An Analytical Tool To Determine The Optimum Counterweights

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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, [email protected]

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

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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

[email protected]

2Dalgakıran Makina, Research & Development, Kocaeli, Turkey

[email protected]

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

mailto:[email protected]

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.


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.


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.


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.


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.


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


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.


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)


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.


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An Analytical Tool To Determine The Optimum Counterweights