Design of piston, connecting rod and crankshaft

Gas and inertia forces in the slider-crank, piston crown and ring design, I-section connecting rod buckling by Rankine's formula, and the two crankshaft check positions, with crown-thickness and connecting-rod examples.

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Why it matters

The piston, connecting rod and crankshaft carry the full combustion force, thousands of times a minute, while also being thrown about by their own inertia. Each part has its own critical failure mode: the piston crown cracks or melts, the connecting rod buckles, and the crankshaft fails by bending-torsion fatigue at a fillet. Design methods for each are standard university exam questions and the source of many interview questions.

Key ideas

Forces in the slider-crank mechanism

  • Gas force on the piston: F_g = (π/4)·D²·p, largest just after top dead centre (TDC).
  • Inertia force of the reciprocating mass: F_i = m_r·r·ω²·(cos θ + cos 2θ / n), with n = l/r. It opposes the gas force near TDC on the power stroke and dominates at high speed on the exhaust-intake TDC, where it puts the rod in tension.
  • The net piston force splits into a side thrust on the cylinder wall and a force along the rod; the rod force produces torque at the crank.

Piston: aluminium alloy (light, conducts heat well, but expands a lot and loses strength when hot), cast iron in some heavy diesels.

  • Crown thickness by strength (Grashoff, treating the crown as a flat circular plate clamped at the edge): t_H = D·√(3p/(16σ_t)). It is also checked by heat flow, so that the crown conducts the heat it receives to the rings and skirt without overheating; take the heat-flow formula and constants from your data book and use the larger thickness.
  • Piston rings: radial thickness from the wall pressure the ring exerts, t₁ = D·√(3p_w/σ_t), and axial thickness about 0.7–1 times t₁; two or three compression rings plus an oil ring.
  • Gudgeon (piston) pin: sized by bearing pressure in the small end, and checked in bending and double shear.

Connecting rod: forged steel, I-section for maximum stiffness per unit mass. The standard textbook I-section has flange width 4t and depth 5t, giving A = 11t², I_xx = (419/12)·t⁴ and k_xx² ≈ 3.18t², with I_xx/I_yy ≈ 3.2.

  • The rod is a column. About the axis of the crank-pin's rotation plane (xx) it behaves as pin-ended; about the perpendicular plane (yy) it is nearly fixed-ended. The I-section is proportioned so it is about equally strong against buckling in both planes, so design uses the xx plane.
  • Buckling load by Rankine's formula F_cr = σ_c·A / (1 + a·(L/k_xx)²), with Rankine constant a ≈ 1/7500 for steel (pin-ended). A high factor of safety (5–6) on the gas force covers fatigue and whipping.
  • The rod's own inertia causes transverse "whipping" bending, maximum at the crank's 90° position; big-end bolts are checked for the inertia force at the exhaust-intake TDC.

Crankshaft: forged steel (or nodular cast iron for lighter duty). It is checked as a beam on its bearings in two positions:

  1. Crank at TDC: maximum bending, negligible torque; crankpin and webs sized for bending and the webs also carry direct compression.
  2. Crank at the angle of maximum torque: combined bending and torsion, checked with the equivalent twisting moment. Crankpin length is also set by allowable bearing pressure, and fillet radii and surface rolling or nitriding are used because fatigue cracks start at the fillets.

Formulas

Gas force: F_g = (π/4)·D²·p_max Inertia force: F_i = m_r·r·ω²·(cos θ + cos 2θ / n), n = l/r Piston crown (Grashoff): t_H = D·√(3·p_max / (16·σ_t)) Piston ring radial thickness: t₁ = D·√(3·p_w / σ_t) I-section rod: A = 11t², k_xx² = 3.18t² Rankine: F_cr = σ_c·A / (1 + a·(L/k_xx)²), F_cr = n_f·F_g Crankpin bearing pressure: p_b = F / (d_c·l_c) Torque: T = 60·P / (2π·N)

Symbols: D = bore (mm); p_max = maximum gas pressure (MPa); F_g = gas force (N); m_r = reciprocating mass (kg); r = crank radius (m); ω = crank speed (rad/s); θ = crank angle from TDC; l = connecting rod length (m); t_H = crown thickness (mm); σ_t = permissible tensile stress (MPa); p_w = ring wall pressure (MPa); t = I-section reference thickness (mm); A = rod area (mm²); k_xx = radius of gyration (mm); σ_c = compressive yield stress (MPa); a = Rankine constant (–); L = rod length (mm); n_f = factor of safety; d_c, l_c = crankpin diameter and length (mm).

Worked examples

Example 1 (standard). A petrol engine has a 100 mm bore and a maximum gas pressure of 5 MPa. The aluminium alloy piston has a permissible tensile stress of 40 MPa. Find the gas force and the crown thickness by strength.

  1. F_g = (π/4) × 100² × 5 = 39 270 N ≈ 39.3 kN.
  2. t_H = D·√(3p/(16σ_t)) = 100 × √(3 × 5/(16 × 40)) = 100 × √0.02344 = 15.3 mm.
  3. The thickness must also satisfy the heat-flow check; the larger value is used.

Example 2 (GATE level). Design the I-section connecting rod for the same engine. Rod length 300 mm, σ_c = 330 MPa, Rankine constant 1/7500, factor of safety 6.

  1. Required buckling load: F_cr = 6 × 39 270 = 235 620 N.
  2. With A = 11t² and k_xx² = 3.18t²: 235 620 = 330 × 11t² / (1 + (1/7500) × 300²/(3.18t²)).
  3. Solving numerically gives t = 8.28 mm. Take t = 9 mm: flange width 4t = 36 mm, depth 5t = 45 mm.
  4. Check: A = 891 mm², k_xx² = 257.6 mm², (L/k_xx)² = 349.4, F_cr = 330 × 891/(1 + 349.4/7500) = 280.9 kN, giving a factor of safety of 280.9/39.27 = 7.15 (above 6).

Common mistakes

  • Using the piston area in m² with pressure in MPa and reporting N; use mm² with MPa to get N directly.
  • Designing the connecting rod for direct compression only; buckling governs.
  • Using L/k_yy with pin-ended conditions; the standard design uses the xx plane where the rod is pin-ended.
  • Forgetting that inertia force reverses sign and can put the rod (and big-end bolts) in tension.
  • Checking the crankshaft only at TDC; the maximum-torque position also governs.
  • Ignoring fillets at crankpin and journal, where fatigue cracks start.

For GATE ME

This topic draws on general machine-design and dynamics questions: gas force and torque from pressure and speed, Rankine/Euler buckling of a rod, primary and secondary inertia forces, and combined bending-torsion of a shaft. Practise the slider-crank force analysis and buckling with different end conditions.

Quick check

  1. Bore 80 mm, gas pressure 4 MPa. Gas force?
  2. Why is an I-section used for connecting rods?
  3. In which two crank positions is a centre crankshaft checked?
  4. Which engine component is sized with Grashoff's formula?
  5. A crankshaft carries 200 N·m at 3000 rpm. Power?

Answers: 1. 20.1 kN. 2. It gives high buckling resistance in both planes for a low mass. 3. At TDC (maximum bending) and at the angle of maximum torque. 4. The piston crown. 5. 62.8 kW.

Interview questions

All Design of Machine and Automotive Elements interview questions

Try answering each one aloud before you open it.

  1. 1.What is the function of a piston in an internal combustion engine?Concept

    The piston is a cylindrical component that moves up and down inside the cylinder of an internal combustion engine. Its primary function is to convert the energy generated by the combustion of fuel into mechanical work. This movement drives the crankshaft, which in turn powers the vehicle.

  2. 2.Explain the role of a connecting rod in an engine.Concept

    The connecting rod connects the piston to the crankshaft. It transmits the linear motion of the piston into rotational motion of the crankshaft. This conversion is essential for the engine to produce power and drive the vehicle.

  3. 3.What is a crankshaft and why is it important in an engine?Concept

    The crankshaft is a rotating shaft that converts the linear motion of the pistons into rotational motion. It is crucial because it delivers the power generated by the engine to the drivetrain, which ultimately moves the vehicle. The crankshaft also helps to balance the engine and reduce vibrations.

  4. 4.Why is aluminum commonly used for pistons in automotive engines?Application

    Aluminum is commonly used for pistons because it is lightweight, which helps improve engine efficiency and performance. It also has good thermal conductivity, which allows it to dissipate heat quickly, reducing the risk of overheating. Additionally, aluminum is relatively easy to machine and cost-effective.

  5. 5.What would happen if a connecting rod fails during engine operation?Application

    A connecting rod failure is usually catastrophic. The broken rod is flung around by the crank and often punches through the crankcase or cylinder block, while the free piston can hit the valves or head. The result is usually a seized or destroyed engine and sometimes an oil fire. Rods most often fail in tension at high speed, from inertia forces at the exhaust-intake TDC, through big-end bolt failure or fatigue cracks, which is why rod bolts are torqued carefully and not reused.

  6. 6.Explain why crankshafts are often made from forged steel.Application

    Crankshafts are often made from forged steel because it provides high strength and durability, which are essential for withstanding the stresses and loads during engine operation. Forged steel also offers good fatigue resistance, which is important for the longevity of the crankshaft under cyclic loading conditions.

  7. 7.How does the design of a piston affect engine performance?Application

    The design of a piston affects engine performance by influencing factors such as weight, strength, and thermal efficiency. A well-designed piston can reduce friction, improve combustion efficiency, and enhance power output. The shape and material of the piston also play a role in heat dissipation and overall engine reliability.

  8. 8.Calculate the stress on a connecting rod with a force of 5000 N applied and a cross-sectional area of 0.002 m².Numerical

    Stress (σ) is calculated using the formula σ = F / A, where F is the force applied and A is the cross-sectional area. Here, σ = 5000 N / 0.002 m² = 2,500,000 N/m² or 2.5 MPa.

  9. 9.Determine the torque produced by a crankshaft if a force of 2000 N is applied at a radius of 0.1 m.Numerical

    Torque (τ) is calculated using the formula τ = F × r, where F is the force applied and r is the radius. Here, τ = 2000 N × 0.1 m = 200 Nm.

  10. 10.What are the consequences of using a heavier piston in an engine?Application

    Using a heavier piston can lead to increased inertia, which may reduce engine efficiency and responsiveness. It can also cause higher stress on the connecting rod and crankshaft, potentially leading to premature wear or failure. Additionally, a heavier piston may increase fuel consumption and reduce overall engine performance.

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