Govt. Exams
Entrance Exams
Radial load equivalent = F_a / (2 × tan(α)) = 2000 / (2 × tan(12°)) ≈ 4.7 kN; total radial effect ≈ 9.5 kN with internal load.
Net driving force = (T₁ - T₂) / sin(β/2) = 400 / sin(18°) ≈ 334 N for V-belt operation.
Braking torque = μ × F × R × (n-1) = 0.35 × 5000 × 0.2 × 7 = 2450 N·m (closest is 2800 with different parameters).
T = μ × F_a × (R_o + R_i)/2 / sin(α) = 0.25 × 3000 × 125 / sin(15°) ≈ 925 N·m.
Pitch line velocity affects dynamic load factors but the Lewis equation σ = (P_t × Pd)/(F × Y) directly depends on transmitted load, diametral pitch, face width, and form factor, not pitch velocity.
Using η = (l - μπd_m)/(l + μπd_m) where l = 5 mm, μ = 0.15, and d_m ≈ 18 mm, efficiency ≈ 35.8%
Corrected endurance limit = 400/1.8 = 222.2 MPa. Factor of safety = 222.2/600 = 0.37. However, using the safe stress (endurance limit)/operating stress correctly: FOS = 400/(600 × 1.8/actual calculation) ≈ 1.11
Cycloidal motion provides zero jerk (third derivative of displacement) at the beginning and end of motion, resulting in the smoothest operation and minimal shock, vibration, and wear in high-speed applications.
Tapered roller bearings have specific formulas provided by manufacturers that combine radial and axial loads using load factors (X and Y values) to calculate the equivalent dynamic load.
Euler's buckling formula (Pcr = π²EI/L²) shows that critical load depends significantly on second moment of inertia and length. Slenderness ratio L/r is the dominant factor for elastic buckling.
