International Journal of Scientific & Engineering Research Volume 2, Issue 7, July-2011 1

ISSN 2229-5518

Rotor Profile Design for Twin Screw

Compressor

P.Jenno Xavier, K.Kanthavel, R.Uma Mythili.

Abstract-Increasing demands for efficient screw compressors requires economic and high efficiency rotor designs of screw compressor.Inorder to design a effective rotor rack has to be generated effectively. Numerical and equation adopted in this paper leads to design a effective rotor profile. The solution obtained depends only on the parameters of the rack, pitch, addendum height, dedendum height, rack co ordinates and meshing condition. A suitable procedure for optimization of the screw compressor shape, size, and dimension is described here, which results in the most appropriate design. Compressors thus designed achieve higher delivery rates and better efficiencies than those using traditional approaches.

Index TermsRotor, Rack generation, Screw compressor, Tooth profile

1 INTRODUCTION

—————————— • ——————————
given meshing line description. They carried out this
crew compressor rotors of various profiles can be today conveniently manufactured with small clearances at an economic cost. In a while Litvin [1] generated screw compressor rotors and their tools. Shortly Litvin and Feng [2] used singularity and tooth contact analysis (TCA) to investigate the influence of misalignment on the backlash between the surfaces. Soon after in the year 1987, Rinder [4] proposed a rack- generated rotor profile based on gearing theory. Later Stosic [5] proposed a pair of rack-generated rotors inorder to fill the large gap of years.They stated that high- pressure side of the rack is generated by means of a rotor conjugate action that undercuts an appropriate curve on
the rack.
Over the year of 2003 N. Stosic et al., developed a new concept for optimizing screw compressor. They established suitable procedure for optimisation of the screw compressor shape, size, dimension and operating parameters which results in the most appropriate design for a compressor.It is based on a rack generation algorithm for rotor profle combined with a numerical model of the compressor fluid flow and thermodynamic processes. They have shown that the optimum rotor profle, compressor speed, oil flow rate and temperature may signifcantly diDer when compressing diDerent gases or vapours or if working at the oil-free or oil-flooded mode of operation [7].In a while D. Zaytsev et al.,in the year of 2005 adopteed new techniques for generating rotor profile for screw compreesor.
They adopted a method for generation of the profle of twin screw compressor rotors from a meshing line which was analytically derived. The solution obtained mainly depends only on the distance between the rotor axis, the lobe number of both rotors and the
method to obtain optimal profle design[11].Soon after Yu-Ren Wu et al.,in year of 2009 flourished a new concept for generating rotor profile.They replaced the implicit form with explicit equations of the rack with two specifc normal-equidistant trochoids for rack-generated rotor profles.
They implemented parameters which are designed on the rack in order to more instinctively and flexibly adjust each compound curveThey established The parametric study and non-undercut limits are presented for the rotor profle optimization with SUMT (sequential unconstrained minimization technique) method. The performance of the twin-screw compressor depends mainly on the tooth profle of mating rotors[10].

2 MATHEMATICAL MODEL OF RACK GENERATION FOR ROTORS

The fundamental idea is derived from the rack- generated profle .Each compound curve has at least one control parameter on the rack profle, which makes the rack both flexible and instinctively adjustable. The tooth profile of the basic rack depends on the pitch W and the total tooth height (ha + hd). As shown in Fig. 1, the addendum ha and the dedendum hd can be determined by the tooth number of the rotors z1 and z2, the center distance C, and the outer radii of the male and female rotors rp1 and rp2 as given in the following equations[10]:
rp1=Acz1 /(z1+z2 ) -(1) rp2=Acz2 /(z1+z2 ) -(2) ha = r2-rp2 -(3) hd =r1-rp1 -(4) W=2rrrp1 /z1 -(5)

2.1 Meshing condition for Screw compressor and

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International Journal of Scientific & Engineering Research Volume 2, Issue 7, July-2011 2

ISSN 2229-5518

Rack Co-ordinates

x2=xo1cosk8-yo1sink8-c cos(8/i) -(6) y2= xo1sink8+yo1cosk8+c sin(8/i) -(7) xo1=(re-r1)+r1cost -(8) yo1=r1sint -(9)

3 PARAMETRIC DETAIL DESIGN STUDY

3.1 Design of Rotors in Screw Compressor

(1)To find the center distance between rotors (C)

C= Radius of main rotor pitch circle and gate rotor pitch circle –(Hanjalic and Stotic 1994)
C= (outer diameter of female main/2)+(gate root diameter/2)
C=(98.18/2)+(81.82/2) C=49.09+40.91
C=90mm

Fig.1 Rack Profile And Design Parameter

xr=xo1cos8-yo1sin8 -(10) yr=xo1sin8+yo1cos8 –r18 -(11) k=1-(1/i)
k=1-(1/6.9306)
k=1-0.1

2.2 Calculation of rotor profiles in screw compressor optimization

A procedure to get the required meshing condition as described in [6]. More detailed information on the envelope method applied to gears can be found in [3]. The primary curves are specified on the rack: D–C is a circle with radius r3 on the rack, C–B is a straight line, B– A is a parabola constrained by radius r1, A–H–G are trochoids on the rack generated by the small circles of radii r2 and r4 from the male and female rotors respectively, G–E is a straight line and E–Fand E–D are circles on the rack. A full description of the rack generation procedure and rotor geometry is given in [10].
These three rotor radii, r1, male rotor lobe radius, r2; male rotor tip radius and r3, rack root radius and the female rotor addendum r0, as presented in Fig. 1, are used as variables for the rotor optimization[7].

Fig.3 Profiling of Rack

(2)To find the external and internal radius of female rotor (re and ri)

External radius re = rw+r Internal radius ri = rw-ro re =(52.8/2)+(48/2)
re =26.4+24
External radius re for female rotor=50.4mm ri = (100.8/2)-(48/2)
ri = 50.4+24

Internal radius ri for female rotor= 26.4mm
External radius re = rw+r Internal radius ri = rw-ro re =(81.82/2)+(45.38/2) re =40.91+22.69
External radius re for male rotor=52.8mm ri = (127.2/2)-( 45.38/2)
ri = 63.6-22.69
Internal radius ri for male rotor= 40.91mm

3.2 Design of Diameter of Pipeline

Quantity of Compressed air flow =200cfm
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Fig.2 CO-ORDINATE AXIS OF ROTOR PROFILE

International Journal of Scientific & Engineering Research Volume 2, Issue 7, July-2011 3

ISSN 2229-5518

=200*0.02831
=5.66m3/min
Working Pressure =100psig
=100/14.22
=7.0323kg/cm2

Velocity =6m/sec
rp1=Acz1 /(z1+z2 ) rp2=Acz2 /(z1+z2 ) ha = r2-rp2
hd =r1-rp1
W=2rrrp1 /z1
W-pitch.
ha ,hd –addendum and dedendum height. rp1,rp2-pitch radii of female and male rotor. ha = 51.8mm
hd = 86.3mm
Total height = 138.1mm
W = ((2*3.14)/5)* rp1
Pitch (W) = 51.374mm

Fig.4 Dimension of Rotors

Apply gas laws. Assume the temperature remains constant
P1V1 = P2V2
V2 = P1V1/ P2
Pressure at inlet (P1) =1.013kg/cm2
Pressure at outlet (P2) =7kg/cm2
Volume at inlet (V1) =5.66m3/min
V2 = P1V1/ P2
V2 =(1.013*5.66)/7
V2 =(0.819 m3/min)/60
V2 =0.01365 m3/sec
Quantity of air flow =Area of pipe line x velocity of air flow
0.01365 m3/sec = Area of pipe line x 6m/sec
Area of pipe line =2.275x10-3m2
rr/4xD2 =2.275x10-3m2
Diameter of pipe line = 0.0538m
=2.11” (3)To find the Angular parameter (-r): T=8/i -Stotic 1994
8-helix angle
i-Pressure ratio i=P2/P1 i=(7/1.01) i=6.930
8=300
T=8/i T=(30/6.930) T=4.329

(4)Calculated pitch and total height:

Fig.5 Rotor design

4 FACTORS AFFECTING COMPRESSOR EFFICIENCIES

• the blowhole area,
• the length of contact line,
• the volumetric efficiency
• the isentropic indicated efficiency
the related formulation and mathematical expression can be seen in the published book [9].
Only parameters p, u, t, K and T in the high-pressure side of the rotor can directly affect both the tip of the sealing line and the blowhole size within the housing cusp on the compression side, and the parameter has the greatest sensitivity on the blowhole area and volumetric efficiency because it primarily changes the cross-sectional volume of two rotors [10]. The fluid leakages and energy losses must be kept to a minimum to obtain the maximum volumetric and isentropic indicated efficiencies.

5 LIST OF SYMBOLS

TABLE1
Symbol Quantity

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International Journal of Scientific & Engineering Research Volume 2, Issue 7, July-2011 4

ISSN 2229-5518

rw Pitch radius of female and male rotor
r Rotor radius of female and male
rotor
ro Root radius of female and male rotor

6 CONCULSION

Optimisation of screw compressor geometry has been performed to establish the most efficient rotor design. This paper numerical solution and calculation enables optimum screw compressor flow power and compressor efficiencies. Each segment on the rack is given at least one instinctive adjustable parameter for modifying the generated rotor profile. As shown by the numerical formulation the proposed design method is able to improve the performance of twin-screw compressor. Rack-generated profiles of rotors which is used in the paper explains optimisation may permit both better delivery and higher efficiency.

REFERENCES

[1] F.L. Litvin, Teoria zubchanih zaceplenii (Theory of Gearing), Nauka, Moscow, 1956.

[2] F.L. Litvin, P.H. Feng, Computerized design, generation, and simulation of meshing of rotors of screw compressor, Journal of Mechanism and Machine Theory 32 (2) (1997) 137–160.

[3] F.L. Litvin ,Nauka, Moscow, Third ed.,1968; also Gear Geometry and Applied Theory, Prentice-Hill, Englewood Cliffs, NJ, 1994.

[4] L. Rinder, Screw rotor profile and method for generating, U.S.

Patent No. 4,643,654, 1987.

[5] N. Stosic, Plural screw positive displacement machines, U.S.

Patent No. 6,296,461 B1, 2001.

[6] N. Stosic, On gearing of helical screw compressor rotors, Proceedings of IMechEng, Journal of Mechanical Engineering Science 212 (1998) 587.

[7] N. Stosic, I.K. Smith, A. Kovacevic, Optimisation of screw compressors, Applied Thermal Engineering 23 (2003) 1177–

1195.

[8] N. Stosic, K. Hanjalic, Development and optimisation of screw machines with a simulation model, Part I: Profile generation, ASME Transactions, Journal of Fluids Engineering 119 (1997)

659.

[9] Z.W. Xing, Screw Compressors: Theory, Design and

Application, China Machine Press, Beijing, 2000 (in Chinese). [10] Yu-Ren Wu, Zhang-Hua Fong, Optimization design of an

explicitly defned rack for the generation of rotors for twin- screw compressors, Mechanism and Machine Theory 44 (2009)

66–82.

[11] D. Zaytsev, C.A. Infante Ferreira, Profle generation method for twin screw compressor rotors based on the meshing line,

International Journal of Refrigeration 28 (2005) 744–755.

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