In a converting line — printing press, slitter-rewinder, laminator, or coating line — a continuous web of material unwinds from a parent roll, passes through one or more process stations, and rewinds onto finished rolls. The tension in the web between each roller pair determines registration accuracy, coating uniformity, and whether the finished roll is tight enough to ship but not so tight that the inner layers crush the core. The control problem is that the roll diameter is constantly changing — the unwind roll shrinks from 1,200 mm to 100 mm core, and the rewind roll grows from 100 mm core to 1,200 mm. At constant angular velocity, the same web speed that requires 50 rpm at full diameter requires 600 rpm at core — a 12:1 speed ratio. The motor torque required to maintain a given web tension varies linearly with diameter: 100 N of web tension at 600 mm diameter requires 30 N·m of motor torque; the same 100 N at 100 mm diameter requires only 5 N·m. The tension controller must vary motor torque in real time as the roll diameter changes, and it must do so without a diameter sensor — the controller infers the diameter from the ratio of line speed to roller rpm.
Open-Loop Diameter Calculation: The Foundation Layer
The controller calculates the instantaneous roll diameter D from the fundamental relationship D = (line speed × gear ratio) / (π × roller rpm). The line speed comes from a draw roller encoder or a laser Doppler surface velocimeter; the roller rpm comes from the motor drive's encoder feedback or a proximity sensor counting gear teeth on the roller shaft. The calculated diameter is noisy — encoder quantization at low rpm produces a diameter signal that jumps ±2–5 mm per calculation cycle — so the controller applies a first-order low-pass filter with a time constant typically 5–20× longer than the diameter update interval. The filtered diameter feeds the torque command: motor torque = target tension × (D/2) / gear ratio.
Taper Tension: Why Constant Torque is Not the Answer
At constant web tension, each layer of material wound onto the rewind roll compresses the layers beneath it. The radial compressive stress at the core can exceed the yield strength of the core material — a 75 mm diameter fiberboard core collapses under roughly 1.5–2.0 MPa of radial pressure, which can be generated by winding 400 layers of 50 µm PET film at constant tension. The failure mode is called telescoping: the inner layers slip radially on the core, and the roll deforms into a cone shape.
Taper tension prevents this by reducing the tension setpoint as the roll diameter increases. A linear taper reduces tension from 100% at the core to a programmable end-taper percentage — typically 50–70% — at full roll diameter. The controller calculates the instantaneous tension setpoint as: T(D) = T_core × [1 − taper% × (D − D_core) / (D_full − D_core)]. A 60% linear taper on a roll winding from 100 mm core to 1,000 mm full diameter reduces tension from 100 N to 40 N over the build. This keeps the radial compressive stress below the core's crush limit while maintaining sufficient interlayer friction to prevent telescoping during transport.
A hyperbolic taper produces a more aggressive tension reduction early in the wind, which is useful for extensible films (polyethylene, stretch wrap) that elongate under tension: if the film stretches by 2% during winding and then relaxes during storage, the inner layers loosen and the roll becomes a "soft" roll that shifts in transit. A hyperbolic taper reduces tension quickly in the first 30% of diameter growth, keeping the in-wound strain below the film's elastic limit. For more on roller drive systems, see our servo drives & motors category.
Inertia Compensation: The Torque That is Not About Tension
During acceleration and deceleration of the converting line, the motor must supply additional torque to overcome the rotational inertia of the roll — and that inertia changes with the fourth power of roll diameter. The moment of inertia of a solid cylindrical roll is J = (π × ρ × W × D⁴) / 32, where ρ is the material density, W is the web width, and D is the instantaneous roll diameter. For a rewind roll growing from 100 mm to 1,000 mm diameter, the inertia increases by a factor of 10,000:1. During a line speed ramp from 0 to 300 m/min at 10 m/min/s, a 1,000 mm diameter roll requires roughly 75 N·m of additional motor torque for acceleration alone — and if the tension controller does not add this inertia compensation torque to the command signal, the web tension drops by that equivalent amount during the ramp.
The DFE EasyWeb digital web tension controller addresses all three control layers in a single device: diameter calculation from line speed and roller rpm, programmable linear or hyperbolic taper tension with automatic diameter-based setpoint scheduling, and inertia compensation using the calculated diameter and the measured acceleration rate from the line speed encoder. Its 0–10 VDC or 4–20 mA output directly commands a pneumatic brake (unwind) or a regenerative drive (rewind), and its MODBUS RTU interface allows the PLC to upload tension setpoints and download actual tension data for production lot tracking.
How do I know if my tension problem is a control issue or a mechanical issue?
Measure the tension at the web with a tension sensing roller — a load-cell-instrumented idler roller — and record the tension signal for 10–20 seconds at constant line speed. If the tension signal shows a periodic oscillation at the same frequency as the roller rotation, the problem is mechanical: an eccentric roller, a misaligned bearing, or an unbalanced roll. The frequency in Hz = line speed in m/min / (π × D_roller in m) / 60. If the tension signal shows a steady drift upward or downward over the roll build (tension at 100 mm core is correct, tension at 1,000 mm diameter is 40% high), the problem is a diameter calculation or taper tension configuration error. If the tension signal spikes during acceleration and dips during deceleration, the problem is missing or misconfigured inertia compensation. The diagnosis is almost always visible in the tension signal — the hard part is isolating the mechanical causes from the control causes. For diagnostic instruments, browse our sensors & instrumentation and pressure sensors categories for tension transducers and load cells.
