Tec de Monterrey, 2020

This project aimed to design and simulate a DC-powered linear motor; a simplified model of the technology behind maglev trains capable of accelerating a conductive bar along two rails using electromagnetic forces. The challenge was not only to model the forward motion but also to integrate a magnetic braking system for controlled stopping.

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The team began by researching the physical principles underlying electromagnetic propulsion, focusing on Maxwell’s equations (Gauss, Gauss-Magnetic, Ampere, and Faraday), the Biot–Savart law, and the Lorentz force. These laws provided the mathematical foundation to describe how electric currents generate magnetic fields, and how these fields exert forces on conductors.

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They studied linear motor architectures, concluding that their design would be a single-sided, direct-current, rail-based motor. Key elements included:

• Two copper rails connected to a DC supply.

• Ferrite or neodymium magnets arranged with uniform polarity to generate a consistent field.

• A non-magnetic aluminum bar acting as the moving conductor.

• An electromagnet-based braking coil to produce a counter-field for stopping.

CAD blueprints were prepared in Shapr3D, specifying the dimensions of the wooden base, support brackets, and alignment of magnets to ensure a uniform field along the track.

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Once the design was defined, the team developed a mathematical model in MATLAB.

• Lorentz Force Calculation: Using F⃗=I⋅L⃗×B⃗\vec{F} = I \cdot \vec{L} \times \vec{B}F=I⋅L×B, they computed the force acting on the conductor based on current, conductor length, and magnetic flux density.

• Biot–Savart Refinement: Modeled the magnetic field generated by current-carrying rails, concluding that the resulting fields cancel symmetrically and do not disturb the main propulsion field, an insight borrowed from maglev safety systems that prevent derailment

• Solenoid Field Calculation: Designed a coil capable of producing a variable magnetic field to serve as a braking mechanism. Using integration of field equations, they determined a theoretical field strength of B≈2.12×10−2 TB \approx 2.12 \times 10^{-2} \, \text{T}B≈2.12×10−2T for a 10-turn coil at 4A.

• Dynamic Simulation: A full set of kinematic equations for position, velocity, and acceleration were solved numerically using the Runge–Kutta method. MATLAB plots showed how the bar accelerated and decelerated over time, with velocity profiles confirming the feasibility of the concept.\

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The theoretical results indicated that even with a relatively weak magnetic field, the bar would move, though with low acceleration and modest final speed, sufficient for a proof-of-concept prototype. The braking coil effectively slowed the bar, validating the ability to stop motion safely.

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Experimentally, the team noted that dimensional tolerances and current supply limitations had a significant effect on results: too little current caused barely perceptible motion, while excessive current risked overheating materials. This highlighted the need for careful design of both electrical and mechanical components to avoid failure.

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The project provided a comprehensive experience in electromagnetic system design, integrating:

• Physics: Application of Maxwell’s equations and Lorentz force in a real system.

• Mathematics: Analytical derivation of forces, fields, and motion equations.

• Simulation: MATLAB modeling of dynamic behavior and braking response.

• Engineering Design: CAD-based prototyping, material selection, and manufacturability considerations.

The team reflected on the broader significance of electromagnetism in modern technology, from maglev trains to wireless charging and transformers, recognizing how even small electromagnetic forces can produce powerful and precise motion when properly harnessed.

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Please find attached below the relevant documents to this project.