Tawjihi Vocational Engineering cheat sheet

First-angle projection places the object between observer and plane; the view from above is drawn below the front view. Third-angle places the plane between observer and object; the top view is drawn above the front view.

ISO A-series sheet areas halve at each step: A0 = 1 m², A1 = 0.5 m², A2 = 0.25 m². A4 = 1/16 m². The ratio of sides is √2 : 1.

Standard scales: full size 1:1; enlargement 2:1, 5:1, 10:1; reduction 1:2, 1:5, 1:10, 1:20, 1:50, 1:100.

Line precedence when lines coincide: visible outlines and edges first, then hidden outlines, then centre lines, then dimension and projection lines.

A dimension line is drawn parallel to the measured feature with arrowheads touching the extension lines; extension lines start about 1 mm from the object and extend about 2–3 mm beyond the dimension line.

Hatching in section views uses thin continuous lines at 45° to the principal outline, equally spaced; adjacent parts are hatched in opposite directions.

A section view removes material in front of the cutting plane; the cutting plane is shown in an adjacent view by a chain line with thick ends and arrows giving viewing direction.

Symbols: Ø diameter, R radius, □ square, SR spherical radius, ⌴ counterbore, ⌵ countersink, M metric thread (e.g., M12×1.75).

A surface roughness value Ra is the arithmetic mean deviation of the profile; smaller Ra means a smoother surface. Typical turning: Ra 1.6–3.2 µm; grinding: Ra 0.4–0.8 µm.

Carbon steel classification by carbon content: low carbon (mild) up to 0.25 % C, medium carbon 0.25–0.60 % C, high carbon 0.60–1.4 % C.

Cast iron contains 2–4 % C; grey cast iron is brittle in tension but good in compression and damping; it is not weldable by ordinary methods.

Brass is a copper–zinc alloy; bronze is a copper–tin alloy (or copper–aluminium in aluminium bronze). Bronze has higher wear resistance than brass.

Hardness scales: Brinell (HB) uses a 10 mm ball for soft to medium metals; Rockwell C (HRC) uses a diamond cone for hardened steel; Vickers (HV) uses a diamond pyramid.

Annealing: heat above the critical temperature, hold, then cool slowly in the furnace. It softens, relieves internal stress, and refines grain structure.

Quenching (rapid cooling in water or oil) followed by tempering produces martensite that is then toughened; full hardening without tempering leaves the part brittle.

A hacksaw blade cuts on the forward stroke; blade pitch is chosen so at least two teeth are in contact with the workpiece thickness.

A file cuts on the forward stroke only; a second-cut file is used for finishing, a bastard file for rough removal.

A twist drill has a point angle of 118° for general steel; 135° is used for hard materials; the helix angle is typically 25–30°.

Equilibrium of a particle: ΣF_x = 0 and ΣF_y = 0. Equilibrium of a rigid body in 2D: ΣF_x = 0, ΣF_y = 0, ΣM = 0.

Moment of a force about a point: M = F × d, where d is the perpendicular distance from the point to the line of action. Units: N·m.

A couple consists of two equal, opposite, parallel forces; its moment is M = F × d and is the same about any point.

Resultant of two perpendicular forces: R = √(F₁² + F₂²); direction θ = tan⁻¹(F₂/F₁) from F₁.

Resolving a force F at angle θ to the horizontal: F_x = F cos θ, F_y = F sin θ.

Friction: limiting friction F = μN, where μ is the coefficient of friction and N the normal reaction. Motion starts when the applied force exceeds μN.

Centroid of a rectangle lies at its geometric centre; of a triangle at one-third of the height from the base; of a semicircle at 4r/(3π) from the diameter.

Work = force × distance moved in the direction of the force (J); power = work / time (W); efficiency = useful output / input × 100 %.

For a simply supported beam with a central point load W and span L: reactions are W/2 each; maximum bending moment = WL/4 at mid-span.

Ohm's law: V = I × R. Power: P = V × I = I²R = V²/R.

Series circuit: R_total = R₁ + R₂ + …; current is the same in all elements; voltage divides in proportion to resistance.

Parallel circuit: 1/R_total = 1/R₁ + 1/R₂ + …; voltage is the same across all branches; current divides inversely with resistance.

Kirchhoff's current law: sum of currents entering a node equals the sum leaving. Kirchhoff's voltage law: algebraic sum of voltages around a closed loop is zero.

A capacitor stores charge Q = C × V; energy = ½CV². A capacitor blocks DC and passes AC; its reactance X_C = 1/(2πfC).

An inductor opposes change of current; its reactance X_L = 2πfL. In a pure inductor, current lags voltage by 90°.

In a series RLC circuit at resonance, X_L = X_C, impedance is minimum and equal to R; resonant frequency f = 1/(2π√(LC)).

A diode conducts when forward-biased (anode positive with respect to cathode) above about 0.7 V for silicon; it blocks in reverse bias.

A transformer changes AC voltage by the turns ratio: V_s/V_p = N_s/N_p. It does not work on steady DC.

Cutting speed for turning: v = πDN/1000 (m/min), where D is workpiece diameter in mm and N is spindle speed in rev/min.

Feed rate in turning is measured in mm/rev; depth of cut is half the reduction in diameter for a straight turning pass.

In a shaping operation, the tool cuts on the forward stroke; the return stroke is idle. Stroke length = job length + approach + overtravel.

Drilling: cutting speed v = πDN/1000; feed is in mm/rev; a reamer is used after drilling to improve hole size and finish, removing 0.1–0.5 mm.

Milling: up (conventional) milling produces chips that start thin and end thick; down (climb) milling starts thick and ends thin and gives a better finish on rigid machines.

Welding: in arc welding the electrode may be consumable (SMAW) or non-consumable (TIG, tungsten electrode with separate filler).

A fillet weld joins two surfaces at an angle; its throat thickness t = 0.707 × leg length s.

Casting: the riser feeds molten metal to compensate for shrinkage; a pattern is made slightly larger than the part by the shrinkage allowance (e.g., 1–2 % for cast iron, about 1.3 % for steel).

Sheet-metal bend allowance depends on bend radius, thickness, and bend angle; the neutral axis lies about 0.3–0.5 of thickness from the inside surface.

A vernier calliper least count = 1 main-scale division − 1 vernier-scale division. For 1 mm main divisions and 50 vernier divisions spanning 49 mm, least count = 0.02 mm.

A micrometer least count = pitch / number of divisions on the thimble. For 0.5 mm pitch and 50 divisions, least count = 0.01 mm.

Zero error: a positive error means the instrument reads too much and must be subtracted; a negative error must be added to the reading.

A dial indicator (plunger type) is used for runout, flatness, and alignment checks; its resolution is commonly 0.01 mm.

A go/no-go gauge checks limits without giving a size value; a plug gauge checks holes, a snap gauge checks shafts.

Tolerance is the difference between the upper and lower limits. A fit is clearance if the hole is larger than the shaft, interference if the shaft is larger, transition if either may occur.

Control charts: X-bar chart monitors the process mean; R chart monitors process variation. Points outside the 3σ control limits indicate an out-of-control condition.

Process capability C_p = (USL − LSL)/(6σ); C_pk accounts for centring and equals min[(USL − μ), (μ − LSL)]/(3σ).

Calibration compares an instrument against a standard of known accuracy; traceability links the standard to a national or international reference.

Hierarchy of controls, most to least effective: elimination, substitution, engineering controls, administrative controls, personal protective equipment (PPE).

Lockout/tagout (LOTO) isolates hazardous energy before maintenance; a personal lock and tag are applied by each worker and removed only by that worker.

Machine guards must prevent access to nip points and rotating parts; a guard should not be removable without a tool.

Electrical safety: earth (ground) the metal frame of equipment; use a residual current device (RCD) rated at 30 mA for personnel protection.

Fire classes: A solid combustibles, B flammable liquids, C gases, D metals, F cooking oils. Water is unsuitable for B, C, D, and live electrical fires.

A fire triangle has three sides: fuel, oxygen, and heat. Removing any one side extinguishes the fire.

Hazardous waste such as used oil, solvents, and batteries must be segregated, labelled, and sent to an approved disposal route; they must not enter drains.

Noise exposure limit commonly used: 85 dB(A) as an 8-hour time-weighted average; hearing protection is required above this level.

Safety signs: red = prohibition/fire equipment, yellow = warning, blue = mandatory action, green = safe condition or first aid.

Preventive maintenance is scheduled by time or usage; predictive (condition-based) maintenance acts on measured condition such as vibration, temperature, or oil analysis.

Bearing failure indicators: increased vibration at the ball-pass frequency, rising temperature, and metallic particles in the lubricant.

Vibration severity is assessed by overall RMS velocity in mm/s; ISO 10816 bands classify machines from good to unacceptable.

Alignment of a motor to a pump: angular misalignment shows as 1× and 2× running speed; parallel misalignment shows mainly at 2× running speed.

Lubrication: too much grease in a bearing raises temperature and can cause failure; the correct fill is about one-third to one-half of the free space.

A centrifugal pump that loses flow may have a worn impeller, a blocked suction strainer, air ingress, or a closed discharge valve; check suction conditions first.

Belt drive troubleshooting: squealing indicates slip or glazing; check tension by deflection (about 1 % of span per 100 N applied) and pulley alignment.

Troubleshooting sequence: observe symptoms, gather data, form a hypothesis, test it, correct the fault, then verify and record the result.

Thermography detects loose electrical connections and overheating bearings by infrared temperature difference before failure occurs.

Pythagoras: c² = a² + b². Trigonometric ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.

Sine rule: a/sin A = b/sin B = c/sin C. Cosine rule: a² = b² + c² − 2bc cos A.

Area formulas: rectangle A = lw; triangle A = ½bh; circle A = πr²; trapezium A = ½(a + b)h.

Volume formulas: cylinder V = πr²h; cone V = ⅓πr²h; sphere V = 4/3πr³; prism V = base area × length.

Percentage change = (new − old)/old × 100 %. Percentage error = |measured − true|/true × 100 %.

Unit conversions: 1 inch = 25.4 mm; 1 kgf = 9.81 N; 1 bar = 100 kPa = 10⁵ Pa; 1 kW = 1.36 hp; 1 kWh = 3.6 MJ.

Stress σ = F/A (N/mm² = MPa); strain ε = ΔL/L (dimensionless); Young's modulus E = σ/ε.

Thermal expansion: ΔL = α L ΔT, where α is the coefficient of linear expansion (e.g., steel about 12 × 10⁻⁶ /°C).

Gear ratio = number of teeth on driven gear / number of teeth on driving gear = speed of driver / speed of driven.

A technical report structure: title, summary, introduction, method, results, discussion, conclusion, references, appendices.

A work order records the job description, location, requested date, assigned technician, parts used, labour hours, and sign-off.

A bill of materials (BOM) lists every component with part number, description, quantity, and unit; it is the basis for purchasing and assembly.

An isometric sketch uses three axes at 120° to each other, with vertical lines vertical and the other two at 30° to the horizontal.

Dimensioning rules: give each dimension once, place it on the view that shows the feature true size, and never dimension a hidden line if a visible view exists.

Email and memo etiquette at work: state subject, purpose, action required, and deadline in the first lines; keep one topic per message.

A standard operating procedure (SOP) is written in the imperative and includes scope, safety precautions, tools, step sequence, and acceptance criteria.

Symbols on P&ID diagrams: a circle with a horizontal line is a field-mounted instrument; a circle with no line is panel-mounted; letters give the measured variable and function (e.g., FT = flow transmitter).

Change control: any modification to a drawing or procedure must be recorded with revision number, date, author, and approval.

Break-even quantity Q = fixed costs / (selling price per unit − variable cost per unit).

Contribution margin per unit = selling price − variable cost; contribution margin ratio = contribution / selling price.

Payback period = initial investment / annual net cash inflow. A shorter payback means faster recovery but ignores cash flow after payback.

Net present value NPV = Σ [cash flow / (1 + r)^t] − initial investment; accept a project when NPV is positive.

A Gantt chart shows activities as bars against time; the critical path is the longest path through the network and determines the shortest project duration.

Float (slack) = latest start − earliest start; activities on the critical path have zero float.

Cost estimation: material cost = quantity × unit price × (1 + waste allowance); labour cost = hours × hourly rate; add overhead and profit margin.

Depreciation by straight line = (cost − salvage value) / useful life. Reducing balance applies a fixed percentage to the book value each year.

A feasibility study covers technical, economic, legal, operational, and schedule feasibility before capital is committed.

Working capital = current assets − current liabilities; it covers day-to-day operating costs such as wages, materials, and utilities.

Newton's first law: a body remains at rest or in uniform motion unless acted on by a resultant force. Second law: F = ma. Third law: action and reaction are equal and opposite.

Weight W = m g, with g = 9.81 m/s². Mass in kg, weight in N.

A simply supported beam with a uniformly distributed load w over span L has reactions wL/2 at each support and maximum bending moment wL²/8 at mid-span.

A cantilever with a point load W at the free end has maximum bending moment WL at the fixed end and maximum deflection WL³/(3EI).

Shear force diagram: the shear force changes slope at each concentrated load; the bending moment is maximum where the shear force is zero.

Moment of inertia of a rectangle about its centroidal axis: I = b h³/12. For a circle: I = πd⁴/64.

Bending stress σ = M y / I; maximum stress occurs at the greatest distance y from the neutral axis.

Torque transmitted by a solid shaft: T = (π/16) τ d³, where τ is the allowable shear stress.

Coefficient of friction can be found from the angle of repose φ: μ = tan φ, where φ is the steepest angle at which a body remains at rest on the plane.