ENGINEERING STUDIES ATAR COURSE DATA BOOK 2017

Transcription

1 ENGINEERING STUDIES ATAR COURSE DATA BOOK 207 Copyright School Curriculum and Standards Authority, 207 This document apart from any third party copyright material contained in it may be freely copied, or communicated on an intranet, for non-commercial purposes in educational institutions, provided that it is not changed and that the School Curriculum and Standards Authority is acknowledged as the copyright owner, and that the Authority s moral rights are not infringed. Copying or communication for any other purpose can be done only within the terms of the Copyright Act 968 or with prior written permission of the School Curriculum and Standards Authority. Copying or communication of any third party copyright material can be done only within the terms of the Copyright Act 968 or with permission of the copyright owners. Any content in this document that has been derived from the Australian Curriculum may be used under the terms of the Creative Commons Attribution 4.0 International (CC BY) licence. This document is valid for teaching and examining until 3 December /806 Engineering Studies Data Book updated January 207

2 ENGINEERING STUDIES 2 Core content Index Data BOOK Core content SI units Standard prefixes Common constant 3 General formulae 4 Selected material properties 5 Specialist Field Mechanical Basic formulae (Mechanical) 6 Basic formulae (Mechanical) 2 Selected SI units Common constants 7 Second moment of area 8 Simple beams 9 Specialist Field Mechatronics Selected SI units Prefixes 0 Standard symbols Resistor colour codes Electrical formula wheel 2 Basic formulae (Mechatronics) 3 Basic formulae (Mechatronics) 2 SI units 4 Diodes Transistors 5 Logic symbols with truth tables and Boolean expressions Flow chart symbols 6

3 DATA BOOK 3 ENGINEERING STUDIES Core content SI units uantity Name SI unit Symbol Length metre m Mass kilogram kg Time second s Energy, work, quantity of heat joule J Power watt W Celsius temperature degree Celsius C Area square metre m 2 Volume cubic metre m 3 Speed, velocity metre per second m s - Mass density kilogram per cubic metre kg m -3 Standard prefixes Factor prefix Symbol Factor prefix Symbol 0 2 tera T 0-3 milli m 0 9 giga G 0-6 micro μ 0 6 mega M 0-9 nano n 0 3 kilo k 0-2 pico p Common constant Item Symbol Value Ratio of the circumference of a circle to its diameter π 3.459

4 ENGINEERING STUDIES 4 Core content Data BOOK General formulae parameter Formula Terms Side lengths of a right triangular plane figure h = o + a h is the hypotenuse o is the opposite side a is the adjacent side a cosθ = h θ is the angle Angular relationships of a o h is the hypotenuse sinθ = right triangular figure h o is the opposite side o a is the adjacent side tanθ = a Perimeter of a circle [p] p = π d d is the diameter Area of a circle [A] 2 A = πr Surface area of open ended cylinder [A] A = π dh Volume of a cylinder [V] 2 V= π rh Surface area of a sphere [A] 2 A = 4πr Volume of a sphere [V] V = 4 π r Density [ρ] of a material Energy [E] Efficiency [η] % 3 m ρ = V E = Pt 3 r is the radius d is the diameter h is the height r is the radius h is the height r is the radius r is the radius m is mass V is volume t is the time taken P is the power Output η % = 00 η is the efficiency (%) Input

5 DATA BOOK 5 ENGINEERING STUDIES Core content Selected material properties Material Density kg m -3 Elastic (Young s) modulus kn mm -2 Ultimate tensile * strength N mm -2 Yield stress N mm -2 Electrical conductivity Ω - m Thermal conductivity W m - K - Structural steel Stainless steel Cast iron Wrought iron Aluminium Brass Copper Zinc Solder (60% lead, 40% tin) Concrete Concrete (steel reinforced) 40 (compressive) Timber (parallel to grain) Polypropylene Polycarbonate ABS plastics Nylon Acrylic Glass Diamond Gold Ice @-5 C @-5 C Pure water 000 Sea water 022 Petrol Crude oil * Unless noted as compressive strength.

6 ENGINEERING STUDIES 6 Specialist field mechanical Data BOOK Basic formulae (Mechanical) parameter Formula Terms Mechanical Advantage [MA] Velocity Ratio [VR] Velocity ratios in drive trains (for gear or pulley train ) [VR] Torque [τ] Moment of a force [M] Stress[σ] or Pressure [p] Strain [ε] Young s (Elastic) modulus [E] Young s (Elastic) modulus [E] expanded formula Factor of Safety [FS] Acceleration [a] Velocity [v] F MA = F d VR = d F VR = D load effort effort load F D 2 2 τ = Fr M = Fd F D σ (p) = F A L ε = L σ E = ε FL E = A L σuts FS= σ a = v u t safeworking v = u + 2as Distance [s] 2 Force [F] Equilibrium conditions Equilibrium conditions (expanded) 2 F load is the output force F effort is the input force d effort is the distance moved by the effort d load is the distance moved by the load F,2 and 3 are the followers D,2 and 3 are the drivers (measured via number of teeth on gears or by pulley diameters) F is the force r is the radius F is the force d is the perpendicular distance F is the force A is the area ΔL is the change in length L is the original length σ is the stress ε is the strain F is the force A is the area ΔL is the change in length L is the original length σ UTS is the ultimate tensile stress σ safeworking is the safe working stress v is the final velocity u is the initial velocity t is the time u is the initial velocity a is the acceleration s is the distance s = ut + at u is the initial velocity F = ma M = 0 Fy = 0 F x = 0 ΣCWM = ΣACWM ΣF( up) = ΣF( down) ΣF( left) = ΣF( right) t is the time a is the acceleration m is the mass a is the acceleration Σ is the sum of M are the moments F y are the vertical force components F x are the horizontal force components Σ is the sum of CWM are clockwise moments ACWM are anticlockwise moments

7 DATA BOOK 7 ENGINEERING STUDIES Specialist field mechanical Basic formulae (Mechanical) 2 parameter Formula Terms Work [W] Power [P] Energy [E] Potential energy [E p] W = Fs Fs P = = t E = Pt Fv E p = mgh Kinetic energy [E k] 2 Potential and kinetic energy conversion Efficiency [η] % Compound gear or pulley system [RPM] Linear velocity of a gear or pulley system [v] Distance around a winch drum [s] E k = mv E 2 = p E k Work done in moving load η % = 00 Work done by the effort input RPM output RPM = VR ( RPM )( 2π r) s v = = 60 t F is the force s is the distance moved F is the force s is the distance t is the time taken v is the average velocity t is the time taken P is the power m is the mass g is the acceleration due to gravity h is the height m is the mass v is the velocity Δ is the change in Work done in moving load is the output Work done by the effort is the input VR is the velocity ratio RPM is the revolutions per minute r is the radius of the gear or pulley s is the distance travelled t is the time taken s = 2πr r is the radius of the drum Selected SI units SI unit Derived quantity Expression Expression Name Symbol in terms of in terms of other SI units SI base units Force newton N m kg s -2 Pressure, stress pascal Pa N m -2 m - kg s -2 Energy, work, quantity of heat joule J N m m 2 kg s -2 Power, radiant flux watt W m 2 kg s -3 Common constants Item Symbol Value Acceleration due to gravity g 9.80 m s 2

8 ENGINEERING STUDIES 8 Specialist field mechanical Data BOOK Second moment of area Shape Dimensions b Second moment of area about centroidal axis 3 Rectangle solid section h bh I (vertical) xx = 2 D D Circular solid section x x 4 πd I xx = 64 D Circular tube section x x I xx 4 4 ( Do Di ) = π 64 D o = cylinder outside diameter D i = cylinder inside diameter t t

9 DATA BOOK 9 ENGINEERING STUDIES Specialist field mechanical Simple beams Beam configuration Maximum bending moment Maximum deflection (y) A F F B BM = max FL at A FL y = 3EI 3 xx at B Here F is the single vertical point load Here F is the single vertical point load F UDL= ωl BM max = F UDL 2 L at A y = FUDLL 8EI xx 3 at B Here F UDL= ωl which is the load per unit length (ω) times the length of the beam (L) Here F UDL= ωl which is the load per unit length (ω) times the length of the beam (L) A F B BM max = FL 4 at C y = 3 FL 48EI xx at C C Here F is the single vertical point load Here F is the single vertical point load F UDL= ωl BM max = FUDLL 8 at C Y 5FUDLL = 384EI 3 xx at C Here F UDL= ωl which is the load per unit length (ω) times the length of the beam (L) Here F UDL= ωl which is the load per unit length (ω) times the length of the beam (L) Terms: L ω FUDL F E Ixx A B C Length of beam between supports A uniformly distributed load per unit length The product of the UDL s applied load/unit length (ω) and the length of the beam (L) An applied vertical point load The elastic (Young s) modulus of the material of the beam The second moment of area of the beam section The left-hand end of the beam The right-hand end of the beam The mid-point of the beam

10 ENGINEERING STUDIES 0 Specialist field mechatronics Data BOOK Selected SI units uantity Unit Abbreviation Symbol Expression in terms of other SI units Voltage volt V V W A - Current ampere A I W V - Resistance ohm Ω R V A - Charge coulomb C A s Capacitance farad F C A s V - Power watt W P J s - Frequency hertz Hz f s - prefixes prefix Abbreviation Multiplier Tera T 0 2 = Giga G 0 9 = Mega M 0 6 = Kilo k 0 3 = = Milli m 0-3 = 0.00 Micro µ 0-6 = Nano n 0-9 = Pico p 0-2 =

11 DATA BOOK ENGINEERING STUDIES Specialist field mechatronics Standard symbols Cell Light dependent resistor (LDR) NPN transistor Battery Thermistor IC Integrated circuit DC Power supply unit (PSU) Non-polarised capacitor Polarised capacitor Diode Voltmeter Ohmmeter Fuse Light emitting diode (LED) Ammeter 78XX Voltage regulator Lamp (also called bulb) SPST switch SPDT switch DC motor Servo DPDT switch Push to make switch SPDT relay Push to break switch DPDT relay Resistor Potentiometer Unipolar stepper motor Variable resistor

12 ENGINEERING STUDIES 2 Specialist field mechatronics Data BOOK Resistor colour codes Band colour st band 2nd band Multiplier Black 0 Brown 0 Red Orange Yellow Green Blue Tolerance band Brown ± % Red ± 2% Gold ± 5% Silver ± 0% Violet 7 7 Grey 8 8 White 9 9 E2 Preferred values: 0, 2, 5, 8, 22, 27, 33, 39, 47, 56, 68, 82 Example: 4 band colour code Electrical formula wheel

13 DATA BOOK 3 ENGINEERING STUDIES Specialist field mechatronics Basic formulae (Mechatronics) Ohm s law parameter Formula Terms Power law 2 2 V Electrical energy [E e] Resistors in series Resistors in parallel Kirchhoff s first law I = 0 Kirchhoff s second law V = 0 Capacitors in parallel Capacitors in series Voltage dividers LED in series with a V = IR V is the voltage I is the current R is the resistance P is the power P = VI = I R = I is the current R V is the voltage R is the resistance E e = VIt V is the voltage I is the current t is the time Rt = R+ R2 + R t is the total resistance R, R 2, are the individual resistances R t is the total resistance = + + R R R R, R 2, are the individual resistances t 2 resistor ( ) Transistor current gain The sum of currents flowing toward that point is equal to the sum of currents flowing away from that point The directed sum of the electrical potential differences around a closed loop in a circuit must be zero C = C+ C2 + C is the total capacitance C, C 2, are the individual capacitances C is the total capacitance = + + C C C C, C 2, are the individual capacitances 2 Vcc = V+ V V 2 cc is the total voltage across the resistor pair R V is the voltage across resistor R V = Vcc V 2 is the voltage across resistor R2 R + R 2 R2 V2 = Vcc R + R 2 V cc is the total applied voltage Vcc VLED V R = LED is the voltage across the LED I I LED is the current through the LED h FE I = I C B LED R is the series resistor I C is the collector current I B is the base current

14 ENGINEERING STUDIES 4 Specialist field mechatronics Data BOOK Basic formulae (Mechatronics) 2 parameter Formula Terms Mechanical advantage (MA) MA = load effort Velocity ratio (VR) Pulley belt ratio Chain and sprocket ratio Gear ratio VR = VR = VR = VR = distance moved by effort distance moved by load Ø follower pulley Ø driver pulley nº teeth follower gear nº teeth driver gear nº teeth follower gear nº teeth driver gear Compound gear ratio Worm and worm wheel ratio VRT = VR VR2.. VR = nº teeth worm wheel VR T is the total velocity ratio VR, VR 2, are the individual velocity ratios Rack and pinion distance = nº teeth pinion nº revolutions nº teeth per metre rack Speed, velocity velocity = distance time = (rpm)(2πr) 60 output rpm = input rpm VR VR is the velocity ratio rpm is the revolutions per minute SI units uantity Name SI unit Symbol Length (distance) metre m Time second s Speed, velocity metre per second m s -

15 DATA BOOK 5 ENGINEERING STUDIES Specialist field mechatronics Diodes Diode model Formula Terms/diagrams VD = VD,on (or VF) On Check: I D > 0 I D = 0 A Off Check: VD < VD,on (or VF) Transistors Transistor model (NpN BJT) Formula Terms/diagrams I B = I C = 0 A Cut-off Check: V BE < 0.7 V V BE = 0.7 V V CE = 0 V Saturation Check: I B > 0 A I C I B < β (or h FE) V BE = 0.7 V I C = β I B Forward-active Check: I B > 0 A V CE > 0 V Transistor current I C gain Gain or β or h FE = I C is the collector current I B I B is the base current

16 ENGINEERING STUDIES 6 Specialist field mechatronics Data BOOK logic symbols with truth tables and Boolean expressions A NOT Gate A 0 0 A B OR Gate A B A B AND Gate AND Gate A B A B NOR Gate A B A B NAND Gate A B A B XOR Gate A B Flow chart symbols End of Data Book

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18 ENGINEERING STUDIES 8 Data BOOK This page has been left blank intentionally

19 DATA BOOK 9 ENGINEERING STUDIES This page has been left blank intentionally

20 ACKNoWlEDGEMENTS page 2 Electrical formula wheel. Retrieved January, 200, from Published by the School Curriculum and Standards Authority of Western Australia 303 Sevenoaks Street CANNINGTON WA 607