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December 2020, Vol. 20, No. 6
MANUFACTURING TECHNOLOGY
ISSN 1213–2489
indexed on: http://www.scopus.com 755
10.21062/mft.2020.119
© 2020 Manufacturing Technology. All rights reserved.
http://www.journalmt.com
Research on Optimization of a High Precision Hydrostatic Turntable
Lai Hu, Yaolong Chen
School of Mechanical Engineering, Xi’an Jiaotong University, 28 Xianning Road, Xi’an, Shaanxi 710049, P.R.
China. E-mail: chenzwei@mail.xjtu.edu.cn (Yaolong Chen)
This paper mainly studies the hydrostatic turntable of precision milling and grinding compound machi-
ning center in aerospace processing equipment, and innovatively designs and analyzes the mesa. It is
proposed to replace the traditional 40Cr with imported marble for the mesa. Firstly, the vibration model
of the hydrostatic turntable is carried out. ANSYS Workbench software is used to compare and analyze
the original and marble materials. In the process, the static characteristics and the difference of first-
order modes of the two materials are compared. In addition, the analytical results are used for manu-
facturing. The results show when the applied force reaches the limitation 29400N, the maximum displa-
cement of 40Cr increases sharply to 8.9406μm; while the marble material reaches 2.6μm. Meanwhile, it is
obtained that the power consumed by marble is reduced by 39.12% compared with 40Cr. The weight of
marble is reduced by 39.36% compared with 40Cr. Marble is about 21.59% higher than 40Cr in the com-
parison of vibration mode results.
Keywords: Milling and grinding compound machining center, Hydrostatic turntable, Innovative design, Com-
pared, Marble
Introduction
The development of aerospace technology always
represents one of the factors of a country's military
strength. Generally speaking, aerospace technology
belongs to high precision equipment. However, there
are many aspects of traditional research on high-pre-
cision equipment, and many scholars have also carried
out research. For example, Brecher C et al. [1]
followed a compact design strategy and developed two
high-precision machine tools by reducing the overall
size of the machine. The development of two kinds of
compact machine tools shows that the compact design
improves the dynamic performance and accuracy.
Chen E P et al. [2] designed a double-axis rotary
milling head with large torque, high precision and high
rigidity with an output torque of 3000Nm. Therefore,
a new design scheme of double-axis rotary milling
head with mechanical spindle, gear transmission and
swing fork structure is proposed. The contradiction
between large reduction ratio and high precision
transmission is solved. Chen W et al. [3] introduced an
integrated system for the conceptual design and basic
design stages of ultra-precision machine tools. This
system is based on dynamics, thermodynamics and er-
ror budget theory. Liang, Y.C [4] proposed a dynamic
design method for ultra-precision machine tools based
on the requirements of workpiece morphology. Star-
ting from the morphological characteristics and
functional requirements of the workpiece, this method
demonstrates how to design and analyze the kinematic
chain and configuration of the machine tool. Chen G
D et al. [5] proposed a dynamic precision design met-
hod for ultra-precision machine tools based on
frequency domain error allocation. The feasibility of
the proposed DAD method is illustrated by an
example.
Of course, there are also scholars who have studied
the hydrostatic turntable in aerospace processing
equipment. For example, Zhao Y.S et al. [6] developed
a simulation model to analyze the influence of guide
rail profile error on the motion accuracy of hydrostatic
turntable. According to Reynolds equation of lubrica-
ting film, the reaction forces of preloaded thrust bea-
ring and hydrostatic circular oil pad are obtained. The
motion equation of static pressure turntable conside-
ring the contour error of the two guide rails is derived.
The results show that wavelength, profile error ampli-
tude, velocity amplitude and turntable offset load can
all affect the motion accuracy of hydrostatic turntable.
Zhaomiao L et al. [7] studied the numerical simulation
of the flow, bearing and carrying capacity of cycloidal
hydrostatic oil chamber under the rotating speed of
0~5 m/s and different boundary conditions.
IWASAKI, Makoto et al. [8] proposed a new research
method of high precision contour control for machine
tool worktable transmission system. The proposed
method has significant performance improvement in
accurate table contour control. Adong Y U et al. [9]
developed a rotary worktable to improve the accuracy
retention of large-scale high-precision vertical nume-
rical control machine tools. The turntable adopts a set
of radial thrust tapered roller bearings, eliminating the
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traditional spindle and complex spindle bearing sys-
tem. The bottom ring and the top ring of the radial
thrust tapered roller bearing are installed on the same
shaft table, which eliminates the clearance between
each bearing ring and its components, realizes interfe-
rence fit, and greatly improves the accuracy retention
of the machine tools. In addition, the author has also
studied the other related components of the turntable,
the purpose of which is also to improve the rotation
accuracy of the turntable. In view of the above autho-
rs' research, this paper proposes an innovative design
of the turntable system. In the mesa optimization, im-
ported marble material are mainly used to replace the
traditional 40Cr. Because the anti-vibration strength
and stability of marble are higher than 40Cr. And with
the increase of the service life of the machine tools,
the overall accuracy maintenance ability of the ma-
chine tools will not be changed basically. In this paper,
the theoretical vibration model of turntable compo-
nents is deduced at first. Secondly, the advantages and
disadvantages of marble and 40Cr are further expla-
ined by means of analysis and comparison. Finally,
processing and production are carried out through the
analysis results, and quantitative conclusions are
drawn.
Theoretical analysis
Before analyzing 40Cr and marble mesa, theoreti-
cal analysis of mesa vibration system is needed. Firstly,
the quality of the turntable top system is simplified, as
shown in Fig. 1.
As shown in Fig. 1, the diagram of the vibration
system consists of three parts: 40Cr table top, marble
turntable and fastening screw. The surface of the
worktable bears gravity, and the lower surface of the
worktable is in a fixed mode and rotates around the Y
axis.
Fig. 1
Simplified diagram of turntable surface vibration sys-
tem.
Therefore, the vibration dynamics analysis Eq. [10-
11] is˖
[ ]
{ }
[ ]
{ }
[ ]
{ }
( )
{ }
K X C X M X F t+ + =
}
[
]
{
}
(
)
}
[
]
{
}
{
F t
(
C X M X
}
[
]
{
}
{
C X M X
M X
}
[
]
{
}
(1)
Considering undamped structure, partial constra-
ints and external load factors, the Eq. (1) can be ex-
pressed as:
[ ]
{ }
[ ]
{ } { }
29400M X K X+ =
}
[
]
M X K X
}
[
]
K X
[
]
(2)
Of which,
( )
{ }
F t
is the external load;
[ ]
K
is the
stiffness matrix;
[ ]
C
is the damping matrix;
{ }
{ } { }
X X X
}
{
}
X X
X
}
{
ǃ ǃ
is the set of displacements of each
node, its first derivative and second derivative re-
spectively, and is also the modal shape;
[ ]
M
is the
mass matrix.
In this research system, the mass matrix includes
the mass and inertia parameters of the powertrain,
which are expressed as follows:
1
2
3
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0
0 0 0
0 0 0
xx xy zx
xy yy yz
zx yz zz
m
m
m
MI I I
I I I
I I I
é ù
ê ú
ê ú
ê ú
=ê ú
- -
ê ú
ê ú
- -
ê ú
- -
ê ú
ë û
(3)
However, through the derivation of Eq. (2), it is
concluded that:
11
1 2 2
2
2
2 2 3 3
3
3
3 3 4 4
4 4 5 5 4
5 5 6 6 5
6 6 6
0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0
0 0 0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0 0
xx xy zx
xy yy yz
zx yz zz
xm
k k k
m
x
k k k k
m
x
k k k k
I I I
k k k k x
I I I
k k k k x
I I I
k k x
+ - ì ü é
é ù ï ï ê
ê ú
- + - ï ï ê
ê ú ï ï ê
ê ú
- + - ï ï +
ê ú í ý - -
- + -
ê ú ï ï
ê ú ï ï - -
- + -
ê ú ï ï - -
-
ê ú ï ï
ë û ë
î þ
{ }
1
2
3
4
5
6
29400
x
x
x
x
x
x
ì ü
ùï ï
úï ï
úï ï
úï ï =
ê ú í ý
ê ú ï ï
ê ú ï ï
ê ú ï ï
ê ú ï ï
ûî þ
ì ü
1
x
1
ï ï
1
ì ü
ì ü
1
ï ï
ï ï
2
x
ï ï
ï ï
x
ï ï
{
29
ï ï
ï ï
ï ï
ï ï
3
x
3
ï ï
ï ï
3
x
3
í ý
ï ï
ï ï
3
ï ï
ï ï
ï ï
{
29
=
í ý
ï ï
4
x
í ý
í ý
{
29
=
í ý
ï ï
x
ï ï
5
x
ï ï
ï ï
x
ï ï
ï ï
ï ï
ï ï
ï ï
ï ï
ï ï
ï ï
î þ
6
ï ï
ï ï
6
x
ï ï
(4)
In Eq. (4), consider that the inertia product
xx yy zz
I I Iǃ ǃ
is expressed by
I
:
xx xy zx
xy yy yz
zx yz zz
I I I
I I I I
I I I
é ù
ê ú
=ê ú
ê ú
ë û
(5)
The Eq. (5) also represents an inertial matrix com-
posed of a rigid body for a spatial coordinate system
Oxyz.
Among them, the table top and worktable of this
turntable are symmetrical models. Therefore, diagonal
elements are moments of inertia, defined as:
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( )
2 2
xx
I y z dm= +
òòò
(6)
( )
2 2
yy
I x z dm= +
òòò
(7)
( )
2 2
zz
I x y dm= +
òòò
(8)
Combining the calculation Eqs. (6-8) of space iner-
tia parameters and triple integral, the following results
are obtained:
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
2 2 2 2 2 2
2 2 2 2 2 2
2 2 2 2 2 2
1
12
1
12
1
12
xx
yy
zz
I y z dm y z dV abc b c
I x z dm x z dV abc a c
I x y dm y x dV abc b a
r r
r r
r r
ì= + = + = +
ï
ï
ï= + = + = +
í
ï
ï= + = + = +
ï
î
òòò òòò
òòò òòò
òòò òòò
(9)
Further analysis shows that:
( )
( )
( )
6
6
6
xx yy zz
move
xx yy zz
move
xx yy zz
move
move
I I I
am
I I I
bm
I I I
cm
m
abc
r
ì- + +
ï=
ï
ï
ï- +
ï=
ï
í
ï+ -
ï=
ï
ï
ï=
ï
î
(10)
Therefore, the size aǃbǃc and density ρ of the
inertial body are derived by combining the inertia pro-
duct
xx yy zz
I I Iǃ ǃ
and the powertrain mass
move
m
.
At the same time, combined with Eqs. (4) and (9)
and deduced, the following results are obtained:
( )
( )
1
1 2 2
2
2 2 3 3
3
3 3 4 4
4 4 5 5 4
5 5 6 6 5
6 6 6
1
2
3
2 2
2 2
0 0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
1
0 0 0 12
1
0 0 0 12
0
xy zx
xy yz
x
k k k
x
k k k k
x
k k k k
k k k k x
k k k k x
k k x
m
m
m
abc b c I I
I abc a c I
r
r
+ - ì ü
é ù ï ï
ê ú
- + - ï ï
ê ú ï ï
ê ú
- + - ï ï +
ê ú í ý
- + -
ê ú ï ï
ê ú ï ï
- + -
ê ú ï ï
-
ê ú ï ï
ë û î þ
+ - -
- + -
( )
{ }
1
2
3
4
5
6
2 2
29400
1
0 0 12
zx yz
x
x
x
x
x
x
I I abc b a
r
é ù
ê ú ì ü
ê ú ï ï
ê ú ï ï
ê ú ï ï
ê ú ï ï =
í ý
ê ú ï ï
ê ú ï ï
ê ú ï ï
ê ú ï ï
ê ú î þ
- - +
ê ú
ë û
ì ü
1
x
ï ï
1
ì ü
ì ü
1
ï ï
ï ï
2
x
ï ï
ï ï
x
ï ï
{
29
ï ï
ï ï
ï ï
ï ï
3
x
ï ï
ï ï
3
x
í ý
ï ï
ï ï
3
ï ï
ï ï
ï ï
{
29
=
í ý
ï ï
4
x
í ý
í ý
{
29
=
í ý
ï ï
x
ï ï
5
x
ï ï
ï ï
x
ï ï
ï ï
ï ï
ï ï
ï ï
ï ï
ï ï
ï ï
î þ
6
ï ï
ï ï
6
x
ï ï
(11)
Finally, the first six modal functions of the simpli-
fied turntable system will be analyzed and expressed
by
( )
{ }
( )
{ }
( )
{ }
( )
{ }
( )
{ }
( )
{ }
1 2 3 4 5 6
A A A A A Aǃ ǃ ǃ ǃ ǃ
.
Simulation analysis of vibration and sta-
tics of different materials
In order to better analyze the excellence of marble
and 40Cr, it is necessary to apply the two materials to
the turntable components and study them respecti-
vely. At the same time, before vibration and statics si-
mulation analysis, the overall structure of the turntable
needs to be analyzed, as shown in Fig. 2.
In the research of traditional high-precision ma-
chine tools hydrostatic turntable, the marble turntable
in Fig. 2 uses 40Cr material. According to Fig. 2, the
vibration mode and statics analysis of the combination
of 40Cr mesa and marble turntable will be separately
carried out. Firstly, the model is imported into the ana-
lysis software ANSYS Workbench and generated
mesh [12-13]. At that same time, marble and 40Cr
were applied to the marble turntable of Fig. 2, re-
spectively. The two material parameter pairs are
shown in Tab. 1.
Tab. 1
Comparison of marble and 40Cr parameters.
Materials
Parameters
Marble 40Cr
Density
3.09g/cm3
7.9 g/cm3
Young's modulus
50GPa
209000GP
Average linear
expansion coeffi-
cient
7.36 10-6°C-
1
11.9 10
-6°C-
1
Poisson's ratio
0.3
0.277
Compressive
strength
366MPa 365.7MPa
Weight
172.003Kg
436.96555Kg
Water absorption
0.026%
Hardness
505HB
207HB
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Fig. 2
Three-dimensional model of hydrostatic turntable.
Fig. 3
Analysis and comparison of marble and 40Cr
(1000N-29400N).
Fig. 4
Maximum displacement of marble (29400N).
As shown in Figs. 1 and 2, a boundary condition is
applied. The lower surface of the marble turntable is
set as a fixed constraint, while only rotating around the
Y axis is reserved, and the rest displacements are set
to 0 mm. A limit force of 29400N is applied to surface
of the 40Cr mesa shown in Fig. 2 in a direction from
top to bottom and a maximum rotational speed of
10.47 rad/s was applied too. After the setting is com-
pleted, force (1000N-29400N) is applied to marble
and 40Cr respectively and maximum displacement
analysis is carried out, as shown in Fig. 3. Meanwhile,
the simulated results of marble and 40Cr at 29400N
are presented separately. As shown in Figs. 4-6 and
Figs. 7-9, respectively.
Fig. 5
Maximum stress of marble (29400N).
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a) First-order mode
b) Second-order mode
c) Third-order mode
d) Fourth-order mode
e) Fifth-order mode
f) Sixth-order mode
Fig. 6
The first six modes of marble (29400N).
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Fig. 7
40Cr maximum displacement (29400N).
Fig. 8
40Cr maximum stress (29400N).
a) First-order mode
b) Second-order mode
c) Third-order mode
d) Fourth-order mode
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e) Fifth-order mode
f) Sixth-order mode
Fig. 9
The first six modes of 40Cr (29400N).
Analyzing the data in Fig. 3 from a macro per-
spective, it can be concluded that although the 40Cr is
about smaller than the marble in terms of the ma-
ximum displacement as a whole, the maximum displa-
cement of 40Cr increases sharply to 8.9406 μm when
reaching the applied force limit of 29400N. In con-
trast, the maximum displacement of marble slowly
increases with the increase of force. When the limit
force is 29400N, it only reaches 2.6 μm, which far me-
ets the processing requirements. Meanwhile, accor-
ding to the analysis of power consumption equation
=9550 9550 9550
T F r m nd r
Pn n n
p
× ×
= =
× × ×
. The power con-
sumption increases with the increase of mass m. Ac-
cording to the density lesson in Table 1, the power
consumed by marble is reduced by 39.12% compared
with 40Cr. From the aspects of weight and material
saving of hydrostatic turntable, the weight of marble
is reduced by 39.36% compared with 40Cr. According
to the analysis of Figs. 5 and 8, the maximum stress of
both is small. However, according to the analysis of
the first mode shapes of the two materials in Figs. 6
and 9, it is shown that marble is about 21.59% higher
than 40Cr. Among them, the most important factor is
that 40Cr will appear oxidation and other inevitable
factors with the increase of machine tools service life.
It will inevitably lead to a sharp drop in machining ac-
curacy. Marble avoids this bad factor.
Test processing
Based on the above analyzed results, processing,
manufacturing and assembly are performed, as shown
in Fig. 10.
1 40Cr table top; 2 marble turntable; 3 bearing bush; 4 seal
oil ring; 5 45° swing head; 6 TDM motorized spindle; 7 oil
pressure regulating hole; 8 foundation bed
Fig. 10
Field assembly drawing of hydrostatic turntable.
As shown in Fig. 10, the uppermost table surface 1
of the hydrostatic turntable is made of 40Cr and
clamps the workpiece in direct contact with the tool
mounted on the motorized spindle 6. However, the
lower surface of the marble turntable 2 is in direct con-
tact with the oil in the hydrostatic turntable to ensure
the rotation accuracy of the hydrostatic turntable.
With the increase of the service life of the machine
tool, the marble turntable in direct contact with the oil
will give full play to its advantages and still maintain
high support and rotation accuracy.
Conclusion
(1) This paper mainly studied the structural inno-
vation of hydrostatic turntable in high precision ma-
chining equipment for aerospace parts. It is proposed
to replace the traditional 40Cr with marble and appled
it to the components of the hydrostatic turntable. The
vibration mathematical model of the components is
analyzed, and the differences between the two mate-
rials are compared through software simulation.
(2) From the analyzed results, it is found that mar-
ble is better than 40Cr for some parts of hydrostatic
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turntable in high precision equipment. From the ana-
lysis of the maximum displacement, when reaching the
applied force limit of 29400N, the maximum displace-
ment of 40Cr increases sharply to 8.9406μm; While
the marble reaches 2.6μm. In particular, it is analyzed
that the power consumed by marble is reduced by
39.12% compared with 40Cr. The weight of marble is
reduced by 39.36% compared with 40Cr. In terms of
vibration mode, marble is about 21.59% higher than
40Cr. At the same time, it is inferred from the analysis
of all the data that with the increase of the service life
of this ultra-precision equipment, the machine tools
made of marble for some parts is better than the ma-
chine tools made of 40Cr in terms of overall accuracy
retention and processing accuracy stability of related
parts. Therefore, through the above analysis and re-
commendation, the actual processing is carried out,
and the hydrostatic turntable is assembled to process
high-precision aerospace parts.
Acknowledgment
This research was funded by [National Key Re-
search and Development Program of China]
grant number [2018YFB2000502] and [National
Science and Technology Major Project of the Mi-
nistry of Science and Technology of China] grant
number [2018ZX04002001] and [National Science
and Technology Major Project] grant number
[2017-VII-0001-0094].
The authors declare no conflicts of interest.
References
CHRISTIAN BRECHER, P UTSCH, R
KLAR, (2010). Christian Wenzel. Compact design
for high precision machine tools, pp. 50(4): 328-334.
International Journal of Machine Tools & Manu-
facture.
CHEN, EN PING, LI, SHAO HUI, WU,
FENG HE. (2014). Structure Design of Biaxial
Rotary Milling Head with High-Torque, High-
Precision and Mechanical Spindle, pp. 621:337-
345.Key Engineering Materials.
CHEN, WANQUN, LUO, XICHUN, SU,
HAO. (2016). An integrated system for ultra-
precision machine tool design in conceptual
and fundamental design stage, pp. 84(5-
8):1177-1183. International Journal of Advanced
Manufacturing Technology.
YINGCHUN LIANG, WANQUN CHEN,
YANG SUN, GUODA CHEN. (2012). Dyna-
mic design approach of an ultra-precision ma-
chine tool used for optical parts machining, pp.
226(11):1930-1936. Proceedings of the Institution of
Mechanical Engineers Part B Journal of Engineering
Manufacture.
GUODA CHEN, YAZHOU SUN, FEIHU
ZHANG. (2018). Dynamic Accuracy Design
Method of Ultra-precision Machine Tool, pp.
031(002):158-166. Chinese Journal of Mechanical
Engineering.
YONGSHENG ZHAO, HONGCHAO WU,
CCONGBIN YANG. (2019). Effect of guide
rail profile errors on the motion accuracy for a
heavy-duty hydrostatic turntable, pp. 233(15).
Archive Proceedings of the Institution of Mechanical
Engineers Part C Journal of Mechanical Engineering
Science.
ZHAOMIAO LIUI, CHENGYIN ZHANG,
FENG SHEN. (2011). Influence of boundary
conditions and turntable speeds on the stability
of hydrostatic oil cavity, pp. 6(3):359-368. Fron-
tiers of Mechanical Engineering.
IWASAKI MAKOTO, MIYAJI MASASHI,
MATSUI NOBUYUKI. (2005). High-Preci-
sion Contouring Control of Table Drive Sys-
tem in Machine Tools Using Lost Motion
Compensation, pp. 125. Ieej Transactions on In-
dustry Applications.
YU ADONG, WANG PINGJUN, LI
XIANGLONG. (2016). Research on New
Turntable Technology for Improving Large
and High Precision Vertical Machine Tool Ac-
curacy Retention, pp. 14. Machine Tool & Hyd-
raulics.
FU ZHIFANG, (1990). Vibration Modal Analy-
sis and Parameter Identification. Beijing: Beijing
Machinery Industry Press.
ZHANG HUA, ZHAO LEI, CHEN HUA
(2019). Research on Hydraulic System Opti-
mization of Loader Based on GA-BP, pp.
19(6):952-958. Manufacturing Technology.
MÁRIA BLATNICKÁ, MIROSLAV
BLATNICKÝ, JÁN DIŽO, MILAN SÁGA.
(2018). Comparison of Analytical Stress Analy-
sis and Numerical Calculation of Mobile Work
Machine Part, pp. 18(2):190-193. Manufacturing
Technology.
LIU CHENGPEI, HU JUNPING. (2018). A
FSI-thermal model to analyze performance
characteristics of hydrostatic turntable, pp.
70(9):1692-1698. Industrial Lubrication & Tribo-
logy.
