**3. The electro-spindle**

In literature can be found examples of air bearing electro-spindles for high speed and high precision applications, see for example references [11-13]. The electro-spindle developed at Politecnico di Torino [14], shown in Figure 10, is composed of a rotor of 7 kg mass, 50 mm diameter and 479 mm length. It is supported by air bearings and accelerated by means of an asynchronous motor mounted on one end of the spindle. On the opposite end of the rotor a clamping tool is mounted.

**Figure 6.** Thermal transient

86 Tribology in Engineering

same supply pressure.

tests have gone up to 80 krpm.

in order to plot the orbits.

**3. The electro-spindle** 

[10].

flange.

**Table 2.** Measured diameters of the supply holes

Tests were carried out to determine the bearing stiffness with the rotor stationary. The radial stiffness measured in correspondence of the nose at 120 mm from the front side of the bearing is 18 N/μm at 0.6 MPa supply gauge pressure. The axial stiffness is 27 N/μm at the

Figure 6 shows the thermal transient at 40 krpm for spindle internal and external temperature measurements. The internal temperature is close to that of the air issuing from the exhaust ports. This is in accordance with the results indicated in the literature, see e.g.

Rotor orbits at the two radial bushings were recorded at speeds up to 50 krpm, although

Figure 7 shows an example of orbits at 45 krpm, both in forward precession. Sensors 1 and 2 are for the bushing on the turbine side, while 3 and 4 are for the bushing on the motor side. These orbits, which were measured with zero radial and axial loads, are synchronous and stable. As signal frequency analysis indicated that no peak appears at a frequency of around

The centrifugal forces effect has been taken into account during the rotor designing. The

The approaching of the external surface of the rotor to the sensors has also been considered

By means of a finite element code a circumferential groove was designed in proximity of the rotor flange in order to compensate the deformation due to the centrifugal force of the

In Figure 9 the calculated deformation with the circular groove (depth 0.5 mm, length 10 mm) is visible. The deformation is enlarged with respect to the rotor profile. Also thermal effects on the relative distance between rotor and sensors, mounted on the housing, have

In literature can be found examples of air bearing electro-spindles for high speed and high precision applications, see for example references [11-13]. The electro-spindle developed at Politecnico di Torino [14], shown in Figure 10, is composed of a rotor of 7 kg mass, 50 mm diameter and 479 mm length. It is supported by air bearings and accelerated by means of an

half the rotation frequency, unstable whirling does not occur.

radial deformation of the rotor far from its flange is visible in Figure 8.

been taken into account in order to individuate the centre of the orbit.

**Figure 7.** Rotor orbits; *ω*=45 krpm

Figure 11 shows a section of the electro-spindle with carter (1), rotor (2), two bushings (3) and double thrust bearing (4). Motor (5) is of the two-pole squirrel-cage type controlled by an inverter. Speed range is up to 75 krpm and power is 2.5 kW. A clamping tool designed for high-speed is screwed onto the left end of the rotor. By mounting a tool on the spindle it is possible to test the dynamic behaviour of the rotor also during the machining process.

High Speed Rotors on Gas Bearings: Design and Experimental Characterization 89

In order to measure radial and axial stiffness of the tool, the electro-spindle is mounted on a test rig designed for the purpose with proper load devices. Radial forces were measured at different supply pressures (Figure 12) at *ω*=0. Figure 13 shows the axial load capacity readings for 0.3, 0.5 and 0.7 MPa supply absolute pressure. The load device was used for positive displacements and weights were applied to obtain the curve with negative

The rotor orbits depicted in Figure 14 were measured at the same supply pressure. Due to the rotor centrifugal expansion these orbits appear not to be centered in the bushings because the relative rotor-sensor distance decreases. The spindle was tested up to 53000 rpm and the tests were stopped because of the high rotor vibration. The permissible residual imbalance should be diminished in order to allow tests at higher speeds. Anyway the whirl

instability did not occur and the imbalance response was only synchronous.

displacements.

**Figure 10.** Photo of the electro-spindle

**Figure 11.** Schematic section of the electro-spindle

**Figure 8.** Centrifugal expansion of the rotor in correspondence of the bushings (diameter 50 mm)

**Figure 9.** Rotor deformation due to centrifugal force in correspondence of the flange at different rotational speeds

The radial bearings feature cylindrical barrels. Each barrel has four sets of supply ports diameter 0.25±0.01 mm arranged 90 degrees apart. The thrust bearing, similar to the one described in [15], is composed of two disks facing the flange on the journal. Each disk has 8 axial nozzles dia. 0.2±0.01 mm positioned on the mean diameter.

The system is provided with a closed cooling circuit that controls the temperature of the motor and of the discharge air. Without refrigeration and with ambient temperature 298 °K, at 60000 rpm the temperature would reach 383 °K after two hours due to power losses on bearings.

An optical tachometer facing the rotor was provided to measure rotational speed. Four capacitance displacement transducers were inserted radially and at right angles in the carter facing the rotor to measure dynamic runout. Two were positioned on motor side, the other two on thrust bearing side.

Clearances were measured moving the rotor axially and radially until contact is made. It was found that axial and radial clearances are about 15 μm and 20 μm respectively.

In order to measure radial and axial stiffness of the tool, the electro-spindle is mounted on a test rig designed for the purpose with proper load devices. Radial forces were measured at different supply pressures (Figure 12) at *ω*=0. Figure 13 shows the axial load capacity readings for 0.3, 0.5 and 0.7 MPa supply absolute pressure. The load device was used for positive displacements and weights were applied to obtain the curve with negative displacements.

The rotor orbits depicted in Figure 14 were measured at the same supply pressure. Due to the rotor centrifugal expansion these orbits appear not to be centered in the bushings because the relative rotor-sensor distance decreases. The spindle was tested up to 53000 rpm and the tests were stopped because of the high rotor vibration. The permissible residual imbalance should be diminished in order to allow tests at higher speeds. Anyway the whirl instability did not occur and the imbalance response was only synchronous.

**Figure 10.** Photo of the electro-spindle

88 Tribology in Engineering

rotational speeds

bearings.

two on thrust bearing side.

**Figure 8.** Centrifugal expansion of the rotor in correspondence of the bushings (diameter 50 mm)

radial deformation [m]

0 2 4 6 8 10

[rpm]

x 104

**Figure 9.** Rotor deformation due to centrifugal force in correspondence of the flange at different

axial nozzles dia. 0.2±0.01 mm positioned on the mean diameter.

The radial bearings feature cylindrical barrels. Each barrel has four sets of supply ports diameter 0.25±0.01 mm arranged 90 degrees apart. The thrust bearing, similar to the one described in [15], is composed of two disks facing the flange on the journal. Each disk has 8

The system is provided with a closed cooling circuit that controls the temperature of the motor and of the discharge air. Without refrigeration and with ambient temperature 298 °K, at 60000 rpm the temperature would reach 383 °K after two hours due to power losses on

An optical tachometer facing the rotor was provided to measure rotational speed. Four capacitance displacement transducers were inserted radially and at right angles in the carter facing the rotor to measure dynamic runout. Two were positioned on motor side, the other

Clearances were measured moving the rotor axially and radially until contact is made. It

was found that axial and radial clearances are about 15 μm and 20 μm respectively.

**Figure 11.** Schematic section of the electro-spindle

High Speed Rotors on Gas Bearings: Design and Experimental Characterization 91

The electro-spindle was also tested in dynamic conditions during machining with high speed milling cutters of diameters in the range 1 to 6 mm. The system depicted in Figure 15, mounted below the electro-spindle, provides the advance along axis *x* of the material under milling. The material under machining was a block of rapid prototyping resin, advanced by means of a motorized slide. The tests were made up to 40000 rpm with feed speeds from 1 to

Gas bearings suffer from instability problems at high speed. A method to increase the stability threshold (the speed at which the unstable whirl occurs) is to increase the damping of the rotor-bearings system by introducing external damping supports [16]. A design guideline for the selection of the support parameters that insure stability in an aerodynamic

The prototype described in this paragraph was designed with the priority of increasing the stability at high speeds [17]. The method adopted for this purpose was the use of rubber O-

The prototype consists on a rotor (1) made of hardened 32CrMo4 steel with mass 0.96 kg, diameter 37 mm and length 160 mm. The rotor is supported by a radial air bearing mounted on rubber O-rings and an axial thrust bearing (Figure 16). It was designed to rotate in stable conditions up to 150 krpm. At one end of the rotor an air turbine (2) was machined and at the other end a nose (3) was screwed to the rotor. The housing (4) is fixed to the base and has four circumferential slots in which the O-rings are inserted. The bushing (5) incorporates the rubber rings and has four sets of supply nozzles (diameter 0.2±0.01 mm) fabricated by EDM. The total length of the bearings is 57 mm. In the middle plane of the bushing a

10 mm/s and chip thickness 1 mm.

**Figure 15.** Motorized slide used for the dynamic tests

rings.

**4. The textile rotor with damping supports** 

journal bearing with damped and flexible support is given in paper [2].

**Figure 12.** Radial force on the tool (measured at 120 mm from the front side of the bearing ) versus radial displacement at different bearing supply absolute pressures

**Figure 13.** Diagram of axial force on tool versus displacement at different bearing supply gauge pressures

**Figure 14.** Rotor orbits in correspondence of a bushing due to the residual unbalance; supply gauge pressure 0.6 MPa

The electro-spindle was also tested in dynamic conditions during machining with high speed milling cutters of diameters in the range 1 to 6 mm. The system depicted in Figure 15, mounted below the electro-spindle, provides the advance along axis *x* of the material under milling. The material under machining was a block of rapid prototyping resin, advanced by means of a motorized slide. The tests were made up to 40000 rpm with feed speeds from 1 to 10 mm/s and chip thickness 1 mm.

**Figure 15.** Motorized slide used for the dynamic tests

90 Tribology in Engineering

pressure 0.6 MPa


axis x [m]

**Figure 12.** Radial force on the tool (measured at 120 mm from the front side of the bearing ) versus

0 2 4 6 8 10 12 14 16

radial stiffness

0.7 MPa 0.6 MPa 0.5 MPa 0.4 MPa 0.3 MPa

displacement [micron]

**Figure 13.** Diagram of axial force on tool versus displacement at different bearing supply gauge pressures

 **Figure 14.** Rotor orbits in correspondence of a bushing due to the residual unbalance; supply gauge


axis x [m]


motor side

10000rpm 20000rpm 30000rpm 34000rpm 36000rpm 40000rpm

axis y [m]

10000rpm 20000rpm 30000rpm 34000rpm 36000rpm 40000rpm

radial displacement at different bearing supply absolute pressures


axis y [m]

tool side

force [N]
