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Purdue University Purdue University
Purdue e-Pubs Purdue e-Pubs
International Compressor Engineering Conference School of Mechanical Engineering
2021
An Analytical Tool To Determine The Optimum Counterweights An Analytical Tool To Determine The Optimum Counterweights
For Multi-Cylinder Reciprocating Compressors For Multi-Cylinder Reciprocating Compressors
Salih Güvenç Uslu Kirpart Automotive, Turkey
Kaan Şengül Dalgakiran Makina, Turkey, kaan.sengul@dalgakiran.com
Follow this and additional works at: https://docs.lib.purdue.edu/icec
Uslu, Salih Güvenç and Şengül, Kaan, "An Analytical Tool To Determine The Optimum Counterweights For Multi-Cylinder Reciprocating Compressors" (2021). International Compressor Engineering Conference. Paper 2677. https://docs.lib.purdue.edu/icec/2677
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.html
1375, Page 1
AN ANALYTICAL TOOL TO DETERMINE THE OPTIMUM COUNTERWEIGHTS
FOR MULTI-CYLINDER RECIPROCATING COMPRESSORS
Salih Güvenç USLU 1, Kaan ŞENGÜL 2
1Kırpart Automative, Research & Development, Bursa, Turkey
guvenc.uslu@kirpart.com.tr
2Dalgakıran Makina, Research & Development, Kocaeli, Turkey
kaan.sengul@dalgakiran.com
ABSTRACT
The industrial air compressor market has been growing fast, thereby compelling the manufacturers to produce
competitive products with less vibration and noise, which also better meet the customers’ expectations and related regulations. Both mechanical and hydrodynamical factors induce vibrations which have substantial negative effects
in the maintenance periods and the lifetime of certain components. This study focuses on the balancing of the
crankshaft by modifying the geometry of the counterweights. It aims at reducing the overall vibration of a
compressor with the outputs of an analytical model which investigates the dynamics of the crankshaft of a W-type
reciprocating compressor. The model predicts the entire motion of the compressor. An interface is created on
MATLAB to ease the use of the model. The theoretical results are validated by both a series of tests and rigid body
dynamics, RBD, simulations on Ansys Workbench. The tests encompass the progressive change of the outer
diameter of the counterweights on the crankshaft. The RMS (root mean square) velocities on several locations on the
compressor head are obtained with a piezoelectric triaxial accelerometer for each outer diameter. The analytical
model, RBD model and experimental results match each other with a maximum deviation of 5%. The conclusion of
the study is that not only the optimization of the resultant forces acting on the crankshaft take a role in reducing the
overall vibration on the compressor head but also the moments on the crankcase bearings alter the vibrational
amplitude. The reciprocating and the centrifugal motions of the crank mechanism, the geometry of the crankshaft in
axial direction and gyroscopic effect due to the crankshaft inertia tensor are considered in the calculation of the
resultant moments on the bearings.
1. INTRODUCTION
The vibration levels are of primary cause that determine the compressor life and accordingly its noise-vibration-
harshness (NVH) characteristics (Hanlon, 2001). This paper focuses on the balanced inertial forces and the inertial
moments created by the vibration in an air compressor which can be caused by natural frequencies, unbalanced
inertial forces and hydrodynamic impacts. The unbalanced inertial forces in a crank mechanism are caused by
reciprocating behavior of components, such as piston and connecting rod, and by centrifugal forces of rotating
components, such as crank webs and counterweights (Olgun, 2010).
There are several methods to reduce the vibration levels in an air compressor. Modifying the counterweights, adding
balance shafts addressing to first and/or first and second order reciprocating forces are of them. This study only
adjusts the counterweights due to the feasibility of this method.
This paper is a complementary study to that of Pisirici et al. (2018). Pisirici et al. studied on the dynamics of a W-
type, three stage reciprocating compressors and presented a mathematical method to calculate the unbalanced
inertial forces on the steady and transient conditions. The recent study contributes to it by evaluating the inertial
moments acting on the crank bearings, creating a tool on MATLAB software, performing RBD analyses on Ansys
Workbench and further experiments to determine the optimum counterweights.
Both this study and Pisirici et al.’s have been shedding light on the on-going design updates of single and multi-
stage reciprocating compressors in Dalgakiran Compressor.
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
Max = -/•~ * cns(fl) * x1 - / •~ * Xz * cns(R ± <p) + Mgy * cns(fl)
May = Fe * sin(e) * X1 + Fa * Xz * s in(e ± </J) - M_qy * sin(e)
Mr= j(Max)2 + (May)2
Fe = -[mh - mbk * r] * w2
mh = mk * hk
1375, Page 2
2. MATHEMATICAL MODEL
Pisirici et al. built a methodology to calculate the resultant inertial forces acting on the crankshaft of the air
compressor. In addition to this finding, in the recent study, using the inertial forces in different directions, the
inertial moments acting on each crank bearing are calculated. The moment along which the crankshaft rotates are
ignored as it is assumed that the moment in this direction was neglectable and it does not contribute to the vibrant
effect to the compressor body.
There are two impacts to calculate the moments on the bearings. One is a component of resultant inertial velocity
field and its axial level arm to the crankcase bearings, the other is due to the gyroscopic effect that arises from the
shape of the crankshaft and accordingly the inertial reference coordinate frame. As seen in Figure 1, the deviation of
z axis from the rotational axis of the crankshaft causes the additional inertial moment as gyroscopic torque on the
crankcase bearings. The gyroscopic torque is calculated using equation (1). The resultant inertial moment on the
crankcase bearings is calculated as in Equations (2-4).
(1)
Figure 1: The deviation of the inertial reference coordinate system from the rotational axis of the crankshaft in z
direction
(2)
(3)
(4)
The centrifugal force produced by the crankshaft rotation is calculated using equation (5). The variable parameter
mh, which is aimed to be found in the software, is calculated using equation (6).
(5)
(6)
The mathematical model computes the resultant terms over one cycle for one mh parametric variable and it repeats
the computation for other mh variables within a given range and an increment. After the model scans the interval of
mh, it highlights the mh variable/s with which the minimum resultant inertial force and moments are acquired.
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
Method
@ 1st method
Q21>C1method
Number of cylinder
QOnecylonde<
0 Two cytlnders
@Thu cytindefs
Component masses (kg]
bt corvod mas.s
2nd conrod mass
3rd corvod mass
bl pslon group mass
2nd piston group mass
3rd pston group mns
1st beanng/crankpn bush
3rd be~crankpn bul-h
Crankshal group mass
Neyman
mh range (kg•mm]
mh_nw, 50
mh_maks 300
mh_increment 02
1254
1254
1254
0827
0827
0827
0'12
0'12
0'12
Operational conditions
Mot0< ,peed (,pm] 2970
TransmsslOO rabo (d2/d1) 3_357
Calculate
Export
Refresh
Ou•
Component dimensions (mm) I (degree)
bt corvod tenglh 214
21ldconiodle~ 214
3rd corvod tenglh 214
1st Conrod Cenlff ol f7M'f 74 331
2nd corvod center ol g,My 74 331
3rd Conrod Ctnltf ol grM'( 74 331
Sltokt 70
ANJ• bttWHn substQU«II s119es 140
(lvlglo - lht lirs/&.«iond 61"90')
Crank Inertia tenSOf [ll:g'mm2)
.)yz. product ol intftr.a
Resuhs
Opimum mh wr1 total force act...g on the crankcase (kg•nvn]
Maxin'l>m total fofte act.ing lhe crankcase at optJmum mh (NJ
Optimum mh wrt total moment acting the ctankcase beanng 1 (kg"mm)
Maxunum total moment acting the aankcase beanng 1 at opbm.im rm (Nm)
Opbmum mh wrt total moment actiog the ctankuse bearing 2 (kg'mm}
Maxunum total moment acting the crankcase beanng 2 at opt1room rm (Nm)
105
· ---- · Pulley side
Bearing 2
' I .Jr-. /1 9727
1986
194 8
153
X
X
J
1375, Page 3
3. THE SOFTWARE
A part of the interface of the software is depicted in Figure 2. The tool was created on MATLAB.
Figure 2: The interface of the software which helps to determine the optimum mh parametric variables
The software consists of six sections. There are two types of solutions under the method section. The first method
determines the optimum mh parametric variable/s. The second one calculates the absolute inertial force and
moments acting on the crankcase bearings. The solution with the second method becomes a guideline in selecting
the proper bearings. The solution can be performed for single-cylinder, V-type and W-type compressor heads. To set
the range of mh parameter, the extremes and the increment are defined. The transmission ratio and the motor speed
are defined in the operational conditions section. It should be noted that the model assumes that the compressor runs
steadily. The other inputs are component masses, component dimensions, the related product of the crankshaft
inertia tensor and the lever arms. An example of a result for the first method can be seen in Figure 2 in the results
section.
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
z QJ
2 .E oi € QJ C
c ~ ::, <JI
~ E ::,
E -~ :2'
1000
900
800
700
600
500
400
300
200
100
0
----------------------------------~ 150
E z <JI
' 100 c
' · '
50
'-------'-------'-------'-------'--------' o
~ 0 E oi € QJ
.£: E ::,
E -~ :2'
50 100 150 200 250 300
mh parametric variable (kg-mm]
1375, Page 4
4. MODEL VALIDATION
The model mentioned in Section 2 was evaluated with two approaches which were the validation with a computer-
based analysis and an experimental method. In the validation process Dalgakiran DBK 30 reciprocating compressor
model was utilized, which is a booster compressor generally coupled with a screw compressor that pressurizes air
from 7 bar to 35 bar and runs at a fixed-speed electric motor. The torque generated by the motor is transmitted to the
compressor head with two V-belts.
Figure 3: The optimum mh values calculated with the software created on MATLAB (F, M_1 and M_2 stand for
the maximum inertial force, the maximum inertial moments on crankcase bearings, respectively, as mh varies).
Figure 3 exhibits the ideal mh values with respect to the total inertial forces on the crankcase and the moments by
different bearings in DBK30 booster compressor. The ideal mh based on the total inertial forces was 198.6 kg-mm.
The ideal mh depending the crankcase bearings were 194.8 kg-mm and 153 kg-mm.
4.1 Rigid Body Dynamics Analysis
DBK 30 has a W-type compressor head. The cylinder heads are identical, but the heads pressurize the sucked air
with a phase shift of 70˚. The crank mechanism of the compressor can be seen in Figure 4.
RBD analysis was run at steady state condition at the fixed speed of 770 rpm. The rotational velocity was defined on
the revolute joint between the crankshaft and the ground.
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
1375, Page 5
Figure 4: DBK 30 booster compressor on ANSYS Workbench RBD module
In order to find the optimum radius of the counterweights, a parametric optimization process was used with a
definition of parametric variable. Figure 5 demonstrates the parts of the counterweight which were split and
suppressed step by step over a given range of radius. At each radius, the analysis was repeated automatically, and
the total inertial forces were obtained on the revolute joint of the crankshaft.
Figure 5: The gradually split and suppressed parts of the counterweights
The total inertial moment on the revolute joint of the crankshaft depended on the origin of the reference axis. The
crankshaft was mounted on the crankcase at two locations. These locations were where the bearings were. As
depicted in Figure 5, one bearing was in the side of the pulley, the other was in the side of radiator. The bearings
were suppressed in Figure 5. Eventually, two total inertial moments were obtained depending on the reference
location.
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
1375, Page 6
Table 1: RBD results with respect to different design points
Design point Counterweight
radius
Total maximum
crankshaft force
Total maximum
crankshaft
moment
Units m N Nm
DP 0 (Current) 0,104 189,17 64,524
DP 1 0,1035 152,84 59,419
DP 2 0,103 118,39 54,563
DP 3 0,1025 84,9 49,725
DP 4 0,102 57,249 44,919
DP 5 0,1015 81,782 40,151
DP 6 0,101 115,79 35,438
DP 7 0,1005 149,56 30,769
DP 8 0,1 183,07 26,145
DP 9 0,0995 216,36 21,572
DP 10 0,099 249,38 17,193
DP 11 0,0985 282,06 13,832
DP 12 0,098 314,43 15,7
DP 13 0,0975 346,48 20,172
DP 14 0,097 378,22 24,603
DP 15 0,0965 409,64 28,992
DP 16 0,096 440,75 33,34
Table 1 displays the results of the parametric solution obtained through the rigid body dynamics analysis. The
column on the left indicates the design points, the second column lists the radius of the counterweights, the others
are the total inertial forces and moments, respectively. Starting from 104 mm radius, the radius of the
counterweights was reduced by 0.5 mm down to 96 mm. The minimum resultant inertial force was obtained at the
third design point where the radius of the counterweights was 102 mm. Similarly, the minimum resultant moment
was obtained at 98.5 mm radius. 98.5 mm radius and 102 mm radius correspond to 195.7 kg-mm and 198.9 kg-mm,
respectively. The difference between the mathematical model results and the RBD results stem from the increment
of the parametric solution and the assumption that in the mathematical solution the inertial coordinate system is
fixed at each radius of the counterweight within the given mh range on MATLAB.
4.2 Experimental Setup
Modelling on MATLAB and Ansys Workbench ran simultaneously, and they validated each other. The computer-
based studies were supported by a series of vibration test using the equipment seen in Figure 6-7.
The tests were performed with a progressive method. The diameter of the counterweights seen in Figure 5 was
reduced by 1 mm in the sequential vibration tests. The ideal mh interval had been determined with the mathematical
and the RBD models prior to testing phase. The number of tests was determined and reduced considering these
models. Figure 8 demonstrates the process of metal removing on the counterweights.
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
1375, Page 7
Figure 6: Dewe 43A data logger
Figure 7: Dytran 3263A2 accelerometer and Dytran 6272 magnetic base used in the tests to measure vibration
levels
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
13
12 ♦- ____._ Head equivalent "' -...... ] 11 - - - ♦- - - -+- Crankcase --.. en
10 ' I ' Q) 9
.... _ -0 -...... _ .a 8 s -,._ - - -• ~
QC)
"" s 7
€ 6 ()
.£ 5 Q)
:> 4
3 105 103,5 103 102 101 100 99 98 97 96 95
Countenveight outer radius [mm]
1375, Page 8
Figure 8: Metal removing process within the successive vibration tests
Figure 9 demonstrates the velocity amplitudes of vibration with respect to the counterweight outer radius on DBK
30 at 12.83 Hz which is equivalent to 770 rpm. 770 rpm is the first order of rotational speed of the compressor head.
A modification on the counterweights directly impacts on the first order, thus the velocity amplitudes at this speed
was studied primarily. One curve in Figure 9 belongs to the tests performed on the crankcase. This location is seen
in Figure 6. The other curve and the mean velocity amplitudes on it belong to the measurements taken in several
locations on the compressor head. As seen in Figure 9, the amplitudes were minimized at 99 mm radius. This
learning complies with the one obtained in the mathematical and the RBD models.
Figure 9: The velocity amplitude of vibration with respect to the counterweight outer radius on DBK 30 at 12.83 Hz
(770 rpm)
It should be highlighted that the sequential tests were carried out by 1 mm radius increment. Therefore, the optimum
counterweight outer radius might have been any value within 98 - 100 mm range. It was certain that the optimum
one was not by 102 mm radius which the resultant inertial force points at.
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
Mgy
]yz
0
1375, Page 9
Table 2 summarizes the results. The mathematical model obtained three different mh values. One of them was 153
kg-mm. As seen in Figure 3, this mh did not lead to a sharp absolute minimum in the curve. Moreover, at 153 kg-
mm mh, the resultant inertial parameters were greater in comparison with those obtained at around 190 kg-mm.
Therefore, 153 kg-mm mh was not involved in this study. Table 2 emphasizes that the experimental result best
matches with those which considered the resultant inertial moment with respect to the bearing in the radiator side.
The pulley seen in Figure 4-5 does not only transmit torque from the motor but also plays the role of flywheel. It
stores inertia, thus preventing velocity fluctuations during an operation. In DBK30, the pulley approximately 50%
heavier than the whole crank mechanism, that is, that its mass is 34.7 kg. In the other side of the crankshaft an oil
filter is mounted as seen in Figure 7. It is named as the radiator side in Table 2. The bearing in this side is exposed to
a lighter mass.
Table 2: mh values and counterweight outer radius with different validation methods
Method Reference parameter mh
[kg-mm]
Counterweight
outer radius
[mm]
Resultant inertial force 198.6 101.8
Mathematical
model
Resultant inertial moment with respect to the bearing
position in the radiator side 194.8 97.7
Resultant inertial moment with respect to the bearing
position in the pulley side 153 62
Resultant inertial force 198.9 102
RBD analysis Resultant inertial moment with respect to the bearing
position in the radiator side 195.7 98.5
Experiment - 196.1 99
5. CONCLUSION
The study was aimed at determining the optimum counterweight for a W-type reciprocating compressor using a
mathematical model and an application created on MATLAB. The model was validated with RBD analysis on
Ansys Workbench and consecutive vibration tests. In this way, an approach which had been created in Dalgakiran
was extended with the conclusion that not only the inertial forces but also the inertial moments on the crankcase
have a significant role in determining the counterweights.
The experimental results supported the findings of the computer-based models with a maximum deviation of 5%. It
can be concluded that the method, which regards the resultant inertial moment calculated with respect to the bearing
position in the lighter side of the crankshaft, best matches with the test results.
Dalgakiran Compressor has over thirty different reciprocating compressor heads and this study will be a guideline in
re-evaluating their vibrational performance. Moreover, this learning will be a tool to be used in the design phase of
new reciprocating compressor crankshafts within the company in the future.
NOMENCLATURE
Gyroscopic torque
(N-m)
Product of crankshaft inertia tensor with respect to global axis
(kg-m)
Rotational speed of crankshaft
(rad/sec)
Velocity of precession
(rad/sec)
Centrifugal force produced by the rotation of the crankshaft
(N)
Crank angle
(deg)
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
Xz
<p
Mr
mh
1375, Page 10
Axial lever arm from the center of gravity of the crankshaft to one of the crankcase bearings
(m)
Reciprocating force
(N)
Axial lever arm from the center of gravity of the crankpin to one of the crankcase bearings
(m)
Angle between subsequent cylinder heads
(deg)
Moment by the horizonal axis in Figure 1 at one of the crankcase bearings
(N-m)
Moment by the vertical axis in Figure 1 at one of the crankcase bearings
(N-m)
Resultant inertial moment
(N-m)
Parametric variable to vary the centrifugal force
(kg-m)
Substitute mass of the connecting rod at the crank end
(kg)
Crank radius
(m)
Mass of the crankshaft including the counterweight/s
(kg)
Distance between the center of gravity of the crankshaft and the rotational axis of it
(m)
REFERENCES
Hanlon, P.C. (2001). Compressor handbook. New York, Mc-Graw-Hill Book Co.
Olgun, M., Kutlar, O.A. (2010). “Tek silindirli bir dizel motorun atalet kuvvetlerinin analizi ve dengeleme
hesaplamaları (Unpublished master’s thesis)”. Istanbul Technical University Institute of Science and Technology.
Pisirici, S. Et Al. (2018). “On the dynamics of a three-stage single acting reciprocating compressor”. International Compressor Engineering Conference. 1700:1-9.
25th International Compressor Engineering Conference at Purdue, May 24-28, 2021
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