Unbalance Force
Calculate the centrifugal force generated by an unbalanced rotor, F = m·e·ω², from the unbalanced mass m, the eccentricity e (distance from the centre of mass to the rotation axis) and the angular velocity ω (rad/s). The result, in newtons, is the rotating force that excites vibration in the bearings and structure — proportional to the square of speed, which is why unbalance becomes critical at high speeds. Quantifying it guides the balancing of rotors, fans, turbines and wheels, reducing vibration, noise and fatigue. Enter the unbalanced mass, the eccentricity and the angular velocity.
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Unbalance force
No real rotor is perfectly balanced: there is always a small unbalanced mass whose centre of gravity fails to sit exactly on the axis of rotation. As the rotor spins, that mass generates a rotating centrifugal force that shakes the bearings and the structure, making it the leading cause of vibration in rotating machinery. The force is F = m·e·ω², where m is the unbalanced mass, e is the eccentricity (the distance between the centre of mass and the geometric axis of rotation) and ω is the angular velocity. The dominant factor is ω squared: unbalance force grows with the square of the rotational speed. A tiny unbalance, harmless at low speed, can therefore produce enormous forces at high speed — doubling the speed quadruples the force. Fast rotors (turbines, compressors, grinding wheels, electric motor rotors, dental burs) thus demand rigorous balancing, in which vibration is measured and small correction masses are added or removed until e is driven down to minute levels. ISO 1940 defines balance quality grades (G) from the admissible e·ω product for each machine type. Quantifying the unbalance force guides that balancing work and the sizing of bearings and foundation, which must withstand and damp this rotating excitation without fatigue or resonance. Enter the unbalanced mass, the eccentricity and the angular velocity.
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Shaft Critical Speed
Calculate the critical speed of a rotating shaft, ω_c = √(k ÷ m), from the shaft stiffness k and the rotor mass m. The result, in rad/s, is the rotational speed that coincides with the shaft's bending natural frequency — at it, any small unbalance causes large-amplitude resonant vibration that can damage the equipment. Shafts should run with a safe margin below the first critical speed (rigid rotors) or pass through it quickly to a range above (flexible rotors). It is an essential calculation in designing high-speed turbines, pumps and motors. Enter the stiffness and the mass.
Belt Centrifugal Tension
Calculate the centrifugal tension in a belt, T_c = m·v², from the mass per unit length m (kg/m) and the belt velocity v (m/s). When the belt wraps a pulley at high speed, its own mass, making the turn, generates a CENTRIFUGAL force tending to 'throw' the belt outward, LIFTING it off the pulley. This creates an additional tension throughout the belt (the centrifugal tension), the same at all points and not contributing to power transmission — it only 'steals' part of the belt's gripping capacity against the pulley. Centrifugal tension grows with the SQUARE of velocity, so it is negligible at low speeds but becomes important in fast belts. The effect is harmful: by lifting the belt off the pulley, centrifugal tension REDUCES the normal contact force and thus the friction available to transmit power — there is an OPTIMAL velocity above which increasing speed reduces transmissible power (the belt starts to 'float'). So belt speed has a practical limit (typically 25-30 m/s for conventional V-belts, more for special belts). Centrifugal tension must be added to the tensions to get the total tight- and slack-side tensions. Enter the mass per unit length and the velocity.
Hoist Rope Tension
Calculate the resultant force in an elevator's hoist rope, F = (Q + M_car − M_counterweight)·g, from the payload Q, the car mass and the counterweight mass (kg). The result, in newtons, is the unbalanced effort the steel ropes must transmit, already net of the counterweight's balancing effect. It is the basis for sizing the ropes (number, diameter and safety factor, typically ≥ 12 in elevator codes) and the traction sheave. When the load is such that car + load ≈ counterweight, the force tends to zero (balanced system). Enter the load, the car mass and the counterweight mass.
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Punching Force (Sheet Cutting)
Calculate the force to punch (cut) a round hole in sheet metal, F = π·D·t·τ, from the hole diameter D (mm), sheet thickness t (mm) and the material shear strength τ (N/mm²). The product π·D is the cut perimeter; times thickness gives the area to be sheared; times shear strength gives the force. Punching (and sheet cutting in general, like blanking) is one of the most common stamping operations: a punch descends against a die, with a small clearance, and shears the material, separating the part or scrap. Computing the force is essential to select the press (whose tonnage capacity must exceed the force with margin) and to size the tooling. Force can be reduced with tricks like adding a shear angle to the punch or die, making the cut progressive instead of simultaneous over the whole perimeter — reducing the peak force (but increasing stroke). Knowing the force also lets you estimate the operation's work and energy. Enter the hole diameter, thickness and shear strength.
Rail Thermal Force (CWR)
Calculate the axial thermal force in a continuous welded rail (CWR), F = E·A·α·ΔT, from the steel elastic modulus E (Pa), the rail section area A (m²), the thermal expansion coefficient α (1/°C) and the temperature change ΔT from the neutral temperature (°C). In CWR — where rails are welded into hundreds-of-metre or kilometre strings, removing joints — thermal expansion is PREVENTED by track fastening, so a temperature change, instead of changing length, generates a huge internal axial force: compression in heat (risk of track buckling, which misaligns the rails) and tension in cold (risk of rail or weld fracture). Since the force does not depend on length (only section and ΔT), it can reach hundreds of kN. So CWR is installed at a neutral (stress-free) temperature chosen mid-range, minimizing compression and tension extremes. This is essential to modern track safety and to set the laying neutral temperature. Enter the elastic modulus, section area, expansion coefficient and temperature change.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.