Design Framework and Manufacturing of an Active Magnetic Bearing Spindle for Micro-Milling Applications

Kazi Sher Ahmed; Bekir Bediz

eess.SYFeb 26, 2026

Design Framework and Manufacturing of an Active Magnetic Bearing Spindle for Micro-Milling Applications

Authors: Kazi Sher Ahmed, Bekir Bediz

Organizations: Faculty of Engineering and Natural Sciences, Mechatronics Engineering Program, Sabanci University, Istanbul, 34956, Turkiye

Abstract

Micro-milling spindles require high rotational speeds where conventional rolling element bearings face limitations such as friction and thermal expansion. Active magnetic bearings (AMBs) address these challenges by providing non-contact and lubrication-free operation at ultra-high speeds with the ability to actively regulate spindle dynamics. The existing literature on AMB spindles has mainly reported specific prototype realizations or control system implementations for specific spindle dynamics. Consequently, design knowledge remains fragmented across isolated successful studies. This paper addresses this gap by presenting a systematic and iterative framework to design and manufacture a micro-milling AMB spindle. The process involves a multidisciplinary design flow with a focus on critical practical aspects of manufacturing. The realized spindle is reported as a case study.

Figures & tables

Fig. 1: Design flowchart for a micro-milling AMB spindle.

Fig. 2: Predicted cutting forces in x , y , and z directions for a slot-milling operation using a two-flute tool.

Fig. 3: Turbine torque as a function of nozzle diameter with turbine power efficiency range 0.18-0.48. Selected nozzle diameter 1.5 mm results in 2.65 N mm of torque with conservative power efficiency of 0.18.

Fig. 4: Air turbine components. (a) Turbine buckets and splitter machined into the rotor. (b) Nozzle plate with push-in pneumatic fittings.

Pitch diameter	$d_{m}$	10 mm
Nozzle diameter	$d_{n}$	1.5 mm
Number of nozzles	$Z$	4
Number of buckets	$Z_{b}$	7
Inlet pressure	$P_{in}$	0.2 MPa
Design operating speed	$N$	114,320 rpm
Turbine output torque	$M$	2.65 N mm

TABLE I: Air turbine parameters.

Fig. 5: Rotor Campbell diagram showing rigid body (cylindrical and conical) and bending modes.

Fig. 7: Radial AMB cross-section with bias and control flux paths.

Stator inner radius	$s_{ir}$	27.1 mm
Stator radial thickness	$s_{rt}$	9.1 mm
Pole length	$p_{l}$	8.4 mm
Pole width	$p_{w}$	4.7 mm
Pole radius	$p_{r}$	8.6 mm
PM thickness	$pm_{t}$	1.5 mm
PM width	$pm_{w}$	8 mm

TABLE II: Radial AMB design variables at selected design point.

Maximum generations	1800
Population size	200
Maximum stall generations	100
Distance measure function	Distance crowding (phenotype)
Pareto fraction	0.35

TABLE III: Optimization algorithm (GA) settings.

Fig. 8: Pareto front with maximization of static radial load capacity and minimization of AMB volume. A selected design point (13.88 N and 3.06

\times

10 -5 m 3 ) is also shown for further analysis and manufacturing.

Fig. 9: AMB load capacities and demands. The AMB capacity envelope is defined by the minimum of both static and dynamic capacities and is shown with a grey thick line. The static and dynamic loads shown are contained within this capacity envelope for proper AMB operation.

Fig. 10: Cross-sections (CS) of AMB (geometry shown in Figure 7 ) with magnetic flux density in T. The white arrows show the direction of the magnetic flux density field. Maximum airgap flux density stayed around 0.664 T. (a) Transverse CS in mid-stator plane normal to rotor axis. (b) Longitudinal CS in plane parallel to rotor axis.

Fig. 11: Manufactured AMB sub-assemblies (not to scale). (a) Radial AMB. (b) Axial AMB (lower half; see Figure 12 ).

Fig. 12: Axial AMB longitudinal cross-section. Two reluctance actuators are placed at either side of the rotor disc for axial levitation control. The dot and cross convention shows the direction of coil currents. Dashed lines show the flux path.

Bias current	$i_{b}$	1.6 A
Axial airgap	$l_{o}$	0.3 mm
Stator pole area	$A_{a}$	1.16 $\times$ 10 -4 m 2
Coil turns per actuator	$n_{a}$	66
Force-displacement dependency	$K_{a}$	6.4 $\times$ 10 4 N/m
Force-current dependency	$K_{ia}$	11.9 N/A

TABLE IV: Parameters for axial AMB.

Fig. 13: Quarter view of longitudinal cross-section of axial AMB showing the magnetic flux density in T (refer to geometry in Figure 12 ) when upper actuator coils were excited with a current of 2.1 A. White arrows represent the direction of the flux density field.

Fig. 14: Backup bearing components. (a) Ceramic plain bearing. (b) Viton O-ring.

Fig. 15: Spindle housing (without end covers).

Fig. 16: Labeled cross-section of AMB spindle CAD assembly.

Manufacturing

Manufacturing research develops methods and systems to design, plan, automate, monitor, and improve industrial production.

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Robust Autonomous Control of a Magnetic Millirobot in In Vitro Cardiac Flow

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Laboratory for Computational Sensing and Robotics, Johns Hopkins University, Baltimore, MD 21218, USA. · Division of Magnetic Manipulation and Particle Research, Weinberg Medical Physics, Inc., Rockville, MD 20852, USA. · Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA.

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Untethered magnetic millirobots offer significant potential for minimally invasive cardiac therapies; however, achieving reliable autonomous control in pulsatile cardiac flow remains challenging. This work presents a vision-guided control framework enabling precise autonomous navigation of a magnetic millirobot in an in vitro heart phantom under physiologically relevant flow conditions. The system integrates UNet-based localization, A* path planning, and a sliding mode controller with a disturbance observer (SMC-DOB) designed for multi-coil electromagnetic actuation. Although drag forces are estimated using steady-state CFD simulations, the controller compensates for transient pulsatile disturbances during closed-loop operation. In static fluid, the SMC-DOB achieved sub-millimeter accuracy (root-mean-square error, RMSE = 0.49 mm), outperforming PID and MPC baselines. Under moderate pulsatile flow (7 cm/s peak, 20 cP), it reduced RMSE by 37% and peak error by 2.4

\times

compared to PID. It further maintained RMSE below 2 mm (0.27 body lengths) under elevated pulsatile flow (10 cm/s peak, 20 cP) and under low-viscosity conditions (4.3 cP, 7 cm/s peak), where baseline controllers exhibited unstable or failed tracking. These results demonstrate robust closed-loop magnetic control under time-varying cardiac flow disturbances and support the feasibility of autonomous millirobot navigation for targeted drug delivery.

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