Question 1

How do I calculate shaft torque from motor power and RPM?

Accepted Answer

Torque (T) relates to power (P) and rotational speed (n) by: T = P × 9550 / n, where P is in kW, n is in RPM, T is in N·m. Derivation: Power = Torque × Angular velocity. P (W) = T (N·m) × ω (rad/s). Since ω = 2π×n/60, we get P = T × 2πn/60. Solving for T: T = P × 60 / (2πn) = P × 9549.3 / n ≈ P × 9550 / n. Example: 37 kW motor at 1480 RPM: T = 37,000 × 60 / (2π × 1480) = 238.9 N·m. This is the fundamental relationship used for shaft, coupling, and gearbox sizing throughout South African engineering.

Question 2

What is torsional shear stress and how is it checked?

Accepted Answer

Torsional shear stress (τ) is the stress induced in a shaft cross-section by the applied torque: For solid round shaft: τ = 16T / (πd³). For hollow round shaft: τ = 16T×d_o / (π(d_o⁴ - d_i⁴)). The maximum shear stress occurs at the outer surface of the shaft. This is checked against the allowable shear stress: τ_allow = S_y / (2 × SF) for ductile materials (von Mises) or τ_allow = S_y / (√3 × SF) (von Tresca). Shafts must satisfy: τ_actual ≤ τ_allow. Typical safety factors: SF = 2–3 for solid shafting under steady torsion. SF = 3–5 for oscillating or shock loading (mining, crushers, conveyors).

Question 3

How do I select the correct shaft diameter for a given torque?

Accepted Answer

Design procedure for solid shaft diameter from torque: 1. T = P × 9550 / n → Calculate torque from power and speed. 2. Apply service factor (SF): T_design = T × SF. 3. Set allowable shear stress: τ_allow = S_y / (2 × SF) or per standard. 4. Solve for diameter: d = ∛(16 × T_design / (π × τ_allow)). 5. Apply standard size (next standard diameter up). South African standard shaft sizes (metric): 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 90, 100, 110, 120, 130, 140, 150, 160, 180, 200, 220, 250 mm. Always provide a minimum keyway depth as a notch allowance and check deflection and critical speed separately.

Question 4

What is angle of twist and why does it matter in engineering?

Accepted Answer

Angle of twist (θ) is the angular deformation of a shaft under torque: θ = TL / (GJ), where T = torque (N·m), L = shaft length (m), G = shear modulus (Pa), J = polar second moment of area (m⁴). For solid round shaft: J = πd⁴/32. For hollow shaft: J = π(d_o⁴ - d_i⁴)/32. Significance: 1. Torsional resonance — shaft natural frequency must exceed operating excitation frequency. 2. Coupling alignment — excessive twist in flexible couplings affects accuracy. 3. Machine tool accuracy — CNC spindle deflection affects machining precision. 4. Conveyor timing — belt conveyors can have cumulative twist causing tracking problems. Maximum recommended twist: General machine shafts: 0.25°/m. High-precision machinery: <0.1°/m. Crankshafts and power transmission: 1°/m maximum.

Question 5

What is combined bending and torsion and how is it analysed?

Accepted Answer

Most real shafts experience both bending (from gear, pulley, or flywheel loads) and torsion simultaneously. Analysis using von Mises (distortion energy) criterion: τ_eq = √(σ_bend² + 3τ_torsion²) / √3 — or equivalently S_eq = √(σ_bend² + 3τ²). Check: S_eq ≤ S_y / SF. For rotating shafts, ASME shaft design equation (DE-Goodman): (16/πd³) × √[(K_f × M_b)² + (K_fs × T)²]^0.5 = S_y/n. In South African mining applications: Gearbox output shafts on crushers and conveyors. Mill pinion shafts (SAG/Ball mills). Pump impeller shafts. Fan shafts at power stations. These shafts are designed using combined loading analysis with dynamic service factors.

Question 6

What is the difference between shear stress in torsion vs direct shear?

Accepted Answer

Two types of shear stress in engineering: 1. Torsional shear stress — acts tangentially on the cross-section due to torque. Distribution: zero at centre, maximum at outer surface. Formula: τ = T×r/J. Circular shaft — parabolic distribution. 2. Direct shear (transverse shear) — stress due to lateral shear forces (reaction forces from supports/loads). Distribution: parabolic — maximum at neutral axis, zero at outer fibre. For most practical shafts, torsional shear dominates over transverse shear (except for very short stubby shafts). Weld shear stress and bolted joint design also use direct shear calculations. South African structural codes (SANS 10162-1) cover structural steel shear design for beams, while ASME codes govern pressure equipment shafts.

Question 7

What shaft material should I use for mining and heavy industrial applications?

Accepted Answer

Shaft material selection by application: Light duty (fans, small pumps, general machinery): EN8 (C45 / 1045) — σ_y = 380 MPa. Standard yield basis: Medium duty (conveyors, crusher drives, pumps ≤110 kW): EN24 (708M40 / 4340) — σ_y = 690 MPa. High alloy, through-hardened. Heavy duty (SAG mill drive shafts, large gearbox shafts): EN36 (665M23) or special alloy steel, case-hardened. Surface-critical (journal bearings, seals): 316 Stainless or EN40B nitrided. Corrosive / food industry: 316L stainless. High rotational speed turbomachinery: Titanium alloy or Incology. South African suppliers: Special Steel Supplies, Grant Mackay, Atlas Copco for standard EN steels. Certification to SANS 50050 or ASTM A108/A564.

Question 8

How do critical speed and shaft resonance affect shaft design?

Accepted Answer

Critical speed (N_c) is the rotational speed at which a shaft resonates due to unbalance. Rayleigh's formula for simple supported shaft: N_c = 42.3 / √δ_st (rpm), where δ_st = static deflection (mm) due to own weight under gravity. General rule: operating speed should be < 75% of first critical speed (below critical) or > 125% of critical speed (supercritical operation). For mining conveyors and horizontal centrifugal pumps in South Africa: Shafts are typically designed to run at 40–70% of first critical speed. VFD-driven machines must pass through critical speed during startup / shutdown — this is managed by rapid acceleration through the critical band. Dynamic balancing is required for all rotating assemblies above 1500 RPM per ISO 1940 Grade G2.5.

Material	Sy	τ_allow
Mild Steel	275	110
Structural Steel	355	142
Medium Carbon Steel	380	190
Alloy Steel	690	276
Case Hardened	620	248
Stainless Steel 304	205	82
Stainless Steel 316	205	82
Aluminium 6061-T6	276	110
Cast Iron	—	35
Phosphor Bronze	200	80

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