In a series-wound DC motor, the field winding and armature are connected in one series circuit, so they carry the same current. In the explicitly unsaturated region where field flux is approximately proportional to current, developed torque is approximately proportional to current squared.
Series-Wound DC Motor Unsaturated Ratio Reference
Compare two current levels using the ideal unsaturated series-motor flux and torque ratios.
Equation Used
- Field and armature carry the same series current.
- Both selected points are in the linear unsaturated magnetization region.
- The proportionality constants are unchanged between points.
- Absolute performance, thermal limits, speed and safety are excluded.
Current percentages share an arbitrary reference and do not imply rated or safe current.
One current path through field and armature
The same current passes through the series field and armature. General DC-machine torque is proportional to field flux times armature current. With Φ ∝ I only in the linear magnetization region, T ∝ I².
The animation shows the continuous electrical path and illustrative rotor motion. It does not calculate speed, voltage, commutation or a specific machine.
What the calculator determines
Enter two currents as percentages of one common reference. The calculator reports current ratio, the corresponding ideal unsaturated flux ratio, ideal unsaturated torque ratio and torque at the final current relative to the hypothetical unsaturated torque at 100% reference current.
No absolute torque, allowable current or machine rating is inferred.
Unsaturated ratio relationship
Because If = Ia = I and Φ ≈ kfI, T = KΦI gives T ≈ KkfI². Therefore Φ₂/Φ₁ = I₂/I₁ and T₂/T₁ = (I₂/I₁)² within the stated unsaturated approximation.
Selected-input arithmetic
Changing from 50% to 100% of the same reference current gives current and ideal flux ratios of 2.0 and an ideal unsaturated torque ratio of 4.0. The 100% final-current point is 100% of the hypothetical unsaturated reference torque.
Model boundary
Magnetic saturation breaks the Φ ∝ I assumption; actual torque then requires the machine's magnetization curve and torque constant. Armature reaction, resistance, voltage, back EMF, speed, load, losses, temperature, commutation, current limits, overspeed protection and generator behavior are absent.
This reference must not be used to select protection, predict safe current, set speed or claim absolute torque.
Questions
Does torque always rise with current squared?
No. The square law is an unsaturated approximation; saturation makes flux rise less than proportionally.
Does 100% mean rated current?
No. It is only a shared reference selected by the user.
Does this model predict speed?
No.
References & Further Reading
- Wikipedia contributors. DC motor. Wikipedia
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