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 DOI: 10.1243/09544062JMES1203

2675 2009 223:Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

S K Mandal, K Dasgupta, S Pan and A Chattopadhyayhydrostatic drives. Part 2: Experimental investigation

Theoretical and experimental studies on the steady-state performance of low-speed high-torque  

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2675

Theoretical and experimental studies on the steady-stateperformance of low-speed high-torque hydrostaticdrives. Part 2: experimental investigationS K Mandal1∗, K Dasgupta1, S Pan2, and A Chattopadhyay1

1Department of Mechanical Engineering and Mining Machinery Engineering, Indian School of Mines University,Dhanbad, Jharkhand, India

2Department of Electrical Engineering, Indian School of Mines University, Dhanbad, Jharkhand, India

The manuscript was received on 4 June 2008 and was accepted after revision for publication on 12 May 2009.

DOI: 10.1243/09544062JMES1203

Abstract: The performance investigations of an open-circuit and a closed-circuit low-speedhigh-torque hydrostatic drive are presented. The modelling of both drives and determination oftheir loss coefficients are presented in Part 1 of this article (pg. 2663 of this issue). This studydetermines and analyses the overall efficiency and slip characteristics of the hydrostatic drivesusing the expressions describing the characteristics of their loss coefficients. The effects of criticalcontrol parameters of the pumps and the motor are investigated on the basis of their steady-stateperformance. This investigation is based on the performance of the hydrostatic transmissiondrives at different torque levels.

Keywords: experimental investigation, steady-state performance, efficiency, critical parameters,low-speed high-torque hydrostatic drive, open circuit, closed circuit

1 INTRODUCTION

The low-speed high-torque (LSHT) hydrostatic trans-mission (HST) drive is an essential part of modernearthmoving machineries. Obtaining the maximumefficiency of an HST drive relies on the performance ofits hydrostatic components – mainly pump and motor,whose efficiencies depend on the operating condi-tions. With the continuous improvement of the designof the pumps and motors, there is an overall increasein the efficiency of the HST drives. The efficiency ofthe drive may be further improved by controlling theexisting hydrostatic components in a creative manner.

Initial work on pump–motor loss characteristicswas developed through extensive experimental workto determine the forms and mathematical repre-sentations of each flow and torque loss term [1–6].Experiments conducted by Helduser [7] indicate thata speed-controlled hydraulic pump offers improved

∗Corresponding author: Mechanical Engineering and Mining

Machinery Engineering, Indian School of Mines University, Dhan-

bad 826004, Jharkhand, India.

email:mandalsantosh2000@yahoo.com, mandalsantosh@hotmail.

com

efficiency compared with a displacement-controlledhydraulic pump, especially at partial load. The steady-state performance of an open-circuit hydrostatic driveusing an orbital rotor LSHT hydraulic motor was inves-tigated by Dasgupta et al. [8], where the effects ofthe loss coefficients on the overall efficiency of thedrive were studied. Using such motor with a pres-sure compensated pump in an open-circuit HST drive,the quasi-static performance was analysed by Das-gupta [9]. In the recent years, Watton [10] has estab-lished an explicit steady-state performance equationof a servo-valve-controlled axial piston motor throughtheoretical and experimental investigations.

In Part 1 of this article, using the Bondgraph sim-ulation technique [11, 12], a mathematical model ofan open-circuit and a closed-circuit LSHT hydrostaticdrives is developed. The slip and the efficiencies of thedrives have been determined in terms of the loss coef-ficients of the hydrostatic components and the statevariables of the model. The variations of the loss coef-ficients of the pumps and the motor with respect tothe state variables are established through experimen-tal investigation. These variations are also recognizedby McCandlish and Dorey [4, 13], Dasgupta et al. [8]and Dasgupta and Mandal [14] in their studies onpiston-type hydrostatic machines.

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2676 S K Mandal, K Dasgupta, S Pan, and A Chattopadhyay

The performance of the hydrostatic drives mainlydepends on the performance of the pump and themotor, which are the basic components of the system.The overall efficiencies and slips of the hydrostaticdrives are predicted and validated experimentally inthis part of the article, using the expressions of theloss coefficients of the pumps and the motor obtainedin Part 1.

The bases for deciding the best combination ofpump and motor of an HST drive are critical param-eters like efficiency η, critical speed ratio αmcr,displacement ratio αpd, speed ratio αps, and loadtorque Tl.

In this article, the effects of αps in case of the open-circuit LSHT drive and that of αpd in case of theclosed-circuit drive on their maximum efficiencies arestudied. A similar theoretical study was proposed byWilson [15] for an HST drive that consists of axialpiston pump and a hydraulic motor.

2 EXPERIMENTAL RESULTS AND DISCUSSIONON THE SLIP CHARACTERISTICS AND TORQUELOSSES ON THE PERFORMANCES OF THEHYDROSTATIC DRIVES

The slip of the hydrostatic drives depends on the over-all leakage losses (Rip1, Rip2, Rem, Req) of the pumpsand the motor. The torque losses of the drives aredue to the valve port resistance Rvm of the motor aswell as to mechanical friction losses Rls of the hydro-static pumps. The nature of these losses are obtainedexperimentally and described in Part 1.

2.1 Slip characteristics of the hydrostatic drives

In Part 1 of this article, equations (38), (39), and (42)to (45) express the leakage resistances of the pumpsand the motor. Using equations (25) and (29) of Part 1,the predicted slip of the open-circuit and the closed-circuit hydrostatic drives are obtained and are shownin Figs 1 and 2. These quantities are also comparedwith the corresponding experimental data.

In general, from Figs 1 and 2, the following observa-tions are made.

1. At a given value of load torque, increasing the motorspeed ωma decreases the slip.

2. At a given value of the hydraulic motor speed,increasing the load torque Tl increases the slip.

3. At a given value of pump speed ratio αps or displace-ment ratio αpd, increasing the load torque increasesthe slip.

4. At a given value of load torque, increasing the αps orαpd decreases the slip.

The slip on the open-circuit hydrostatic drive issmaller than the slip corresponding to the closed-circuit drive at a given value of load torque. This is

due to the higher pump leakages in the closed-circuitdrive. This also attributes to the lower efficiency ofthe closed-circuit drive compared to the open-circuitdrive, the details of which are discussed in section 3.2.

2.2 Torque loss characteristics of the hydrostaticdrives

Using equations (30) and (32) of Part 1, the pre-dicted overall torque losses of the open-circuit andthe closed-circuit hydrostatic drives are obtained andare shown in Figs 3 and 4. These quantities are alsocompared with the corresponding experimental data.

The general observations made from the torque losscharacteristics, which are shown in Figs 3 and 4, are asfollows.

1. At a given value of motor speed ωma, increasing theload torque Tl decreases the torque loss.

2. At a given value of Tl, increasing ωma increases thetorque loss.

3. At a given value of αps or αpd, increasing Tl decreasesthe torque loss of the drives.

Comparing the torque loss characteristics of bothhydrostatic drives, it is found that the variation oftorque loss with the motor speed in an open-circuitHST drive at a given value of torque is greater thanthe case of the closed-circuit drive. This is particularlysignificant for medium- to high-speed range of opera-tion of the drives (50–140 r/min). This behaviour is dueto the higher variation of overall efficiency of open-circuit drive compared to the closed-circuit drive asdiscussed in section 3.2.

3 EXPERIMENTAL RESULTS AND DISCUSSIONON THE OVERALL EFFICIENCY OF THE LSHTHYDROSTATIC DRIVES

The overall efficiencies of the hydrostatic drivesdepend on the slips and the torque losses. Such lossesvary with the pump speed ratio αps or the pump dis-placement ratio αpd of the respective drives as well asthe load torque Tl. Considering the characteristics dis-cussed in section 2, the predicted overall efficienciesof the drives are compared with the correspondingexperimental data.

3.1 Open-circuit LSHT hydrostatic drive

Using equation (23), the predicted efficiency ηpo ofthe open-circuit HST drive is calculated, and it iscompared with its actual efficiency ηa in Fig. 5.

Figure 5 shows the variation of the efficiencies ofthe drive with respect to the motor speed ωma atthree different torque levels Tl and various pumpspeed ratios αps. The results are plotted using best-fit lines to the data points. The dotted and solid

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Fig. 1 Slip characteristics of open-circuit hydrostatic drive

Fig. 2 Slip characteristics of closed-circuit hydrostatic drive

lines correspond to the experimental and predictedresults, respectively. It is seen that the experimentalefficiencies throughout the test speed range of themotor at any torque level between 170 and 542 Nmare smaller than the predicted efficiencies. Within thetest range of operation, the efficiency of the HST drivevaries from 52 to 84 per cent and it is observed thatincreasing the motor speed decreases the efficiencyof the drive. The results show reasonable correla-tions between the predicted and the experimentalvalues. The predicted efficiencies are higher than theactual efficiencies by about 3–4 per cent. Therefore,the estimation of loss coefficients given by equations(38), (40), (42), (44), and (46) of Part 1 seems to bereasonable.

The overestimation may be attributed to severalaspects not accounted for in the modelling of thepump and the motor of the HST drive. Such aspectsare additional leakage paths, thermodynamic effects,

distortion around the contact surfaces, quality of thesurface finish, additional flow path around the rollersof the motor because of its distortion, etc. Further, itmay be noted that the loss coefficients of the pumpsand the motor are the major parameters influencingthe drive’s efficiency and these are estimated based onexperimental observations.

Consideration of the effects ignored in the stud-ies requires further refinement of the model, whichneed a detailed analysis of the above-mentioned fac-tors sensitive to micro-constructional variations frommachine to machine and for each unit reassembledafter overhaul and repair.

The following observations are made from the pre-dicted characteristics of the open-circuit HST drive.

1. At constant torque level and low speed range(about 30–50 r/min), increasing the motor speedωma increases the efficiency of the drive (from 80

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2678 S K Mandal, K Dasgupta, S Pan, and A Chattopadhyay

Fig. 3 Torque loss characteristics of open-circuit hydrostatic drive

Fig. 4 Torque loss characteristics of closed-circuit hydrostatic drive

Fig. 5 A comparison of predicted and experimental efficiencies

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to 84 per cent). However, the efficiency of the drivegradually decreases as its speed increases.

2. At a given value of drive speed, increasing thetorque level increases the efficiency of the trans-mission.

3. At a given value of αps, increasing the torque levelincreases the drive efficiency.

At lower torque level, with the increase in pumpspeed ratio αps, the torque losses increase (Fig. 3),which mainly predominate the overall efficiency ofthe HST drive. At the LSHT level, the slip of the drive(Fig. 1) mainly determines its overall efficiency. Lowtorque and high efficiency at comparatively high out-put speed may not be possible to achieve in such typeof hydrostatic drive because of the characteristic of thetorque loss of the motor.

However, because of the lower torque loss at highertorque level (Fig. 3), the HST drive exhibits betterperformance throughout its speed range.

With the increase in αps, the efficiency of the HSTdrive decreases. At low value of αps such type of driveexhibits better efficiency.

3.2 Closed-circuit LSHT hydrostatic drive

Using equation (27), the predicted efficiency ηpc ofthe closed-circuit HST drive is calculated. It is com-pared with its actual efficiency ηa. The variations ofthe efficiencies with motor speed at different torqueTl levels and displacement ratios are shown in Fig. 6.Such characteristics are plotted using best-fit lines tothe data points.

The dotted and solid lines indicate the experi-mental and the predicted efficiencies, respectively, ofthe HST drive. It has been observed that the actual

efficiencies throughout the test range of motor speedare lower than the predicted efficiencies. However, theresult shows a close agreement between predicted andexperimental values, which are within 4–5 per cent.Therefore, the estimation of the pump and the motorloss coefficients given in equations (39), (41), (43), (45),and (47) of Part 1 seems to be reasonable.

The higher values of predicted efficiencies over theexperimental ones are because of the several aspectsexplained in section 3.1. The predicted efficiencies asfunctions of output speed of the drive are shown inFig. 7.

The following observations are made from the pre-dicted performance of the closed-circuit HST drive.

1. In general, at a given value of load torque, increas-ing the displacement ratio decreases the efficiencyand increases the speed ωma of the drive. However,the efficiency of the HST drive decreases slightlywhen the speed of the motor decreases from 36to 20 r/min. The nature of the efficiency character-istics remains almost flat. This behaviour may bedue to the characteristics of the torque loss of thedrive discussed in section 2.2. As a conclusion, thedisplacement-controlled HST drive maintains goodefficiency for a wide range of speed and torque.

2. The maximum efficiency of the HST drive is about78 per cent, which is smaller than the speed-controlled open-circuit HST drive; this may be dueto a higher slip and torque losses.

3. At a given value of displacement ratio αpd, increas-ing the load torque Tl increases the drive effi-ciency.

As observed in Fig. 4, at a lower value of torquelevel, increasing the displacement ratio αpd, the torquelosses increase, which mainly influences the efficiency

Fig. 6 A comparison of predicted and experimental efficiencies

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2680 S K Mandal, K Dasgupta, S Pan, and A Chattopadhyay

Fig. 7 Predicted efficiency as a function of output speed

of the closed-circuit drive. At LSHT operation, thehigher slip of the drive (Fig. 2) mainly influences itsoverall efficiency.

Referring to Fig. 6, with the increase in αpd, the effi-ciency of the closed-circuit HST drive decreases. Atlow values of αpd, such type of drive exhibits betterefficiency due to its lower torque loss.

The characteristics shown in Fig. 7 indicate that therange of maximum efficiency of the drive is 72–78 percent for the test range of operation, which is smallerthan the efficiency of the open-circuit HST drive. Themaximum efficiency range of the open-circuit HSTdrive is 72–84 per cent. However, comparing the resultsshown in Figs 5 and 6, it may be concluded thatthe closed-circuit HST drive provides small variationin efficiency throughout its range of operation. Themaximum efficiency line indicated in Fig. 7 shows themaximum that can be attained at output speed from 20to 130 r/min by varying the displacement ratios from0.28 to 1.0.

4 MAXIMUM EFFICIENCY OPERATION OF THEHYDROSTATIC DRIVES

The maximum efficiency lines indicated in Figs 5 and 6give an idea about a scheme for maximum energyefficient operation of the HST drives in steady-statecondition. For a constant load torque Tl, the maximumefficiency line gives the values of the prime moverspeed ωp in case of the open-circuit drive, or the dis-placement ratio αpd in case of the closed-circuit drive,for the maximum efficiency operation. In this way, incase of open-circuit drive the pump speed is to be setand in case of closed-circuit drive the pump displace-ment ratio is to be adjusted to obtain the maximumefficiency at a given steady-state load.

4.1 Open-circuit hydrostatic drive

In Fig. 8, the maximum efficiency line has beenobtained for the output speed range from 30 to130 r/min by varying the pump speed ratio αps from0.33 to 1.0. The maximum efficiency with a given αps

occurs at a critical speed ratio (αmcr = ωma/ωmmax). Forexample, in Fig. 8, for αps = 0.41, the maximum effi-ciency obtained is 84 per cent at motor speed ωma =50 r/min and the corresponding critical load torqueTlcro = 636 Nm. In Fig. 9, αmcr is shown as a functionof αps for the open-circuit HST drive considered in thepresent investigation.

It is observed that in the HST drive considered inthe present example, a minimum value of αps = 0.15 isneeded to compensate the leakages of the pump andthe motor and to build up pressure to overcome theminimum load torque connected with the motor.

From the predicted performance of the HST driveshown in Fig. 8, the variation of critical speed ratio αmcr

with respect to critical load torque Tlcro is plotted inFig. 10, where the pump speed ratio αps varies from 0.33to 1.00. The best-fit line connecting the data pointsindicates that decreasing Tlcro increases αmcr.

From the characteristics shown in Figs 9 and 10,the following expressions of αmcr are obtained for themaximum efficiency operation of the HST drive

αmcr = −10−5T 2lcro + 0.0088Tlcro − 0.6055 (1)

and

αmcr = −0.3404α2ps + 1.488αps − 0.2182 (2)

To operate the drive at maximum efficiency, for a givenload torque, the critical output speed ωmcr and inputspeed ωp of the drive can be predicted from equations(1) and (2).

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Fig. 8 Predicted efficiency as a function of output speed

Fig. 9 Critical output speed ratio as a function of pumpspeed ratio

Fig. 10 Critical output speed ratio as a function ofcritical load torque

4.2 Closed-circuit hydrostatic drive

From the characteristics shown in Fig. 7, the variationof αmcr with respect to αpdcr is obtained and it is shownin Fig. 11, where Tlcr varies from 475 to 541 Nm.

It indicates that a minimum value of αpdcr = 0.18 isneeded to compensate the leakages of the pump and

Fig. 11 Critical output speed ratio as a function ofcritical displacement ratio

the motor of the closed-circuit hydrostatic drive and tobuild up sufficient pressure to overcome the minimumload torque connected with the motor.

Figure 12 shows the variation of the critical loadtorque Tlcrc with respect to the critical output speedratio αmcr, where the pump displacement αpd variesfrom 0.28 to 1.0. The best-fit line connecting the datapoints indicates that with increase in αmcr, the criticalload torque Tlcr increases.

From the characteristics shown in Figs 11 and 12,the following expressions of αmcr and αpdcr are obtainedfor maximum efficiency operation of the closed-circuitHST drive

αmcr = 0.0003T 2lcrc − 0.2624Tlcrc + 63.359 (3)

and

αpdcr = −0.0394α2mcr + 0.8673αmcr + 0.1765 (4)

The critical output speed and the displacement ratioof the drive are obtained from equations (3) and

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2682 S K Mandal, K Dasgupta, S Pan, and A Chattopadhyay

Fig. 12 Critical output speed ratio as a function ofcritical load torque

(4) to operate the displacement-controlled drive atmaximum efficiency.

The discrepancies found while comparing the the-oretical and the test results of the efficiencies are dueto the minor losses, such as additional leakage paths,thermodynamic effects, distortion around the contactsurfaces, quality of the surface finish, and additionalflow path around the rollers of the motor because ofits distortion. Consideration of these effects requiresmore detailed theoretical analysis and wider rangeof test.

5 CONCLUSION

In Part 1 of this article, with the help of the bondgraphtechnique, a reduced model to study the steady-stateperformance of an open-circuit and a closed-circuitLSHT hydrostatic drives has been proposed. The losscoefficients of the HST drives are identified and theircharacteristics are determined experimentally.

In this Part 2 of this article, using the nature of theloss coefficients that vary with the operating param-eters of the drive, the models are validated experi-mentally and the performances of both HST drives arestudied.

The slip of the open-circuit HST drive is smaller thanthe closed-circuit drive due to the higher leakages ofthe pump of the closed-circuit drive. This results in ahigher efficiency of open-circuit drive particularly athigh load torque.

The steady-state performance of the open-circuitHST drive indicates the following.

1. At constant torque level and low speed of the motor,there is a small increase in efficiency when themotor speed increases.

2. The efficiency of the HST drive increases when theload torque at a particular motor speed increases.

3. The drive efficiency decreases when the torque levelat a constant pump speed ratio decreases.

4. At a lower torque level, the overall efficiency ofthe drive mainly depends on its torque loss, which

increases with the increase in supply flowrate. Thisinfluences the overall efficiency of the drive.

The steady-state performance of the closed-circuitHST drive indicates the following.

1. When the motor speed increases, the efficiencydecreases gradually.

2. The characteristic curve of the efficiency almostremains flat and it indicates that displacement-controlled HST drive exhibits good efficiency for awide range of speed and torque.

3. The maximum efficiency of the closed-circuit HSTdrive is about 78 per cent, which is less than thespeed-controlled open-circuit HST drive, which isabout 84 per cent. This is because of the factthat the volumetric efficiency of the displacement-controlled pump is less than that of the fixeddisplacement pump, which attributes to the higherslip of the closed-circuit drive.

The low torque and the high efficiency at high motorspeed may not be possible to achieve in these typesof hydrostatic drives because of the role of valve portresistance of its motor.

It is observed that at a given value of load torque, themaximum efficiency of the drive occurs at a particularαps or αpd and are shown in Figs 7 and 8. Accordingly,the concerned components of the HST drive shouldbe chosen to achieve the maximum possible efficiencyfor all operating conditions. The method of achievingmaximum efficiency may be further scope of the work.

This method of predicting the performance maybe useful to the practicing engineers and it may alsobe useful for the selection of similar HST drives. Thesteady-state models proposed here would have con-siderable value to study the control aspects of theplants where such hydrostatic drives are the integralpart. It also may be useful for initial design and selec-tion of similar machine for a given application, whereone can easily obtain more economical solutions usingthe idea developed here. By measuring load torque andspeed from the slip characteristics of the HST drivesshown in Figs 1 and 2, suitable control schemes may beformulated for varying the pump speed ratio or pumpdisplacement ratio to reduce the slip of the respectivehydrostatic drives. This may be a potential future work.

ACKNOWLEDGEMENTS

The Research & Development Project Grant for1999–2004 from University Grants Commission, Gov-ernment of India, under Special Assistance Pro-gramme for carrying out the research work on thistopic is acknowledged. The authors are thankful toDr M. Rahman, Indian School of Mines University, forchecking the language of the manuscript. The authorswish to offer special thanks to the learned reviewers

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The steady-state performance of LSHT hydrostatic drives. Part 2 2683

for their valuable suggestions during preparation ofthe manuscript.

REFERENCES

1 Wilson, W. E. Performance criteria for positive displace-ment pumps and fluid motors. In Proceedings of theASME Semi-annual Meeting, 30 May–June 1948, paperno. 48-SA-14.

2 Schlossor, W. M. J. A mathematical model for displace-ment type pumps and motors. Hydraulic power trans-mission, April 1961, pp. 252–253 and p. 269; May 1961,pp. 324–328.

3 Bowns, D. E., Rolfe, A. C. J., and Chappel, P. J. A. A discus-sion of factors which affect motor torque under startingconditions, In Proceedings of the Fifth BHRA Fluid PowerSymposium, Durham, UK, 1978, paper B6.

4 McCandlish, D. and Dorey, R. E. Steady-state losses inhydrostatic pumps and motors, In Proceedings of theSixth BHRA Fluid Power Symposium, Cambridge, UK,1981, pp. 133–144.

5 Blackburn, J. F., Reethof, J. L., and Shearer, J. L. Fluidpower control, 1960 (Technology Press of MIT and JohnWiley, New York).

6 Merritt, H. E. Hydraulic control systems, 1967 (JohnWiley, New York).

7 Helduser, S. Electric-hydrostatic drive – an innovativeenergy-saving power and motion control system. Proc.IMechE, Part I: J. Systems and Control Engineering, 1999,213(I5), 427–437. DOI: 10.1243/0959651991540250.

8 Dasgupta, K., Mukherjee, A., and Maiti, R. Theoreticaland experimental studies of the steady-state perfor-mance of an orbital rotor low speed high torque hydraulicmotor. Proc. IMechE, Part A: J. Power and Energy, 1996,210(A6), 423–429. DOI: 10.1243/PIME_PROC_1996_210_70_02.

9 Dasgupta, K. Analysis of hydrostatic transmission sys-tem using low-speed-high-torque motor. Mech. Mach.Theory, 2000, 35, 1481–1499.

10 Watton, J. An explicit design approach to determinethe optimum steady-state performance of axial pistonmotor drives. Proc. IMechE, Part I: J. Systems and Con-trol Engineering, 2006, 220(I2), 131–143. DOI: 10.1243/09596518JSCE157.

11 Thoma, J. U. Simulation by bondgraph, 1990 (Springer-Verlag, Berlin).

12 Mukherjee, A. and Karmakar, R. Modelling and simu-lation of engineering systems through bondgraph, 2000(Narora Publishing House, New Delhi, India).

13 McCandlish, D. and Dorey, R. E. The mathematical mod-elling of hydrostatic pumps and motors. Proc. IMechE,Part B: J. Engineering Manufacture, 1984, 198(B3), 165–174. DOI: 10.1243/PIME_PROC_1984_198_162_02.

14 Dasgupta, K. and Mandal, S. K. Analysis of the steady-state performance of a multi-plunger hydraulic pump.Proc. IMechE, Part A: J. Power and Energy, 2002, 216(A6),471–479. DOI: 10.1243/095765002761034249.

15 Wilson, W. E. Mathematical models in fluid power engi-neering. Hydraul. Pneum. Power, 1967, 1, 136–147.

16 BS 4617. Methods of testing hydraulic pumps and motorsfor hydrostatic power transmission, 1983 (British Stan-dards Institution, London).

APPENDIX 1

Notation

Dm motor displacement rateDpc pump displacement rate in a

closed-circuit HST driveDpc max maximum pump displacement rate in a

closed-circuit HST driveDpo pump displacement rate in an

open-circuit HST driveRem external leakage resistance of the motorReq equivalent leakage resistance of the motorRvm valve port resistance of the motorRip1 internal leakage resistance of the fixed

displacement pumpRip2 internal leakage resistance of the variable

displacement pumpTl load torque of the motor shaftTlcrc critical load torque of the motor shaft

(closed circuit)Tlcro critical load torque of the motor shaft

(open circuit)Tplc predicted torque loss of a closed-circuit

HST driveTplo predicted torque loss of an open-circuit

HST driveV̇plkg leakage flowrate of the pumpV̇s supply flowrate

αmcrc critical output speed ratio of the motor(closed circuit)

αmcro critical output speed ratio of the motor(open circuit)

αpd pump displacement ratio (Dpc/Dpc max)

αpdcr critical displacement ratio (pump)αps pump speed ratio (ωp/ωp max)

η generalized efficiency of the HST driveηa actual efficiency of the HST driveηpc predicted efficiency of the closed-circuit

HST driveηpo predicted efficiency of the open-circuit

HST driveωma actual speed of the hydraulic motorωmcr critical output speed of the hydraulic

motorωmmax maximum rotational speed of the

hydraulic motorωmp predicted speed of the HST driveωp actual speed of the pumpωp max maximum rotational speed of the pump(•) time derivative of a variable

APPENDIX 2

Experimental test set-up

Before validating the steady-state models of the HSTdrives, the characteristics of various loss coefficients of

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Fig. 13 Experimental test set-up

Table 1 List of components used in test set-up

S/n Item description S/n Item description

1 Electric motor 2 Variable displacement pump3 Charge pump 4 Pressure transducer (system)5 LSHT motor 6 Gear box (1:20)7 Loading pump 8 Pressure relief valve9 Flow transducer (inlet) 10 Flow transducer (outlet)

11 Pressure transducer (outlet) 12 Pressure transducer (loading pump)13 Speed indicator (electric motor) 14 Torque indicator (electric motor)15 Flow indicator (motor return) 16 Pressure indicator (system)17 Flow indicator (motor inlet) 18 Pressure indicator (motor outlet)19 Speed indicator (motor) 20 Torque indicator (motor)21 Pressure indicator (loading pump) 22 Data acquisition system

the pumps and the motor are determined experimen-tally. Using them, the proposed models are validated. Asimplified representation of the experimental test set-up is shown in Fig. 13 for ready reference. The list ofcomponents used in the test set-up is given in Table 1.The experiment has been conducted over a wide rangeof speed and torque levels, following a standard testprocedure [16].

In investigating the performance of the HST drives,the experiments have been conducted at differenttorque levels Tl, maintaining the outlet pressureof the motor at atmospheric level. Constant loadtorque is maintained by adjusting the set pressureof the proportional relief valve of the loading unit.

As such, the transmission considered in the presentinvestigation which is used in LSHT drive, the testspeed of the motor is limited to 30–140 r/min tocover its maximum efficiency zone. The high speedof the transmission could not be achieved due tothe limitations of the test unit. Viscosity of thefluid has been kept constant by maintaining oiltemperature at 50 ± 2 ◦C. The parameters like loadtorque Tl, motor speed ωma, supply flowrate V̇s,and system pressure Pp are measured through suit-able sensors and recorded in the respective instru-ments. Summary of the major components andinstruments used in the test set-up are given inTable 2.

Proc. IMechE Vol. 223 Part C: J. Mechanical Engineering Science JMES1203 © IMechE 2009

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The steady-state performance of LSHT hydrostatic drives. Part 2 2685

Table 2 Summary of the major components and instru-ments used in the test set-up

Components Parameters

Pressure compensated axial piston pumpMake Bosch Rexroth, GermanyModel A10VSO28DR/3XRPPA12N00Displacement 4.45 × 10−6 m3/rad

Variable displacement swash plate controlled pumpMake Bosch Rexroth, GermanyModel A4VG28EP2DM1/3X–RPZC10F02DDisplacement 4.45 × 10−6 m3/rad

Radial piston LSHT motorMake Bosch Rexroth, GermanyModel MCR 3F 280 F 180 Z 32 B2 MDisplacement 4.45 × 10−5 m3/rad

Torque transducerMake Honeywell Sensotec, USAModel 2100A series data telemetry systemMaximum torque range 1000 NmAccuracy Less than ±0.05% full-scale torque

TachometerMake Syscon Instruments Pvt. Ltd, IndiaModel ST-60r/min range 0–500Accuracy Within 0.1%, FSR ±1 count

FlowmeterMake Rockwin Flowmeter India Pvt. Ltd, IndiaModel TFM 1015Flow range 0–50 l/mAccuracy ±0.5% over 10 to 100% flow range

Pressure transducerMake Wika, GermanyModel S-10Pressure range 0–200 barAccuracy �0.25%

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