TECHNICAL REVIEWPower Reduction of Hydrostatic Bearings for Grinding Machines
H. YAMATO

F. SUGIMOTO

Hydrostatic bearings used in the grinding wheel spindles of grinding machines have high stiffness and highdamping against load fluctuation, as well as high rotating accuracy during grinding, however have larger power
loss than other types of bearing. Therefore, the mechanism of power loss is elucidated using fluid analysis and ahydrostatic bearing with minimal power loss is developed. As a result, a developed bearing has reduced power lossby 24%.
Key Words: hydrostatic bearing, grinding wheel spindle, power loss reduction, CFD

1. Introduction

2. Overview of Hydrostatic Bearings

Hydrostatic bearings are bearings that support a spindleby the pressure of lubricant so that the spindle andbearing can maintain a constant state of non-contact. As
a result, there is no wear or deterioration of the bearing
components, and the life of the bearing is extremely longcompared to other types of bearings. Moreover, the error
averaging effect of the oil film can mitigate shape errors,roughness, and other anomalies of the spindle and bearing
for achieving a rotational accuracy that is one order ofmagnitude more precise than the machining accuracyof these parts1). Also, the squeeze effect of the oil film
provides a large damping force against dynamic external
forces to ensure high dynamic rigidity.
At JTEKT, we have established a unique design
theory for hydrostatic bearings and have developed thehydrostatic bearing with internal return flow shown in
Fig. 12), a hydrostatic bearing with hydrodynamic effect3),
and a hydrostatic bearings with flow control system4).
These technologies have enabled excellent accuracy
and high productivity through grinding. However, in agrinding machine with a high peripheral velocity for
attaining high productivity, the viscous resistance of the
lubricant causes a large power loss. This paper presents
our efforts to reduce the power loss in these hydrostatic
bearings.

2. 1 Principle of Hydrostatic Bearings

Sink (discharge hole) Nozzle LandLand

As shown in Fig. 2, hydrostatic bearings have a recess,which is a few millimeters deep, formed on the innersurface. The outer circumference of the recess has lands
that hold the lubricant and typically form a clearance of
20 to 30 Pm with the opposing spindle.
Lubricant pressurized by a pump passes through therestrictor and is supplied to each recess, and then flows
out of the bearing through the clearance between thespindle and the land.During this process, the hydraulicforce in the recess is determined by the outflow resistanceof the restrictor and clearance, and this pressure supports
the spindle. As shown in Fig. 3, by constructing therecesses with large cavity, the pressure drop in the bearing
can be reduced, and a larger loading capacity can beobtained for a bearing of the same dimensions.
When an external force acts on the spindle and theclearance changes, the hydraulic force in the recess alsochanges to balance the external force. The relationshipbetween this clearance and the hydraulic force is thestiffness of the hydrostatic bearing.
RecessLand
RecessSpindleud

Land

Restrictor
Pump

Pump

Fig. 2 Schematic drawing of hydrostatic bearing
Hydrostatic bearing
with internal return flow

Hydrostatic bearing
with hydrodynamic effectFig. 1 JTEKT hydrostatic bearing technologies

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JTEKT ENGINEERING JOURNAL English Edition No. 1018E (2022)

Power Reduction of Hydrostatic Bearings for Grinding Machines

Table 1 Main dimensions of hydrostatic bearing
Pump(a) When recess is not included

Land
RecessRestrictor

Speciﬁcation
Pump(b) When recess is included

Bearing diameter, mm

60

Bearing width, mm

50Bearing clearance, mm

0.0175

Recess depth, mm

1Fig. 3 Effect of recesses in hydrostatic bearing

2. 2 Power Loss in Hydrostatic Bearings
Because the entire loading surface of a hydrostatic
bearing is in contact with lubricant, power loss due toviscous resistance occurs when the spindle rotates. The
power loss can be approximated by Petrov’s equation in
Equation ⑴.

Bearing supply pressure, MPa

1.5

Rotational speed, min1

10 000Coeﬃcient ofMineral oil

1.627

viscosity, mPa·s

Distilled water

0.890

Mineral oil

802

Distilled water

997

Density, kg/m3⑴

where,
P : Power loss
D : Bearing diameter
L : Bearing width
N : Rotational speed
H : Bearing clearance
l: Coefficient of viscosity
From Equation ⑴, reducing the bearing diameter andwidth and increasing the bearing clearance are effective in
reducing power loss. However, since these measures also
reduce the stiffness of the bearing, they must be combinedwith measures to achieve higher stiffness. For example,
there are hydrostatic bearings with hydrodynamic
effect that use the wedge effect of rotation to generate
hydraulic force in combination with the hydraulic forceof hydrostatic bearings, and hydrostatic control systems
that use flow control valves to optimally control the flowrate of lubricant according to the load for reducing theeccentricity of the spindle.
Similarly, in Equation ⑴, the power loss can be
reduced by lowering the coefficient of viscosity of the
lubricant, which has traditionally been addressed byusing low-viscosity mineral oil. Figure 4 compares thepower loss during rotation when low-viscosity mineral oil
and distilled water are used as lubricants in hydrostatic
bearings. The specifications of the bearing are shown in
Table 1. The coefficient of viscosity for distilled water isapproximately 1/2 that of low-viscosity mineral oil, but
the power loss was reduced by about 10%5). Consequently,
technology must be developed that reduces the power
loss regardless of the size of hydrostatic bearings and thecoefficient of viscosity of the lubricant.

JTEKT ENGINEERING JOURNAL English Edition No. 1018E (2022)

1.2
Power loss (ratio)

P =plD 3 N 2 L /H

Value

Reduction of
about 10%

1.0
0.8
0.6
0.4
0.2
0

Mineral oil
l 1.6 mPa･s

Distilled waterl 0.9 mPa･s

Fig. 4 Power loss with different lubricant

3. Reducing Power Loss in Hydrostatic Bearings
3. 1 Understanding the Causes of Power Loss inConventional Hydrostatic Bearings
First of all, computational fluid dynamics (CFD)
simulation of hydrostatic bearings was conducted
to identify the area where power loss occurs in thehydrostatic bearing. The power losses are calculated
from the two-dimensional models for the bearing recess
and for the land, and the sum of the two values is usedas the power loss of the entire bearing. A comparisonof the fluid resistance of the land and recess at 10 000
min1 is shown in Fig. 5. The vertical axis in Fig. 5 isthe shear stress acting on the spindle and shows the fluid
resistance per unit area. The depth of the recess is several
millimeters, which is about 50 times the bearing clearanceof the land. Generally, the fluid resistance decreases ininverse proportion to the size of the clearance, but thefluid resistance of the recess is about the same as that of
the land.
As indicated by the simulation of the flow in the recess
shown in Fig. 6, the flow accompanying the spindle(“forward flow” below) occurs within about 1/3 of therecess depth, and the flow in the opposite direction to therotation (“reverse flow” below) occurs in the remaining
range. Due to the effect of this reverse flow, the forward
flow does not have a gradual velocity change, but instead,it has a rapid velocity change near the spindle. Because25Power Reduction of Hydrostatic Bearings for Grinding Machines

Shear stress, kPa

5.0
4.0
3.0

2.0

1

0.1

350 min1

0.01

0.001

10

100

1 000

10 0001

Rotational speed, min

1.0
Land

RecessFig. 5 Shear stress on land and recess

Rotation direction of spindle

Simulation result(including turbulent flow)
Calculated values forlaminar flow

2.7

2.0

0

10

Shear stress, kPa

the fluid resistance and power loss are proportional tothe velocity gradient, a recess with a large clearance isconsidered to have a larger fluid resistance.

Flow accompanying
the spindle(forward flow)

Fig. 7 Shear stress on recess

3. 2 Reducing Power Loss in Hydrostatic Bearings
The simulation up to the previous section showed thatin order to reduce the power loss of hydrostatic bearings,
it is effective to separate the reverse flow at the bottomof the recess so that it does not affect the forward flow.
To achieve this, we devised a hydrostatic bearing with aseparating plate inside the recess to separate the forward
and reverse flows as shown in Fig. 86).

Flow in the opposite
direction to rotation(reverse flow)

Fig. 6 Velocity vector plot in recess
Separation of forward and reverse flows
Separating plate structure

For the shear stresses at the recess when the rotational
speed of the spindle is varied from 50 to 10 000 min1,
Fig. 7 shows a comparison of the simulation results
and the calculated values assuming laminar flow. The
rotational speed on the horizontal axis and the shear stresson the vertical axis are both shown in logarithmic form.
When the rotational speed reaches 350 min1, the solidline for the simulation results begins to deviate from thedashed line for the calculated value that assumes laminar
flow, and it becomes about 10 times larger at 10 000
min1. This indicates that the power loss is affected by the
turbulence.
As described above, it was found that both forward andreverse flows occurred at the recess, and their interference
and turbulence caused a large power loss.

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Fig. 8 Schematic of proposed hydrostatic bearing

To determine the position of the separating plate,the effect on the power loss of the size of the clearance
between the plate and the spindle was simulated. The
results are shown in Fig. 9. From this figure, we can seethat there is a position for the separating plate where thepower loss is minimized. Since the Reynolds number issmall in the range where the distance between the spindle
and the separating plate is small, the flow is laminar, andthe viscous resistance is expected to decrease inversely
proportional to the increase in the clearance. On the other
hand, in the range where the distance between the spindle
and the separating plate is large, the resistance due toturbulence and the pressure resistance due to the increasein forward flow rate are expected to increase.

JTEKT ENGINEERING JOURNAL English Edition No. 1018E (2022)

1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0

1.2

Conventional bearing
power loss

Conventional bearing
1
Power loss (ratio)

Bearing power loss (ratio)Power Reduction of Hydrostatic Bearings for Grinding Machines

Power loss minimum value
0

1

2

3

4

Distance H between spindle and separating plate(when distance at power loss minimum value is H 1)

Developed bearing

34%
reduction

0.8
0.6
0.4
0.2
0

H

0

2

4

6

8

10
1

Rotational speed, u1 000 min

Fig. 9 Power loss by position of separating plate

Figure 10 shows the simulation results of the shear
stress acting on the spindle surface under the conditionsof minimum power loss in Fig. 9. For comparison,
the simulation results of shear stress for conventional
bearings are also shown. The horizontal axis of Fig. 10 isthe circumferential angle of the bearing. In the developed
bearing with a separating plate inside the recess, the shear
stress at the center separating plate is reduced by half
compared to shear stress in a conventional bearing.

Shear stress, kPa

5.0

Conventional bearing

4.0

Developed bearing

3.0
2.0

½

1.0
0.0

0

30
60
Circumferential angle, °90

Fig. 10 Power loss reduction by separating plate

Based on the results of the above simulation, a newhydrostatic bearing was built as a prototype. The results ofthis power measurement are shown in Fig. 11. The power
loss was measured using a torque meter by measuring thefluid resistance generated in the hydrostatic bearing. As
shown in Fig. 11, the power loss of the developed bearing
started to decrease around 3 000 min1, and at 10 000
min1, the power loss was reduced by about 34%.
The structure of the bearing with a separatingplate described above is achieved by combining twoparts. If we can Integrate two parts into one, we canreduce the manufacturing cost and improve the ease of
assembly. Consequently, by applying the power loss
reduction principles in this technology and using asingle-component hydrostatic bearing, we were able tosuccessfully reduce the power loss by 24%.

JTEKT ENGINEERING JOURNAL English Edition No. 1018E (2022)

Fig. 11 Power loss of proposed hydrostatic bearing

3. 3 Verification Using a Grinding Wheel Spindle
This technology was installed on a grinding wheel
spindle to evaluate the power loss. The evaluation bench
is shown in Fig. 12. The grinding wheel spindle uses
journal bearings primarily to support radial loads, suchas the grinding force in the normal direction, and thrustbearings to support axial loads. Among these, the power
loss of the grinding wheel spindle was compared with thatof a journal bearing equipped with the developed bearing.
A comparison of the power loss of the grinding wheel
spindle, the temperature rise of the lubricant, and thethermal displacement of the grinding wheel spindle isshown in Fig. 13. The power loss of the grinding wheel
spindle was reduced by 13%, as shown in Fig. 13. The
reduction in power loss for the grinding wheel spindle issmaller than a single bearing, but this is because power
loss for the grinding wheel spindle includes the power lossof the thrust bearing, whose geometry is unchanged. The
reduction in power loss also suppressed the temperaturerise of the lubricant, which in turn reduced the amount ofthermal displacement in the front-back direction of thegrinding wheel head. Therefore, this technology reduces
not only the power loss of the grinding wheel spindle,
but also the power consumption of the oil cooler and thethermal displacement stabilization time.

Fig. 12 Experimental apparatus of wheel head

27

1.4

1.2

13% reduction

1.0
0.8
0.6
0.4

1.00

0.87

0.2
0

Conventional
bearing

Developed
bearing

Temperature rise (ratio)

Power loss (ratio)

1.4

1.2

27% reduction

1.0
0.8
0.6

1.00

0.4

0.73

0.2
0

Conventional
bearing

Thermal displacement (ratio)Power Reduction of Hydrostatic Bearings for Grinding Machines

Developed
bearing

1.4
1.2

22% reduction

1.0
0.8
0.6
0.4

1.00

0.78

0.2
0

Conventional
bearing

Developed
bearing

Fig. 13 Performances of existing hydrostatic bearing and proposed hydrostatic bearing

4. Conclusion
This paper presented a case study of power loss
reduction by flow optimization of hydrostatic bearings.
A camshaft grinding machine that used this technology
received the 2020 Minister’s Award for Excellent Energysaving Equipment and Systems from the Ministry of
Economy, Trade and Industry (METI). We will continue
to improve the performance of our products and contributeto realizing carbon neutrality due to the ongoing need toreduce the power consumption of machine tools.

References
1)

2)

3)

4)

5)

6)

A. KANAI, M. MIYASHITA: Seiatsujikuuke ni okeru
buhinseido to kaitenseido, Journal of the Japan Society
for Precision Engineering, Vol. 45, No. 538 (1979) 11741176 (in Japanese).
M. HIRANO: The development history and technologicaltransition of Grinders in JTEKT, The Proceedings ofConference of Tokai Branch (2011) 455 (in Japanese).
K. SUGITA: Chouseimitsu seiatsujikuuke, Journal of theJapan Society for Precision Engineering, Vol. 50, No.
5(1984) 796-801(in Japanese).
S. UETAKE: Approach to Energy Saving in Machine
Tools, JTEKT ENGINEERING JOURNAL, No. 1010E(2013) 9-12.
H. YAMATO, F. SUGIMOTO, M. HIRANO: Reductionof fluid resistance in Hydrostatic Bearing for Machine
Tools, Proc. of Tribology conferences 2015 Spring
Himeji (2015) 467-468 (in Japanese).
H. YAMATO, F. SUGIMOTO, M. HIRANO: Reductionof fluid resistance in Hydrostatic Bearing for Machine
Tools, Proc. of Japan Society for Precision Engineering
Annual Meeting Spring (2016) 487-488 (in Japanese).
H. YAMATO**

28

F. SUGIMOTO*

Innovative Processing R&D Dept., Research &Development Division

JTEKT ENGINEERING JOURNAL English Edition No. 1018E (2022)