V4 90° Engine — Kinematics, Dynamics & Machining

The Engine: V4 at 90°

This project studies a V4 engine at 90° — a four-cylinder engine in a V configuration with a 90° angle between the two cylinder banks. This architecture is used in performance motorcycles and sports cars. The 90° V-angle has specific dynamic properties that make it naturally balanced in some orders but not others — which is precisely what this project analyses.

Part 1 — Kinematics

Kinematic Model

The mechanism is modelled with the complete crank-connecting rod geometry:

• Crankshaft (input: constant angular velocity)
• Two pairs of connecting rods (bielles) at 90°
• Four pistons in translational motion

Joint positions, velocities, and accelerations were computed analytically for every 2° of crank rotation (360° full cycle) and tabulated in a calculation spreadsheet.

Kinematic Results

The position analysis yields the piston displacement law, velocity, and acceleration as a function of crank angle. At 90° V-angle, the two cylinder banks produce force pulses with a defined phase relationship — the starting point for the dynamic analysis.

Part 2 — Dynamic Analysis

Inertial Forces

Using Newton's second law applied to each moving element, the inertial forces generated over one full crank cycle were computed. The oscillating masses (pistons + connecting rod portions) produce forces transmitted directly to the engine block:

• First-order forces: sinusoidal, at engine rotation frequency
• Second-order forces: at twice the rotation frequency

Moments on the Engine Block

The global moments on the engine mount (Galop = pitching moment, Lacet = yawing moment) were computed from the force and position data. Both are periodic, with significant amplitudes that would cause vibration if uncontrolled.

Part 3 — Counterbalancing

To reduce the transmitted forces and moments, a counterbalancing strategy was developed — adding counterweights to the crankshaft at calculated positions.

Optimal counterbalance parameters:

• Mass: 6 kg
• Radius: 0.145 m
• Phase offset: 4.69 rad (≈ 269°)

After adding the counterweights, residual forces drop from ±21 kN to near zero — a reduction factor of ~650.

Part 4 — Machining Study (PFMC)

Isostatism

Part V4a90 was positioned and clamped using the isostatism method:

• 3-2-1 positioning: 3 points on the reference face, 2 on a perpendicular face, 1 on an orthogonal stop
• Clamping force calculated to exceed the maximum cutting force without over-constraining

Process Planning

Machining sequence defined to propagate the tolerance chain correctly:

1. Facing operations to establish reference datums
2. External turning and shouldering
3. Milling and pocket operations
4. Drilling and boring of functional surfaces
5. Finishing passes to final tolerances

Cutting Conditions

For each operation, cutting parameters were calculated from:

• Material grade and tool coating
• Required surface roughness (Ra)
• Tool life (Taylor's equation: Vc × T^n = C)
• Machine power limits

What This Demonstrates

From mechanism kinematics to inertial force computation, counterbalancing optimisation, and CNC machining — this project covers the full mechanical engineering analysis chain applied to a real engine architecture. The forces involved (21 kN) are physically meaningful, and the counterbalancing result is verified analytically.