Why is this not a full conveyor-belt FEA?

Real belts have bending stiffness, creep, and different slip physics on the driver vs driven side. This page isolates the textbook capstan inequality and torque limit from mean tension, which is enough to motivate why preload and friction matter.

Belt Drive & Slip

Two pulleys: tension difference limited by μ and wrap θ (e^{μθ}); load torque vs τ_max and simple slip on ω₂.

About this model

A flat open-belt drive is modeled with two cylindrical pulleys. Mean belt tension T₀ and a symmetric tight/slack split T₁ = T₀ + ΔT/2, T₂ = T₀ − ΔT/2 are assumed. The friction limit T₁/T₂ ≤ e^{μθ} caps the transferable tension difference and therefore the torque τ ≈ ΔT·R on the driven wheel. When the requested load torque exceeds this limit, the visualization marks slip and scales the driven angular speed with a simple linear teaching rule.

Who it's for: Intro machine elements and friction drives; complements the capstan rope simulator.

Key terms

Euler belt formula
wrap angle
tension ratio
torque capacity
belt slip

How it works

Open-belt drive caricature: the driver pulls the tight side, the driven resists with torque τ. Friction over wrap angle θ limits how large the tension difference ΔT = T₁ − T₂ can be before the belt slips on the pulley. The steady-state torque on the driven sheave is approximately τ = ΔT · R₂ when there is no slip; beyond the friction limit, real belts slip, heat up, and wear — here we only show a simple scaled ω₂ to signal overload.

Key equations

T₁/T₂ ≤ e^(μθ) ⇒ ΔT_max = 2T₀(e^(μθ) − 1)/(e^(μθ) + 1) for symmetric ±ΔT/2 about T₀

τ = ΔT · R₂, ω₂/ω₁ = R₁/R₂ when no slip

Frequently asked questions

Why is this not a full conveyor-belt FEA?: Real belts have bending stiffness, creep, and different slip physics on the driver vs driven side. This page isolates the textbook capstan inequality and torque limit from mean tension, which is enough to motivate why preload and friction matter.

Continue with similar topics in this category — or all 85 in Classical Mechanics.

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