DESIGN OF AIR DRIVE SPINDLE

Yohichi Nakao1, Tomohiro Mizoi1 and Yuzo Minowa2 1Mechanical Engineering

Kanagawa University Yokohama, Japan

2PENTAX Corporation, Tokyo, Japan

INTRODUCTION A spindle of the ultra-precision machine tools, such as diamond turning/grinding machines, is an important component that determines the machining accuracy. Therefore, improvement of the spindle performance is a critical issue in designing the machine tools in order to accomplish further improvement of the machining accuracy. In addition, producing small and precise parts is another important requirement. Thus, a small spindle with improved performance is needed to meet the requirements in the precision machining. In order to develop small in size and precise spindle, a spindle driven by water flow, named the water drive spindle, has been proposed and developed[1]-[3]. The performance of the water drive spindle has been evaluated in the theoretical and experimental studies. The water drive spindle uses water flow for driving, supporting and cooling the spindle rotor. A small number of flow channels are specially designed inside the spindle rotor so that the water flow energy through the channels can be transformed into torque that makes the spindle rotational motion. This simple structure works as a motor, thus it is named the water drive motor. The water flow is used as the lubricant flow for the water hydrostatic bearings, as well. Water is the incompressible fluid as well as oil. In addition, the viscosity of water is smaller than that of oil, thus the water hydrostatic bearing is considered to be suitable for precision machine tools. By the combination of the water drive motor and the water hydrostatic bearing, it is accomplish to design the small size and high performance spindle for the precision machining. In fact, the size of the water drive spindle is 22 mm in diameter and 112.5 mm in length. In addition, stiffness of the water drive spindle is 374 N/µm, as well. The bearing stiffness and rotational accuracy are,

in general, important concerns in designing the spindle for precision machine tools. In some applications, however, high speed spindle rotation becomes at the most important requirement, even bearing stiffness will degrade or the spindle size will be large. In this case, air pressure bearing is still the suitable choice for the spindle. The present paper introduces a newly designed air drive spindle. The air drive spindle uses similar driving principle to the water drive spindle, for instance, it uses some flow channels to produce the torque to spin the rotor. However, a modification for integrating additional function to the spindle has been made so that the water/air drive spindle can rotate for both rotational directions. In the following sections, the structure and working principle of the air drive spindle are presented. A mathematical model for designing the air drive spindle is introduced, and the spindle performance is discussed through the simulation. Developed air drive spindle is evaluated through experimental studies. AIR DRIVE SPINDLE A basic structure of the air drive spindle is depicted in Fig. 1. The air drive spindle uses air flow for driving and supporting the spindle rotor. The spindle rotor is supported by air pressure bearings in the axial and radial directions. Since the designed air drive spindle is the prototype, the thrust air pressure bearings are located at both end surfaces of the spindle rotor for ease of the design and fabrication. The air drive spindle is designed to be basically bilateral symmetry, except for exit channels as described later. As the water drive motor, the air drive motor is composed of a small number of flow channels inside the spindle rotor. The supplied air first enters the rotor through the channels, named the inlet channels, in the radial direction. The inlet channels are located between the outer rotor surfaces and the main channel that is formed at the center of the rotor in the

axial direction. The main channel is made so as to lead air flow to outside of the rotor through exit channels from the inlet channels. As shown in Figs. 1(b) and (c), the exit channels form bend-shaped channels. The direction of the air flow changes significantly in the exit channels. Consequently, the torque used to spin the rotor is generated by the large change in the angular momentum of the air flow.

22

4

23

432

ωρ

ωµπωµπωρ

exexd

th

th

j

rr

m

ml

RAnC

hR

hLRRq

AlqnT

−

−−

−=

slj LLL += where n is the number of the bend channels of each air drive motor, hj and hth are the clearance of journal and thrust bearings, respectively. q is the flow rate through each bend channel of the exit channels, ρ is the density of air, µ is the coefficient of the viscosity of air. Cd is the drag coefficient and Aex is the projected area of the part formed on the rotor surface.

The direction of the exit channels determines the direction of the produced torque. In order to produce torque in the opposite direction, another couple of the air drive motor structure is designed in the other side of the rotor, as shown in Fig. 1. Both air drive motor structures are the same except for the direction of the exit channels, as depicted in Figs. 1(b) and (c).

In Eq. (1), the first term represents the produced torque by the air drive motor. The second and third terms are the negative torques due to the air viscosity at the clearances between the rotor and the sleeve and journal bearing, as well as the thrust bearings. The last term represents the air resistance acting on the small parts which are placed on the rotor surface forming the exit channels, as shown in Fig. 1.

R If the load acting on the spindle rotor is negligibly small, the relationship between the supplied air flow and the angular velocity of the air drive spindle can be expressed as

0

42

2

2

422

3

=−

+

++

qAln

hRR

hRL

qnRAnC

m

m

th

thr

j

jjexexd

ρ

ωµπµπρωρ

(2)

Exit channels (A, B)

Main channel

th

hth

Air supply port

Rotor

Rr

hj

hsl_r

hsl_c

b

Inlet channel

Casing

Drain port (a) Spindle structure

Air bearing

Rc

Lj Collar Sleeve Lsl Air bearing

ω

w

Fig. 1 Structu

THEORY FOR SPINDLE A mathematical mothe air drive spindleprincipal spindle clearance between nozzle size of thetorque produced byexpressed as

lm

q

Am

Thus, the angular velocity can be obtained by

ααγββ

ω2

42 −+−=∴ (3)

here,

23exR

AnCρ

α = (4)

(b) Exit channel (A)

re of a

DESIG

del is and it paramethe sle exit the air

(c) Exit channel (B)

ir drive spindle

NING AIR

derived for deuses to determters, such

eve and rotor channel. The drive spindle

ω

2exd

th

thr

j

jj

hR

Rh

RLqn

424 µπµπ

ρβ +

+=

2qAl

nm

mργ −= DRIVE

signing ine the

as the and the driving

can be

If minor pressure losses can be neglectedcontrol pressure, pc, is determined by the nsizes of the exit channels as well as the flowq, through the nozzle. Consequently, the cpressure is given by

(1)

(5)

(6)

, the ozzle rate, ontrol

diameter and 165 mm in length. Air pressure bearings using porous media are used in the spindle. Stiffness of the bearings at the supply pressure of 0.4 MPa are nominally 36.0 N/µm for the journal bearing and 17.7 N/µm for the thrust bearing, respectively.

2

2

=

mc cA

qp ρ (7)

where Am is the area of the nozzle and c is the discharge coefficient. The clearances between the sleeve and the rotor, and between the casing and the sleeve are important parameters in controlling both leakage flow in the clearances and negative torque, due to the viscosity of the air in the clearance. The leakage flow at the clearances can be written by

( ) ( )[ ]

+−+

−−+=

c

cslc

ccslcccslc

sl

coutsl

RhR

RhRRhR

Lpq

_

222_44

__

ln4µπ

(8)

( ) ( )[ ]

+−+

−−+=

r

rslr

rrslrrrslr

sl

cinsl

RhR

RhRRhR

Lpq

_

222_44

__

ln4µπ

(9)

Nozzle diameter of the exit channels was designed to be 1.4 mm. However, actual diameters of the eight nozzles are varied from 1.458 to 1.501 mm. Since the nozzle diameter is a principal design parameter that affects spindle performance, the exit channels are designed to be exchangeable. Thus, optimum nozzle diameter will be chosen so as to meet requirement of the spindle application. In addition, the direction of the discharge port of the exit channel can be changed, which enables all the discharge ports to set in the same direction. This setting accomplishes high speed rotation.

Table 1. Determined parameters

b 4.0 mm w 4.0 mm d 1.4 mm Aex b･w=16 mm hj 9.5 µm Lj 50.5 mm

hsl_c 9.5 µm Lsl 1.3 mm hsl_r 11 µm Rc 13 mm hth 5 µm Rex Rr+b/2=12 mm lm 11 mm Rr 10 mm n 4 Rth 13 mm

Thus, the total flow rate is given by outslinsld qqnqQ __ ++= (10)

Important spindle parameters were determined using the derived equations as shown in Table 1. Before developing the air drive spindle, performance of the designed spindle was examined through simulation. Calculated output power is given in Fig. 2. The spindle speed under no load condition is also shown in Fig. 3. Because of the air pressure limitation of the compressor for supplying air flow to the spindle, driving air pressure, pc, is calculated. As shown in Fig. 4, it is verified that the air pressure for driving the spindle can be supplied by the commercial air compressor.

Servo valve Rotary encoder

DESIGNED AIR DRIVE SPINDLE Spindle Air bearingThe developed air drive spindle is shown in Fig. 5. Dimensions of the spindle rotor are 20 mm in Fig. 5 Developed air drive spindle

Fig. 4 Calculated driving pressure Fig. 2 Calculated output power Fig. 3 Calculated spindle speed

EXPERIMENTS

The relationship between the supplied flow rate and the spindle rotation was given in Fig. 6. It is verified that bidirectional rotation was accomplished by switching the supply ports. In addition, it can be observed that the calculated spindle speed shown in Fig. 3 simulates the actual spindle speed, though it is slightly higher than the actual speed. Driving pressure, pc, was

addition, it can be observed that the calculated spindle speed shown in Fig. 3 simulates the actual spindle speed, though it is slightly higher than the actual speed. Driving pressure, pc, was also measured, as shown in Fig. 7. It is verified that the calculated pressure, pc, also simulates the actual pressure.

also measured, as shown in Fig. 7. It is verified that the calculated pressure, pc, also simulates the actual pressure.

Fig. 6 Spindle speed vs. flow rate

As mentioned, the nozzle of the exit channels is a key parameter that determines the spindle speed. In addition, theoretical and experimental studies indicate that the derived mathematical model can simulate the characteristics the air drivel spindle. Thus, the influence of the nozzle diameter on the spindle speed was studied through the simulation using the derived mathematical model. In the simulation, the spindle speed, when the driving pressure reaches 0.5 MPa, was evaluated. In addition to the supply pressure limitation, maximum flow rate of the compressor, qmax, was considered in the calculation. The calculation result is presented in Fig. 8. From the result, it is verified that the designed nozzle diameter, d=1.4 mm, is rather large to attain high spindle speed. Since the exit channels was designed to be exchangeable, the exit channels with optimum diameter can be introduced to increase the highest spindle speed.

As mentioned, the nozzle of the exit channels is a key parameter that determines the spindle speed. In addition, theoretical and experimental studies indicate that the derived mathematical model can simulate the characteristics the air drivel spindle. Thus, the influence of the nozzle diameter on the spindle speed was studied through the simulation using the derived mathematical model. In the simulation, the spindle speed, when the driving pressure reaches 0.5 MPa, was evaluated. In addition to the supply pressure limitation, maximum flow rate of the compressor, qmax, was considered in the calculation. The calculation result is presented in Fig. 8. From the result, it is verified that the designed nozzle diameter, d=1.4 mm, is rather large to attain high spindle speed. Since the exit channels was designed to be exchangeable, the exit channels with optimum diameter can be introduced to increase the highest spindle speed.

Fig. 7 Driving pressure vs. flow rate

Fig. dle

REFERENCES

[1] Y. Nakao, M. Mimura and F. Kobayashi,

nd Y. Sagesaka,

. Sagesaka, Water Drive

(Nagoya, 2005-10).

SUMMARY SUMMARY In the present paper, an air drive spindle was proposed and mathematical model was derived for designing the air drive spindle. The air drive spindle uses the same driving mechanism with the water drive spindle that has been developed. Spindle performances were investigated through simulation studies. Then, the developed air drive spindle was tested and the result was compared to the simulation. From these investigations, it is verified that the mathematical model simulates the characteristics of the air drive spindle. Thus, optimum nozzle diameters of the exit channel were obtained for various driving conditions based on the mathematical model.

In the present paper, an air drive spindle was proposed and mathematical model was derived for designing the air drive spindle. The air drive spindle uses the same driving mechanism with the water drive spindle that has been developed. Spindle performances were investigated through simulation studies. Then, the developed air drive spindle was tested and the result was compared to the simulation. From these investigations, it is verified that the mathematical model simulates the characteristics of the air drive spindle. Thus, optimum nozzle diameters of the exit channel were obtained for various driving conditions based on the mathematical model.

8 Influence of nozzle diameter on spinspeed

Water Energy Drive Spindle Supported by Water Hydrostatic Bearing for Ultra-Precision Machine Tool, Proc. of ASPE 2003 Annual Meeting, pp. 199-202, (Portland, 2003-10). [2] Y. Nakao, F. Kobayashi aPerformances of Water Energy Drive Spindle Supported by Water Hydrostatic Bearing, Proc. of ASPE 2004 Annual Meeting, pp. 241-244, (Orlando, 2004-10). [3] Y. Nakao and Y

ACKNOWLEDGMENT ACKNOWLEDGMENT

Spindle for Diamond Turning Machine, Proc. of the third international conference on leading edge manufacturing in 21st century, pp. 449-454,

This research work is financially supported by the Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science.

This research work is financially supported by the Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science.