finite element analysis of screw compressor ansys2006

Finite Element Analysis of Screw Compressor

Technology Development of 19 Elgi Equipments Ltd


M. Selvaraji Technology Development,

Elgi Equipments Ltd Abstract

There is a growing demand for all types of screw compressors in the industry due to user requirements.

Design and construction of screw compressors are demanding tasks that require advanced calculations and theoretical knowledge. The clearances in screw compressors play a major role in performance and reliability.

Screw compressors operate with tip speeds up to 100 m/sec and the discharge temperature up to 250 °C. A theoretical approach was needed in order to minimize the clearances while avoiding contact between the rotors and the casing. It was established to calculate the clearances accurately by considering the structural and thermal deformations. It is essential to incorporate the Computer Aided Engineering in the Screw Compressor design and development process to validate the theoretical model. Analysis of the stress and deflection caused by external force and pressure, analysis of the thermal stress and deformation caused by heat transfer has been performed in the screw compressor rotors, rotor and bearing housings by using Ansys. Based on the analysis results, a prototype compressor was built and tested. The reliability and performance of screw compressor was established. The design based on this procedure makes the screw compressor to reach the customer without any teething troubles. Results of the analysis are presented in the paper.

(Key words: Screw compressor, clearance management, and structural, heat transfer and thermal analysis)

Introduction

Screw Compressor

A set of intermeshing helical screw rotors is housed in the housing of the screw compressor. The rotor with profile outside the pitch circle is called male or main rotor, the rotor with profile inside the pitch circle is called female or gate rotor. The ball bearing on the rotors takes axial forces of the screw compressor. Similarly, the cylindrical roller bearing on both ends of the rotor receives radial forces from the screw compressor.

Screw compressors are same as piston compressors in the principle of the rise of the air pressure, one rotor acts as piston and other forms as cylinder in screw compressor and both belong to positive displacement compressors.



Types

Screw Compressors are classified based on principle of working, type of gas to be compressor and principle of application as below.

��

�

��

�

�

��

��

�

��

��

�

scompressor Injected -Water

scompressorDry scompressor free Oil

scompressor Gas Processscompressorion Refrigerat

scompressorAir scompressor flooded Oil

scompressor Screw

Design

In oil-free screw compressors, air does not contact the lubricating oil and the rotors don’t contact directly and remain space between each other. Male rotors drive female rotors through timing gear and it keeps the space between rotors. The main components of screw compressors like bearings, gears etc are lubricated by methods of normal lubrication, and isolating shaft seals are applied between these lubricated parts and the compression chamber.

In oil-flooded screw compressors, the lubricant is injected into the compressed air, which helps to lubricate, compress, cool and reduce noise. There is no timing gear in oil-flooded screw compressors, for the pair of rotors can work the purpose, the male rotor drive the female rotor directly.

In water-injected screw compressors, the water is injected to the compression chamber in order to reduce the discharge temperature in dry screw compressors and raise the single stage discharge pressure. As water can not be used for lubrication, timing gear is also designed in these compressors



Theoretical approach to calculate the clearances

The performance of any screw compressor depends on the following design and operating parameters.

1. Sealing line length

2. Blow hole area

3. Radial clearance

4. Interlobe clearance

5. Axial clearance

Sealing line When the male and female rotors of screw compressors mesh, the surfaces of two rotors contact with each other forming a space curve which is Sealing line.

Blow hole Area The tip of the contact line of the rotor usually can not reach the intersecting line between the cylinder holes of the male and female rotors, and form a space curve triangle between the top of contact line and rotor cylinder hole of the case, which is called blowhole area.

The significance of the sealing line length and blow hole area is depends on the type of the profile and type of application and if the profile is optimized for certain application, these parameters are fixed once for all.

The calculation of manufacturing and operating clearances namely, radial, interlobe and axial clearances are directly depend on the following parameters.

1. Structural deflection of the rotors due to pressure

2. Structural expansion of the housing bores due to pressure

3. Torsional twist of the rotors

4. Backlash of the synchronizing gears (incase of dry and water injected compressors)

5. Thermal expansion of rotors due to the thermal loading due to compression

6. Thermal expansion of housing bore due to the thermal loading due to compression

7. Thermal expansion of the housing center distance of the bores due to thermal loading

In the above list, first 3 parameters can be calculated by using the theoretical formulae with simplified geometry with assumption and can also be verified using analysis.



Structural deflection of the rotors due to pressure The screw compressor rotor is a stepped shaft with variable cross section from one end to the another end due to the assembly requirements of gears, bearings and seals in to the screw compressor.

The deflection of the stepped shaft can be calculated using moment area method as shown below.

��

�

��

�

�=

��

�

��

�

�

−2

112

x

x

dxEIM

xx dxdv

dxdv

First moment area theorem ------------ Equation No.1

( ) ��

�

��

�

�=−−

��

�

��

�

�

−2

11212

12

x

x

dxEIM

x

xx

vvxdxdv

xdxdv

Second moment area theorem ------------ Equation No.2

Solving the above two equations after applying the known boundary conditions the maximum deflection of the rotor and as well the location can be calculated.

Structural expansion of the housing bores due to pressure

Based on the casting feasibility the wall thickness is higher than one twentieth of the bore diameter, the Lame's theory for thick cylinder can be used to calculate the stress induced at inner and out walls and the corresponding expansion as below.

( ) ( )��

�

��

�−+−

−= 212

22

212

112

2221

22

1pp

rrr

rprprrrσ

Lame's Equation for radial stress ------------ Equation No.3

( ) ( )��

�

��

�−+−

−= 212

22

212

222

1121

22

1pp

rrr

rprprrcσ

Lame's Equation for hoop stress ------------ Equation No.4



Torsional twist of the rotors The angle of twist of the screw rotors is the sum of individual twist of each step of the rotors based on the torsion theory as below.

� �

��

�=

n

nn

n

JCl

T1

θ Torsion Equation ------------ Equation No.5

Backlash of the synchronizing gears

The amount by which the width of a tooth space exceeds the thickness of the engaging tooth on the pitch circles

Manufacturing Backlash - sum of tooth thickness tolerances of mating gears

21 ssm AA +=β ------------ Equation No.6

Operating Backlash - it is different from manufacturing backlash due to the center distance change and thermal expansion.

)(2 αββ CTanmo += ------------ Equation No.6

C= center distance tolerance + thermal expansion

Thermal expansion of rotors The rotors are subjected to pressure which causes the structural deformation and also they are subjected to variable thermal loading which causes the thermal expansion at profile which affects the operating radial, interlobe and axial clearances and thermal expansion of shaft t end affects seal and bearing clearances.

Radial thermal expansion of rotor

( )frrr TTRrr −= αδ ------------ Equation No.7

Axial thermal expansion of rotor

( )frrr TTLar −= αδ ------------ Equation No.8

Thermal expansion of Housing bores and CD The housings are subjected to variable thermal loading which causes the thermal expansion rotor bores which affects the operating radial, interlobe and axial clearances and thermal expansion of bosses affects seal and bearing clearances.

Radial thermal expansion of rotor bore

( )fhhh TTRrh −= αδ ------------ Equation No.9

Radial thermal expansion of Housing CD

( )fhhh TTCDcdh −= αδ ------------ Equation No.10



Axial thermal expansion of boss

( )fhhh TTLah −= αδ ------------ Equation No.11

Operating axial clearance

It is the function of cold clearance set during the assembly, internal clearance of the axial bearing, thermal expansion of the shaft and housing between axial bearing and discharge end face.

Operating Inter-lobe clearance

It is the function of cold clearance set during the assembly, internal clearance of the radial bearing, thermal expansion of the rotor, thermal expansion of housing bore, torsional deformation of rotors and operating backlash of the gears.

Operating Radial clearance

It is the function of cold clearance set during the assembly, internal clearance of the radial bearing, thermal expansion of the rotor and housing bore.

Finite Element Analysis

Flow diagram

Structural Analysis of rotors

Thermal Analysis of rotors

Thermal Analysis of Housings

Results



Structural Analysis of rotors

GEOMETRY

The equivalent circular cross-section of the screw rotor profile has been calculated and modeled instead of the actual helical rotor, because the helical rotor is symmetric about its axis. (Ref fig .1)

ELEMENT / MESH CONSIDERATIONS

Beam elements are used to create a mathematical one-dimensional idealization of a 3-D structure. They offer computationally efficient solutions when compared to solid and shell elements.

Beam 188, used here, has 6 degrees of freedom- 3 translations, 3 rotations; at each of its two nodes and can support 3-D displacement plots/contours. It also supports line/3-D plots. Circular Beam Sections were attributed to each line, with the same no. of elements in radial and circumferential directions. (Ref Fig.1)

BOUNDARY CONDITIONS

The model was constrained at two keypoint locations, with pure radial support at one end and with radial & axial support at the other. The loads were previously estimated point loads for the resultant gas & gear loads in 2 locations. (Ref Fig.2)

Thermal Analysis of rotors

GEOMETRY The equivalent 3D-stepped shaft model was made.


3D ELEMENTS were used with the free mesh option to obtain a sufficiently fine Mesh.

BOUNDARY CONDITIONS

Convective heat transfer coefficients were calculated using the equations 12 -15 and input to areas where heat transfer was known to take place. Bulk temperatures were also given.

Theoretical calculation of the thermal distribution of the rotors at different locations is very complex due to the geometry, loading and boundary conditions and the Computer Aided Engineering assistance become mandatory to determine the steady state temperature distribution.



Heat transfer coefficient of hot medium Reynolds number

h

hh

Dvγ

=Re

Nusselt number

4.08.0 PrRe023.0 hhhNu = ------------ Equation No.12

Heat transfer coefficient of air

DNu

h hhh

λ= ------------ Equation No.13

Heat transfer coefficient of cold medium Reynolds number

o

oo

Dvγ

=Re

Nusselt number

4.08.0 PrRe023.0 oooNu = ------------ Equation No.14

Heat transfer coefficient of oil

DNu

h ooo

λ= ------------ Equation No.15

The boundary condition obtained from the above calculation is applied in the thermal analysis and found the temperature distribution of the rotors and the average value at required locations.

Thermal Analysis of Housings GEOMETRY

The equivalent 3D model was imported. (Ref Fig. 6)


3D ELEMENTS were used with the free mesh option to obtain a sufficiently fine Mesh. (Ref Fig. 7 & 12)

BOUNDARY CONDITIONS

Convective heat transfer coefficients were calculated using the equations 12 & 16 and input to areas where heat transfer was known to take place. Bulk temperatures were also given. (Ref Fig. 7 &13)

Theoretical calculation of the thermal expansion of the housing bores at different location is very complex due to the geometry, loading and boundary conditions and the Computer Aided Engineering assistance become mandatory.



Heat transfer coefficient of cooling medium

Reynolds number

c

cc

Dvγ

=Re

Nusselt number

4.08.0 PrRe023.0 cccNu = ------------ Equation No.16

Heat transfer coefficient of water

DNu

h ccc

λ= ------------ Equation No.17

The thermal boundary condition obtained from the above calculation is applied in the thermal analysis and found the temperature distribution of the discharge end of the housing, bearing bore and seal bore. The analysis result is shown in the figure no.3

The above model is verified with temperature testing at many locations in the housing and found that the comparison shows a close match with prediction and actual testing values.

Analysis results and discussion

The structural analysis of rotor shows that the deflection of the rotor is 18 microns, refer the fig. 3&4, which correlates with the theoretical calculation.

The thermal analysis of the rotor shows that the maximum temperature due to convection is about 207 degC for the bulk temperature of 250 degC, refer the figure no. 5.

Based on the thermal analysis of the bearing housing, the bearing bore temperature is about 60 degC against the measurement of 61 degC and the seal bore temperature is about 75 degC against the measurement of 80 degC, refer the figure no. 8-11

Based on the thermal analysis of the rotor housing, the rotor bore temperature is about 160 degC, fig. 14.

The above analysis indicated the hot and cold zones of the housings and hence the operating clearance is depending on the surface temperature.

Based on the model, the compressor clearances are calculated and tested with and without the above procedure and found the performance improvement, which is shown in the figure no.15

Conclusion Theoretical model has been developed and the same is verified by structural, thermal analyses using ANSYS 8.1. Based on the analysis results, the clearances have been designed and tested the machine reliably and there is a significant performance improvement by using this procedure.



Nomenclature

M - Bending moment, m

E - Young's modulus, N/m2

C - Shear modulus, N/m2

I - moment of Inertia, m4

J - Polar moment of Inertia, m4

rσ - Radial stress in casting wall, N/m2

θσ - Hoop stress in casting wall, N/m2

P1, P2 - Pressure acing at the radii r1, r2

θ - Angle of twist, rad

L - Length of shaft, m

As1, As2 - Tooth thickness tolerance for mating gears, m

mβ - Backlash of the gear under manufacturing, m

oβ - Operating backlash, m

C - Variation in center distance of gears, m

α - Pressure angle, deg

rh,α - Thermal expansion coefficient of housing and rotor material, m/mdegC

R1,2 - Housing and rotor radii, m

Th,r,f - Temperature of housing, rotor and reference, degC

Vh,c - Velocity of hot and cold fluid and oil, m

D - Hydraulic mean diameter, m

hh,c, o - Heat transfer coefficient of hot, cold fluid and oil, W/m2K

och ,,λ – Thermal conductivity of hot, cold fluid and oil, W/mK

Reh,ec,eo - Reynolds number of hot, cold fluid and oil

Prh,rc,ro - Prandtl number of hot, cold fluid and oil

Nuh,c,o - Nusselt number of hot, cold fluid and oil



References

1. Ahmed kovacevic, Nikola Stosic, Ian K. Smith, Numerical analysis of the fluid-solid interaction in twin-screw positive displacement machines, ICNPAA 2004: Mathematical Problems in Engineering and Aerospace Sciences, June 2-4, 2004, The West University of Timisoara

2. Dr A Kovacevic, CFD and stress analysis in screw compressor design, City University London, UK

3. C. Zamfirescu, N. Nannan, M. Marin and C. A. Infante Ferreira OIL FREE TWO PHASE AMMONIA (WATER) COMPRESSOR, FINAL REPORT, DELFT UNIVERSITY OF TECHNOLOGY Faculty of Design, Construction and Production , Contract BSE-NEO 0268.02.03.03.0002 , Report K-336

4. Takao Inoue, Tomokazu Nakagawa, Eiji Fujita, Hisao Hamakawa, Thermo-elastic analysis of Oil free screw compressors, Kobe steel Engineering reports, Vol.49, No.1 April 1999. (Translated from Japanese)

5. Mikio Oi,Mariko Suzuki,Natsuko Matsuura, Structural Analysis and Shape Optimization in Turbocharger Development, Ishikawajima-Harima Heavy Industries Co., Ltd.

6. N.Seshaiah, Subrata Kr. Ghosh, R.K. Sahoo, Sunil Kr. Sarangi, MATHEMATICAL ANALYSIS OF OIL INJECTED TWIN SCREW COMPRESSOR, Mechanical Engineering Department, National Institute Of Technology, Rourkela, Orissa

7. N.Seshaiah, Subrata Kr. Ghosh, R.K. Sahoo, Sunil Kr. Sarangi� �� , Mechanical Engineering Department, National Institute Of Technology, Rourkela, Orissa

8. Xing Ziwen, SCREW COMPRESSOR-Theory, Design and Application, Mechanical Industry Publishing House (Translated from Chinese)



Figures

Fig.1 Force system and Simply Support Constraints on Equivalent 3D BEAM model

Fig .2 Reaction Solution



Fig.3 Structural analysis of rotor – Vector sum of Displacement

Fig.4 Structural analysis of rotor – Von Mises stress check



Fig.5 Thermal analysis of rotor- Temperature Plot



Fig.6 Thermal analysis of Bearing Housing- Meshed Model

Fig.7 Thermal analysis of Bearing Housing- Convective Boundary Conditions



Fig.8 Thermal analysis of Bearing Housing- temperature plot (looking from top)

Fig.9 Thermal analysis of Bearing Housing- temperature plot (looking from bottom)



Fig.10 Thermal analysis of Bearing Housing- temperature plot (looking from back)

Figure no.11 Thermal analysis of Bearing Housing-Temperature Plots (looking from back)



Figure no.12 Thermal analysis of Rotor Housing – Mesh

Fig.13 Thermal analysis of Rotor Housing- Convective Boundary Conditions



Fig.14 Thermal analysis of Rotor Housing- Temperature plot

Figure no.15 Performance improvement using the above procedure

Performance improvement with respect to specification

0.0

2.5

5.0

7.5

10.0

12.5

15.0

1 1.5 2 2.5 3

pressure (BarG)

% d

evia

tion

from

Spe

c

beforeAfter

finite element analysis of screw compressor ansys2006

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