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Recent Patents on Mechanical Engineering 2009, 2, 179-192 17

1874-477X/09 $100.00+.00 2009 Bentham Science Publishers Ltd.

A New System for Testing Gears Under Variable Torque and Speed

Athanassios Mihailidis* and Ioannis Nerantzis

Laboratory of Machine Elements and Machine Design, Department of Mechanical Engineering, Aristotle Universi ty of

Thessaloniki, Thessaloniki, Greece

Received: June 22, 2009; Accepted: July 30, 2009; Revised: August 26, 2009

Abstract: In many applications, the transmitted power by a gearbox is fluctuating strongly. For example, in wind energy

converters the rotor torque depends on the wind velocity and therefore varyies over a wide range, whereas the rotor speed

is constant. In automotive applications, both torque and speed vary according to the driving conditions. It is evident, that

in order to test such gearboxes, test rigs are needed that enable torque and speed to vary during the test according to the

testing requirements and simulate the actual loading conditions as accurately as possible. The first part of this paper is a

review of the many known mechanical devices developed to load gears. Their advantages and disadvantages are

commented and presented. The second part describes a novel system designed and built by the authors (patent pending),

which makes it possible to apply the test torque and speed according to a given load pattern during the test of the gears. It

can further be implemented in close power loop test rigs (known also as back-to-back test rigs) such as the FZG test rig.

The gearboxes of the test rig may be similar enabling thus the measurements of the power loss and efficiency of the gear

pairs. It can also be used in the research of fatigue related surface failures, such as pittings and micro-pitt ings. The system

consists mainly of a self-locking planetary Wolfrom gear train. Its sun gear is connected to a high starting torque electric

motor, while its two ring gears are connected to the shafts ends of the two gearboxes. The operation of the motor iscontrolled by a computer. The software compares the actually applied torque, which is measured by a contactless torque

meter, with the required torque, which has been already prescribed.

Keywords: Back-to-back gear test rig, gear testing machine, FZG test rig, Ryder gear machine & IAE test machine.

INTRODUCTION

The requirements set to modern gear boxes are reallytough to meet: They need to be even more efficient, stronger,smaller, quieter, easier to produce and finally they need tocost less. Despite the impressive progress made in the lastyears regarding the analysis and simulation, experiments arestill essential. There are many modes of failure that may

appear when the load carrying capacity of a gear pair isexceeded. Tooth breakage, pittings and micro-pittings aswell as excessive wear or even scuffing are the most com-monly met. Besides the load carrying capacity, there are alsoother important parameters like efficiency and dynamicbehavior that need to be experimentally investigated. There-fore, test rigs that allow gears to operate under predefinedspeed and torque conditions are needed.

An apparently simple way to design such a test rig is toplace the test gearbox between a motor and a brake as shownin Fig. (1a). However, this design has many disadvantages:First, the motor has to supply all the power under which thegearbox has to be tested. Then, the brake has to transform itto heat that is often difficult to dissipate. High installation

cost and high energy consumption are the result. Therefore,the implementation of such designs is rather limited and suchsystems are not further discussed hereafter.

A more efficient way to load gears is to include the testgear box in a closed power loop, which can be either

Address correspondence to this author at the Laboratory of Machine

Elements & Machine Design, Department of Mechanical Engineering,Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece;Tel: +30-2310-996073; Fax: +30-2310-996037;E-mail: [email protected]

electrical or mechanical as shown in Fig. (1b) & (1c). In thfirst case, an electric motor drives the input shaft of the tes

gearbox. Its output shaft is coupled to a generator that feeds

the power back to the network. In this way, the total energy

consumption is significantly reduced. However, the draw

back of the big size of both motor and generator remains

since they have to be chosen according to the maximum tes

power, which is usually higher than the nominal. In the

second case, the input and output shafts of two gearboxe

that have exactly the same transmission ratio are connected

to each other by intermediate shafts building a closed loop. A

torque applying device can be included in the power loop

Then the applied torque loads both gearboxes. An externa

motor is used to rotate the system. In steady state, it has to

supply only the total power loss of the system and therefore

its power rating is much lower than the power that actually

loads the gears.The advantages of such test rigs are: Installation cost i

significantly reduced, since no generator or brake is neededand the driving motor has to be rated according only to thetotal power loss.

The energy consumption is also much less compared tothe simple motor - test gearbox - brake design mentionedabove. Another important advantage is that it permits thedetermination of the efficiency of the gearboxes directly bymeasuring the rotational speed and torque of the drivingmotor. Considering the high efficiency of modern gearboxeit seems extremely difficult to obtain the power loss of gearbox with acceptable accuracy just by measuring theinput and output power. For example, if the deviation of thepower measurement is + 2%, and the efficiency of the


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180 Recent Patents on Mechanical Engineering 2009, Vol. 2, No. 3 Mihailidis and Nerantzi

gearbox about 98%, the error in the determination of thepower loss is almost + 100%!

One of the firsts, who used a test rig with closed powerloop, was Rikli [1] who reported about his gear efficiencymeasurements almost a century ago. Since then, such testrigs are widely employed in a vast variety of designs to testnot only gears and gearboxes, but also other power trans-mitting machine elements such as shafts, couplings anduniversal joints.

In many applications, the power transmitted by a gearboxfluctuates strongly. For example, in wind energy convertersthe rotor torque depends on the wind velocity and therefore itvaries over a wide range, whereas the rotor speed is constant.In automotive applications both torque and speed vary

according to the driving conditions. In order to test suchgearboxes, the test rig should enable torque and speed tovary during the test according to the testing requirements and

simulate the actual loading conditions as accurately aspossible. The variation of speed can be achieved in convenient way by using either a DC motor or an invertecontrolled AC motor. A review of the relevant electric andelectronic systems used to control the speed of the drivingmotor of gear test rigs is outside the scope of the currenpaper. However, to vary the torque according to a predefined load spectrum is a challenging design task. Manypatents have been published addressing this requirementThe first part of this paper includes a review of many knowngear and gearbox test rigs showing the historical evolutionwith particular emphasis on their torque applying devices

Fig. (1). Gear test rig layouts. (a) Open power loop, (b) closed electrical loop and (c) closed mechanical power loop.


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New System for Testing Gears Recent Patents on Mechanical Engineering 2009, Vol. 2, No. 3 181

Although some of them are quite old, they are included inthe review because new materials and manufacturingtechnologies could make their implementation much morefeasible. Their advantages and disadvantages are commentedand presented. The second part describes a novel systemdesigned and built by the authors that enables to apply thetest torque and speed according to a given load patternduring the test of the gears. It can further be implemented in

closed power loop test rigs (known also as back-to-back testrigs) such as the FZG test rig. The gear boxes of the test rigmay be similar enabling thus the measurement of the powerloss and efficiency of the gear pairs. Additionally, it can beused in the research of fatigue related surface failures, suchas pittings and micro-pittings as well as wear and scuffing.

CLOSED MECHANICAL POWER LOOP GEAR TESTRIGS AND TORQUE APPLYING DEVICES

According to the way in which the torque load is applied,closed mechanical loop gear test rigs can be classified inmechanical and hydraulic systems. Other known mechanicalsystems to load and test gears having elastic elements,chains, inertial devices are not included in the reviewbecause they have not been applied to a closed mechanicalpower loop design.

Mechanical Systems

One of the most widespread test rigs is the FZG(Forschungsstelle fr Zahnrder und Getriebebau of theTechnical University Munich) back-to-back test rig, [2]. Itsprinciple of operation is shown in Fig. (2). The gears of the

two gearboxes have equal teeth numbers and consequentlythe same transmission ratio. The slow shafts are connectedby an intermediate torque measuring shaft. The fast shaftare connected by a load flange coupling that permits bothends to rotate relative to each other. When the rig is out ooperation and the coupling bolts are loose, one flange can befixed and the required test torque can be applied to the otheby means of a lever and weights. Then, the bolts are tighten

ed prohibiting thus the relative movement of the couplingflanges and entrapping in this way the applied torque in thesystem. The flanges of the torque measuring flange rotateagainst each other according to the torsional deformation othe intermediate shaft proving thus the readout of the testorque. The previously fixed flange of the load coupling cannow be released and the test rig set in operation. The powerwhich the gearboxes have to transmit, is equal to the producof the applied torque and the rotational speed. The drivingmotor has only to supply the power losses. This feature is noonly energy saving, but it also allows for the determinationof the efficiency of one test gearbox. Provided that bothgearboxes are identical, it can be assumed with sufficienaccuracy that they have the same power loss. Since no othe

sources of significant power loss are present in the poweloop, the power loss of a single gearbox can be easilyobtained by dividing the total power loss by two.

Apart from research, the FZG test rig is widely used todetermine the scuffing load carrying capacity [3-7] and thewear behaviour [8] of oils and greases, as well as theirinfluence on the friction coefficient and efficiency [9, 10and on the formation of micro-pittings [11] and pittings [1213]. The same design concept has also been used in other tes

Fig. (2). Layout of the FZG test rig.


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rigs like the IAE gear machine [14], a test rig for hypoidgears [15] and a crossed helical gears test rig [16]. Fresen etal. [17] showed an interesting test rig consisting of fouridentical test gearboxes that allows for the deter-mination ofthe power loss.

The torque applying clutch of the above test rigs issimple and reliable; however it has the drawback that theapplied torque cannot be controlled during the test. As

mentioned above, a device is needed which enables to varythe test torque during the test without interrupting it, in orderto simulate the actual loading conditions accurately. Suchdevices often employ planetary gear trains.

Lanahan [18], Klinger [19], Langenbeck [20] andBasedow [21] presented such systems. The most simple ofthem consists of a simple planetary gear train and is shownschematically in Fig. (3). Torque is applied to the planetcarrier by an auxiliary worm gearing during the test eithermanually or by a numerically controlled stepper motor. Thetest torque results from the difference in the rotation direc-tion and rate of the sun and ring gears. Figure 4 shows afurther development that employs a double planetary gear

train without ring gears. The teeth numbers of the gears arechosen in such a way that for a given rotation angle of theplanet carrier the suns rotate in the same direction but atdifferent angles applying thus the test torque. Load is appliedin the same manner to the planet carrier. The maindisadvantage of these systems is that they cannot be used if itis required to determine the power loss of one test gearboxbecause of the following reasons: First, the power flowsthrough the gears of the planetary system and causes addi-tional power losses. Second, the transmission ratios of thetest gearboxes must be exactly adapted to the transmissionratio of the planetary system and therefore, they cannot beidentical. Consequently, the power loss of one test gearboxcannot be obtained accurately from the total power loss of

the test rig. In order to tackle this drawback, Gruscka andHerrmann [22] proposed to include in the power loopanother identical double planetary system, as shown in Fig.(5). In this configuration, both test gearboxes can be iden-tical. However, the power flows through the planetary geartrains and causes additional losses making thus difficult toobtain the power loss of a single test gearbox.

Instead of using planetary gear trains, Schrderet al. [23implemented a strain wave gearing which has been previously presented by Musser [24] and was called by himstrain-wave gearing-tubular shaft. Such devices are nowadays commonly called harmonic drives and are commercially available. Their main part is a ball bearing whose crossection is elliptical instead of cylindrical as shown in Fig(6). The outer ring of this bearing has an external gearing. I

is actually a flexible gear which engages with the internagearing of a ring gear at the points near the major diameteof the ellipse. The teeth number difference is usually smaland therefore the transmission ratio is high, usually in therange 1:50 to 1:320. In the proposed configuration the shafof an auxiliary motor is connected to the inner ring. The testorque results from the difference in the rotation angles othe outer bearing ring and the ring gear. If both tesgearboxes have the same transmission ratio, the auxiliarymotor has to rotate during the test with the same speed. Thiis a drawback because the power loss of the auxiliary motoris usually unknown and decreases the accuracy in the determination of the efficiency of a test gearbox. An interestingdesign, based on the same principle, was presented by

Brggemann et al. [25]. They employed a cycloidal drivinstead of the harmonic drive as shown in Fig. (7). In thiway, they succeeded to extend significantly the upper limiof the test torque.

Besides load couplings and planetary gear trains oharmonic and cycloid drives, another interesting way to loadthe test gear boxes is to include in the power loop anadditional gear pair that generates the test torque when it imoved in the transverse direction as shown in Fig. (8)Haraldet al. [26] as well as Yano et al. [27] presented tesrigs based on this concept. These test rigs do not allow forthe determination of the efficiency of the test gear box. However, they have the advantage that they enable very rapid testorque variations.

Bader [28] succeeded in designing a test rig that did noinclude any torque applying device in the closed power loopThe simplest version of this test rig consists of twogearboxes that have exactly the same transmission ratio andare connected by two universal joints shafts, as shown in Fig(9). One of the gearboxes rests on a separate base that ismounted by a joint, which permits it to rotate around an axi

Fig. (3). Simple planetary system used to impose the test torque.


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Fig. (4). Double planetary system without ring gears used to impose the test torque.

Fig. (5). Two identical planetary gear trains without ring gears used to impose the test torque and compensate the rotational speed

respectively.

Fig. (6). A harmonic drive used to impose the test torque.


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Fig. (7). A cycloidal drive used to impose the test torque.

Fig. (8). Application of the test torque by pushing the auxiliary gear pair in the transverse direction.


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Fig. (9). Application of the test torque by rotating the complete gearbox.

parallel to the shafts of the gearboxes, applying thus the testtorque. Considering the high torsional stiffness of themachine elements included in the power loop, the resultingdeflections are small and therefore the power loss in theuniversal joints can be neglected. Hence, this test rig can beused for efficiency measurements provided that the two gear-

boxes are identical. However, this concept has the limitationthat it is not applicable in gearboxes with transmission ratioequal to 1:1.

Hydraulic Systems

Many designers replaced the simple load clutch of themechanical systems by a hydraulic torque applying device inorder to adjust the test torque by controlling the hydraulicpressure. One of the first attempts to design such a devicewas presented by Collins [29] and it is shown in Fig. (10).Collins included in the power loop an intermediate shaftwhich was provided on its both ends with helical splines thathad opposite directions. This shaft was mounted by ball

bearings inside a case that was designed to operate as abidirectional hydraulic piston. By imposing pressure in oneof the pressure compartments, an axial load was applied onthe intermediate shaft and the test torque was generated dueto its helical splines. Although it was not initially foreseen, atorque meter should be included in order to measure theactually applied test torque, since the friction on the flanks ofthe splines is proportional to the applied torque and thereforeintroduces a difficulty in controlling the torque accuratelyonly by the pressure. The device can be integrated in a testrig with two identical gearboxes. However, it does not permitthe measurement of the efficiency, because of the consi-

derable power loss in the piston bearings which are axiallyloaded.

Based on the same operating principle, Hennings [30designed a torque applying clutch consisting of a drum and disk with mating helical splines. It was controlled by ahydraulic piston, as shown in Fig. (11). However, this designhas the same disadvantages as the one previously mentionedSchneider et al. [31] used hydraulic cylinders in order toapply the test torque. One end of the cylinders was attachedto pins located on a flange assembled on the gear shaft, whilethe other end was attached to pins placed on the gear, asshown in Fig. (12). The friction in this design is no longeaffected by the test torque.

Ryder [32] replaced the helical splines by helical gearsand built a gear tester consisting of a single gearbox with twoshafts as shown in Fig. (13). These shafts are connected bytwo spur gear pairs having exactly the same transmissionratio building a closed power loop. The helix angle of thesegear pairs is different. In the original configuration, the

narrow gears were straight while the wide ones were helicalThe hub of a wide gear was designed to operate as ahydraulic piston. Therefore, by applying hydraulic pressurean axial force is imposed and the required test torque igenerated. The Ryder test rig has been widely adopted [33and is still being used in oil and gear tests especially in theUnited States. It effectively enables the variation of the testorque during operation by controlling the hydraulic pressure, but does not allow for the determination of the efficiency of a single gear pair. Obviously, complete gearboxecannot be tested in the Ryder test machine.


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Fig. (10). Intermediate shaft with helical splines mounted inside a hydraulic piston used to impose the test torque.

Fig. (11). Torque applying clutch with helical spline controlled by a hydraulic cylinder.

Fig. (12). Circumferentially located hydraulic cylinders used to impose the test torque.


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Fig. (13). The Ryder gear testing machine.

Shipley [34] introduced a torque applying device consis-ting of a drum and a rotor. Both were provided with radialwings forming pressure chambers, as shown in Fig. (14) Testtorque is generated by pressing oil in the even numberedchambers. By properly designing the unit with needle

bearings and contactless seals, friction can be minimized andtest torque can be accurately controlled by oil pressure. Thisconcept proved quite successful. The design of such devices,which are now called hydraulic rotary cylinders, has beenenhanced and they include an angle sensor, slip rings,rotating oil connector couplers and servo-valves. They arecommercially available for up to 8000 Nm torque. Klinger[19] presented test rigs equipped with a hydraulic rotarycylinder. Kugler [35] designed such a cylinder inside the hubof a test gearbox gear in order to apply the test torque, asshown in Fig. (15).

NEW TEST TORQUE IMPOSING SYSTEM

The main part of the proposed system [36] is a planetarygear train, as shown in Fig. (16). It was originally designedby Wolfrom [37] and consists of a sun gear, two sets ofplanetary gears attached to the same planet carrier and tworing gears. They are used in a many industrial, automotiveand aeronautical applications.

Loomann [38] and Mller [39] include a comprehensive

analysis; therefore, only the results will be mentioned here.

The rotational speeds of the sun gear, carrier and ring gears

fulfill the following relationship, that enables one to calcu-

late the transmission ratio according to which member drives

and which is driven.

1

zr1

zp2

zp1

zr2

s +

zr1

zp2

zp1

zr2

zr1

zs

r1 +

zr1

zs1

r2 = 0 (1)

z refers to the number of teeth and the indices s, p1, p2, r1 and

r2 to the sun, planetary and ring gears respectively. It should

be noted that the teeth number of internal gearings is always

negative.

When the Wolfrom system operates as a reducer, the sun

gear is driving, one ring gear is fixed and the other is the

driven. In this case the transmission ratio is given by the

following equation obtained directly from Eq. (1):

i =

s

r2 r1

=0

=

1zr

1

zs

1zr

1

zp2

zp1

zr2

(2

If the ring gear with the smaller teeth number is fixed, thetransmission ratio is negative, meaning that the sun gear and

the free ring gear rotate in opposite directions. By designing

the ring gears with proper profile modification it is possible

to have the planets of both sets with the same number o

teeth. In this case, very high transmission ratios can be

achieved by choosing the teeth numbers of the ring gears

close to each other.

The efficiency of such a gear train depends strongly on

which member is driving. If the sun drives, the first ring gea

is fixed and the second driven, then the efficiency ratio i

given by the following equation [38]:

red.

=

1 zr1

zs

1z

r1

zr2

1

2

1 zr1

zr2

1z

r1

zs

(3

In the above formula the power loss caused by the

bearings is neglected and the efficiency ratios of all gea

pairs are considered constant and equal to . If a ring gear i

the driving part, then the efficiency can be estimated by the

following equation [38]:

inc.

=

12

zr1

zr2

1 zr1

zr2

(4)

From the above Eqs. (3) and (4), it can be clearly seenthat the efficiency of a Wolfrom system depends strongly onthe operation mode. Further, Eq. (4) shows that the efficiency of the system, when it operates as speed increasermay become negative, which means that the Wolfromsystem is in this case self locking. This is an essentiaproperty of the system because otherwise, if the Wolfromgear train was not self locking it would not be possible todetermine the efficiency of the test gearboxes.


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Fig. (14). Hydraulic rotary cylinder used to impose the test torque.

Fig. (15). Hydraulic rotary cylinder designed inside the gear hub.


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Fig. (16). Wolfrom planetary gear train.

The above calculation of the efficiency of the Wolfromsystem is simplified, since the power loss of the bearings isnot taken into account. Nevertheless, the results of this calcu-lation are on the safe side since the decisive feature of the

proposed system is that the Wolfrom gear train is self-locking. The simplified calculation shows that the system hasthis feature. A more detailed calculation considering thepower loss of the bearings would yield an even lowerefficiency ratio.

Figure 17 shows the concept of the proposed torqueapplying system. The transmission ratio calculated by Eq. (2)is 1: 385. Assuming that the efficiency of a single gear pairis about 98.5%, the overall efficiency when the sun geardrives is 49% as obtained by Eq. (3). This means that inorder to impose a test torque of 1000 Nm only 5.29 Nm haveto be imposed to the sun gear. Consequently, it can be drivenby a small size stepper motor. When one of the ring gears

attempts to drive, the efficiency obtained by Eq. (4) is 1.02%. Consequently, the planetary gear train is locked andno braking torque is required to be applied to the sun gear.The stepper motor has to operate only while applying orvarying the test torque. Otherwise, the whole planetary geartrain, including the non-operating stepper motor rotates as ablock. Consequently, the proposed system can be used toobtain the efficiency of the gearboxes by simply measuringthe torque applied by the main motor since no power loss

occurs in the torque applying system which operates as arigid shaft.

An important design issue concerns the clearance of the

planetary gear train. Figure 18 shows some ways that havbeen proposed in order to address this issue. Butsch et al[40] proposed a cost effective way to minimize the clearanceby adjusting the relative radial position of the r ing gears andthe planet carrier during the assembly. Orlowski [41presented a Wolfrom system whose ring gears had helicagearings in opposite directions. Each planet consisted of twoparts, which had also helical gearing in opposite directions inorder to engage with the corresponding ring gear. During thassembly, they were adjusted to each ring gear. The planetwere supported on the carrier pins by needle bearings beingthus able to self-center between the two ring gears. Cesaron[42] applied the same principle to the final wheel drive oelectric trucks. Sulz [43] designed later a Wolfrom system

with bevel gears. The axes of the carrier pin were inclined bya small angle relative to the sun axis. By adjusting the axiaposition of the carrier and one ring gear, it was madepossible to minimize the clearance.

Another problem, which is common to all planetary geatrains, concerns the load distribution across the planetsOften, the sun and ring gears are left unsupported in thradial direction so that they can self-center between theplanets.

Fig. (17). Proposed torque applying system.


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In the proposed design, shown in Figs. (19) & (20), theabove issues are addressed by the following features: First,the tolerance of the planet - ring gears engagement waschosen tight and the rims of the ring gears were made thin.Second, no bearings are provided to support the carrier.Instead, it is left unsupported in the radial direction, so that itcan self-center to the ring gears. Third, the sun gear ismachined at the free end of the thin and relatively longdriving shaft, which can be easily deformed, allowing thusthe sun gear to center itself between the planetary gears. Asmentioned earlier, the stepper motor has to operate only

when an adjustment of the test torque needs to be done. Inthis case only a few rotations of the stepper motor shaft areneeded. For example, 3 rotations of the sun gear aresufficient in order to apply the maximum torque, whichcorresponds to 3.11 degrees relative movement of the ringgears. Therefore, grease lubrication proved sufficient.Current and control signals are transmitted to the steppermotor by the brushes shown also in Figs. (19) & (20). Theproposed system includes further a speed and torque mea-suring flange that measures the applied test torque duringoperation of the test rig and feeds its signals to the controlsystem of the test rig. If it is out of the predefined range, it isautomatically corrected by driving the stepper motor towardsthe appropriate direction. A user defined matrix that includes

rotational speed of the main motor, test torque and time isstored in the control system, enabling thus the testing of thegears accordingly. A significant feature of the proposedsystem is that it can be fitted in a standard FZG test rig dueto its compact dimensions.

CURRENT & FUTURE DEVELOPMENTS

The design of test rigs has improved extensively andmany layouts have been proposed, each one of them havingits particular advantages and drawbacks as outlined in thispaper. However, most of them are designed for industrial

applications and high power ratings, especially the hydraulicones. Their application range should be extended to covethe need for testing mini or even miniature gears andgearboxes.

Modern applications demand to design gears and gearboxes even more compact in order to save costs and materials. Consequently, more research has to be done on fatigueinduced failures and adapt the service life of the transmissionsystem to the service life of the complete machine. Modernlubricants should be friendly to the environment and whethepossible bio-degradable. Therefore, it has to be investigatedfurther how their lubrication properties evolve over operationtime. In order to save energy, the efficiency of power transmission systems has to be increased. New materialsincluding plastics and composites as well as coatings, havepromising properties and are becoming available. Theiapplication to gear design often seems attractive and theyneed to be experimentally evaluated. Therefore, new test righave to be designed accordingly.

The proposed torque applying system is simpler andcosts less than the hydraulic ones. Preliminary tests provedthat it can successfully impose the test torque according to given load pattern. Further, it can be easily mounted in aFZG test rig. An inherent limitation of the system is that i

does not allow for the extremely rapid load changes neededto simulate operation under heavy shocks. Forthcoming workincludes the optimization of the control system, investigationof the dynamic behavior and verification that standardizedtests can be accurately carried out.

ACKNOWLEDGEMENTS

None reported.

CONFLICT OF INTEREST

The authors declare no conflict of interest.

Fig. (18). Patented ways to reduce backlash in planetary gear trains: (a) By adjusting the radial position of carrier and ring gear relative toeach other, (b) By split double helical planets and (c) By beveled planets.


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Fig. (19). Cross section and exploded view of the new test torque imposing system.

Fig. (20). General view of the proposed test torque imposing system.


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