THERMAL RATING CALCULATION AND DESIGN OF IMPROVED FAN FOR H2-200 TYPE GEAR BOX

Customer: M/s Greaves Ltd., Pune

MULTIFACET TECHNICAL CENTRE# 33, SVK Layout, West of Chord Road,

BANGALORE – 560 079.Tel.: 3225394, Tel/Fax: 3224006

E-mail: multifacet@vsnl.net

REPORT No : 0181 PREPARED BY: Murali K.S Jaiprathap N.S

Date : Jun – 2003 APPROVED BY: B.V.Nagendrakumar

THERMAL RATING CALCULATION AND DESIGN OF IMPROVED FAN FOR H2-200 TYPE GEAR BOX

Abstract:

This report summarises the estimation of Thermal rating of H2 type – foot mounted gearbox and design of improved fan to maximize the heat dissipation and hence thermal rating. Based on the study of literatures a procedure for estimation of the thermal rating was established. In order to validate the procedure thermal ratings of four sizes of gear box viz H2-180, H2-200, H2-225, H2-250 were calculated and compared with the values given in Catalogue. The performance of the existing and improved fan was also compared.

List of symbols:

Q = Heat generation in Gear Box (kW) = efficiency of Gear box T.R = Thermal Rating of Gear Box (kW)hoia = Heat transfer co-efficient of oil to ambient air (kW/m2K)hoiw = Heat transfer co-efficient of oil to inner surface of Gear Box (kW/m2K)hnv = Convective heat transfer co-efficient of air for vertical plates

(Natural Convection) (kW/m2K)hnh = Convective heat transfer co-efficient of air for Horizontal plates

(Natural Convection) (kW/m2K)hnc = Convective heat transfer co-efficient of air (Natural Convection) (kW/m2K)hfc = Convective heat transfer co-efficient of air (Forced Convection) (kW/m2K)hr = Heat transfer co-efficient of air (Radiation) (kW/m2K)A = Total surface area of Gear box (m2)Anc = Total surface area of under natural convection (m2)Afc = Total surface area of Gear box under fan cooling (m2)T = Rise in oil temperature (K)X = Length of Gear Box (m)Y = Width of Gear Box (m)Z = Height of Gear Box (m)t = Thickness of Gear Box plate (m) = Density of air in kg/mm3

= Co-efficient of absolute viscosity (kgs/m)K = Thermal conductivity of air (KW/mK)k = Thermal conductivity of gear box material (KW/mK)Gr = Grashof No.Nu = Nusselt No.Pr = Prandtl No.g = Acceleration due to gravity (m/s2) = Emissivity of Gear Box material = Stefan Boltzmann Constant (W/m2K4)d = Diameter of Fan (m)Vf = Peripheral velocity of fan (m/s)fk = Fan constant

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CONTENTS

AbstractList of symbolsContents1.0 Introduction2.0 Analysis procedure3.0 Performance of existing and improved fans4.0 Thermal rating with new fan5.0 Conclusion6.0 References

1.0 INTRODUCTION

The main objective of this exercise was to enhance the thermal rating of H2-200 gearbox. A systematic study was commissioned to analyse the above problem while focusing the attention on improving the fan performance, which would help in increased cooling. In the process of the above analysis, it was found that the thermal rating calculations form the core of the above study and it was also found that the methods available are empirical. Therefore, an attempt has been made to incorporate basic heat transfer equations to estimate the heat dissipation by natural convection and by fan cooling. To start with it was necessary to correctly define “thermal rating” of gearboxes. Because, depending on the definition of thermal rating, actual thermal rating calculations will have to be made.Thermal rating of a gearbox depends on the methods of cooling employed. If the gearbox cools by natural convection then for the same mechanical rating, thermal rating would be far lower. And by the same logic, by improved methods of heat dissipation, thermal rating of the given gearbox could be enhanced.After establishing the methodology for one size of gearbox and comparing it with catalogue values, the same procedure was adopted for validating the methodology on different sizes of gearbox and compared with catalogue ratings. Separate graphical representations have been made for natural convection and fan cooled or ‘blown gearboxes’ with comparisons shown for calculated and catalogue figures for the different models analysed.The next step was to have a close look at the fan with the idea of redesigning the fan to increase its performance and hence improve the thermal ratings. After a preliminary study, it became apparent that

a) the fan impeller will have to be centrifugal radial bladed only andb) the cowl that is presently in use cannot be disturbed and that, the improved

design for the impeller will have to work within the cowl space. Obviously, this is a serious constraint for placing a larger size impeller. Fan performance calculations have been also been included along with thermal rating improvement calculations. Manufacturing drawing for the improved impeller is also provided.

Future work would involve, building a gearbox with the improved fan and testing the performance on a test rig.

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2.0 ANALYSIS PROCEDURE

2.1 Assumptions:

1. The mechanical power lost in the gearbox is transformed as heat.2. Ambient temperature and rise in oil temperature are assumed to be 30C and

65C respectively.

2.2 Definition of Thermal rating Ref 1

“Thermal rating is defined as the maximum power that a Gear Box can transmit for 3 hours with out the oil temperature exceeding 93C when the ambient air temperature is not exceeding 30C.”

2.3 Specification of the existing gear box

Gear box size : H2-200Mechanical Rating : 213 KWInput speed : 1500 RPMSpeed Ratio : 1:5.6Efficiency : 98%

2.4 Heat generation in the Gearbox

--------------------- 1

2.5 Thermal rating of gearbox without fan (Heat dissipation by Natural convection):

Thermal rating of gearbox is given by,

---------------- 2

Where, TR = Thermal Rating in KWh0ia= Over all heat transfer coefficient of oil to ambient airA = casing area open to the air in m2

T = Rise in oil Temperature in C = 65C

2.5.1 Estimation of over all heat transfer coefficient of oil to air

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From the Catalogue and drawings the following dimensions are taken

Fig 1. Gearbox casing dimensions

Length of the gear box (X) = 0.68mWidth of gear box (Y) = 0.31mHeight of gear box (Z) = 0.45m

Total Surface area (A) = 2[X*Y+Y*Z+Z*X] -------- 3

A = 2[0.68*0.31+0.31*0.45+0.45*0.68] = 1.3126 m2

Taking 25% extra area to consider the curvature, cavities etc., A = 1.25*1.3126 = 1.641 m2

Properties of air at 30C (Ref 2) are

= 1.165 kg/m3 Pr = 0.701, k=26.75x10-6 kW/mK = 16x10-6 m2/s Cp = 1.005 kJ/kgK = 18.63x10-6 kg/m-s = 1/T =1/(273+30) = 0.0033 /K

Grashoff No is given by,

------------------------ 4

a) Convective heat transfer co-efficient

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i) Vertical plates

L = Z = 0.45m

= 0.75 x 109

Gr*Pr = 0.75 x 109 X 0.701 = 0.526x109 < 1 x 109 => laminar flow

Nusselt No. is given by

------------ 5

= 103.6

Heat Transfer Co-efficient is given by

----------------------------- 6

= 0.0062 kW/m2K

ii) Horizontal plates

L = sqrt (X*Y) Ref3

= Sqrt (0.68*0.31) = 0.46m

= 0.801 x 109

Gr*Pr = 0.801 x 109 X 0.701 = 0.561x109 < 1 x 109 => laminar flow

Nusselt No. is given by

Nu = 0.15*(GrPr)0.333 ------------------------- 7

Nu = 0.15*(0.561x109)0.333

= 123.75

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Heat Transfer Co-efficient is given by

= 0.0072 kW/m2K

The convective heat transfer co-efficient of air is given by

=

= 0.00652 kW/m2K

b) Heat transfer co-efficient due to radiation

Heat transfer by radiation is given by

qr = **(T24 – T1

4) -------------------------- 8

where = Emissivity of gear box material = 1.0 (assumed) = Stefan Boltzmann constant = 5.669x10-8 W/m2K4

T1 = Initial Temperature of oil in K = 303KT2 = Final Temperature of oil in K = 368K

Substituting the above values in equation 8, we get

qr = 1.0*5.669x10-8 *(3684 – 3034) = 561.84 W/m2 = 0.562 kW/m2

Heat transfer co-efficient due to radiation is given by

hr = qr/(T2-T1) = 0.562/65 = 0.00865 kW/m2K

The over all heat transfer co-efficient is given by

------------------------- 9

Where,

hoiw= heat transfer co-efficient of oil to inner surface of wall = 0.08 kW/m2K (From table 3.3 of Ref 3)

hnc = Convective heat transfer co-efficient = 0.00652 kW/m2Khr = Heat transfer co-efficient due to radiation = 0.00865 kW/m2K

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t = Thickness of gear box plate = 13 mm (Taken from drawing)

k = Thermal conductivity of Gear box material = 56 W/mK

Substituting the above values in equation 9 we get

= 0.01271 kW/m2K

Substituting the values in equation 2 we get

= 67.8 kW

2.6 Thermal rating of gearbox with fan (Heat dissipation by Forced convection):(As per the procedure given in Ref3)

Refer to the above fig,

Area under fan cooling is given by,

Af = 2*[X/2*Z] = 2*[0.68/2*0.45] *1.25 = 0.3825 m2

Area under natural convection (An) = A-Af = 1.641-0.3825 = 1.2585 m2

Fan diameter (d) = 0215m

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Peripheral speed of fan = = 16.89 m/s

Fan factor (fk) = [Vf/1.25]0.6 ---------------- 10 = [16.89/1.25]0.6 = 4.77

Heat transfer co-efficient with fan cooling is given by

--------------------- 11

= 0.0782 kW/m2K

Thermal rating with fan is given by

--------------------- 12

= 152 kW

2.7 Validation of the procedure

In order to validate the above procedure thermal ratings of few more models were calculated and compared with the values given in catalogue. The values are tabulated in the following table: Sl

No.Gear Box

modelThermal Rating with out Fan

(kW)Thermal Rating with Fan

(kW)Calculated Catalogue value Calculated Catalogue Value

1 H2-180 55.6 45.7 116.2 127.02 H2-200 67.8 82.0 149 153.03 H2-225 83.3 102.0 190.6 186.04 H2-250 102.6 125.0 245.9 254.0

The values tabulated in the above table are compared graphically as follows:

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3.0 PERFORMANCE OF EXISTING AND IMPROVED FAN

The following table gives the design and comparison of new fan with the existing fan. From the table it is clear that the airflow in new fan is increased by 23% when

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compared to the present design. Refer to figs 3 and 4 for manufacturing drawing and 3D model of new fan.

Radial Blade Fan Design    CASES: Present Design New DesignINPUT DATA    1. IMPELLER OUTSIDE RADIUS (d2) in mm 215 2282. IMPELLER INSIDE RADIUS (d1) in mm 41.5 41.53. BLADE WIDTH AT IMPELLER OUTSIDE RADIUS(b2) in mm 11.6 12.74.BLADE WIDTH AT IMPELLER INSIDE RADIUS(b1) in mm 19.7 225. N - FAN SPEED IN RPM 1500 1500     CALCULATIONS:    PERIPHERAL VELOCITY U2 = (pi x N x d2)/60 m/s 16.8855625 17.90655Vm2 = 0.2 x U2 m/s 3.3771125 3.58131     VOLUME FLOW    Q = pi x d2 x b2 x Vm2 m3/s 0.0264601 0.032578418     IMPELLER TOTAL PRESSURE    p = RHO x U2**2 Kfg/m2 RHO , Density of air in Kgf/m3 342.1466651 384.7734395     

POWER P = Q x p in watts 88.81223553 122.97139     Performance of Old design v/s New design    1.% increase in Q from old design   23.122806362.% increase in Air Power from old design.   38.46221668

Stress Analysis of fan back plate and blades.    INPUT DATA    1.Wb = Weight of Blades in Kg 0.207 0.2822.Wbp = Weight of Back Plates in Kg 1.554 1.773. W = Density of material in Kgf/mm^3 8000 80004. Impeller inlet diameter d1 in mm 41.5 41.55. Impeller outlet diameter d2 in mm 215 2286. Impeller width at Inlet b1 in mm 19.7 227. Impeller width at outlet b2 in mm 11.6 12.78. Fan speed N in rpm 1500 1500

1. Radial StressFr ={wc * Omega^2 / 8*g}* {(pis+3)(r2 - r1)^2} in Kgf/mm^2  Present Design New Design Wbe = Wb/2 0.1035 0.141

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wc = W * {(Wbp+ Wbe)/Wbp}where , wc = Corrected weight Density in Kgf/m^3Wbe = Effective Blade weight Wb/2 in Kgs. W = Density of material in Kgf/m^3 8532.818533 8637.288136Omega = 2 * pi * N / 60 rads/s 157.075 157.075pis = poision ratio 0.3 0.3 0.3g = accelration due to gravity 9.81 m/s^2 9.81 9.81r1 = d1/2 in M 0.02075 0.02075r2 = d2/2 in M 0.1075 0.114omega^2 24672.55563 24672.55563(r2-r1)^2 0.007525563 0.008695563Therefore radial stress Fr in Kgf/mm^2 0.066619376 0.0779191442. Hoop Stress    Fh = {wc*Omega^2/4*g}*{(pis+3)r2^2+(1-pis)r1^2} in Kgf/mm^2 0.206218367 0.234545763. Bending Stress in Blade    

Fb = b^2*W*r*Omega^2 --------------------------- 2*t*gWhere,Fb = Bending Stress in baldes ,Kgf/mm2b = width of blade at inlet and outlet in mm W = weight density of the material in Kg/m3r = radius of impeller at inlet and outlet in mmOmega = angular velocity in rads/st = thickness of blade in mmg = acceleration due to gravity.         Input data at Impeller inlet    r = r1 in mm 20.75 20.75t in mm 3 3b1 in mm 25 25Fb in Kgf/mm^2 0.043489257 0.043489257     Input data at Impeller Output.    r = r2 in mm 107.5 114t in mm 3 3b1 in mm 11.6 12.7Fb in Kgf/mm^2 0.048507435 0.061658955     Material : SG600/3  1.Allowable Stress for alternating load in Bending , ab in Kgf/mm2 3.3 3.32.Allowable stress for alternating stress in tension, at in Kgf/mm2 3.3 3.3Conclusion :1.Fh,Fr is less than allowable stress hence designs is safe.2.Fb is also less than allowable stress hence designs is safe.

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4.0 THERMAL RATING WITH NEW FAN

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From the comparison of the existing and new fan, we have the following data

Existing fan New Fan

i) Fan Dia (m) 0.215 0.228ii) Flow ,Q (m3/s) 0.020 0.0325iii) Speed (RPM) 1500 1500

Equivalent diameter of fan :

From fan laws we have Flow diameter3

i.e Q1 d13 ------------- 13 (For existing fan)

Q2 d23 ------------- 14 (For new fan)

Dividing eqn 13 by eqn 14, we get

=> ------------- 15

= 0.232 m > actual dia of new fan

Area under fan cooling is increased by factor = (d2/d1)2 = (0.232/0.215)2 = 1.164

Area under fan cooling with new fan = 1.164 * Area with existing fanAfc = 1.164*0.3825

= 0.4454 m2

Area under Natural convection Anc = A – Afc = 1.641 – 0.4454 = 1.1956 m2

Repeating the procedure given in section 2.6, we get

Thermal rating of Gear Box with new fan = 168 kW

5.0 CONCLUSION

1. This report represents the results of a systematic study of the problem of improving the heat dissipation from helical gearboxes.

2. We observe that Thermal rating predictions for the case of gear box with out fan cooling show departure from catalogue figures. Whereas for the case of fan cooled gearbox the mathematical predictions show good agreement with catalogue values. The reasons for this will have to be determined based on the proposed experimental study.

3. Manufacturing drawing for the improved fan has been provided. As per theoretical predictions, we expect the improvement in the Thermal rating to an extent of 10%. The actual improvement in the thermal rating of H2-200 gearbox will have to be established on the test rig itself. 6.0 REFERENCES

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1. Darle W.Dudley “Handbook of Practical Gear Design”McGraw-Hill Book Company

2. C.P.KOTHANDARAMAN and S.SUBRAMANYAN “HEAT AND MASS TRANSFER DATA BOOK” Fourth Edition, Wiley Eastern Limited 3. Dr.T.H Frost “HEAT DISSIPATION FROM GEAR BOXES” Data item submission (008) to the British Gear Association4. WILLIAM C. OSBORNE “FANS” First Edition, PERGAMON PRESS LTD

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