Radial Ball Bearing Material

Radial Ball Bearing frameworkYou atomic number 18 tasked with selecting a existent that is sui flurry for the wraps in a radiate-ply tire ball bearing much(prenominal) as the one shown in Fig. 1. Radial ball bearings although intended primarily for radial loads, will in any case keep a certain amount of thrust. Ball intent 1 Ball bearingThe following details are cognise in relation to radial ball bearing designYoungs modulus should have a minimum of cc GPa.The compressive cleverness should have a value 300 MPa.The balls must not go against under load. It female genital organ be assumed that the contact centering can be modelled for a sphere on a flat (see Fig. 1). An assumption should be made that the hearty for the ball and the raceway are the same and therefore they have the same moduli and Poissons ratio has a value of 1/3.The balls should be light.Material selection process. This refers to selecting a material that cope withs all the constraints and objective a t a lower place.Design requirementsTable 1 Table of design requirementsFunctionSuitable for balls in a radial ball bearingConstraintsYoungs modulus must be greater than 200 Gpa.Compressive specialisation should not have a value of less than 300Mpa.(Assumption)Moduli and Poissons ratio being the same (ratio of ).ObjectivesThe balls must not fail under load, contact should be modelled for a sphere on a flat.The balls should be light.Free variablesCross sectional subject fieldMaterial choiceMass of ballBelow is a figure of all materials with a mechanical property (Youngs modulus greater than 200Gpa and Compressive strength greater than 300Mps) against engrossmentSeen below is a table of the materials and their corresponding Youngs modulus.Table 2 Table of materials severaliseYoungs modulus (GPa)Tungsten carbides625 700Boron carbide440 472Silicon carbide400 460Alumina343 390Tungsten alloys310 380 aluminium nitride302 348Silicon nitride290 318Zirconia200 250Nickel-based overse er alloys150 245Nickel-chromium alloys200 220Nickel190 220 rugged alloy steel205 217Medium carbon steel200 216Low carbon steel200 215High carbon steel200 215Stainless steel 210Although seen to a higher place, 16 values have passed the requirements so far, pass on analysis will be conducted, and this can be seen belowThe below table illustrates the materials that meet the design requirements, the table is ranked based on Youngs modulus, from highest modulus to lowest. The Compressive strength of the material must also be considered, a minimum compressive strength of 300MPa must apply.The table below illustrates each materials Youngs modulus and corresponding compressive strength.Table 3 Materials with Youngs modulus and compressive strengths that meet design requirements (density also noted)NameYoungs modulus (GPa)Compressive strength (MPa)Tungsten carbides625 7003.35e3 6.83e3Boron carbide440 4722.58e3 5.69e3Silicon carbide400 460690 5.5e3Alumina343 390690 5.5e3Tungs ten alloys310 380555 800Aluminium nitride302 3481.97e3 2.5e3Silicon nitride290 318524 5.5e3Zirconia200 2503.6e3 5.2e3Nickel-based super alloys150 245300 1.9e3Nickel-chromium alloys200 220365 460Nickel190 22070 1e3Low alloy steel205 217400 1.5e3Medium carbon steel200 216305 1.76e3Low carbon steel200 215250 395High carbon steel200 215335 1.16e3Stainless steel189 210170 1e3Below is a bubble chart of Youngs modulus versus compressive strengthFigure 2 Bubble chart of Youngs modulus of Compressive strengthThe above figure is on a logarithmic scale. Only materials that have passed the requirements were plotted.When bob ups are placed in contact they touch at one or a few discrete points. If the surfaces are loaded, the contacts flatten elastically and the contact areas grow until failure of some style occurs. (Duffy, 2010) Compressive stress causes this. As the requirements state should be modelled as a sphere on a flat, this allows the student to use following fo rmulae (contact stresses)Figure 3 subject on a flat(Duffy, 2010)(Yield Stress) The following is subbed in to produce the below x x x x = = The mass of the sphere must be derived, this is done belowWhere is density and is legerVolume of a sphere is denoted as m= The student knows the objective is to minimise the mass of the ball, the derivation above is done on that basis and results in the equation being flipped above.From the material selection index above, the equation can be related in the logarithmic scale = This results in This now means the slope can be known to be = 0.222The above value is known as an index bendIndex lines can be used to compare the sufficeance of different materials, and to find replacement materials. Materials that are on the line will all perform equally well in each design. Materials above the line have a higher performance index and will therefore perform repair those below the line have a lower index value. (Edupack, 2006)The below bubble char t illustrates the material selection process using the slopeFigure 4 Material selection with material indexAs seen from above, with a material index of 0.222 the following two materials passed (whole record is within the selection was used)NameIndex slope =0.2222Silicon nitride6.55e101Zirconia1.66e speed of lightAs seen from above the materials are both ceramic.An additional chart plotting the materials costs can also be seen belowFigure 5 Price of selected materialFigure 6 Price of selected material Pass preciselyA table of the materials cost can also be seen belowTable 4 Table of costsNamePrice(EUR/kg)Zirconia17.1-24.7Silicon nitride32.3-49.4(i)It has been identified that both Youngs modulus and compressive strength are important material properties when selectin ball bearings, below is a detailed summary of why each property is importantYoungs modulus refers to a materials elastic modulus. This determines the stiffness of a solid material. This is a proportional (constant) betwe en stress as long as stress is less than the yield point. This results in a smaller strain with the same stress in a stiffer material. In relation to a ball bearing Youngs modulus of Silicon nitride is about 1.5 times that of steel, meaning a smaller contact surface is present when there is a high contact pressure. Hertz theory means the maximum load for combination steel- Silicon nitride reduced with 30%.In relation to the contact of the bearing we know it will be a sphere on a flat. The balls within a bearing are vent to experience both an axial and radial force. If the force is too great for the material this whitethorn result in deformation (changing of shape). This affects the ball bearings ability to perform, this can be compared to as a wheel on a car, if it is flat may result in a pulling motion. If severe deformation occurred this may result in the bearing not allowing for rotation. This means that Youngs modulus is important when selecting materials for ball bearings.Youn gs modulus mathematical representation It is noted from CES EduPack that atomic number 14 nitride is used mostly for ball bearings the Youngs modulus is known to be 290-318 GPa (Edupack, 2006)Compressive strength refers to a materials resistance to compressive stress. This is when a force is applied in an inwards direction in the material. It is inverse to tensile stress. As a ball bearing is going to have one point of contact, (below) compressive strength is an important element in choosing the material. This is due to the radial forces applied when the ball is in the raceway. Once again, if the radial force is greater than the materials compressive strength abilities this will result in deformation. This will affect the bearings performance. Compressive strength can be up to 10 times greater than tensile stress. Ceramic material has a good compressive strength due to crack propagation, since there are more intrinsic cracks in ceramics (than most materials) if placed under tension cracks will propagate and produce failure where if it is placed under compression it works in the opposite manner.Compressive strength mathematical representation It is noted from CES EduPack that silicon nitride is used mostly for ball bearings the compressive strength is known to be 524-5.5e3 MPa (Edupack, 2006)(ii)The other material properties of Silicon Nitride which take aim to superior operating performance can be seen belowGeneral propertiesDensity3.1e3-3.4e3kg/m3Price*32.3-49.4EUR/kgDate first used1958Mechanical propertiesYoungs modulus290-318GPa shear modulus*100-128GPaBulk modulus*210-232GPaPoissons ratio0.26-0.28Yield strength (elastic limit)*600-720MPaTensile strength600-720MPaCompressive strength524-5.5e3MPaElongation0% strainHardness Vickers1.4e3-1.6e3HVFatigue strength at 107 cycles*300-500MPa go toughness4-6. 7MPa.m0.5Mechanical loss coefficient (tan delta)*2e-5-5e-5 thermal propertiesMelting point2.39e3-2.5e3CMaximum service temperature1e3-1.2e3CMinimum service t emperature-272271Cthermic conductor or insulator?Good conductorThermal conductivity22-30W/m.CSpecific heat capacity670-800J/kg.CThermal expansion coefficient3.2-3.6strain/CElectrical propertiesElectrical conductor or insulator?Good insulatorElectrical resistivity1e20-1e21ohm.cmDielectric constant (relative permittivity)7.9-8.1Dissipation factor (dielectric loss tangent)*5e-4-7e-4Dielectric strength (dielectric breakdown)*11-131000000 V/mOptical propertiesTransparencyTranslucentRefractive index1.95-2ProcessabilityMoldability2-3Weldability1-2Eco propertiesEmbodied heartiness, primary production116-128MJ/kgCO2 footprint, primary production4.63-5.12kg/kgRecycleRecycle(Edupack, 2006)The above characteristics result ceramic materials being the optimum material for ball bearingsHigh speed, faster acceleration this is because ceramics are only 40% as dense as steel. However, the material can deliver 30-50% higher running speeds with reduced skidding and less lubrication needed.Lighter in weight ceramic ball bearings are more rigid to that of steel ball bearings and lighter in weight. This allows for lower coefficients and a higher overall RPM (rotation per minute)Greater accuracy since ceramics has 50% higher modulus of elasticity than steel. This means less of a deformation which leads to vibration and spindle deflection, this increases components productivity and quality.Reduced friction benefits of this include longer life, energy efficiency reduced noise levels, less heat and less lubrication needed.Non-conductive materials like Silicon nitride eliminate the pitting and fluting of raceways which ic common in electric motor applications. If steel is used in bearings the electricity could cause magnetic field (EMF) and this could act as a conducted damaging the bearings over time. Ceramic materials are immune to EMF, which mean they perform well even when electricity is present.Corrosion resistance Silicon nitride more effective than steel balls in the presence of liquids such as water or corrosive materials. Corrosion resistance can be enhanced when ceramic balls are used with dry fil, lubricant on the ring and retainer components.Longer operating life Up to 5 to 10 times longer than standard metal bearings.Higher temperature operation ceramic ball bearings can operate in high temperatures (up to 1,800 F) Less noise and vibration due to a lower coefficient of friction(Ibsco, 2011)The two materials chose were Silicon Nitride and Zirconia. A brief description can be seen below outlining why the individual ceramic is the optimum choiceSilicon NitrideThis material contains high temperature capabilities, meaning it has a low thermal expansion coefficient which gives good thermal impact resistance compared to other ceramic materials. The material is up to 58% lighter than steel silicon (Carter, 2009). As the material is lighter it means a smaller force is needed to roll the element. The main advantage to this is that silicon nitride can carry similar loads to that of silicon steel with less force needed.ZirconiaZirconia was made for high performance duties such as (atmospheric journeys). This means the material has the highest temperature ability. However, this material has a high thermal expansion (almost like steel) but weighs less so it does not have the same weight saving and thermal shock resistance found in other ceramic materials. (Carter, 2009)Zirconia is used when low loads are applied or when high temperature capabilities are needed (corrosive too).(iii)Porosity refers to a measure of void (empty spaces in a material) and is a fraction of the pile of voids over the total volume between 0% and 100% (Quora, 2003)Technical ceramics do not have open porosity. To achieve porosity manufacturing process must be done (use of additives). This then allows closed and open pores to be created, ranging from nm to m.Porosity can have various effects on the mechanical properties of ceramics (as chosen). The following proper ties are effectedCompressive strengthDensityFatigueYoungs modulusFracture toughnessShear modulusTensile strengthAny residual porosity will influence elastic properties and strength. For some materials, the magnitude of the modulus of elasticity E decreases with volume fraction perIt is known that porosity affects flexural strength as it reduces cross-sectional area. It also results in pores acting as stress concentrates. (Duffy, 2010)(iv)Below is a completed table for ceramic materials having 20vol% porosity. This is done by using the followingThe below calculation for silicon nitride is done for clarity )= 199.424 GPaWhere is the modulus of elasticity and is the porosity volume.Table 5 Ceramic materials with 20vol%MaterialModulus of Elasticity GPaPorosity at 20vol%E(20%) Porosity GPaSilicon nitirde3040.2199.424Zirconia2050.2134.48Silicon carbide3450.2226.32Aluminum oxide3930.2257.808Glass-ceramic1200.278.72Mullite1450.295.12Spinel2600.2170.56 magnesium oxide2250.2147.6Fused sili ca730.247.888Soda-lime glass690.245.264As seen from the above, silicon nitride is the ceramic material resulting in a modulus of elasticity when having a porosity volume of 20%.ReferencesCarter, 2009. Carter. Online Available at http//www.carterbearings.co.uk/unasis/hybrid-and-ceramic-bearings/ceramic-matericals-and-their-properties-part-2/Accessed Saturday Feburary 2017.Duffy, J., 2010. Moodle. Online Available at http//moodle.itb.ie/pluginfile.php/115304/mod_resource/content/0/CES%20EduPack%20-%20USEFUL%20SOLUTIONS%20to%20COMMON%20PROBLEMS%202008%20-%2001Jan13.pdfAccessed Wednesday Feburary 2017.Edupack, C., 2006. s.l. s.n.Ibsco, 2011. Ibsco. Online Available at http//www.ibsco.com/ceramic-ball-bearings.phpAccessed Saturday Feburary 2017.Quora, 2003. Quora. Online Available at 2017Accessed Wednesday Feburary 2017.