Compufcrs & Sfructurer. Vol. 4. pp. 193-204. Pergamon Press 1974. Printed in Chat Britain

PROPELLER BLADE STRESSES, APPLICATION OF FINITE ELEMENT METHODS

TERJE SBNTVEDT

Det norske Vcritas, P.O. Box 6060, Etterstad, Oslo 6, Norway

Abstract-This paper presents results from application of shell elements for prediction of quasi static and dynamic stresses in marine propeller blades.

Stresses and deformations calculated for ordinary geometry and highly stewed propellers are compared with experiments.

Specially designed data generators are employed to facilitate the helicoidal geometry involved.

1. INTRODUCTION

IN 1969 a research project was initiated by DnV with the main object of studying stresses and deformations in marine propeller blades when operating in the behind conditions of a ship. The research project was sponsored by A/S Strermmen Staal and NTNFt. Extensive experiments have been conducted to assess detailed quasi static and dynamic response characteristics of blades with realistic stew and aspect ratio. Various theoretical models have been developed to observe correlations with the said experiments.

Details connected with the research project are fully documented in [l]. In this paper we will concentrate on application of finite element methods for frequency response and response to the frozen type of hydrodynamic loading.

In 1970 Genalis [2] reported a study of Conolly’s experiments [3] by use of thin shell elements. At that time DnV had worked for two years with the SESAM-69 program com- lex [4]. Promising results obtained when simulating complex shaped bodies led to inclusion of such methods in our striving towards proper assessment of response characteristics for blades of all known shapes. The basic tools involved in this paper namely the thin shell element of the triangular type and the sdperparametric shell element are properly described in [5-81 and will only be referred to here.

2. RESPONSE OF PROPELLER BLADES TO FROZEN TYPE OF HYDRODYNAMIC LOADING. THEORETICAL MODELS AND

EXPERIMENTS

2.1 Moderarely scewedpropeller

In Fig. 1 is indicated the procedure employed by. DnV to determine the stresses and deformations in propeller blades. The procedure is based on the normal propeller drawing and the hull wake field. The load module produces the pressure distribution on punched cards for required generator positions in the wake field [19]. In the data generating module

t The Royal Norwegian Council for Scientific and Industrial Research

193

194 TERJE S~NTVED~

the coordinates for the camber, blade thickness and element loading are found by function interpolation [lo]. Triangular elements with constant thickness subjected to normal pressure have been found to match well with the actual blade shape when dealing with ordi- nary propellers. Since all nodes in an element must be situated in plane, triangular elements only, could be used for our helical surfaces. For the propeller shown on Fig. 2 the card out- put amounted to 550 with cpu time on UNIVAC 1108 Iess than 12 sec. The handling process from given propeller geometry and wake to the latter mentioned card output serving as input to the SESAM 69 system appeared to be simpie and quick. Unless direct interactive design is desired, card output may be used-for everyday application.

The module NV331 thin shell analysis [Ill then determined the desired stresses and deformations.

MATERI AL

’ DATA

GENERATION OF INPUT FOR

t--i NVS52 1 NV331 (NV3321

STRESSES AND

OEFORMATIONS IN

PROPELLER BLADES

Fro. 1. calculation of stresses and deformations in propeller blades,

t-

I PLANES: II 12 Jl JZ Ml Ict I 10 1 9 1 i

_ -. -_ ..x

FIG. 2. Control plot of model used.

Propeller Blade Stresses Application of Finite Element Methods 19.5

Figure 2 is an illustration of a data check on the element mesh as plotted by our Calcomp plotter. This plotter has also’been used to produce stresses and deformations such as are shown in Figs. 3-7. The net cpu, time for the described thin shell analysis is less than 2 min when employing the UNIVAC 1108 computer.

PROPELLER

FIG. 3. Stresses and strains, computer plots,

The propeller blade in question is of the controllable pitch type with diameter 2,044 m, pitch ratio 0.65, area ratio 0.4 number of blades 3. This propeller was subjected to experi- ments in our laboratory together with other propellers of diverging geometry,

Tension pads were loaded by soft springs Figs. 8-10 and strains recorded in 32 rosettes together with observation of deformations. The flow diagram exhibited on Fig. 11 helps to identify components applied for stress recording. On Figs, 12-13 calculated and measured principal stresses are compared. 1x1 general, the principal stress q1 is directed along the radius while a2 points approximately along the propeller helix. Calculated and observed axial deflections are included in Fig. 14. Apparently the blade Gxation at the bed pIate for this cpu propeiter is not properly simulated by the calculated degree of fixation. There is little doubt that ex~~mental~theoret~~l stress correlations obtained are satisfactory.

196 TERJE SWTVEDT

Y i

FIG. 4. Propeller. Deformed shape.

For the propeller referred to in Section 3 which is built in one piece the degree-of-fixation at the root is more accurately predicted (refer Fig. 15).

Similar results were obtained for all other propellers tested. Also Conolly’s experiments -indicated in the introduction to this paper [3] were adequately simulated by thin shell elements-as may be observed in Fig. 16.

2.2 Highly scewedpropeller

Stress measurements carried out on a highly stewed propeller (120”) with diameter 0.305 m, pitch ratio 1.071 and expanded area ratio 0.202 are reported in [12]. Air pressure provided external loading to this propeller. The procedure outlined in Section 2.1 led to control plot and results given in Figs. 17 and 19. Possibly the steep tangential stress grad- ient experienced necessitates a finer element mesh.

Propeller Blade Stresses Application of Finite Element Methods 197

PROPELLER.

GEFORNEC SHRPE .

LORDCRSE 1. ZCRLE I :50

fiISFLR:EME!;TS 3X fiY DZ

FIG. 5. Propeller. Deformed shape,

Also elements with arbitrary thickness distribution limited by 8 nodes have been used to observe whether rather more “sophisticated” elements would improve accuracy indicated above. In the plots on Figs. 20 and 21 the mesh used for simulation of the highly stewed propeller is subject to control. With the module NV331 “Thick/thin shell analysis” a c p u time of approximately 4 min was found to yield results given in Figs. 22 and 23. Apparently, the mesh distribution used is not optimum. Calculations recently completed employing said superparametric elements and reportedin [13]exhibited excellent agreement with experiments described.

3. NATURAL FREQUENCES AND FORCED RESPONSE

A 6 bladed large propeller with diameter 8.8 m, pitch ratio 0.78 and expanded area ratio 0.6 was excited in air and the primary flexural mode recorded by strain gauges.

In a finite element approach the blade was divided into elements as illustrated in Fig. 24. As generating system was used the procedure outlined in Section 2.1 The module NV461 ‘Shell Vibration Analysis’ was employed to establish the natural frequencies and corres- ponding shapes. The calculated and recorded frequencies of the primary flexural mode compare well-as is indicated on Fig. 24.

198 TERJE SBNWEDT

PROPELLER. PROPELLER.

PLOT OF STRESSES. PLOT OF STRESSES.

121 i /23[ Srs.3 SCQLE 1 :50 12/l/-23cso-1 SCRLE 1 :scl

ISOFRCTOR: IO*%-2 ISOFRCTOR: lOr~-Z

FIG. 6. Equivalent stresses, pressure side. FIG. 7. Equivalent stresses, suction side.

STRAIN GAUGES

POWER

SUPPLY

4

STRAIN GAUGE

BRIDGE UNIT

c

DATALOGGER

ti STRESSES

FIG. 11. Flow chart. stress recording.

FIG. 8. Propeller in teat bt&.

FIG. 9. Strain gauges and tension pads on prop&er, item 2.

_ -..

FIG. 10. Arrangement for static load experiments.

Propeller Blade Stresses Application of Finite Element Methods 199

r/R= 1.0 -

0.9 -

---*-- 0.6 -

_e-.--em,. 07 &

0.6 -

0.5 -

01 &

z -

---c, F.E.M. ’ =1

x t MEASURED - G2 2

PRESSURE SIDE

FIG. 12. Principal stresses in model propeller, item 2. Pressure side.

--_ ct - (72

F. E.M.

-2J

SUCTION SIDE

FIG. 13. Principal stresses in model pmpeller, item 2. Suction side.

200 -t-EWE 80NTVEDT

Forced response of a propeller blade may be found by applying the structurai damping characteristics determined as illustrated in [l] based on experiments carried out in the DnV

Iaboratory and on approximated hydrodynamic damping characteristics.

0.L 0.6 0.8 r/R

FIG. 14. Axis1 deflection at chord center line.

Fro. 15. Calculated viz measured axial deflection propeller No. 1.

Pr~pllcr Blade Strekxx Application of Finite Element Methods

- FlNIKE ELE!‘+ENT’J

FTC% 16. Propeller blade stresses at max. thickness.

FIG. 17. Element mesh NV331,

202 TERJE SSNTVEDT

- F. EM. - NV 331

1000 PSI -COMPRESSION

SUCTION SIDE

FIO. 19. Principal stresses in model propeller. Suction side.

PLANES:11 12 Jl J2 Kl K2

FIG. 20. Element mesh NV332.

PLANES: 11 12 Jl J2 Kl K2

FIO. 21. Element mesh NV332.

Propeller Blade Stresses Application of Finite Element Methods 203

. MEASURE0

L F EM. - NV 332

1000 PSI -TENSION

PRESSURE SIDE

FIG. 22. Principal stresses in model propeller Pressure side.

- 17 EM - NV 332

1000 PSI - cOMPREWON

SUCTION SIDE

FJG. 23. Principal stresses in model propeller Suction side.

PRIMARY FLEYURAL

MODE IN AIR.

EXPERIMENTS 20.8

20.6

FJG. 24. Plot of mesh.

204 TERJE Smrv~~r

4. CONCLUSION

Thin-thick shell analysis can be employed together with simple datagenerator systems to solve the every day stress and deformation problems experienced with given hydrodynamic loading on marine propellers. This statement applies to all known blade shapes. The element mesh required leads to cpu time less than 2 min when modelling orthodox geometry propellers.

Together with FE techniques available for added mass estimates aspects related to more unorthodox propulsors may also be dealt with.

REFERENCES

[l] T. SBNWEDT, NTNF project B0930. 2916 Response of propeller blades to given hydrodynamic load- DnV report No. 72-4-M.

[2] P. GENALIS, Elastic strength of propellers-an analysis by matrix methods. The University of Michigan ing. Publ. No. 101. Nov. (1970).

(31 J. E. CONOLLY, Strength of propellers. Trans. R. I. N. A. 103,139 (1961). [4] P. 0. AFLUDSEN, SESAM-69-A general purpose finite element method program. (51 I. HOLAND and K. BELL, Finite element methods in stress analysis. Trondheim Jan. (1969). [6] 0. C. ZIENKIEWICZ, The Finite Element Methodin Engineering Science. MC Graw-Hill, New York (1971). [7j 0. C. ZIENKIEWICZ, R. L. TAYLXX, and J. M. Too, Reduced integration technique in general analysis

of plates and shells. Znt. J. num. Meth. Engng 3, 275-290 (1971). [8] S. F. PAWSEY and R. W. CLOUOH, Improved numerical integration of thick shell finite element. Znt.

J. num. Meth. Engng 3 (1971). [9] K. HOLDEN, Type and extent of cavitation on propeller blades and hydrofoils. DnV report No. 72-2M.

[lo] A-E. RIESTAD, User’s Manual NV552. Stresses and deformations in marine propeller blades. Data generation for SESAM-69 system. DnV report No. 72-36-M.

[ll] 0. EOELAND, P. 0. ARALDSEN, B. AAMOT and G. GUDBRANDSEN, NV331 Thin SheN Analysis. User’s Manual.

[12] R. J. BOSWELL, Static stress measurements on a highly-skewed propeller blade. Naval Ship Research and Da-elopment Center. Report 3247. December (1969).

[13] A-E. -TAD and T. SBNTVEDT, Response of Marine propeller blades to frozen loading, Norwegian Maritime Research, Voi 1, No. 3 (1973).

(Received 11 December 1972)