Electric motors (rotor magnetic pull)

What it is for

In an electric machine, the magnetic field pulls the rotor towards the closer side of the air gap. The pull grows as the gap closes, so it acts as a negative radial spring on the shaft: it softens the shaft, lowers the critical speeds and amplifies any eccentricity. The Motors module (under "Motion and drives"; its workspace is titled "Electric machines") puts that spring, the rotor's mass and inertia and its torque on a shaft. The bearing loads, deflections and critical speeds in the Shaft and Bearings modules then include them.

The electric-motor template is a 15 kW induction motor shaft. A Ø150 × 160 mm rotor stack sits between a 6309 drive-end bearing and a 6208 non-drive-end bearing, with an air gap of 0.5 mm, at 1 460 rpm.

Inputs

+ Rotor adds a rotor. The inspector has three groups.

Rotor

• Shaft: the shaft the rotor sits on.
• Stack centre (mm from the shaft's left end) and Stack length (mm). The pull, mass and inertia are spread over the stack length at three points, so a tilting stack also meets the pull.
• Rotor diameter (mm), the outside diameter of the stack.
• Rotor mass (kg). It enters the critical speeds as a solid cylinder's mass and inertia. Its weight counts in the static loads only when gravity is switched on in the shaft settings.

Magnetic pull

• Air gap (mm), the radial gap between rotor and stator.
• Air-gap flux density (RMS) (T), typically about 0.6–0.7 T for induction machines.
• Static eccentricity (× gap), the rotor's offset as a share of the gap. 0.1 means 10 % of the gap, as in the template.
• Eccentricity direction (°), measured about +x from +y.
• Pull reduction factor, 1 by default. Values below 1 account for saturation and parallel winding paths, which reduce the real pull. It must be greater than zero.

The negative stiffness is $k=\frac{\pi \cdot D\cdot L\cdot B^2}{2{\mu }_0\cdot g}$, times the pull reduction factor, with D the rotor diameter, L the stack length, B the flux density and g the air gap. The static eccentricity e adds a steady pull k·e in its direction.

Drive

• Electromagnetic torque (N·m). Balance it with the coupling: on the coupling load in the Shaft module, tick "Takes the torque that balances the shaft (e.g. the output coupling)".
• Speed (rpm).
• Max deflection / gap, the largest rotor deflection allowed as a share of the air gap (0.1 by default). It is checked against the largest deflection anywhere along the stack, not only at its centre.

Results

The results show the Magnetic stiffness (N/µm) with the static pull, the Rotor deflection (µm) with its share of the air gap, and the Power (torque × speed).

The rotor deflection is the largest radial deflection of the shaft anywhere under the stack, from one end of the stack to the other, in both planes together. A shaft that tilts under the stack moves one end of the stack more than its centre. A stack centred on a bearing of an overhung shaft can have no deflection at its centre while its outer end closes the gap. The results say where the largest deflection is, and give the centre's deflection as well when it differs.

The electric-motor template gives:

The pull grows with the deflection it causes. That is why the two bearings carry 1 430 N together, a little more than the static pull.

Changing the inputs shows how the pull works:

A smaller gap raises k. With the eccentricity given as a share of the gap, the static pull k·e stays the same.

Rotor view

The Rotor view card above the details has two tabs:

• 2D draws the shaft from its sections with the bearings, and the rotor stack at its position and length inside the stator. The section lies in the plane of the eccentricity, which points up. The air gap is too small to see at scale, so it is drawn at least 12 % of the rotor radius; the label gives the true gap and how much larger it is drawn. With a static eccentricity the rotor sits off centre by the same enlarged amount, and amber arrows show the magnetic pull spread over the stack as $q=F/L$. A spring symbol marks the negative magnetic stiffness −k. An End view below shows the rotor off the stator bore's centre and the pull towards the narrow gap.
• 3D shows the rotor stack with its laminations, bars and end rings on the shaft, inside a stator cut open by a quarter so the gap shows. Point at it (or move the keyboard focus to it) and the rotor turns for a moment. Drag to turn the view, scroll to zoom.

The 3D tab needs WebGL. Where the browser has none, the view stays on the 2D tab and says why. With reduced motion set in the system, nothing moves.

Checks and how to fix them

The stability value is the pull's negative stiffness as a share of what the shaft and its supports hold, with the bearings taken as in the critical speed analysis. If the pull exceeds the stiffness of the static solve, the shaft cannot be solved at all; the rotor's facts then say so.

Standards and scope

• The pull follows the classical uniform-gap formula with the RMS flux density. It is not a magnetic finite element analysis. Saturation and parallel winding paths enter only through the pull reduction factor.
• Only static eccentricity is an input. A rotating pull from dynamic eccentricity is not modelled.
• The rotor's inertia is that of a solid cylinder of the given mass and diameter.
• In the unbalance response, the magnetic springs are not damped.
• The calculation does not follow a standard. Treat it as an engineering estimate for stiffness and critical speed studies.

From the command line

axm new motor.axm.json --template electric-motor
axm solve motor.axm.json

Related

• Shaft dynamics: deflection, critical speeds, whirl
• Shaft
• Shaft vibration
• Bearings
• Housings (seat stiffness)
• Open the electric-motor example