Elevator Traction Ratio: T1/T2 Formula, Rope-Sheave Friction, EN 81-50 Design Check and Safety Gear Traction Condition

Traction ratio (also called traction factor or T1/T2 ratio) is the fundamental criterion governing traction elevator operation and safety. The traction sheave transmits force to the ropes by friction; if the ratio of tensions on either side of the sheave exceeds the available friction (which depends on the rope-sheave groove geometry, contact arc, and rope material), the rope will slip on the sheave. The traction condition: T1/T2 ≤ e^(μα), where T1 = heavier side tension, T2 = lighter side tension, μ = coefficient of friction between rope and sheave groove, α = angle of wrap (contact arc) in radians, and e is Euler's number (~2.718). Typical values: μ ≈ 0.09–0.12 for wire rope on cast-iron sheave (round groove), μ ≈ 0.12–0.18 for wire rope on polyurethane-lined sheave (undercut groove); α typically 150–180° (2.62–3.14 rad). The traction condition must be checked for: (1) Normal operation — car with rated load descending (maximum T1) vs empty car ascending (minimum T2); (2) Safety gear actuation — the sheave must not pull the suspension ropes upward through the sheave during safety gear arrest. EN 81-20/50 requires a traction calculation at the design stage. Counterweight balance factor affects T1/T2; if overloaded (e.g. due to miscalculation), traction failure is possible. Modern VVVF drives with closed-loop speed control can detect rope slip via encoder feedback.

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