Kinematics · torque · cycle arithmetic
Motion duty & energy
Inputs
User-entered total inertia referred to the stated motor/axis; no load inertia is inferred.
Initial angular speed for the declared acceleration or deceleration interval.
Final angular speed for the declared acceleration or deceleration interval.
Time over which the stated speed change occurs.
User-entered torque magnitude during the constant-torque segment.
Duration assigned to the declared running torque.
User-entered torque magnitude during the deceleration segment for RMS arithmetic.
Duration assigned to the declared deceleration torque.
Results
Angular acceleration
471.24
rad/s²Inertia acceleration torque
5.6549
Declared total cycle time
2
Declared-duty RMS torqueTrms
3.2847
Kinetic energy released if decelerating
0
α = (ω1−ω0)/tacc; Tacc = Jα; Trms = √(ΣTᵢ²tᵢ/Σtᵢ); Ereleased = ½J(ω0²−ω1²)
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Axial response · Beam deflection & reactions · Elastic stability · Solid-shaft torsion
Method
Formula, when it applies, and when it does not
Calculate angular acceleration, inertia torque, duty-cycle RMS torque, total cycle time, and a kinetic regenerative-energy upper bound from motion conditions.
α = (ω1−ω0)/tacc; Tacc = Jα; Trms = √(ΣTᵢ²tᵢ/Σtᵢ); Ereleased = ½J(ω0²−ω1²)
When
- User-entered reflected inertia
- Piecewise constant torque segments
- No inferred load/friction torque
- Kinetic-energy upper bound
Don’t
- This is declared-duty arithmetic: inertia acceleration torque from user-entered reflected inertia and speed change; RMS torque from three user-entered constant-torque segments; and a kinetic-energy upper bound only when the stated interval decelerates. It does not infer friction, gravity, cutting/process load, reflected inertia, motor capability, drive current, thermal limits, braking hardware, bus capacity, power regeneration, safety category, or motion-profile suitability.