Light stiff beam Support structure for concave parabolic mirrors Flywheel Energy Storage systems

Transcription

1 ase Studies in aterials Selection Light sti beam Support structure or concave parabolic mirrors Flywheel Energy Storage systems For this problem : Beam : inimize mass Example: Light-sti Beam Select the best material or a light and sti column o length L supports a load o F onstraints: Length L, Bending Stiness S aterial, cross-sectional area Sti beam o length L and minimum mass During the delection o the beam under three-point loading is b L Square section, area A b 2 The stiness is ore ino: aterials Selection in echanical Design, hapters 5 and 6 E Winter 2008 Slides 5 - E Winter 2008 Slides 5-2 Analysis To minimize mass: Eliminate A to get To minimize mass, the material perormance index to be maximized is 0 Slope Young's modulus ^ ( /2 ) E^(/2) versus E Winter 2008 Slides 5-3 E Winter 2008 Slides 5-4 E versus aterial indices 00 Slope 2 Young's modulus (GPa) e E Winter 2008 Slides FUNTION Tie Beam Shat olumn echanical, Thermal, Electrical... Each combination o ONSTRAINTS Stiness speciied Strength speciied Fatigue limit Geometry speciied onstraint Free variable OBJETIVE inimum cost inimum weight inimum volume inimum eco- impact has a characterising material index INDEX / 2 E aximize this! E Winter 2008 Slides 5-6

2 Support structure or concave parabolic mirrors Support structure or parabolic mirrors oncave parabolic mirrors are used in telescopes both optical and radio The shape is critical. Thereore the material used should be relatively sti and dimensionally stable. A ground based telescope will be subject to gravity A space telescope will have to be launched ass is also an important actor odel the support structure as a circular disk o radius R and thickness t onstraints Precision mirror inimize mass Radius R is speciied ust not distort more than δ under sel weight High dimensional stability no creep, low thermal expansion aterial Thickness Relective surace E Winter 2008 Slides 5-7 E Winter 2008 Slides 5-8 Support structure or parabolic mirrors Support structure or parabolic mirrors Appendix A lists relationships among various types o loading and the response o dierent basic structures. For this problem, we need Appendix A-7 The delection o a disk under a pressure dierential Δp is The mass o the mirror is For delection under sel load, replace Δp by the weight per unit area gt to get The lightest mirror is the one with the greatest value o or a material with a Poisson s ratio o 0.3 For an optical mirror, this delection should be o the order o 0μm or less This depends on the wavelength Other properties o importance could include the thermal expansion coeicient, high melting point, low moisture sensitivity, etc. E Winter 2008 Slides 5-9 E Winter 2008 Slides 5-0 E versus 00 0 Slope 3 0. Young's modulus (GPa) 0.0 e-3 Flexible Polymer Foam (VLD) Flexible Polymer Foam (LD) E Winter 2008 Slides 5 - Also speciy E min 00GPa using Limit Stage Select aterials - All Stages Name Identity Alumina Aluminum nitride Aluminum/Silicon carbide composite Boron carbide FRP, epoxy matrix (isotropic) Silicon Silicon carbide Silicon nitride E Winter 2008 Slides 5-2 2

3 A lywheel is an energy storage system in which energy is stored as the kinetic energy o a spinning mass. hildren s toy cars typically made o lead Gyrobus Switzerland in the 950s large steel disks spinning at 3000 rpm Uninterruptible power supply (UPS) Regenerative braking systems Smooth out uneven energy delivery (lywheels in I engines) A typical lywheel energy storage system consists o rotor suspended by bearings inside a vacuum chamber to reduce riction, connected to a combination electric motor/electric generator The rotors are generally made o steel on smaller systems, but large systems use high-tensilestrength ibers (such as carbon ibers) embedded in epoxy resins, or some other high-strength composite material. Energy is stored by using an electric motor to increase the speed o the spinning lywheel. The system releases its energy by using the momentum o the lywheel to power the motor/generator. E Winter 2008 Slides 5-3 E Winter 2008 Slides 5-4 There are a wide range o materials that have been used or making the rotors in lywheel systems Lead (very high density) Steel (high density) Fiber reinorced composites (relatively light) What drives the choice o these diverse materials or similar applications? There are actually two dierent objectives or the above applications ommercial and space based energy storage systems need to maximize energy stored per unit mass Flywheels in toys are required to maximize energy storage per unit volume or a given angular velocity aximum energy storage per unit mass onstraints Flywheel aximize kinetic energy per unit mass Outer radius R is ixed ust not burst ust not crack aterial t R E Winter 2008 Slides 5-5 E Winter 2008 Slides 5-6 aximum energy storage per unit volume at ixed ω Kinetic energy o a spinning mass is given by onstraints Flywheel aximize kinetic energy per unit volume Outer radius R is ixed ust not burst ust not crack aterial R Kinetic energy per unit mass is t E Winter 2008 Slides 5-7 E Winter 2008 Slides 5-8 3

4 Since KE is to be maximized Increase angular velocity Increase length o the shat Increase density o the material onstraints Should not burst. Thereore the tensile hoop stresses that develop due to centriugal orces should not exceed the ailure stress The maximum principal stress that develops when a solid disk is spinning is Rearranging the terms in the above two equations gives The Poisson s ratio or most engineering materials is about (/3). So in order to maximize the energy stored per unit mass, one needs to maximize the material index given by E Winter 2008 Slides 5-9 E Winter 2008 Slides aterials or Energy FRP, epoxy Storage matrix (isotropic) Silicon Flywheels nitride Wrought magnesium alloys Similar to Figure 4.4 Beryllium GFRP g Alloys FRP Hi-strength Steels eramics σ 00 Ti-Alloys ast Irons Lead alloys Al-Alloys Guidelines or inimum weight Design Yield strength (elastic limit) (Pa) Sheet molding compound, S, polyester matrix Polyamides (Nylons, PA) Sotwood: pine, along grain Rigid Polymer Foam (D) Rigid Polymer Foam (LD) Plaster o Paris Zinc die-casting alloys Lead alloys Sandstone oncrete Guidelines or inimum weight Design σ σ 2/ 3 σ / 2 E Winter 2008 Slides σ σ / 2 σ 2 / E Winter 2008 Slides 5-22 aterial eramics omposites: FRP omposites: GFRP Beryllium High Strength Steels High Strength Al alloys High Strength g alloys Ti alloys Lead ast iron andidate aterials or lywheels (kj/kg) (in compression only) omments Brittle and weak in tension unsuitable The best perormance Good perormance, Less expensive than FRP Good perormance, expensive, toxic All about the same perormance. Steel and Al alloys are less expensive than g or Ti alloys Traditional Traditional Lead and cast iron have very low material indices compared to the other materials Why are they used in applications like toy cars? ommercial energy storage systems spin at very high angular velocities. Thereore the danger o developing tensile stresses o the order o the ailure stress is real In a toy car, the lead lywheel is usually spun by a pulled string. The speeds are no where near that which can cause tensile ailure. The volume o the toy is however limited. The objective then becomes to maximize energy storage or minimum volume, and the constraint o the lywheel alling apart can be removed E Winter 2008 Slides 5-23 E Winter 2008 Slides

5 The kinetic energy per unit volume is The material index now becomes simply So materials with the highest density are best lead, cast iron (tungsten, molybdenum, gold, silver?) ost eliminates the last ew elements in the above list E Winter 2008 Slides