Gear design

Mechanical Engineering (B.E./B.Tech) · Machine design · free study notes for exams, placements and interviews

In short

Gear design is the sizing and selection of toothed wheels that transmit power and motion between shafts at a constant speed ratio, so that the teeth survive bending, surface wear and dynamic shock for the required life. It starts from power, speed and ratio, and ends with module, number of teeth, face width, material and heat treatment. It is a near-certain long question in Machine Design papers (Lewis equation, beam and wear strength, interference) and a standard GATE numerical area, and it is asked in interviews at Maruti Suzuki, Tata Motors, Mahindra, Ashok Leyland, Bharat Gears, ZF, Elecon, Shanthi Gears, TAFE, BHEL and L&T. Indian practice follows the IS 2458/IS 2535 (basic rack and modules), IS 4460 (spur and helical capacity) and IS 7443 (worm gear) families, with AGMA and ISO 6336 used in export work.

Explained

Gear types, nomenclature and the law of gearing

Spur gears - straight teeth, parallel shafts, no axial thrust, cheapest, noisier at speed. Helical - teeth at a helix angle ψ (usually 15-30°), quieter and stronger because contact begins gradually, but produces axial thrust; double helical / herringbone cancels that thrust.
Bevel gears - intersecting shafts (usually 90°): straight, spiral (quieter, higher capacity) and hypoid (offset axes, used in car rear axles). Worm and worm wheel - non-intersecting perpendicular shafts, very high ratio (10:1 to 100:1) in one step, compact, can be self-locking, but sliding contact means low efficiency and heat.
Rack and pinion converts rotation to translation (lathe carriage, steering, CNC long-travel axes). Internal gears give compact, same-direction drives (planetary sets, automatic transmissions).
Nomenclature: pitch circle (the imaginary circle where gears "roll"), module m = d/z (mm), circular pitch p = πm, diametral pitch P = z/d (inch system), addendum (1 m), dedendum (1.25 m), clearance (0.25 m), whole depth (2.25 m), tooth thickness ≈ p/2, pressure angle φ (standard 20° full depth in India; older 14½°), face width b, backlash, pitch line velocity v.
Law of gearing: for constant angular velocity ratio, the common normal at the point of contact must always pass through the pitch point. Involute and cycloidal profiles satisfy it; the involute dominates because the ratio is unaffected by small changes in centre distance, cutters are simple and a single rack cutter makes all tooth numbers of a module.
Interference - the tip of one tooth digging into the non-involute flank (fillet) of the mate. Avoided by increasing the number of teeth, increasing the pressure angle, using stub teeth, or undercutting. Minimum teeth to avoid interference on a 20° full-depth pinion is 17-18 (14½° needs 32); below that, use corrected (profile-shifted) teeth.
Contact ratio = average number of tooth pairs in contact; must exceed 1, and 1.4-1.8 is normal for spur gears. Higher contact ratio means smoother, quieter running and lower load per tooth.

Forces, materials and the design procedure

Spur gear force split: tangential Ft = 2T/d (transmits power), radial Fr = Ft tan φ (separates the gears, loads the bearings), resultant Fn = Ft/cos φ. Helical: Ft = 2T/d, axial Fa = Ft tan ψ, radial Fr = Ft tan φn/cos ψ.
Bevel gear: the tangential force acts at the mean pitch radius; radial and axial components swap between pinion and gear, so both need thrust-capable bearings. Worm: the wheel's tangential force equals the worm's axial force and vice versa - that is why a worm shaft needs a strong thrust bearing.
Materials: grey cast iron (FG 200/FG 260) for large low-speed wheels, good damping; plain carbon steels C40, C45, 40C8 for general gears; alloy steels 20MnCr5, 16MnCr5, 15Ni4Cr1 (case-carburised, 58-62 HRC) for automotive and high-duty gears; 40Cr1Mo28 / 42CrMo4 induction-hardened or nitrided; phosphor bronze for worm wheels against a hardened steel worm (dissimilar materials to resist scuffing); nylon, acetal and fabric-reinforced phenolic for light, quiet, unlubricated drives.
Heat treatment ladder: through-hardening (up to ~350 BHN) → induction/flame hardening → case carburising and grinding (best bending and surface strength; standard for gearbox gears) → nitriding (low distortion). Surface hardness governs wear; core toughness governs bending and shock.
Design steps: (1) fix power, speed, ratio i = z₂/z₁ and life; (2) choose material and pressure angle; (3) take z₁ ≥ 17-18 and compute z₂ = i z₁; (4) estimate module from beam strength with a service factor, then round up to a standard module; (5) take b = 8m to 12m (10m typical, 9.5m for helical); (6) check beam strength (Lewis with velocity/service factors) against the dynamic load; (7) check wear strength (Buckingham) against the dynamic load; (8) check for interference and contact ratio; (9) fix accuracy grade, backlash, lubrication and heat dissipation (critical in worm drives).
Standard modules (IS 2535): 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20 mm preferred (choice I); never leave a module like 4.37 mm in the answer - round up.
Accuracy grades: IS 3681/ISO 1328 grades 1-12 (1 finest). Commercial gears are grades 8-10, automotive transmission gears 5-7, instrument gears 3-5. Finer grade = lower dynamic load but higher cost.

Strength checks - beam, dynamic and wear

Lewis beam strength: treats the tooth as a cantilever loaded at the tip with the load on one tooth, giving Fb = σb · b · m · Y (Y = Lewis form factor, a function of z and φ). It ignores stress concentration at the fillet, load sharing between teeth and radial force - so it is conservative in some ways and optimistic in others, and AGMA/IS methods correct it with factors.
Velocity (Barth) factor Cv derates the allowable stress for pitch-line speed: Cv = 3/(3+v) for ordinary cut gears up to ~10 m/s, 6/(6+v) for carefully cut gears up to ~20 m/s, 5.6/(5.6+√v) for precision gears above that (v in m/s).
Dynamic load (Buckingham): Fd = Ft + Fi, with the increment Fi = 21v(Cb + Ft)/(21v + √(Cb + Ft)) (v in m/s, Cb and Ft in N), where C is the deformation factor in N/mm of face width, set by the tooth error e, the tooth form and the moduli of the two materials. The error e comes from the accuracy grade.
Wear (surface contact) strength - Buckingham: Fw = d₁ · b · Q · K, where Q = 2z₂/(z₁+z₂) is the ratio factor and K the load-stress factor derived from the surface endurance limit σes and the elastic moduli: K = σes² sin φ (1/E₁ + 1/E₂)/1.4. An empirical estimate is σes ≈ 2.8 (BHN) − 70 MPa.
Design is safe when both Fb ≥ Fd × (factor of safety) and Fw ≥ Fd × (factor of safety), typically 1.5-2 on the dynamic load. If beam strength fails, increase module or face width; if wear strength fails, harden the surface (raise BHN) or increase diameter - module hardly helps wear.
Equivalent (virtual) teeth for helical gears: z' = z/cos³ψ, used with the Lewis equation on the normal module mn = m cos ψ. Beam strength Fb = σb · b · mn · Y (with Y for z').
Bevel gears (Tredgold's approximation): use the equivalent spur gear of the back cone, z' = z/cos γ (γ = pitch cone angle); face width b ≤ L/3 (L = cone distance) and Lewis is applied with a factor (L − b)/L for the tapering tooth.

Failure modes, lubrication and gearbox practice

Tooth bending fatigue - a fatigue crack at the root fillet leading to a broken tooth; the catastrophic failure, controlled by module, fillet radius, shot peening and material strength.
Pitting - surface fatigue from repeated Hertzian contact stress; initial pitting may stop after run-in, progressive (destructive) pitting does not. Controlled by surface hardness, better finish and higher viscosity oil.
Scoring / scuffing - metal-to-metal welding and tearing when the oil film fails from high sliding velocity and temperature; controlled by EP (extreme pressure) additives, better cooling, lower load.
Abrasive and corrosive wear - dirt in the oil, or acidic/oxidised oil; controlled by filtration, sealing and oil changes.
Lubrication: splash/dip lubrication below about 4-5 m/s, oil bath with slinger disc at medium speeds, forced circulation (pump, filter, cooler) in high-speed and high-power boxes. Worm reducers need the highest attention to heat - their efficiency, 50-95% depending on lead angle, turns the loss into heat in a small casing.
Worm gear specifics: the ratio i = z₂/z₁ where z₁ is the number of worm threads (1-4); efficiency η = tanλ(1 − μ tanλ)/(tanλ + μ) with λ the lead angle; self-locking when tanλ < μ (roughly λ below 5-6°), useful in hoists but never to be relied on as the only brake.
Backlash is deliberate - typically 0.03-0.3 mm depending on module and size - to allow for thermal expansion, tooth errors and lubricant film; zero backlash means jamming, excess backlash means noise, shock on reversal and lost motion in indexing drives.
Gear trains: simple, compound, reverted and epicyclic (planetary). Train value = product of driving teeth / product of driven teeth; for epicyclic trains use the tabular or relative-velocity method. Multi-stage reduction keeps each stage at 4:1 to 6:1 (spur/helical) so sizes stay reasonable.
Manufacture: forming (milling with form cutters, broaching), generating (hobbing, gear shaping with a pinion cutter, rack planing), and finishing (shaving, grinding, lapping, honing). Hobbing is the Indian workhorse; grinding after carburising gives grades 5-6. Plastic gears are injection-moulded.

Codes, standards and current Indian practice

IS 2458 - basic rack tooth profile for cylindrical gears; IS 2535 - standard modules; IS 3681 - accuracy/tolerance grades for spur and helical gears (aligned with ISO 1328).
IS 4460 (Parts 1-3) - calculation of load capacity of spur and helical gears, the Indian equivalent of the ISO 6336 approach; IS 7443 - worm gearing; IS 5037 / bevel gear standards for straight bevel practice.
AGMA 2001/2101 and ISO 6336 are used for export and OEM work; they replace the plain Lewis equation with a bending stress number σ = (Ft/(b·m)) · Kv Ko Ks Km KB / J and a comparable pitting formula with an elastic coefficient and geometry factor. Universities examine Lewis-Buckingham; industry software (KISSsoft, Romax, MASTA) implements ISO/AGMA.
Lubricant grades follow IS 12225 / ISO 3448 viscosity grades (VG 150-460 common in industrial gearboxes); automotive axle oils are specified by API GL-4/GL-5 and SAE viscosity.
Standards are revised periodically; before quoting a clause number in industry work, check the current amendment on the BIS portal rather than relying on a textbook reprint.

Key points

Module m - m = d/z in mm; the single size parameter that must be a standard value; the metric replacement for diametral pitch.
Law of gearing - the common normal at contact must pass through the pitch point for a constant velocity ratio.
Involute profile - insensitive to centre-distance error, generated by a simple rack cutter; the universal choice.
Pressure angle - standard 20° full depth; higher φ gives stronger teeth and fewer interference problems but larger bearing loads.
Minimum teeth - 17-18 on a 20° full-depth pinion to avoid interference; 32 at 14½°.
Contact ratio - must be > 1; 1.4-1.8 typical; higher means quieter and lower load per tooth.
Tangential force - Ft = 2T/d = P/v; the only component that transmits power.
Lewis equation - Fb = σb·b·m·Y; sizes the tooth against bending fatigue at the root.
Lewis form factor Y - depends on tooth number and pressure angle; increases with z, so pinions are weaker than wheels of the same material.
Weaker member - compare σb·Y for pinion and gear; the smaller product governs the design, and it is usually the pinion.
Velocity factor Cv - 3/(3+v), 6/(6+v) or 5.6/(5.6+√v) by manufacturing class; derates allowable stress for speed.
Dynamic load - Fd = Ft + Fi (Buckingham); the increment comes from tooth error, inertia and stiffness, not from the transmitted torque.
Wear strength - Fw = d₁·b·Q·K; governed by surface hardness and diameter, barely by module.
Ratio factor Q - Q = 2z₂/(z₁+z₂); approaches 2 for a large reduction.
Helical equivalent teeth - z' = z/cos³ψ with normal module mn = m cos ψ; axial thrust Fa = Ft tan ψ.
Worm self-locking - occurs when tanλ < μ; efficiency falls as the lead angle falls, so self-locking worms run hot.
Face width - b = 8m to 12m (10m typical); wider than ~12m risks uneven load from misalignment.
Failure modes - bending fatigue (breakage), pitting, scoring, abrasive wear; the first is sudden, the rest are progressive.

Formulas and examples

m = d/z (mm); p = πm; d = m z; centre distance a = m(z₁+z₂)/2 (mm)
Velocity ratio i = ω₁/ω₂ = z₂/z₁ = d₂/d₁ ; pitch line velocity v = πdN/60000 (d in mm, N in rpm, v in m/s)
Ft = 2T/d = 1000 P / v (Ft in N, T in N·mm, P in kW, v in m/s); Fr = Ft tan φ; Fn = Ft/cos φ
Torque T = 9.55 × 10⁶ P / N (T in N·mm, P in kW, N in rpm)
Lewis beam strength: Fb = σb · b · m · Y (σb = permissible bending stress, MPa = σut/3 for typical FOS; Y = form factor)
Velocity factor: Cv = 3/(3+v) ordinary cut; 6/(6+v) carefully cut; 5.6/(5.6+√v) precision. Effective load Feff = Cs·Ft/Cv
Buckingham dynamic load: Fd = Ft + Fi, Fi = 21 v (C·b + Ft) / (21 v + √(C·b + Ft)) (v in m/s, b and e in mm, C in N/mm)
Deformation factor C = k·e / [(1/E₁) + (1/E₂)] (k = 0.111 for 20° full depth, e = total tooth error in mm)
Buckingham wear strength: Fw = d₁ · b · Q · K ; Q = 2 z₂/(z₁+z₂) ; K = σes² sin φ (1/E₁ + 1/E₂)/1.4
Surface endurance limit (empirical): σes ≈ 2.8 (BHN) − 70 MPa
Helical: mn = m cos ψ ; z' = z/cos³ψ ; Fa = Ft tan ψ ; Fr = Ft tan φn / cos ψ
Bevel (Tredgold): z' = z/cos γ ; tan γ₁ = z₁/z₂ for 90° shafts ; Lewis with factor (L−b)/L
Worm: i = z₂/z₁ ; tan λ = z₁ m / d_worm ; η = tan λ (1 − μ tan λ)/(tan λ + μ)
Gear train value = (product of teeth on drivers)/(product of teeth on followers)

Example 1 - basic geometry and forces. A spur pair transmits 10 kW; pinion z₁ = 20, gear z₂ = 60, module 4 mm, pinion at 1,000 rpm, φ = 20°.

d₁ = 4 × 20 = 80 mm, d₂ = 4 × 60 = 240 mm, centre distance a = 4(20+60)/2 = 160 mm.
v = π × 80 × 1000/60000 = 251.33/60 ≈ 4.19 m/s.
Ft = 1000 × 10/4.19 ≈ 2,387 N. Check by torque: T₁ = 9.55×10⁶ × 10/1000 = 95,500 N·mm; Ft = 2 × 95,500/80 = 2,388 N (agrees).
Fr = 2,388 × tan 20° = 2,388 × 0.3640 = 869 N; Fn = 2,388/cos 20° = 2,388/0.9397 = 2,541 N.
Gear speed N₂ = 1000/3 = 333.3 rpm; torque on gear = 3 × 95,500 = 286,500 N·mm.

Example 2 - module from the Lewis equation. Same duty: 10 kW, pinion 1,000 rpm, i = 3, z₁ = 20, C45 steel σut = 600 MPa, FOS 3 → σb = 200 MPa, carefully cut gears, b = 10 m, service factor Cs = 1.5. Y for z = 20 at 20° full depth ≈ 0.320.

Trial: take v from an assumed m. With m = 4, v = 4.19 m/s → Cv = 6/(6+4.19) = 6/10.19 = 0.589.
Effective load Feff = Cs·Ft/Cv = 1.5 × 2,388/0.589 = 6,082 N.
Beam strength available with m = 4: Fb = 200 × 40 × 4 × 0.320 = 10,240 N > 6,082 N, so m = 4 is safe (ratio 1.68).
Try m = 3: d₁ = 60 mm, v = π×60×1000/60000 = 3.14 m/s, Ft = 2×(9.55×10⁶×10/1000)/60 = 3,183 N, Cv = 6/9.14 = 0.656, Feff = 1.5×3,183/0.656 = 7,279 N; Fb = 200 × 30 × 3 × 0.320 = 5,760 N < 7,279 N - unsafe.
Answer: m = 4 mm, b = 40 mm, z₁ = 20, z₂ = 60, d₁ = 80 mm, d₂ = 240 mm, a = 160 mm.

Example 3 - dynamic and wear check on the Example 2 design. Both gears steel, E = 2.06×10⁵ MPa, φ = 20°, b = 40 mm, m = 4, d₁ = 80 mm, z₁ = 20, z₂ = 60, v = 4.19 m/s, Ft = 2,388 N, error e = 0.04 mm, pinion 350 BHN.

C = 0.111 × 0.04 / (2/2.06×10⁵) = 0.00444/(9.709×10⁻⁶) = 457.3 N/mm.
C·b = 457.3 × 40 = 18,292 N; C·b + Ft = 18,292 + 2,388 = 20,680 N; √20,680 = 143.8.
Fi = 21 × 4.19 × 20,680/(21 × 4.19 + 143.8) = 87.99 × 20,680/(87.99 + 143.8) = 1,819,633/231.79 = 7,850 N.
Fd = 2,388 + 7,850 = 10,238 N. Beam strength Fb = 10,240 N → FOS = 10,240/10,238 ≈ 1.0 - too low; the grade of accuracy must improve (smaller e) or m increased.
With precision gears, e = 0.015 mm: C = 171.5 N/mm, C·b = 6,860, +Ft = 9,248, √ = 96.2; Fi = 87.99 × 9,248/(87.99+96.2) = 813,732/184.19 = 4,418 N; Fd = 6,806 N → FOS = 10,240/6,806 = 1.50, acceptable.
Wear: σes = 2.8 × 350 − 70 = 910 MPa; K = 910² × sin20° × (2/2.06×10⁵)/1.4 = 828,100 × 0.3420 × 9.709×10⁻⁶/1.4 = 2.7498/1.4 = 1.964 N/mm².
Q = 2 × 60/80 = 1.5; Fw = 80 × 40 × 1.5 × 1.964 = 9,427 N > Fd (6,806 N), FOS = 1.39 - marginal; raising hardness to 400 BHN gives σes = 1,050 MPa, K = 2.613 N/mm², Fw = 12,543 N, FOS = 1.84. Note how module did not enter the wear check.

Example 4 - helical gear. 15 kW at 1,440 rpm, ψ = 25°, normal module mn = 4 mm, z₁ = 24, φn = 20°.

m (transverse) = mn/cos ψ = 4/0.9063 = 4.413 mm → d₁ = 4.413 × 24 = 105.9 mm.
v = π × 105.9 × 1440/60000: π × 105.9 = 332.7 mm; × 1440 = 479,088; / 60000 = 7.98 m/s.
T = 9.55×10⁶ × 15/1440 = 99,479 N·mm; Ft = 2 × 99,479/105.9 = 1,879 N.
Fa = 1,879 × tan 25° = 1,879 × 0.4663 = 876 N (the thrust the bearing must take); Fr = 1,879 × tan20°/cos25° = 1,879 × 0.3640/0.9063 = 755 N.
Equivalent teeth z' = 24/cos³25° = 24/0.7443 = 32.2 → Y ≈ 0.364, so the helical tooth behaves like a 32-tooth spur tooth and is stronger than the 24-tooth spur equivalent (Y ≈ 0.337).

Example 5 - worm reducer. Single-start worm (z₁ = 1), worm wheel z₂ = 40, axial module 5 mm, worm pitch diameter 50 mm, μ = 0.06.

Ratio i = 40/1 = 40:1 in one stage.
tan λ = z₁ m/d_worm = 1 × 5/50 = 0.10 → λ = 5.71°.
η = tanλ(1 − μ tanλ)/(tanλ + μ) = 0.10 × (1 − 0.006)/(0.10 + 0.06) = 0.0994/0.16 = 62.1%.
Self-locking check: tan λ = 0.10 vs μ = 0.06 → tanλ > μ, so it is not self-locking; a brake is needed for a hoist.
If input is 5 kW, output = 5 × 0.621 = 3.1 kW and about 1.9 kW becomes heat - the casing must dissipate it.

Gear type	Shafts	Ratio per stage	Efficiency	Typical use
Spur	Parallel	up to 6:1	98-99%	Gearboxes, pumps, machine tools
Helical	Parallel	up to 8:1	97-98%	Automotive transmissions, turbines
Straight bevel	Intersecting	up to 5:1	97-98%	Differentials, hand drills
Spiral bevel / hypoid	Intersecting / offset	up to 10:1	90-96%	Truck and car rear axles
Worm	Perpendicular, non-intersecting	10:1 to 100:1	50-95%	Hoists, conveyors, lift drives
Planetary	Coaxial	3:1 to 10:1	97-98%	Automatics, wind turbines, hubs

Check	Formula	Improved mainly by
Beam (bending)	Fb = σb·b·m·Y	Larger module, wider face, stronger material, bigger fillet
Wear (pitting)	Fw = d₁·b·Q·K	Higher surface hardness, larger diameter, better finish
Dynamic load	Fd = Ft + Fi	Finer accuracy grade (smaller e), lower speed, flexible coupling

Where it is used

Automotive transmissions and axles: Maruti Suzuki, Tata Motors, Mahindra, Ashok Leyland and TAFE use case-carburised 20MnCr5 helical gears (grades 5-7) and hypoid final drives; suppliers include Bharat Gears, ZF India and Sona Comstar.
Industrial gearboxes and reducers: Elecon, Shanthi Gears, Radicon, Greaves and Bonfiglioli India build helical, bevel-helical and worm units for cement, steel, sugar and paper plants, specified by IS 4460 capacity and ISO VG oils.
Machine tools and robotics: lathe headstocks, CNC rack-and-pinion long axes, harmonic and planetary reducers in robot joints where backlash specification matters most.
Power and renewables: three-stage planetary-helical gearboxes in wind turbines (Suzlon, Siemens Gamesa India), turning gears in thermal plants, BHEL turbine auxiliaries.
Railways and heavy equipment: traction gear pairs in locomotives (Chittaranjan and Banaras works), final drives in BEML and JCB India earthmovers.
Job roles: design engineer (gear sizing in KISSsoft/Romax), manufacturing engineer (hobbing and grinding setup), NVH engineer (gear whine, transmission error), reliability engineer (oil analysis, pitting diagnosis).

Interview questions

Q: Why is the involute profile preferred over cycloidal? A: The velocity ratio stays constant even if the centre distance varies slightly, the cutters are simple, and one rack-type cutter produces all tooth numbers of a given module.
Q: What is interference and how is it avoided? A: The tip of one tooth fouls the non-involute root of its mate; it is avoided by using at least 17-18 teeth on a 20° pinion, raising the pressure angle, using stub teeth, or undercutting the flank.
Q: Which member of a gear pair do you design, and why? A: The weaker one, found by comparing σb × Y for both; it is usually the pinion because it has fewer teeth (smaller Y) and sees more load cycles.
Q: Why does the module not help against pitting? A: Wear strength Fw = d₁·b·Q·K depends on diameter, face width and surface hardness - contact stress is set by the radii of curvature and load, not by tooth size, so hardening or a bigger diameter is the remedy.
Q: Why are helical gears quieter than spur gears? A: Contact starts at one end of the tooth and spreads gradually, so more teeth share the load and the load transfer is smooth instead of an abrupt line contact.
Q: What is the penalty of a helical gear? A: Axial thrust Ft tan ψ, which needs thrust bearings; a double-helical or herringbone gear cancels it.
Q: Why is a worm wheel made of bronze and the worm of hardened steel? A: The contact is mainly sliding, so dissimilar materials with the softer, conformable bronze resist scuffing and let the wheel wear in preference to the costlier worm.
Q: When is a worm drive self-locking, and would you rely on it in a hoist? A: When tan λ < μ (lead angle roughly below 5-6°); it should never be the only brake, because vibration, running-in and better lubrication reduce μ and can release the load.
Q: What causes the dynamic load increment in Buckingham's equation? A: Tooth profile and spacing errors, tooth and shaft deflection, and the inertia of the masses accelerated by that error - not the transmitted torque, which is already in Ft.
Q: Why is backlash deliberately provided? A: To allow for thermal expansion, manufacturing errors and the lubricant film; zero backlash would jam the teeth, though preloaded split gears are used where lost motion is unacceptable.
Q: Why does the Lewis equation assume the load at the tooth tip? A: It is the worst bending case for a single tooth; real pairs share load (contact ratio > 1), so AGMA/ISO methods apply load-sharing and stress-concentration factors instead.
Q: How would you reduce gear whine in a gearbox? A: Improve accuracy grade and surface finish, use helical teeth with a higher contact ratio, apply profile crowning and tip relief, stiffen the housing and bearings, and check alignment and backlash.

Common mistakes

Leaving a calculated module like 4.37 mm in the answer instead of rounding up to the next standard IS 2535 value.
Applying the velocity factor Cv to the load and the service factor to the strength, or using the wrong Cv expression for the manufacturing class and speed.
Taking the Lewis form factor Y for the gear when the pinion is the weaker member, or mixing the y (circular pitch) and Y (module) forms of the factor.
Using the transverse module instead of the normal module, or forgetting z' = z/cos³ψ, in helical calculations.
Checking beam strength only and declaring the design safe - pitting kills more industrial gears than tooth breakage.
Ignoring the axial thrust from helical and worm gears when selecting bearings, and ignoring heat dissipation in worm reducers.
Confusing module with circular pitch or diametral pitch (p = πm; P = 25.4/m), and using mm for v when pitch-line velocity must be m/s.