Machine Design Interview Questions

Spur gears have teeth parallel to the axis of rotation and are simpler to manufacture but produce more noise due to sudden engagement. Helical gears have teeth at an angle (helix angle) to the axis, providing gradual engagement, smoother operation, quieter performance, and higher load-carrying capacity, but they generate axial thrust forces requiring thrust bearings.

Module (m) is the ratio of pitch circle diameter to number of teeth (m = D/Z) and represents the size of gear teeth in metric system. It is crucial because two gears must have the same module to mesh properly. Module determines tooth size, strength, and load-carrying capacity. Standard modules (1, 1.5, 2, 2.5, 3, etc.) are preferred for interchangeability and manufacturing economy.

Roller bearings are preferred when higher radial load capacity is needed because they have line contact with races instead of point contact like ball bearings. Use roller bearings for heavy-duty applications like gearboxes, rolling mills, and conveyor systems. Ball bearings are better for higher speeds, lower friction, and combined radial-axial loads in applications like electric motors and pumps.

Factor of safety (FoS) is the ratio of allowable stress (or yield/ultimate strength) to actual working stress. It accounts for uncertainties in loading, material properties, manufacturing variations, and environmental factors. FoS typically ranges from 1.5-3 for ductile materials under static loads, 3-5 for brittle materials, and higher for impact or fatigue loading. Selection depends on consequences of failure, load predictability, and industry standards.

Helical compression springs are used in valves, shock absorbers, and clutches for resisting compressive loads. Helical tension springs are used in garage doors and weighing machines. Torsion springs provide angular force in clothespins and mousetraps. Leaf springs are used in vehicle suspensions. Disc (Belleville) springs provide high force in compact space. Spiral springs store energy in watches and clocks.

A coupling permanently connects two shafts to transmit power, allowing for some misalignment compensation but not engagement/disengagement during operation. A clutch allows engagement and disengagement of shafts while in motion, enabling controlled power transmission. Couplings are used in pumps and compressors; clutches are used in vehicles and machinery requiring frequent starting/stopping.

Preload is the clamping force created when a bolt is tightened, which holds the joint members together before any external load is applied. Proper preload prevents joint separation under external loads, reduces bolt fatigue by minimizing load fluctuation, prevents loosening due to vibration, and ensures consistent joint behavior. Insufficient preload causes joint failure; excessive preload can damage threads or yield the bolt.

Medium carbon steels (C40, C45, EN8) are most common due to good strength, machinability, and cost-effectiveness. Alloy steels (EN19, EN24, AISI 4140) are used for higher strength and fatigue resistance in critical applications like crankshafts. Stainless steel is used in corrosive environments. The choice depends on required strength, surface hardness, fatigue life, and operating conditions like temperature and corrosion.

L10 life (or B10 life) is the rating life in million revolutions at which 90% of a group of identical bearings will survive (10% will fail due to fatigue). It is calculated using the formula L10 = (C/P)^p, where C is dynamic load rating, P is equivalent dynamic load, and p is 3 for ball bearings and 10/3 for roller bearings. This statistical measure helps engineers predict bearing replacement intervals.

A gear train is a combination of two or more gears used to transmit motion and power from one shaft to another. Its purposes include speed reduction or increase (changing RPM), torque multiplication, direction change, and transmitting power between non-coaxial shafts. Types include simple gear trains, compound gear trains, reverted gear trains, and epicyclic (planetary) gear trains used in automobile transmissions and machinery.

Sunk keys (rectangular, square, and tapered) are most common, fitting into keyways cut in both shaft and hub. Woodruff keys are semi-circular, used for tapered shafts. Saddle keys sit on the shaft without a keyway. Feather keys allow axial sliding while transmitting torque. Splines (internal and external) are used for high torque transmission. Key selection depends on torque magnitude, hub movement requirements, and manufacturing considerations.

Spring rate (k) is the force required to deflect a spring by unit length, measured in N/mm. For helical compression springs, k = Gd^4 / (8D^3N), where G is shear modulus, d is wire diameter, D is mean coil diameter, and N is number of active coils. Higher wire diameter and lower coil diameter increase stiffness. Spring rate is crucial for selecting springs that provide desired force at specified deflections.

Flexible couplings accommodate shaft misalignment (angular, parallel, and axial), absorb shock and vibration, and protect connected equipment from overloads. Common types include jaw/spider couplings (elastomer insert, general purpose), disc couplings (high precision), gear couplings (high torque), oldham couplings (parallel misalignment), and bellows couplings (zero backlash). Selection depends on misalignment type, torque, speed, and environment.

Coarse threads have larger pitch and are standard for general applications, offering faster assembly, better tolerance to damaged threads, and stronger threads for tapped holes in softer materials. Fine threads have smaller pitch, providing higher tensile strength, better resistance to loosening under vibration, finer adjustment capability, and are used in precision applications and thin-walled components. Fine threads are more susceptible to cross-threading.

Interference fit (press fit) is used when the bearing ring rotates relative to the load direction - inner ring to shaft when shaft rotates, outer ring to housing when housing rotates. This prevents creep (relative movement) between ring and mating part. Clearance fit is used for the stationary ring, allowing easy assembly and accommodating thermal expansion. Improper fits cause ring creep, fretting corrosion, or bearing damage.

For a compound gear train, the overall gear ratio is the product of individual stage ratios. If gears are numbered 1,2,3,4... with 1 as driver, Gear Ratio = (Z2/Z1) x (Z4/Z3) x ... where Z is the number of teeth. For a two-stage reduction with 20-tooth driver meshing 60-tooth gear (shaft 1), and 18-tooth gear on same shaft meshing 54-tooth output gear, ratio = (60/20) x (54/18) = 3 x 3 = 9:1 speed reduction.

The ASME code considers combined bending and torsion with shock factors. The equivalent torque Te = sqrt((Km x M)^2 + (Kt x T)^2), where M is bending moment, T is torque, Km is bending shock factor (1.5-2.0), and Kt is torsion shock factor (1.0-1.5). Shaft diameter d = (16Te / (pi x tau_allowable))^(1/3). For fluctuating loads, fatigue factors are applied. This ensures shaft withstands combined stresses with adequate safety margin.

Equivalent dynamic load P = X.Fr + Y.Fa, where Fr is radial load, Fa is axial load, X is radial load factor, and Y is axial load factor. X and Y values depend on the ratio Fa/(V.Fr) and bearing geometry (from manufacturer catalogs). For light axial loads (Fa/Fr < e), typically X=1, Y=0. For significant axial loads, X decreases and Y increases. V is rotation factor (1 for inner ring rotating, 1.2 for outer ring rotating).

Joint stiffness determines how external loads are shared between bolt and clamped members. The bolt stiffness Kb = Ab.Eb/Lb and member stiffness Km (calculated using pressure cone method) affect load distribution. Load factor C = Kb/(Kb+Km), typically 0.15-0.25. External load on bolt = C x External Load. Higher member stiffness means lower portion of external load goes to bolt, reducing fatigue. This analysis is critical for fatigue-loaded joints like cylinder heads.

For fatigue loading, use Soderberg or Goodman criteria. Calculate mean stress tau_m and alternating stress tau_a from operating load range. The Wahl factor K = (4C-1)/(4C-4) + 0.615/C accounts for curvature and direct shear (C = D/d). Apply fatigue strength reduction for surface finish, size, and reliability. Ensure tau_a/Se + tau_m/Ssy < 1/FoS. Shot peening improves fatigue life by inducing compressive residual stresses. Design for at least 10^6 cycles minimum.

Bending fatigue at tooth root is prevented by adequate module and fillet radius. Pitting (surface fatigue) is prevented by proper hardness and lubrication. Scoring/scuffing occurs due to lubricant film breakdown at high speeds/loads - use EP additives. Wear is minimized by adequate hardness and filtration. Plastic flow occurs in soft gears under overload. Design involves Lewis equation for bending strength and Buckingham equation for surface durability, with appropriate factors of safety.

For shafts with gears, lateral deflection should be less than 0.01 x module at gear location to prevent uneven tooth contact. Angular deflection at gear should be less than 0.05 degrees. At bearings, angular deflection should be less than 0.04 degrees for ball bearings and 0.1 degrees for roller bearings. For precision machinery, limits are halved. Excessive deflection causes gear noise, vibration, bearing damage, and premature failure. Use Macaulay's method or FEA for deflection analysis.

Grease is preferred for sealed bearings, low-medium speeds (DN value < 300,000), infrequent relubrication, and simple housing design. Oil is required for high speeds, high temperatures (>120C), when heat dissipation is needed, or when other components need oil. Calculate DN value (bore in mm x RPM) to determine suitability. Grease fill should be 30-50% of free space; overfilling causes overheating. Consider operating temperature, contamination, and maintenance access.

Tightening torque T = K x D x Fi, where K is torque coefficient (0.2 for dry steel, 0.15 for lubricated), D is nominal bolt diameter, and Fi is desired preload. Preload is typically 75-90% of bolt proof load for reusable connections. For M12 Grade 8.8 bolt (proof load ~48kN) with 80% utilization and lubricated threads: T = 0.15 x 0.012 x 38,400 = 69 Nm. Always verify with torque-angle method for critical joints.

Clutch size depends on torque capacity T = mu x p x n x 2pi x (ro^3 - ri^3) / (3 x (ro^2 - ri^2)) for uniform pressure assumption, where mu is friction coefficient, p is allowable pressure, n is number of friction surfaces, ro and ri are outer and inner radii. Design considerations include heat dissipation capability (temperature rise per engagement), service factor for shock loads (1.0-2.5), wear allowance, cooling arrangement, and actuating force required.

Spring surge occurs when the natural frequency of a spring coincides with the operating frequency, causing resonance. This leads to coil clash, high stresses, noise, and early failure. Natural frequency fn = (d/pi.D^2.N) x sqrt(G.g/32.rho). To prevent surge, design fn to be at least 15-20 times the operating frequency. Remedies include changing wire diameter, using variable pitch springs, adding friction dampers, or using nested springs. Critical in valve springs and high-speed machinery.

For a planetary system with sun gear (S), planet gears (P), and ring gear (R), using the fundamental equation: Ns/Nr = 1 + Zr/Zs. With ring fixed and sun as input, carrier output ratio = 1 + Zr/Zs. With carrier fixed and sun input, ring output ratio = -Zr/Zs (reverse). Planetary systems achieve high ratios (3:1 to 10:1 per stage) in compact space, used in automatic transmissions, wind turbines, and heavy machinery.

Stress concentration factors (Kt for static, Kf for fatigue) multiply nominal stresses at geometric discontinuities like keyways, shoulders, and holes. For fatigue, Kf = 1 + q(Kt-1), where q is notch sensitivity (material dependent, 0 to 1). A keyway might have Kt=2.0, reducing fatigue strength significantly. Design strategies include generous fillet radii (r/d > 0.1), gradual diameter transitions, avoiding sharp corners, and surface treatment like shot peening at critical locations.

In a locating-non-locating arrangement, the locating bearing (usually near the drive end) is axially fixed on both shaft and housing to position the shaft. The non-locating bearing (at the other end) allows axial movement to accommodate thermal expansion. For a 1m steel shaft with 50C temperature rise, expansion is about 0.6mm. Without this arrangement, thermal stresses could overload bearings. Alternative: cross-located arrangement with back-to-back angular contact bearings.

Metric bolt grades like 8.8, 10.9, 12.9 indicate mechanical properties. The first number times 100 gives tensile strength in MPa (8.8 = 800 MPa). The second number times 10 gives yield/tensile ratio percentage (8.8 = 80%, so yield = 640 MPa). Grade 8.8 is standard for automotive, 10.9 for high-strength applications, 12.9 for maximum strength but lower ductility. Proof load is approximately 90% of yield strength. Grade marking is stamped on bolt head for identification.

A single universal joint (Hooke's joint) causes cyclic speed variation in the output shaft - at operating angle theta, output speed varies as omega_out = omega_in x cos(theta)/(1-sin^2(theta)sin^2(phi)), creating 2x frequency fluctuation. This causes vibration and torsional stress. To eliminate this, use two universal joints with equal angles in the proper phasing arrangement (yokes in same plane). Maximum recommended angle is 25-30 degrees for continuous operation. Critical in automotive driveshafts.

Design involves determining load capacity, deflection, and stress distribution. For a semi-elliptic leaf spring, deflection delta = 6PL^3/(Enbt^3) and stress sigma = 6PL/(nbt^2), where P is load, L is span, n is number of leaves, b is width, t is thickness. Graduated leaves contribute partially to bending resistance. Include nipping (initial curvature difference) to equalize stress. Consider rebound clips, center bolt strength, and interleaf friction. Material is typically 55Si7 or 50Cr4V2 spring steel.

Backlash is the clearance between mating gear teeth when they are in mesh, necessary to prevent jamming due to thermal expansion and manufacturing tolerances. Excessive backlash causes noise, vibration, and positional inaccuracy. It is controlled by tighter manufacturing tolerances (AGMA quality class), center distance adjustment, spring-loaded split gears, or anti-backlash gear mechanisms. For precision applications like CNC machines, backlash should be less than 0.04mm. Zero backlash is achieved using preloaded duplex gears.

Critical speed is the rotational speed at which a shaft's natural frequency of lateral vibration equals the rotation frequency, causing resonance with potentially destructive amplitudes. Calculated as Nc = 30/pi x sqrt(g/delta_static) RPM for simple cases, or using Rayleigh-Ritz method for complex systems. Operating speed should be at least 20% away from critical speed. Rigid rotors operate below first critical, flexible rotors (like turbines) operate above. Critical speed increases with stiffness and decreases with mass.

Fatigue spalling shows pitting on raceways, indicating normal end-of-life or overload. Abrasive wear shows polished surfaces from contamination - check sealing and filtration. Corrosion shows rust and etching from moisture ingress. Electrical erosion shows fluting or pitting from stray currents in motor bearings. Overheating shows discoloration (blue/brown) from lubrication failure or misalignment. Brinelling shows indentations from static overload or vibration during transport. Each pattern suggests specific corrective actions.

AGMA surface durability uses contact stress equation: sigma_c = Cp x sqrt(Wt x Ko x Kv x Km x Cf / (d x F x I)), where Cp is elastic coefficient, Wt is tangential load, Ko is overload factor, Kv is dynamic factor, Km is load distribution factor, Cf is surface finish factor, d is pitch diameter, F is face width, and I is geometry factor. Compare with allowable stress: sigma_c_allowable = Sc x Cl x Ch / (Kt x Kr), where Sc is contact endurance strength, Cl is life factor, Ch is hardness ratio factor. Design iterations balance bending and surface strength.

For fluctuating loads, separate mean (Mm, Tm) and alternating (Ma, Ta) components. Apply Soderberg: 1/FoS = (32/pi.d^3) x [sqrt((Kf.Ma/Se)^2 + (3/4)(Kt.Ta/Syt)^2) + sqrt((Mm/Syt)^2 + (3/4)(Tm/Syt)^2)]. Kf is fatigue notch factor, Se is corrected endurance limit (Se = Se' x ka x kb x kc x kd x ke). Account for surface finish (ka), size (kb), reliability (kc), temperature (kd), and miscellaneous effects (ke). For keyway, Kf approximately equals 2.0. Iterate diameter until FoS requirement is met.

For a system with n bearings, combined L10 life is calculated using: (1/L10_system)^e = sum(1/L10_i)^e, where e = 10/9 (Weibull slope for bearings). For different reliability R, use Lna = a1 x L10, where a1 is reliability factor (0.62 for 95%, 0.33 for 97%). For two bearings with L10 = 5000 and 8000 hours, system L10 = [(1/5000)^1.11 + (1/8000)^1.11]^(-0.9) = 3,400 hours. Consider load distribution, speed variations, and adjusted rating life a_ISO for lubrication and contamination effects.

Design follows ASME method: Operating bolt load W_o = H + Hp = (pi/4)G^2.P + 2.b.pi.G.m.P, where H is hydrostatic force, G is gasket diameter, P is pressure, b is effective gasket width, m is gasket factor. Gasket seating load W_g = pi.b.G.y, where y is minimum seating stress. Required bolt area Ab = max(W_o, W_g)/Sa. Verify gasket crushing: actual seating stress must exceed y but not crush stress. Account for flange rotation, bolt spacing, and thermal effects. Select appropriate gasket material (m, y values) for media and temperature.

For two concentric springs sharing load equally, each carries P/2. For simultaneous bottoming, deflections must be equal: delta_1 = delta_2. Using k = Gd^4/(8D^3N), this gives (d1^4.N2.D2^3)/(d2^4.N1.D1^3) = 1. To avoid interference, D1_inner > D2_outer + clearance. For opposite hand winding, clearance should exceed wire diameter to prevent tangling. Stress in each spring: tau = 8PD.K/(pi.d^3). Check buckling: free length/D < 4 for stable operation. Total rate k_total = k1 + k2. Often used in valve springs for surge prevention.

Worm drives have low efficiency (40-90%), generating significant heat. Thermal power rating Pt = K.A.(t_s - t_a), where K is heat transfer coefficient (13-18 W/m2K natural convection, higher with fan), A is housing surface area, t_s is allowable sump temperature (80-90C), t_a is ambient. Mechanical power rating Pm = Pi x eta where eta = tan(lambda)/(tan(lambda + phi)), lambda is lead angle, phi is friction angle. Actual rating is minimum of mechanical and thermal ratings. Cooling fins, forced convection, or oil coolers increase thermal capacity.

The bolt experiences cyclic stress due to portion of external load (determined by joint stiffness ratio C). Mean stress sigma_m = Fi/At + C.Fe_max/(2At), alternating stress sigma_a = C.Fe_a/At, where Fi is preload, At is tensile stress area, Fe is external load, C = kb/(kb+km). Apply fatigue criteria: sigma_a/Se + sigma_m/Sut < 1/FoS (Goodman). For rolled threads, Kf approximately equals 2.2-3.0. Include endurance limit modifications. Critical design parameters: increase preload (reduces alternating stress), reduce C (stiffer joint members), use higher grade bolts, specify rolled threads after heat treatment.

Tapered roller bearings generate induced axial thrust Fa_induced = 0.5.Fr/Y from radial loads. For back-to-back or face-to-face arrangement under radial loads Fr1 and Fr2, compare 0.5.Fr1/Y1 with 0.5.Fr2/Y2. The bearing with smaller induced thrust carries the net external axial plus reaction. For bearing 1: Fa1 = 0.5.Fr2/Y2 + Ka (if this bearing carries net axial). Bearing life calculation uses equivalent load P = 0.4Fr + Y.Fa when Fa/Fr > e. Preload setting is critical: insufficient causes skidding, excessive reduces life. Adjust with shims or threaded adjusters.

Static imbalance occurs when the center of mass is offset from the rotation axis - single plane correction suffices. Dynamic imbalance involves a couple from masses in different axial planes, requiring two-plane correction even if statically balanced. For rigid rotors (operating below 0.7x first critical), balance in two planes using vector calculation: m1.r1 + m2.r2 = 0 (force balance) and m1.r1.l1 + m2.r2.l2 = 0 (moment balance). ISO 1940 specifies balance quality grades G1 to G4000 based on e.omega where e is specific unbalance. Precision machinery requires G2.5 or better.

Heat generated per engagement Q = 0.5.I.omega^2 where I is inertia, omega is angular velocity difference. Temperature rise delta_T = Q/(m.c) where m is effective mass, c is specific heat. Limit delta_T to 10-15C per engagement. Energy capacity per unit area E'' = Q/(n.pi.(ro^2-ri^2)) should be less than 0.3-0.5 MJ/m^2 for wet clutches. Number of friction surfaces n = 2.T/(mu.p_mean.pi.(ro^2-ri^2).rm) where rm is mean radius. Allow 60-70% engagement time for heat dissipation. Oil flow rate for continuous slip: Q_oil = P_heat/(rho.c.delta_T_oil). Material: sintered bronze or paper-based friction.

Profile shift (x coefficient) modifies gear tooth geometry by shifting the cutting tool during manufacturing. Positive shift (+x) strengthens teeth (thicker at root), reduces undercut in small gears (<17 teeth for 20deg pressure angle), but increases tip interference risk. Negative shift (-x) weakens teeth but allows closer center distances. Sum of profile shifts (x1+x2) determines center distance modification: delta_a = m.(x1+x2).cos(alpha)/cos(alpha'). Use balanced shifts (x1 = x2) to maintain sliding velocity balance. Applications: avoiding undercut, matching non-standard center distances, optimizing specific sliding, and improving load distribution.

Belleville (disc) springs follow: P = (4E/(1-nu^2)) x (t^3/MRd^2) x [(h-delta)(h-delta/2).t + t^3], where P is load, E is modulus, t is thickness, h is cone height, delta is deflection, Rd is outer radius, M is a constant. h/t ratio controls characteristic: h/t < 0.4 gives linear, h/t approximately equals 1.41 gives flat portion (constant force), h/t > 1.41 gives negative rate region (snap-through). Stack in parallel for higher load (add forces), in series for higher deflection (add deflections). Widely used for preloading bearings, bolted joints, and overload protection. Material: spring steel, Inconel for high temperature.

Involute splines are designed per SAE/ANSI B92.1. Torque capacity T = p.L.r_m.z.h.phi where p is allowable pressure (7-21 MPa depending on fit), L is effective length, r_m is mean radius, z is number of teeth, h is tooth height, phi is load sharing factor (0.5-0.75). Check shear stress in teeth: tau = T/(pi.D.L.t.phi) < tau_allowable. For side-fit splines, verify wear and surface durability. Include factors for misalignment, edge loading, and sliding wear in loose splines. Press-fit major diameter for better concentricity. Specify profile tolerance and hardness (50-60 HRC case) for wear resistance.

Hydrodynamic bearings develop pressure through viscous fluid film. Key parameters: L/D ratio (0.5-1.5), clearance ratio c/r (0.001-0.002), and Sommerfeld number S = (mu.N.D.L/W).(r/c)^2. From Raimondi-Boyd charts using S, determine eccentricity ratio, minimum film thickness h_min, friction coefficient, and oil flow. Ensure h_min > 3x(Ra_shaft + Ra_bearing) for full film. Heat balance: heat generated P_f = f.W.pi.D.N must equal heat dissipated by oil flow. Check for thermal instability (hot oil carryover). Specify lubricant viscosity considering temperature rise. Used in turbines, compressors, and large rotating machinery at L&T, BHEL.

Energy absorption: E = 0.5.m.v^2 + m.g.h for vehicle of mass m from velocity v and height h. Average heat flux q'' = E/(A.t_stop). Temperature rise using lumped mass: delta_T = E/(m_disc.c). For repeated braking, use thermal time constant tau = rho.c.V/(h.A) to check cooling between applications. Surface temperature affects friction coefficient (fade). Verify against material limits: cast iron <650C, carbon-carbon <1000C. CFD or FEA for detailed analysis including thermal gradients causing disc coning. Ventilated discs improve h (heat transfer coefficient) by 50-100%. Critical design at Tata Motors, Bajaj for vehicle safety.