Vibration Analysis of a Low-Power Reduction Gear
Free vibrations of a low-power reduction gear engaged with a hydraulic pump of the test rig are discussed. Vibration analysis is performed with the finite element representation and commercial ANSYS program. Vibration analysis of an examined system is conducted in the two stages. The natural frequen...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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irk-123456789-1735052020-12-08T01:26:55Z Vibration Analysis of a Low-Power Reduction Gear Noga, S. Markowski, T. Научно-технический раздел Free vibrations of a low-power reduction gear engaged with a hydraulic pump of the test rig are discussed. Vibration analysis is performed with the finite element representation and commercial ANSYS program. Vibration analysis of an examined system is conducted in the two stages. The natural frequencies of free transverse vibrations of the gears are first generated, and on the basis of the Campbell diagrams, the excitation speeds for several natural frequencies of examined gears are calculated. Then the free vibrations of a reduction gear are analyzed, and two computational cases are presented. In the first case, only the mass and geometry of all parts of the body are considered. In the second case, the mass of tooth gears is also taken into account. Based on the FE models, the first ten natural frequencies and natural mode shapes of a reduction gear are calculated. Then, these results are used to estimate the stress level in the walls of the body for a permissible acceleration value. As expected, smaller stress values for a permissible acceleration value are obtained for the second finite element model of the system. The problems discussed here can be helpful for engineers dealing with the dynamics of gear systems. 2016 Article Vibration Analysis of a Low-Power Reduction Gear / S. Noga, T. Markowski // Проблемы прочности. — 2016. — № 4. — С. 45-53. — Бібліогр.: 15 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/173505 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Free vibrations of a low-power reduction gear engaged with a hydraulic pump of the test rig are discussed. Vibration analysis is performed with the finite element representation and commercial ANSYS program. Vibration analysis of an examined system is conducted in the two stages. The natural frequencies of free transverse vibrations of the gears are first generated, and on the basis of the Campbell diagrams, the excitation speeds for several natural frequencies of examined gears are calculated. Then the free vibrations of a reduction gear are analyzed, and two computational cases are presented. In the first case, only the mass and geometry of all parts of the body are considered. In the second case, the mass of tooth gears is also taken into account. Based on the FE models, the first ten natural frequencies and natural mode shapes of a reduction gear are calculated. Then, these results are used to estimate the stress level in the walls of the body for a permissible acceleration value. As expected, smaller stress values for a permissible acceleration value are obtained for the second finite element model of the system. The problems discussed here can be helpful for engineers dealing with the dynamics of gear systems. |
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Noga, S. Markowski, T. |
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Noga, S. |
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Vibration Analysis of a Low-Power Reduction Gear |
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Vibration Analysis of a Low-Power Reduction Gear |
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Vibration Analysis of a Low-Power Reduction Gear |
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Vibration Analysis of a Low-Power Reduction Gear |
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Vibration Analysis of a Low-Power Reduction Gear |
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vibration analysis of a low-power reduction gear |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Vibration Analysis of a Low-Power Reduction Gear / S. Noga, T. Markowski // Проблемы прочности. — 2016. — № 4. — С. 45-53. — Бібліогр.: 15 назв. — англ. |
| series |
Проблемы прочности |
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AT nogas vibrationanalysisofalowpowerreductiongear AT markowskit vibrationanalysisofalowpowerreductiongear |
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2025-07-15T10:14:20Z |
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UDC 539.4
Vibration Analysis of a Low-Power Reduction Gear
S. Noga
1
and T. Markowski
2
Rzeszów University of Technology, Rzeszów, Poland
1 noga@prz.edu.pl
2 tmarkow@prz.edu.pl
Free vibrations of a low-power reduction gear engaged with a hydraulic pump of the test rig are
discussed. Vibration analysis is performed with the finite element representation and commercial
ANSYS program. Vibration analysis of an examined system is conducted in the two stages. The
natural frequencies of free transverse vibrations of the gears are first generated, and on the basis of
the Campbell diagrams, the excitation speeds for several natural frequencies of examined gears are
calculated. Then the free vibrations of a reduction gear are analyzed, and two computational cases
are presented. In the first case, only the mass and geometry of all parts of the body are considered. In
the second case, the mass of tooth gears is also taken into account. Based on the FE models, the first
ten natural frequencies and natural mode shapes of a reduction gear are calculated. Then, these
results are used to estimate the stress level in the walls of the body for a permissible acceleration
value. As expected, smaller stress values for a permissible acceleration value are obtained for the
second finite element model of the system. The problems discussed here can be helpful for engineers
dealing with the dynamics of gear systems.
Keywords: gear resonance, transverse vibration, resonant frequencies, mode shapes.
Introduction. The progress of modern engineering requires technical facilities of high
stability and operational reliability. This is especially important for the components and
assemblies used in aviation, pharmaceutical industry biotechnology, and biomedical
designs. One of the important factors that could upset the normal operation, of the devices
(reduction gears and others) are vibrations of the components or assemblies of those
systems. The rapid development of computational techniques based on the finite element
method (FEM) allows vibration analysis of the systems of complex geometry and design to
be conducted [1]. In [2], the finite element (FE) models are used to analyze the static and
dynamic behavior of the EDM (electrical discharge machining) machine. The authors [3]
analyzed cyclically loaded gear vibrations with a power circulation test rig configuration
using FEM techniques. In [4], the simulation method (with FEM solutions) of the fatigue
life prediction for dynamic structures is presented. In [5], the FE technique is used to
analyze the steady-state vibrations of axisymmetric structures (e.g., toothed wheel with a
ring damper). The friction damping effect is also studied. In [6], the FE model of a
planetary spur gear designed for vibration analysis is proposed. In [7, 8], the authors
examined the dynamic behavior and vibrations of a planetary spur gear with analytical
methods. Numerical and experimental investigations focused on assessing the infuence of
the local surface damage on the natural vibration frequencies of a full-scale compressor
rotor blade are described in [9]. In [10], the transverse vibrations of spur and bevel gears
are studied. The FE models of examined wheels are verified by experimental investigations.
In [11, 12], the FE technique is employed to solve the problem of transverse vibrations of a
tooth gear with complex geometry. Here the algorithm to identify the distorted mode shapes
is discussed. The transverse vibrations of tooth gears with complex geometry and critical
rotational speeds of rotating systems are further discussed [13]. Tooth gears made of
nanocomposites are investigated in [14]. In [15], the problem for the transverse vibrations
of circular plates with complex geometry is solved with the modified boundary element
© S. NOGA, T. MARKOWSKI, 2016
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 45
method. The free vibrations of a low-power reduction gear are studied. Analysis is
performed with the FE representation and ANSYS program. The major components of the
reduction gear are tooth gears and the main body with the cover. At the first stage, the
natural frequencies of free transverse vibrations of the gears are determined and the
Campbell diagrams are plotted. Then the problems for the free vibrations of a reduction
gear are discussed, and the stress level in the walls of the body for a permissible
acceleration value is estimated.
1. Statement of the Problem. Vibration analysis of a low-power reduction gear
engaged with the hydraulic pump, which is an important auxiliary device of the test rig in
aviation industry, is discussed. The reduction gear consists of three meshing tooth gears
(Fig. 1a–c). They are supported the by roller bearings, which are located in the bearing
block of the body. The body is a complex structure consisting of the main body and the
cover (Fig. 1d, e). The cover is attached to the main body with 21 screws, which connect
both elements with a designated tightening moment.
The entire unit is attached to the body of the actuating device with the matching
sleeve. Power take-off and transfer take place through the additional center shafts, which
mate with the gears through the spline couplings. As mentioned above, from the point of
view of the considered aspects, the tooth gears (Fig. 1a–c) and the main body with the
cover (Fig. 1d, e) are the key component parts. The tooth gears comprise homogeneous
material parts with hollow shafts. Moreover, gears Nos. 1 and 3 are adapted to receive and
transfer the rotational motion and power to the external devices through the spline
couplings. Those gears possess essential geometric similarity (Fig. 1a–c).
2. Finite Element Representations. The numerical FE models of the major component
parts of the structure (tooth gears, main body and cover) are first constructed. Simulation
and analysis are conducted with an ANSYS program. To build the geometrical models with
an optimum number of elements, the surfaces, arising as a result of softening the feather
edges, are neglected. In the case of gears, it is mostly applied to softening the tooth points
and roots, the splines and undercut of bearing journals. In the case of body elements, the
clamping screw holes and geometry of the grease channel are also neglected. In the mesh
generation for selected parts, the ten-node tetrahedral element (solid 187) with the three
degrees of freedom in each node is used. The FEM models of gears Nos. 1 and 3 (Fig. 2a, c)
contain 73,028 elements and 118,848 nodes each. The FE model of gear No. 2 (Fig. 2b)
includes 49,810 elements and 89,013 nodes. The numerical model of the main body with
the cover (Fig. 2d, e) includes 137,579 elements and 212,388 nodes. In the tooth gear
models, the boundary conditions for the nodes are established. In each model, the degrees
of freedom related to the radial displacement of the nodes are subtracted from those of the
nodes located on the surface of bearing journals. Moreover, in the models of gears Nos. 1
S. Noga and T. Markowski
46 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4
a b c d e
Fig. 1. Geometrical model of the tooth gears: (a) gear No. 1; (b) gear No. 2; (c) gear No. 3;
geometrical model of the body (d, e).
and 3, the degrees of freedom related to the longitudinal displacement and rotation of the
nodes about the rotation axis of the gears, are subtracted from those of the nodes located
on the surface of the spline heads. The mating of the cover and the main body becomes
possible due to gluing both elements on the mating surface. Thus, the FEM mesh
generation for both elements (adequate for that surface) is provided. Next, the degree of
freedom related to the displacement along the rotation axis of gear No. 1, the degree of
freedom related to the rotation about that axis and the degree of freedom related to the
radial displacement of the mating surface nodes (joint, Fig. 1e) of the same axis, are
subtracted from those of the nodes located on the mating surface between the reduction gear
and the external device (Fig. 1e or Fig. 2e marked as joint). In the numerical calculations,
the two FE models of the reduction gear assembly are examined. In the first model, the
geometry and mass of the main body and cover are taken into account.
In the second FE model, the mass of the tooth gears of the reduction gear is also taken
into account. In this case, the tooth gears are simulated as rigid regions, which include the
points wherein the concentrated gear masses are located [1, 3].
3. Numerical Analysis. Vibration analysis of the reduction gear unit was conducted
in two stages. First, the natural frequencies of transverse vibrations of the tooth gears are
generated. During this process, the centrifugal effect is considered. Then the free vibrations
of the reduction gear are analyzed. In the case of the tooth gears, the calculation is
performed in two steps. The first step is related to static analysis and evaluation of the
rotation-induced stress distribution. This distribution is taken into account in the second
calculation step, which is related to modal analysis. In compliance with the standards of the
circular and annular plate theory [1], each natural frequency is denoted by �mn , where m
is the number of nodal circles and n is the number of nodal diameters. On the basis of the
analysis, the Campbell diagram for examined tooth gears is plotted. The occurance of
transverse vibrations is most dangerous for the normal operation of the system. The forced
frequencies due to the gear meshing may become the source of their excitation [10, 11,
13]. We distinguish the primary forced frequency due to the gear meshing (first harmonic
frequency) derived from the equation [10, 13]
k n z1 0 60� , (1)
and the secondary frequency due to the gear meshing (second harmonic frequency) derived
from the equation [10, 13]
k n z2 02 60� , (2)
where n0 (rpm) is the rotational speed of the gear and z is the number of gear teeth.
Vibration Analysis of a Low-Power Reduction Gear
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 47
a b c d e
Fig. 2. FE models of the following gears: (a) gear No. 1; (b) gear No. 2; (c) gear No. 3; FE models of
the body: (d) first FE model; (e) second FE model.
The resonance may occur when one of the two forced frequencies is equal to one of
the frequencies of free vibrations with the change in the rotational speed. The possibility of
excitation of vibrations induced by forced frequency (1) is of paramount importance. In
this case, the forced frequency due to the meshing is additionally derived from the equation
[10]
k n z n1 0 60* ( ) ,� � (3)
where n is the number of nodal diameters. Here straight line (1) can be treated as the
nominal primary forced frequency due to the meshing. The technical data and operational
range of rotational gear speeds are summarized in Table 1.
The numerical calculations for the gears were restricted to determining the natural
frequencies, which would be lower or equal to �16. The calculations are conducted with the
assumption that the gears rotate with the speed within the range from 0 to n2 (Table. 1). To
account for the centrifugal effect in the calculations, the angular speeds of gears Nos. 1
and 3 increased by 1146 rpm and of gear No. 2 by 859 rpm, which gave seven results for
gears Nos. 1 and 3 (natural frequencies and corresponding mode shapes) and five ones for
gear No. 2, which requires further interpretation. The calculation results are used to plot the
Campbell diagrams for each gear. The method of plotting the Campbell diagrams was
described in [10, 13]. Gears Nos. 1 and 3 exhibit significant structural similarity. The
calculation results for those gears are also essentially similar. The results of calculations of
free vibration frequencies for gears Nos. 1 and 2 are presented in Tables 2 and 3. The
analysis of the results demonstrates a marginal impact of rotational speeds on an increase in
respective frequencies of free vibrations (moderate increase in the flexural rigidity of the
gears).
Moreover, in the case of gear No. 2 we can observe the separation frequency values
�13 , �23 , and �16. It is caused by the presence of the port holes in the wheel disk. This
problem is further discussed in [11, 12, 13, 15].
Next, the results (Tables 2 and 3) are employed to plot the Campbell diagrams for
examined tooth gears. The diagrams are used to establish the excitation speeds of
respective free vibrations frequencies of examined gears. The Campbell diagram for the
range of frequencies from 4600 to 5600 [Hz] for gear No. 1 is shown in Fig. 3.
The diagram analysis demonstrates that the vibration resonance induced by the
secondary forced frequency may occur due to the meshing [Eq. (2)] in the operational
range of the gear (intersection points of straight line (2) and the curves for the free
vibration frequencies). The vertical lines nkw1, nkw2, and nkw3 in Fig. 3 refer to the
excitation speeds of the frequencies �11, �12, and �10. The excitation speeds of natural
frequencies for gear No. 1 are given in Table 4.
The Campbell diagram for the range of frequencies of 2000–3500 [Hz] for gear No. 2.
is illustrated in Fig. 4. In this case, the resonance induced by the forced frequency due to
48 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4
T a b l e 1
Technical and Operational Data for Tooth Gears
Gear
number
Mass
(kg)
z Rotational speed
(rpm)
Module
(mm)
Poisson’s
ratio
�
Young
modulus
E, Pa
Density
�,
kg/m3
n1 , n2 ,
1 1.29 41 3400 6500
2.5 0.3 2 06 1011. � 78502 2.75 83 1680 3211
3 1.29 41 3400 6500
S. Noga and T. Markowski
the meshing [Eq. (1)] with the frequency �13 in the operational range of the gear can be
observed. Therefore, it is necessary to plot additional straight lines [Eq. (3)].
The lines nw2 and nw3 refer to the nominal excitation speed of the frequency �13,
and the lines nw1 and nw4 correspond to the excitation speed caused by forced frequency
(3). Table 5 presents the excitation speeds of the frequency �13.
Then the free vibrations of a reduction gear body (Fig. 1d) are analyzed. As
mentioned above, at the first step only the mass and geometry of the body are considered,
and at the second step the mass of the reduction gear wheels and their location are
additionally taken into account. The body was made of an aluminum alloy, having the
following characteristics: E � �725 1010. Pa, � � 033. , �� 2790 kg/m3. The estimated body
mass is 14.7 kg. The mass of each gear is set according to Table 1. The numerical
calculations are conducted with the FE models. In both cases, the first ten natural
frequencies and corresponding mode shapes of free vibrations are determined. The results
are summariged in Table 6.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 49
T a b l e 2
Impact of Rotational Speeds on Natural Frequencies (Gear No. 1)
RS
(rpm)
Natural frequencies (Hz)
�11 �12 �10 �13 �14 �20 �21 �15 �22 �16
0 4726 5347 5430 10111 16821 21037 24025 24199 28128 31731
1146 4726 5347 5430 10111 16822 21037 24025 24199 28128 31731
2292 4727 5347 5430 10111 16822 21037 24025 24199 28128 31731
3400 4727 5348 5430 10112 16822 21037 24026 24199 28129 31732
4584 4727 5348 5431 10112 16822 21037 24026 24200 28129 31733
5730 4728 5349 5431 10113 16823 21037 24026 24200 28129 31733
6500 4728 5350 5431 10113 16823 21038 24027 24200 28130 31734
Note. RS = rotational speed.
T a b l e 3
Impact of Rotational Speeds on Natural Frequencies (Gear No. 2)
RS
(rpm)
Natural frequencies (Hz)
�11 �10 �12 �13 �20 �21 �14 �22 �23 �15 �24 �30 �31 �16
0 443.2 626.2 978.9 2706
2741
4782 5045 5107 5811 6402
8811
7994 9594 10347 10443 11134
11186
859 443.5 626.3 979.2 2706
2741
4783 5045 5107 5811 6402
8811
7994 9594 10347 10443 11134
11186
1680 444.3 626.6 980.0 2707
2742
4783 5046 5108 5812 6403
8812
7994 9595 10348 10444 11134
11187
2578 445.8 627.3 981.5 2708
2743
4784 5047 5109 5813 6405
8813
7995 9596 10349 10445 11135
11187
3211 447.2 627.8 983.0 2709
2744
4786 5048 5109 5815 6406
8814
7996 9597 10350 10446 11136
11188
Vibration Analysis of a Low-Power Reduction Gear
The first two mode shapes generated with the constructed models are shown in Fig. 5.
It should be noted that the shapes of corresponding natural modes obtained with the first
and second FE models were similar. The natural frequencies obtained with the second FE
50 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4
T a b l e 4
Excitation Speeds of Natural Frequencies (Gear No. 1)
Forced frequency Excitation speed (rpm)
nkw1 nkw2 nkw3
3460 3914 3975
k2 �11 �12 �10
Fig. 3. The Campbell diagram of gear No. 1.
Fig. 4. The Campbell diagram of gear No. 2.
S. Noga and T. Markowski
model (despite larger mass) are much higher than those calculated with the first one
(Table 6). The mobile parts of the reduction gear operate within the range of rotational
speeds from 1679 to 6500 rpm, which is equal to the following number of cycles: 28–108 Hz.
The rotational speeds exciting the natural frequency �13 of gear No. 2 falls into this range.
All frequencies of free vibrations of the body (Table 6) are above the operational range of
the mobile parts of the reduction gear.
At the next step of calculations, the stress level for permissible acceleration is
estimated. For the reduction gear operation (stationary stand) the permissible acceleration
equals 2g , where g � 9.81 m/s 2. For several natural frequencies the relative acceleration
p0 is calculated by the equation
p b0
2
� � , (4)
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 51
T a b l e 5
Excitation Speeds of the Natural Frequency �13 (Gear No. 2)
Forced
frequency
Excitation speed (rpm)
nw1 nw2 nw3 nw4
1889 1959 1984 2056
k1 �13 �13
k1
* �13 �13
T a b l e 6
Natural Frequencies and Mode Shapes of Free Vibrations of the Reduction Gear
Mode
number
First FE model
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
�
p, Hz 419 596 1153 1750 1864 2081 2265 2807 2996 3113
Mode
number
Second FE model
D1 D2 D3 D4 D5 D6 D7 D8 D9 D10
�
d , Hz 679 830 1601 2291 2997 3115 3701 3967 4757 4969
Vibration Analysis of a Low-Power Reduction Gear
a b c d
Fig. 5. Mode shapes: (a) P1; (b) P2; (c) D1; (d) D2.
where b is the maximum relative displacement for a given mode shape and � is the
natural frequency for a given mode shape. Next, the coefficient kw is calculated by the
equation
k
p
g
w �
0
2
. (5)
Dividing the maximum value of the relative von Mises stress by kw , which is
established for a given natural frequency by the FE solution, a so-called maximum stress
value for permissible acceleration is obtained. This value is compared with the ultimate
fatigue strength of the body material. Maximum stresses for permissible acceleration
values set for given natural frequencies are presented in Table 7.
Analysis of the results demonstrates slightly smaller stresses for permissible
acceleration values in the second FE model. For each natural frequency (Table 7) the
maximum stress for a permissible acceleration value is smaller than the ultimate fatigue
strength of the body material.
Conclusions. The design and developinant of modern facilities (e.g., modern
reduction gears) require advanced computational techniques based on the finite element
method. It permits considering the specific features and complex geometry of those
facilities at the design stage. Here the free vibrations of a low-power reduction gear of a
complex design and geometry are analyzed. The free transverse vibrations of rotating tooth
wheels of the reduction gear and free vibrations of the reduction gear assembly are
discussed. Two FE models for the reduction gear are considered. As is shown, the
Campbell diagram is a very useful tool for the vibration analysis of rotating systems
(especially tooth gears). The possibility of exciting the natural frequency �13 of gear
No. 2 by the primary forced frequency due to the meshing in the operational range does
exist. Slightly smaller stresses for permissible acceleration values of the second FE model
for the reduction gear can also be noticed. For verifying the system vibration levels in the
52 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4
T a b l e 7
Stress Levels for Permissible Acceleration Values
First FE model Second FE model
Mode
number
b,
m
� Mises
rel ,
Pa
� max ,
Pa
Mode
number
b,
m
� Mises
rel ,
Pa
� max ,
Pa
P1 0.5807 2 95 1011. � 144 106. � D1 0.5308 4 20 1011. � 8 53 105. �
P2 0.4864 193 1011. � 5 56 105. � D2 0.4850 4 29 1011. � 6 39 105. �
P3 0.6479 3 78 1011. � 218 105. � D3 0.7389 5 02 1011. � 132 105. �
P4 0.5406 5 72 1011. � 172 105. � D4 0.3597 8 43 1011. � 2 22 105. �
P5 0.5791 510 1011. � 126 105. � D5 0.6402 132 1012. � 114 105. �
P6 0.5099 6 33 1011. � 142 105. � D6 0.5046 117 1012. � 119 105. �
P7 1.0980 8 86 1011. � 7 82 105. � D7 1.5620 128 1012. � 2 97 104. �
P8 0.9429 5 52 1011. � 3 69 105. � D8 2.5880 184 1012. � 2 25 104. �
P9 0.6480 5 74 1011. � 4 90 105. � D9 1.8410 131 1012. � 156 104. �
P10 0.6799 8 59 1011. � 6 48 105. � D10 0.8737 142 1012. � 3 27 104. �
Note: b is the relative displacement, � Mises
rel is the relative von Mises stress, and � max is the
maximum stress value corresponding to a permissible acceleration value.
S. Noga and T. Markowski
rotational speed range, the experimental tests are recommended. It should be noted that the
this investigation can be helpful for design engineers dealing with the dynamics of complex
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Received 10. 08. 2016
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 4 53
Vibration Analysis of a Low-Power Reduction Gear
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/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|