1 Introduction

The increasing miniaturization of components and the functionalization of surfaces with microstructures cause a high demand on economic micro-technical products like micro-optics, micro-reactors and medical implants [1]. This growing demand on micro-components and -structures requests suitable series production systems and processes with high economic feasibility [2]. The machining of these micro-components and -structures can be afforded with high precision and ultraprecision machine tools [3, 4]. But most of these machine tools need a high available space and are restricted in their dynamic, because of their motion of high masses. High manufacturing and operational costs result from the dimension of these machines. Furthermore, the machine tools are mostly high specific or cannot cope with high accuracy standards.

An important requirement for the production of micro-components and -structures with machining manufacturing methods is to provide fast and accurate tool-spindles. Thereby, two basic requirements are made to the tool-spindle of the machine tool [1, 5]. First, a very high rotational speed of the spindle rotor is needed to provide an adequate cutting speed by using micro milling and grinding tools with a diameter smaller than 100 μm. Second, a low run-out error is simultaneously needed to get good cutting conditions. Both requirements are seldom fulfilled together. In most cases the conflict between low run-out error and high rotational speed results from the design and size of the spindle. Large spindles have a very small run-out error but are usually slow, small high speed spindles with compact dimensions, reach rotational speeds above 400,000 rpm, but have a run-out error over 1 μm. An ultra-high-speed electronic drive system with 100 W and a rotational speed of 500,000 rpm has been developed by Zwyssig [6]. With dimensions of 22 × 60 mm² the size of the drive system is convenient for micro-technical applications, although the run-out error of this spindle is still unknown.

2 Related work

To achieve a low run-out error with a simultaneously high rotational speed, an air bearing spindle, propelled by an air turbine, has been developed by the Institute for Manufacturing Technology and Production Systems (FBK). This spindle (FBK-micro-spindle) has a rotational speed up to 450,000 rpm and a run-out error under 0.4 μm [7]. With small dimensions of 25 × 35 mm2 and a weight of 150 g, the FBK-micro-spindle is well adapted for the requirements of micromachining. A cemented carbide tool shank, with a micro-tool directly ground onto the shank, is used as a rotor and thus a functional part of the radial spindle-bearing. This form of radial bearing corresponds a direct guiding of the tool shank. A tool-holder or a collet chuck is no longer needed. Thereby the total run-out error depends only on the accuracy of the grinding process of the end mill on the monolithic rotor-module and the accuracy of manufacturing the air bearing stator [8]. The axial bearing is designed as a ball to plate plain bearing preloaded by magnetic force. This bearing design has less wear resistance and tends with increasing abrasion to axial vibration excitation. Furthermore, a tool change by replacing the rotor-module is rather difficult because for each tool change the turbine has to be removed [9]. This FBK-micro-spindle creates the initial point of the novel high-frequency tool-spindle described in this paper.

3 High-frequency tool-spindle

The high-frequency tool-spindle is a further development of the FBK-micro-spindle. Therefore, some fundamental components of the FBK-micro-spindle or their functions have been applied or have to be suited to the new design. Furthermore, the high-frequency tool-spindle has to meet the following requirements for good performance and multifunctional usage in desktop sized machine tools.

  • Radial and axial air bearing

  • Rotational speed higher than 450,000 rpm

  • Run-out error less than 1 μm

  • Small overall size and mass

  • Low number of components

To implement this, the radial air bearing design of the FBK-micro-spindle was applied unchanged. This bearing, allows a high rotation speed with low run-out error.

4 Spindle design

The developed high-frequency tool-spindle (Fig. 1) is composed of seven different components (Fig. 2).

Fig. 1
figure 1

High-frequency tool-spindle demonstrator

Full size image
Fig. 2
figure 2

Components of the high-frequency tool-spindle 

Full size image

The rotor-module consists of the spindlerotor (1) and the turbine wheel (2). The spindlerotor is guided in the air bearing stator (3). On the front end (tool side) the turbine wheel is fixed.

This wheel has two air bearing surfaces. In combination with an air bearing surface in the front side of the air bearing stator and an air bearing surface in the bearing cover (4), the turbine blade forms the axial air bearing (Fig. 3). Besides the axial air bearing two nozzles for propelling the turbine are integrated in the bearing cover. For tool changing the front cover (7), with integrated bearing cover (4), can be removed from the housing (5) and the rotor module can be replaced. The air bearing stator is fixed in the housing by a back cover (6). In the following chapters the different components of the high-frequency tool-spindle and their design are described.

Fig. 3
figure 3

Bearing concept of the high-frequency tool-spindle

Full size image

4.1 Rotor-modules

A rotor-module is a functional component of the high-frequency tool-spindle, which is guided in the axial and radial air bearing. Every rotor-module consists of a monolithic tool-rotor body, made of cemented carbide and a turbine wheel to drive the rotor. For micro machining, the micro tools for example micro pencil grinding tool or micro end mills could be directly ground onto the shank (Fig. 4).

Fig. 4
figure 4

Rotor-module with micro end mill and micro-pencil grinding tool

Full size image

4.2 Air bearing stator

The air bearing stator includes the radial air bearing and the back part of the axial bearing. The radial air bearing is implemented as stage type or groove type air bearing. The axial air bearing is a stage type air bearing. Both air bearing surfaces are supplied by compressed air through holes in the spindle housing. These holes distribute the compressed air evenly over the air supply grooves (Fig. 5). Three feed holes direct the air into the air bearing supply nut of radial air bearing surface. The back side axial bearing surface is machined in the front side of the air bearing stator. Two feed holes guide the compressed air through a V-supply nut in the axial bearing surface. To decouple the axial a radial air bearing, between the bearings a conical transition is manufactured. In these area four holes provides the vent of the used air from the air bearing stator out of the spindle.

Fig. 5
figure 5

Air bearing stator (model, half section)

Full size image

4.3 Axial bearing

In the bearing cover of the high-frequency tool-spindle the front end of the axial bearing and the turbine drive is integrated. In Fig. 6 a model of the bearing cover with turbine wheel is shown.

Fig. 6
figure 6

Bearing cover with turbine wheel (model, half section)

Full size image

Two feed holes guide the compressed air through a V-supply nut in the axial bearing surface. The air vents through the gap between turbine blade and axial air bearing surface and the turbine wheel floats on the air cushion. The used air vents through exhaust holes. When assembling the bearing cover and the air bearing stator, the contact surfaces of both components have to be in a precise contact. These surfaces align the axial air bearing surfaces in bearing cover and air bearing stator together and define an optimal air gap of the axial bearing and ensure the function of the axial air bearing. In addition to the axial bearing structures, supply and exhaust holes in the bearing cover the whole turbine drive within air nozzles and turbine exhaust are integrated in the bearing cover.

4.4 Turbine drive

The turbine wheel combines the axial bearing blade and the turbine drive together. For this reason the turbine blade has to meet the requirements of the axial air bearing and of the turbine drive. The dimensions of the needed air bearing surfaces are determined by the axial air bearing design. For application, the high-frequency tool-spindle in micro machining, the turbine drive has to provide enough power. Therefore, the dimensions of the turbine must be estimated. Based on the friction energy in the radial and axial air bearing (P RB , P AB ) in addition with the process power P P , the power dissipation P d can be calculated by:

$$ P_{d} = P_{RB} + P_{AB} + P_{P} $$
(1)

Thereby, the friction power in the axial bearing P AB is calculated by [10]

$$ P_{AB} = \frac{{\eta \cdot \pi^{3} \cdot L \cdot D^{3} \cdot f^{2} }}{c} $$
(2)

with the dynamic viscosity of air η, the length of the radial air bearing L, the air bearing diameter D, the frequency of the spindle f and the radial air gap c. For the axial bearing the friction power P AB is calculated by

$$ P_{RB} = \frac{{\eta \cdot \pi^{3} \cdot f^{2} \cdot D_{e} \cdot D_{a}^{3} }}{c} $$
(3)

with the equivalent diameter D e , which is \( (D_{a} - D_{i} )/2 \), the inner radius of the bearing surface Di and outer radius of the axial air bearing surface D a [11]. The process power P P can be calculated with:

$$ P_{P} = \left( {v_{c} + v_{f\hbox{max} } } \right) \cdot F = \left( {\pi \cdot d \cdot f + v_{f} } \right) \cdot F $$
(4)

Thereby F is the process force, d the tool diameter, f the rotation frequency of the spindle, \( v_{c} = d \cdot \pi \cdot f \) the cutting speed and v fmax the maximum feed speed of the process [12]. Calculations, with known process forces and geometry data of the spindle, show that the power supplied by the turbine drive has to be higher than 8.6 W. This turbine power can be calculated with the rotation frequency and impulse transmission [13]:

$$ P_{A} = 2 \cdot \mathop {m^{*} }\limits^{ \cdot } \cdot \left( {c_{e} - u_{D} } \right) \cdot \left( {1 - \cos \left( \tau \right)} \right) \cdot u_{D} $$
(5)

With \( \mathop {m^{*} }\limits^{ \cdot } \) the mass flow, ce the velocity of approach, τ the deflection angle (150 °) [13], u D the turbine blade velocity (\( d_{T} \cdot \pi \cdot f \)) and d T the middle diameter of the turbine wheel, the turbine power results with 26 W. From this follows that 15 W of the turbine power can used for micro machining. Based on the values which depend on the axial air bearing dimension, the turbine wheel is designed. For better impulse repeating at the turbine wheel, the turbine is propelled by two opposite air nozzles. For a better performance of the air turbine, the turbine wheel with different numbers of turbine blades are simulated by CFD. The turbine blade design with 15 blades is the most efficient design and promises the best spindle performance (Fig. 7).

Fig. 7
figure 7

CFD-Simulation (Contour-plot of velocity in m/s)

Full size image

5 Experimental setup

To characterize the attributes of the new developed high-frequency tool-spindle and validate the CFD-Simulation of the turbine drive, the manufactured demonstrator (Fig. 1) has been metrologically documented and analyzed concerning axial stiffness, tilt stiffness and run-out error. For the experimental test of the stiffness the rotor-module of the high-frequency tool-spindle has been loaded with a force, generated with different weights. Thereby the rotor-module deflected from his equilibrium position. The resulting deflection of the spindle was measured with a capacitive measuring sensor. The capacitive sensor was also used to measure the run-out error of the rotor-module. The characteristic signal resulting from the rotor rotation can also be used to determine the rotational speed.

6 Results

6.1 Axial stiffness

The axial bearing stiffness has been measured in both directions with a supply pressure of 7.5 bar. The measured stiffnesses are 0.16 N/μm in tool direction and 0.11 N/μm against tool direction (Fig. 8). Both measured stiffnesses are below the before calculated stiffnesses, because of manufacturing errors by using a conventional lathe for machining the parts. So the parallelism deflects between the axial bearing washer and axial bearing surfaces. Therefore the air cannot flow over a constant parallel bearing gap. Instead it flows over an irregular high air bearing gap, thereby the flow profile of the bearing is clearly changing. Furthermore, the bearing gap of the demonstrator is much bigger than the design of the bearing. Calculations show that a stiffness of 1.2 N/μm in both directions is reachable with manufacturing in tolerances. So the axial bearing meets his requirements.

Fig. 8
figure 8

Measured axial bearing stiffness in N/μm

Full size image

6.2 Tilt stiffness

A tilt stiffness of 2·10−5 Nm/μrad was measured (Fig. 9). If the deflection is higher than 370 μrad, a contact of the rotor-module and the air bearing stator and/or the bearing cover occurs. In the diagram this contact is viewable by a rapid increase of the tilt stiffness up to 370 μrad deflection. The measured tilt stiffness is about a factor of ten smaller than the tilt stiffness of the existing FBK-micro-spindle. This depends on the inaccuracies in manufacture and the resulting difference in the air bearing gaps of the spindles.

Fig. 9
figure 9

Measured tilt stiffness in Nm/μrad

Full size image

6.3 Run-out error and maximal rotational speed

The run-out error of the rotor-module shaft has been measured in an operational system test of the demonstrator and is near 0.7 μm. The maximal rotation speed of the demonstrator has been determined using the structure-borne sound measurement method and is near 222,000 rpm, limited by the half-frequency-instability of the rotor stator system. Both values are worse than the design of calculated values and can be also returned to the default of the machining tolerances.

7 Conclusions and outlook

In the article a novel high-frequency tool-spindle for replaceable rotor-modules was described. With this spindle it will be possible to manufacture micro components by using several production processes with different tool-rotor-modules in a first step and measure the manufactured microstructures, after changing to a measuring-rotor-module, in a subsequent second step. Thereby reclamping operations of the micro component will be dispensed and also the influence of chucking errors and handling problems. Machining with this spindle occurs with monolithic tool-rotor-modules axial and radial guided in air bearings. Thus the air bearing acts as a precision interface, which is aligning the rotor-modules automatically in the spindle. Driven by a pneumatic air turbine, it’s possible to reach a high rotational speed with a simultaneous low run-out error. The combination of these properties affords the use of micro machining tools with a diameter of 10–100 μm.

For the manufactured demonstrator it wasn’t possible to reach the required manufacturing tolerances for the air bearing components by using a conventional lathe for machining the parts. So the previously calculated stiffnesses of the bearings could not be achieved. To achieve the required tolerances for the air bearing components, further machined components will be made on an ultra-precision lathe. Thereby it will be possible to reduce the air bearing gaps and to increase the stiffnesses. As a result, it will be possible to reach higher rotational speeds and a lower run-out error. Based on the corresponding findings the multifunctionality of the already developed high-frequency tool-spindle will be increased by developing new rotor modules (e.g. μ-EDM-module and confocal chromatic measuring module). Additional the development of a “spindle-family” will be used to enlarge the functional boundaries of the existing system. Furthermore the developed high-frequency spindles and its components should be integrated in a small multifunctional machine system.