
Some relevant information about thermodynamics was gathered to be able to understand the heating behaviour of the test rig and to dimension the new heating construction.
3.6.1. Thermodynamic system
A thermodynamic system is an object strictly defined by its boundaries, analysed from a thermodynamic point of view. This means that all space inside the boundaries belongs to the investigated object, the system, and everything outside the boundaries belongs to the environment of the system (Burden, 2011, p.3). A system can be a sub-system to a larger system or an assembly of sub-systems which can consist of only a few or an infinite amount of systems working together, all depending on where the boundaries for the systems are set. The environment of a system can often be seen as such assembly. By this, one can conclude that almost anything can be considered a thermodynamic system depending on how the boundaries are defined for the studied object.
There exist three main types of thermodynamic systems; the closed system, the open system and the isolated system. The systems noteworthy for this report are the closed and the open system which are briefly explained below.
Closed system - A closed system does not exchange any mass with its environment but can
exchange energy in the form of heat or work with its environment. This means that the closed system has a constant mass and allows no mass flux in or out of the system boundaries, i.e. the system always consists of the same amount of matter.
Open system - An open system is a system that can exchange both mass and energy with its
environment. An open system is often viewed as a control volume where energy and mass flux are allowed to pass the defined boundaries of the control volume (Burden, 2011, p.3). The control volume is often considered fixed in space, in which fluid can flow through it, see
Figure 15. Fluid flowing in a section of a conduct, where the section is defined by specified
boundaries, is a good example of an open system.
Figure 15: A thermodynamic open system viewed as a control volume
3.6.2. Incompressible steady state flow
A fluid flow in which the density of the fluid can be considered constant is called incompressible flow. This means that if a volume of incompressible fluid enters a fixed control volume, an equal amount of volume must also leave the control volume. The input and output volume flow rates are of the same size. Since the density of the fluid is constant for incompressible flow, the input and output mass must also be equal.
20 The relation between mass flow rate and volume flow rate for incompressible flow is shown in equation (3).
𝑚̇ = 𝜌𝑉̇ = 𝜌𝑣𝐴 (3)
Where 𝑚̇ is the mass flow rate [kg/s], 𝜌 is the density [kg/m3], 𝑉̇ is the volume flow rate [m3/s], 𝑣 is the flow velocity [m/s] and 𝐴 is the cross-sectional area of the conduct [m2]. Steady state flow means that the flow velocity does not change over time at a fixed point in space, the time derivative is zero. By this one can conclude that the mass flow rate for incompressible fluids is constant during steady state flow.
3.6.3. Steady state and thermal equilibrium
If a system keeps a constant local temperature it is said that the system has reached steady state (Kurowski, 2007). This means that heat entering the system is equal to heat leaving the system and no macroscopic changes occur. The system is in balance with its environment. If two bodies with different temperatures where put in thermal contact with each other they would eventually reach the same temperature. The warmer object would transfer heat to the colder object and if given enough amount of time thermal equilibrium would occur. If no heat transfer occurs between two objects connected by a thermal contact path, it is said that they are in thermal equilibrium (“Thermal Equilibrium”, 2017). All systems strive to reach thermal equilibrium over time.
One law of thermodynamics discussing this phenomenon is the zeroth law, the zeroth law is defined as followed: If two systems are in thermal equilibrium with a third system, then they
are in thermal equilibrium with each other.
3.6.4. Energy of a system
The first law of thermodynamics says that energy cannot be created nor destroyed; it can only
go from one form to another. This means that the change of energy of a system is equal to the
energy added or removed from the system and it is possible to setup an energy budget for it. One way to describe the first law of thermodynamics for a closed system mathematically is shown below in equation (4) (Burden, 2011, p.10).
Δ𝐸 = 𝑄 − 𝑊 (4)
Where 𝐸 is the total energy of a system [J], Δ𝐸 is the change of total energy of the system, 𝑄 is the heat transferred to the system [J ] and 𝑊 is the work performed by the system acting on its environment [J]. This means that if no work is done by the system on its surrounding environment, or vice versa, the change of total energy of the system will be equal to the heat added to the system.
21
3.6.5. Specific heat capacity
To be able to calculate how much heat that is needed to increase the temperature of a system, an empirical formula is often used, equation (5).
𝑄 = 𝐶Δ𝑇, 𝐶 = 𝑄
Δ𝑇 (5)
Where 𝐶, the heat capacity of the system, is the amount of heat needed to increase the temperature of the system with one degree Kelvin [J/K] and Δ𝑇 is the change of temperature [K]. Often the heat capacity of a system is unknown and may be difficult to retrieve since one needs to know the net heat transfer into the system and the temperature change of the system to retrieve it.
The heat capacity of a pure substance is, on the contrary to a system, widely known and is a material specific property that can be found in common thermodynamics tables and handbooks, often stated in the unit [J/kgK]. The specific heat capacity of a material 𝑐, often only called specific heat, is denoted 𝑐𝑣 or 𝑐𝑝 depending on if it is defined for a constant volume respectively a constant pressure. For incompressible fluids and solids, 𝑐𝑣 and 𝑐𝑝 can often be assumed to be the same if not for rare cases such as extreme temperatures.
To calculate the heat needed to change the temperature Δ𝑇 degrees Celsius of a specific amount of material, the following formula, equation (6), is widely used.
𝑄 = 𝑚𝑐𝑝Δ𝑇 (6)
Where 𝑚 is the mass of the material [kg].
3.6.6. Conduction
When heat transfers between two objects that are in physical contact with each other and when heat travels within bodies it is due to conduction. The transfer of energy is on the microscopic level and arises because of electron movements and collisions of particles within the material. A materials ability to transfer heat due to conduction is called the thermal conductivity of a material and is denoted 𝑘 [W/mK]. For insulation applications, materials with a low thermal conductivity are used.
3.6.7. Thermal radiation
Heat can escape from a system by thermal radiation which means that the internal energy of the system decreases. Thermal energy converts into electromagnetic energy and the system suffers energy loss in the form of reduced heat. One must regard the heat losses of the system for systems intended to be heated or kept at a constant temperature or otherwise the temperature of the system will decrease.
A perfect emitter is called a black body and it absorbs all incoming electromagnetic radiation. Thermal radiation from such a body is called black body radiation and radiation from other types of bodies is viewed in relation to this idealized body and is called grey body radiation. Grey body radiation is a fraction of the radiation from a black body and depends on a material
22 surface coefficient, the emissivity coefficient ε, for the studied object which can be found in common thermodynamics and physics handbooks.
The equation (7) for black body radiation is shown below,
𝑞𝑏𝑙𝑎𝑐𝑘𝑏𝑜𝑑𝑦= 𝜎𝑇4𝐴 (7)
Where 𝑞 is heat transfer per unit time [W], 𝑇 is the temperature of the object [K], 𝐴 is the emitting area of the object and 𝜎 is the Stefan-Boltzmann constant. 𝜎 = 5.6703 ∙ 10−8 [W/m2K4].
To calculate the net thermal radiation loss of an object positioned in cooler surroundings, where the object is seen as a grey body, the equation (8) below can be used.
𝑞𝑔𝑟𝑒𝑦𝑏𝑜𝑑𝑦 = 𝜀𝜎(𝑇4− 𝑇
𝑒𝑛𝑣4 )𝐴 (8)
Where 𝜀 is the emissivity coefficient of the object and 𝑇𝑒𝑛𝑣 is the temperature of the environment surrounding the object [K].
3.6.8. Radiation losses for insulated objects
Since the black body and grey body equations are for non-insulated objects and the test rig have parts that are insulated, two more equations for thermal radiation losses are needed. Insulated pipe losses are as followed (VärmeKabelTeknik, 2017 p.12)
𝑞𝑝𝑖𝑝𝑒𝑙𝑜𝑠𝑠 =2𝜋 ∙ Δ𝑇 ∙ 𝑘 ∙ 1.16 ∙ 𝑠
ln(𝑑𝑦/𝑑𝑖) (9)
Where 𝑞 is the losses of the insulated object [W], Δ𝑇 is the temperature difference between the pipe and the environment [°C], 𝑘 is the insulation materials thermal conductivity value [W/mK], 𝑑𝑦 is the outer diameter of the insulation [mm], 𝑑𝑖 is the inner diameter of the insulation and 𝑠 is a safety factor (1.2 inside, 1.5 outside).
Insulated tank losses are as followed (VärmeKabelTeknik, 2017 p.20)
𝑞𝑡𝑎𝑛𝑘𝑙𝑜𝑠𝑠= 𝐴 ∙ Δ𝑇 ∙ 𝑘 ∙ 𝑠
𝑆 ∙ 𝐸 (10)
Where 𝐴 is the total cooling area [m2], 𝑆 is the thickness of the insulation [m] and 𝐸 is a correction factor which normally has the value 0.8.
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3.7. Heating element
There are many different product on the market that could be used to heat motor oil because it’s a fairly common application. Many of those product are used for much larger volumes and flows compared to what the test rig uses, such standard components oil heating system are for example flow heaters.
Considerations when searching the market were taken according to how the test rig was built, also the amount of 𝐶𝑚𝑊2 that the products was delivering. The search led to that heating by cable was a good option, due to its flexibility and good control over the effect.
3.7.1. Parallel circuit heating cables
The parallel circuit heating cable has constant effect in the cable zones that are typical around one meter as displayed in Figure 16 below. This makes it possible to shorten the cable easily. The cable is built up by two bus-wires conductors within a silicone rubber sheath as seen in
Figure 16 below.
Figure 16: Left figure shows the heat cable zones, and to the right an parallel circuit heating cable
The usage for parallel circuit heating cables are many for example temperature maintenance, hot oil lines, external and internal freeze protection, heating tanks and in hazardous environments. The cables usually have limitations in bending radius due the heating zones that the cable have.
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3.7.2. Self-regulating heating cables
The purpose with self-regulating heating cable are that they have resistance that varies with ambient temperatures. The cable is built with two bus-wire conductors inside semi-conducive self-limiting heater core as seen in figure Figure 17 below. So with other words will the cable
change the inner resistance after its temperature and thereby the effect, this is illustrated in
Figure 17 displayed underneath.
Figure 17: Left figure shows the structure of the cable, to the right is a typical one
The typical applications areas for the cable are frost protection and temperature maintenance. The self-regulating heating cable are possible to shorten to suitable length but the bending radius of the cable have to be in mind due to its properties.
3.7.3. Heating Tape
Heating tapes are built up by resistance wires that are creating heat when a current is passing through. There are a great amount of different varieties both in dimensions and cases. The bending radius are determinant rather by the case and not the resistance wire according to (Ericsson, 2017). This gives a good advantage when it’s used on pipes with small radius. The cables often have the option to have a grounded metal braided case that will protect the insulating material as seen in Figure 18 below.
Figure 18: A metal braided heating tape
The cables effect have to be decided before purchase due to its not possible to shorten the total length afterwards.
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3.8. Temperature regulation
To be able to control the temperature of the motor oil in the test rig according to the stated requirement specification was some sort of control unit necessary to control the new heating element. The two ways that were investigated further was a thermostat with an on-off control unit and a proportional-integral-derivative controller (PID Controller) with a sensor. The two different units were chosen due to their widely usage in the field of working with heating elements.
3.8.1. Proportional-integral-derivative controller
PID-regulator is a general name where a linear combination of proportional, integral and derivative action of a regulating error are used to calculating a control signal. PID-controllers are the most common controller in the industries, and are estimated that it’s used in over 95% of all control circuits (Häggblom, 2015, p.7-1).
A PID is good option to use when controlling a process with slow dynamic, especially temperature and vapour pressure due to the derivative part is “predicting” the future inputs. (Häggblom, 2015, p.2-10). Figure 19 below is an example of how a PID could look like.
The PID will thereof change its actual value rapidly and continuously to try to obtain the set point value.
Figure 19: PID-regulator
3.8.2. On-off regulation
An on-off control unit works in two modes, on or off. Common usage are the thermostat to an electric heating element. The thermostat are usually a mechanical switch that switches mode with the temperature. The way an on-off regulation works leads to a low accurate due to adopting max and minimum values on the control signal (Wahlfrid, 2007).
That means that when the control signal is on will the heating element deliver full effect until the thermostat reaches the set point value, and when its reached turn off the heating completely until a lowest accepted value are reached. This process will then repeat itself. There are different designs of how the control unit can function. For example Analog control units where the temperature set point value are adjusted via a manual knob or with digital display.
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3.9. Start-stop journal bearing test rig
Under a series of different projects at KTH in collaboration with Scania have a start stop test rig been developed for creating controlled start stop cycles at hydrodynamic journal bearings. Different conditions within the lubrications regimes as seen in chapter 3.1.2 are produced to study the results. Parameters that can be tampered with are the applied load on the bearing (0-5000 N), oil temperature, the oil pumps capacity and duty cycles design. A computer that is connected to the test rig is recording the friction torque that is created, duty cycle, oil pressure and temperature via different sensors and load cells. In Figure 20 below can the overall design
of the start-stop test rig be seen.
Figure 20: Overall design of the start-stop test rig
The test rig works by a shaft is rotating under different speeds via a servomotor that is following the programmed duty cycle. The shaft is connected to a servo motor through a bellow coupling and supported via two bearings as seen in Figure 21
27 On the end of the motor shaft is a metal sleeve as seen in Figure 22 below connected that are commutable instead of stationary as the motor shaft. This enables it to be removed an inspected and changed to another one with different properties e.g. different surface finish.
Figure 22: Metal sleeve
The sleeve then acts as the journal in the hydrodynamic journal bearing. The bearings shells are inserted in the bearing house parts as seen in Figure 23 that are connected to each other and
then loaded by a spring in the loading mechanism. The whole assembly as seen in Figure 23
below is also called yoke. The support holder for the bearing shells are designed in such a way that they are suspended by thin sheet metal that allow it to flex in only one direction, this entails that the friction torque that is created can be measured as seen in Figure 23.
Figure 23: To the left is the design of bearing housing and to the right is the whole assembly called yoke.
The motor oil that is needed in the hydrodynamic journal bearing is supplied by an oil pump through a series of hydraulic pipes and valves to the top of the bearing house as seen in Figure 24. It can be redirected through an oil filter if wanted.
28 The oil is circulating in the system and is supposed to be able to have different temperatures to imitate the conditions in the real motor. The temperature is raised through a 360 W heating mat that are located under the oil tank as seen in Figure 24. The temperature is then controlled
by an analogue controlled on-off temperature unit by the help of a thermostat.
Figure 24: Shows the lower parts of the test rig with its heating mat
The maximum working temperature that could be reached was not mimicking the real conditions in the motor and needed further development. The top temperature reached under test was 72 °C according to (Sölvason, Gralde, 2014)
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4. Implementation
This chapter presents the implementation phase of the project. It includes calculations, concept development, manufacturing and test planning.
4.1. Estimation of needed heat
Simplifications and assumptions have been made during this part to be able to estimate the required energy to heat the oil. This part of the project has been performed under pressure of time to make sure having enough time to execute the main focus of this master thesis, the experiments, and due to lead times of construction materials. It was understood that it would not exist enough time to learn and understand various simulation programs and therefore a mathematical model was created by using Matlab. Safety factors were introduced to not underestimate the required input power of the heating elements. Heat gained or lost in the form of work energy is neglected. In this part; the word power, energy per unit time and heat per unit time are used as synonyms for each other.
4.1.1. Test rig before redesign
The main problem when dimensioning the new design of the heating construction was to get a good understanding of the current heating design, as it was previously to this thesis, and how the system behaves. If one knew how much energy were put into the system and what temperature the subject parts reached, one could have retrieved the efficiency for the system and by this dimension the required input power of the new heating construction. Problems here were that it was unknown what parts got heated due to conduction, what temperature those parts reached and how much energy got transferred into the system.
Even if the maximum power of the current heating mat was known, 360 W, the energy put into the system was unknown because of several reasons; the efficiency of the heating mat and the time the thermostat allowed the mat to heat was not known. Even though tries where made to find the efficiency of the heating mat, i.e. how much of the power put into the heating mat is transferred to the system, by searching different technical sheets and by talking to companies within the field, no efficiency value was found. It was noticed when doing tests that the heating mat was turned on and off by the thermostat even though the target oil temperature was not reached. The reason for this was probably because the temperature sensor, placed between the heating mat and the tank, reached a higher temperature than the oil itself and therefore regulated the heating mat around that temperature.
Since the power put into the system and the temperature of different parts where not known, another solution to estimate the required heat needed where sought. It was decided to make a simplified mathematical model of the test rig to use as a guideline when dimensioning the new heating construction.
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4.1.2. Defining the system
To be able to estimate the needed energy input to the system, the system itself had to be defined. There were two main problems when defining the system; what parts of the test rig shall be included in the system and what are their sizes and weights. No well-defined parts list existed and there was no possibility to open the CAD-files of the test rig to extract data due to not having access to the needed software.
The problem when choosing what parts to include in the system was mainly because of not knowing how the heat spread across the test rig. The current test rig design lacked insulation between connectors and attachment points between different parts of the test rig and made it difficult to set the borders of the system.
To solve the issue without knowing the size and weight of the parts included in the system, estimations and simplifications were made. The dimensions of the parts were produced by interpretations from looking at pictures of the test rig, technical sheets and by discussing what was remembered from an earlier visit to the test rig at KTH. The idea was to be a bit conservative to not underestimate the required energy input.
An example of one of these simplifications is for the oil pump. The pump has a rather complex geometry, as seen in Figure 25, with a hollow core to be able to displace fluid. No
weight of the pump was found and therefore the weight was estimated by simplifying the pump as a solid cylinder. The pump is made of cast iron and stainless steel. The density of steel is 7850 kg/m3, the density of cast iron is between 6800 – 7800 kg/m3 (“Metals and Alloys – Densities”, 2017), the specific heat of carbon steel is 0.49 kJ/kgK and the specific heat of cast iron is 0.46 kJ/kgK (“Metals – Specific Heats”, 2017). Since steel weighs a bit more than cast iron and has a slightly higher specific heat capacity, the choice of material for the pump was decided to be steel for its mass estimation.
Figure 25: A drawing of the oil pump used in the test rig, measurements in inches
Another example was when choosing the oil volume for the system. The standard operation oil volume is 4 litres but was chosen to be 6 litres when defining the system to be heated, an amount 50% greater than the operating volume.
31 The defined system to be heated can be seen in Table 2 below. A mass of 7 kg steel extra was added to the system to be extra cautious, to include parts as the brackets for the pipes, the bearing house etc. and to consider some of the material heated through conduction.
Table 2: The parts considered in the system to be heated
Detail Mass [kg] Size [kg/mDensity 3] Specific heat
[J/kgK] Oil 5.4 6 litres 890 1800 Pipe 0.08 D=10, d=8 mm, L=3000 7850 490 Tank 3.8 A=200*200*6 mm2, t=2 mm 7850 490 Pump 1.2 d=50, L=80 mm 7850 490 Shaft 3 D=40, L=300 mm 7850 490 Oil filter 0.5 7850 490 Extra 1 7 kg 7850 490
4.1.3. Estimating heat needed
When the system was defined, it was possible to calculate the heat needed to raise its temperature to the target temperature.
From the defined system, a mathematical model was created to calculate how much the needed heat energy is to increase the defined systems temperature from ambient temperature to the target temperature. The specific heat capacity equation, which is explained in chapter 3.6.5, was used to calculate the heat needed for each part in Table 2. When the required heat needed for each part is known, one also has the required heat for the total system which simply is the sum of the heat needed for all parts in the system. The equation to calculate the total heat needed is shown in equation (11) below where 𝑖 denotes each part of the system.
𝑄𝑖 = 𝑚𝑖𝑐𝑝,𝑖Δ𝑇 ⇒ 𝑄𝑡𝑜𝑡 = ∑ 𝑄𝑖 = 𝑖
Δ𝑇 ∑ 𝑚𝑖𝑐𝑝,𝑖 𝑖
(11) Since watt is energy per unit time one can also calculate the time it would take to increase the temperature of the system to a target temperature when transferring a constant positive net watt into it. Heat losses are usually temperature dependant and therefore a system would not normally behave like this, but since a first hinge was needed about what regions the input power would end up in, a plot showing what temperature the system reaches in one hour with different net watts put into it were produced, Figure 26.
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Figure 26: Temperature reached in 1h for the defined system, no losses considered
4.1.4. Estimating losses in the system
New assumptions had to be made regarding the heat losses of the system to keep the mathematical model simple. Losses due to heat conducting to areas and parts outside of the system were neglected and the extra mass added when defining the system were assumed to cover the rest of these losses. All losses considered for the system are therefore of the thermal radiation nature.
As stated before, the dimensions of the parts were unknown and therefore the areas active of thermal radiation and the insulation thickness also had to be estimated. Assumptions were made at this stage that all emitting areas will have the same temperature and the estimated insulation thickness of the insulated parts was 25mm. It was later found out that the existing insulation thickness was 20mm. The estimated radiation area of parts considered in the system can be seen in Table 3.
Table 3: Parts considered as radiators for the defined thermodynamic system Detail Amount Surface area / Length Insulation thickness
Pipe 1 L=3000 mm 25 mm Tank 1 A=200*200*6 mm2 25 mm Pipe brackets 6 A=70*100*2 mm2
Couplings 6 d=20, L=80 mm Pump 1 d=50, L=130 mm Bearing cover 1 A=10*10*6 mm2
Oil filter 1 d=100, L=100 mm Shaft 1 D=40, L=100 mm Base plate 1 150*150 mm2
There are noteworthy differences between Table 3 and Table 2. This is partially because some of
33 between the parts masses and their emitting areas. The dimension differences for the pump is because of its complex geometry, one must estimate its mass for the heat needed and one must estimate its emitting surface area for the thermal radiation. The difference of the estimated shaft dimension is due to the bearing cover considered in Table 3, the bearing cover overlaps a
part of the shaft and since this cover is regarded as an emitter, the emitting length of the shaft is assumed to be shorter than the shaft length used for calculating the mass of the shaft.
When calculating the total loss due to thermal radiation, the equation for grey body radiation is used together with the two equations for thermal radiation loss of insulated objects given in chapter 3.6.8. The same principle as when estimating the total required heat for the system is also applied here. The total thermal radiation loss is the sum of the thermal radiation from each part separately. The assumed emissivity coefficient for all parts is the one for weathered stainless steel, 𝜀 = 0.85 (“Emissivity Coefficients of some common Materials 2017), and the insulations conductivity coefficient used for the equations is 𝑘 = 0.045. This 𝑘-value is an approximate value for mineral wool. The calculations to estimate the total loss due to thermal radiation are described below. (12) – (14).
First the contribution for the non-insulated parts were calculated. 𝑖 denotes each of the non-insulated parts of the system. The temperature is stated in the unit Kelvin.
𝑞𝑛𝑜𝑛𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 = ∑ 𝑞𝑔𝑟𝑒𝑦𝑏𝑜𝑑𝑦,𝑖 𝑖 = 𝜀𝜎(𝑇4− 𝑇 𝑒𝑛𝑣4 ) ∑ 𝐴𝑖 𝑖 = 𝜀𝜎(𝑇4− 𝑇 𝑒𝑛𝑣4 )𝐴𝑡𝑜𝑡 (12)
Then the contribution from the insulated parts where calculated. The safety factor 𝑠 is set to 1 during these calculations because a safety factor for the total loss of the system will be introduced later. 𝑞𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 = 𝑞𝑝𝑖𝑝𝑒𝑙𝑜𝑠𝑠+ 𝑞𝑡𝑎𝑛𝑘𝑙𝑜𝑠𝑠 = 2𝜋 ∙ Δ𝑇 ∙ 𝑘 ∙ 1.16 ∙ 𝑠 ln(𝑑𝑦/𝑑𝑖) + 𝐴 ∙ Δ𝑇 ∙ 𝑘 ∙ 𝑠 𝑆 ∙ 𝐸 (13)
Finally, the total estimated loss of the system, 𝑞𝑙𝑜𝑠𝑠, is acquired by combining equation (12)
and (13). 𝑞𝑙𝑜𝑠𝑠 = 𝑞𝑛𝑜𝑛𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 + 𝑞𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 = = 𝜀𝜎(𝑇4− 𝑇 𝑒𝑛𝑣4 )𝐴𝑡𝑜𝑡+ Δ𝑇 ( 2𝜋 ∙ 𝑘 ∙ 1.16 ∙ 𝑠 ln(𝑑𝑦/𝑑𝑖) + 𝐴 ∙ 𝑘 ∙ 𝑠 𝑆 ∙ 𝐸 ) (14)
A safety factor had to be introduced. By an interview (Ericsson, 2017) it was found out that a commonly used safety factor for estimated losses is 1.4. The total heat loss of the system at different system temperatures, with and without the introduced safety factor are shown in
