Mechanical behaviour simulation for synchromech mechanism ... · 4 Mechanical behaviour simulation for synchromech mechanism improvements Fig. 2 Deﬁnition of working phases during

1

Mechanical behaviour simulation for synchromechmechanism improvementsL Lovas1, D Play1*, J Marialigeti2, and J F Rigal1

1INSA-Lyon, Genie Industrial, Villeurbanne Cedex, France2Budapest University of Technology and Economics, Hungary

The manuscript was received on 10 November 2004 and was accepted after revision for publication on 30 March 2006.

DOI: 10.1243/09544070D21604

Abstract: This paper deals with the synchromesh behaviour of the manual car gearbox. Firstly,the state of the art on Borg–Warner-type synchronizers is presented. Then, the gear-changingprocess is studied and eight main operating phases are defined. The phases are described usingclassical tribological, mechanics and thermodynamics theories. Models are interconnectedto describe synchronizer behaviour and they are included in a numerical simulation soft-ware. Measured data are compared with the results of simulation software. Then, stick-slipphenomenon during gear changing is studied. Stick-slip is supposed to be present in twocontact zones: sleeve splines and the synchronizer cone. The effects in both zones are discussed.Finally, double bump phenomenon is studied. Double bump is assumed to be the maximumaxial operating force coming from short successive phases at the end of the gear-changingprocess. Due to the angular integer division of splines and to the non-definite angular positionof mechanical parts, sliding sleeve displacement into the ring and gear claw clutch splinesgives secondary angular rotation and large increases in the axial operating force. The modelcan explain large variations and random dispersion of the measured double bump force peaks.

Keywords: manual gearbox, synchronization, second bump, numerical simulation

1 INTRODUCTION 1. To make the angular velocity difference betweenthe synchro hub and the gear to be engaged at

Manual car gearbox synchronizers are complicated zero. This task is called ‘synchronization’;mechanical structures. They ensure the connection 2. To prevent gear changing when there is aof three main parts of the transmission (Fig. 1; see difference of angular velocity. This task is calledalso Fig. 31). The synchronized side of the trans- ‘interdiction’;mission is made up of the disengaged plate clutch, 3. To move the synchro sleeve between the syn-the input shaft of the gearbox, and the connected chronizing splines;gears. The synchronizing side is composed of mech- 4. To allow power transmission when gear changinganical parts up to the wheels of the car. The manual occurs.gear-changing mechanism consists of forks andshafts moved either by actuators or by hand. Variations in the angular velocity difference are

As the dynamical behaviour of these three mech- usually obtained by conical friction clutches, whileanical parts is complicated to simulate, owing to the the power transmission is usually done by splinelarge number of elements involved, it is not easy coupling. One, two, or three conical surfaces areto study the entire gear-changing process in detail. considered, depending on the torque transmitted.The following study considers only synchronizer Clearly, a wide variety of technical solutions existsbehaviour, with the four following aims: but the same types of problem are found. In this

paper, the Borg–Warner-type synchronizer with oneconical surface clutch is considered (Fig. 1). Note also* Corresponding author: INSA-Lyon, Genie Industrial, Bat Jules

that only three centring mechanisms are taken intoVerne, 20 Av. Albert Einstein, Villeurbanne Cedex, F-69621,

France. email: [email protected] account.

D21604 © IMechE 2006 Proc. IMechE Vol. 220 Part D: J. Automobile Engineering

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The Charlesworth Group, Wakefield 01924 204830

2 Mechanical behaviour simulation for synchromech mechanism improvements

Fig. 1 Main parts of a gearbox transmission

2 STATE OF THE ART effects of different linings on cone surfaces andthe effects of grooves on the synchro ring conical

Although synchronizers have been used since the surface. The proposed linings allow the shift forcelate 1920s, it was not until several years later that to decrease as well as time for speed changing.scientific papers describing their behaviour appeared. At the same time, linings are not so sensitive toIn the late 1960s, a global description was given [1] variations of oil type and to less severe manu-and used extensive technical experience to formulate facturing tolerance requirements for conical parts.simple mechanical equations to describe synchron- They also have a significant damping effect onization and interdiction. In the early 1980s, the effect changing force. The study of conical surface grooveof different linings on the conical surface clutch was effects has led to proposed optimized values forstudied [2–4] and the increase of transmitted power groove dimensions [1, 15, 16]. The grooves mayhas led to new developments such as multicone have either an axial or circumferential geometricsynchronizers, once again using simple mechanical position. The axial grooves are shown to needtheory [5–8]. During the last decade, simulations of less changing force, but are more influenced byglobal mechanical behaviour have called on classical geometrical errors due to manufacturing and wearsoftwares (Matlab Simulink, Adams) [9–11]. All these occurring during operation.contributions can be classified into the following 3. The description of synchronizer behaviour duringcategories: gear changing, using numerical simulation soft-

ware models, with a comparison of experimental1. The description of new synchronizers, with littleresults including the study of the dynamicaltheory and the main focus on discussion of experi-behaviour of the gear-changing mechanism, syn-mental behaviour [12–14]. These papers placechronizing, and the synchronized parts of theemphasis on the structure of the synchronizer andtransmission. The gear-changing process has beendescribe its advantages. Synchronizing solutionsstudied using various models, and is distinguish-usually permit decreasing either the shift force orable by various working phases. The comparisonthe time needed for gear changing.between measured data and the results from2. The description of angular velocity synchron-numerical simulation highlight the effect of para-ization. Hydrodynamic calculations and a tribo-

logical approach are introduced, such as the meters such as conicity angle, conicity angle error,

D21604 © IMechE 2006Proc. IMechE Vol. 220 Part D: J. Automobile Engineering

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3L Lovas, D Play, J Marialigeti, and J F Rigal

cone friction coefficients, spline chamfer angle, 3 A STUDY OF SYNCHRONIZER WORKINGnumber of cones [8], and number of splines [9]. PHASESThe dynamics of the manual changing mech-anism, joining the gear lever and the gearbox by Studying synchronizer behaviour requires a detailedcables [10, 9] and rods [17, 18, 8] have been knowledge of the gear-changing process. Differentshown to have an effect on gear-changing force. relative positions of the synchronizer parts, as wellThe effect of torsional dynamics of the trans- as the characteristic points of both synchronizedmission has also been studied [19, 20] with the angular velocity and the axial force variation, enableintroduction of the gear backlash effect. To con- successive phases to be distinguishable. The numberclude, widely recognized problems exist, such as of phases depends on the limits of the relative studiessecond bump, gear-changing noise, or impossible and on the type of model formulated for the gear-gear changing, the reasons for which are still changing process. Thus, the number of phases variesunknown. in the literature from four [20] to eleven [10]. In this

4. The study of shift feel and approach from the study, the gear-changing process is described fromdriver’s point of view. A simple dynamical study the neutral-gear lever position to the position whenof the transmission is performed in order to the sleeve has meshed the gear. The gear-changingexplain gear-changing problems such as noise and process is divided into eight phases, illustrated inimpossible gear changing. Usually, these problems Fig. 2. The model limitations are given either byare attributed to the torsional vibrations of the synchronizing torque variations, angular velocitytransmission, torsional backlashes [20], or are variations, or variation of the relative position of thededuced from variations of the force applied on mechanical parts.the sleeve during gear changing [18]. The difficulty In numerical simulations, synchronizer behaviourof obtaining objective measurements was dis- was studied in two environments [22]: either mountedcussed [21]. All these papers give an idea about on a test rig or working in a given gearbox archi-the variety of gear-changing problems and define tecture. Each environment has its own dynamicalthe characteristics of optimal gear changing and power loss characteristics. Many synchro ringfrom the user’s point of view. They attempt to link, geometries and materials were tested in bothas far as possible, human perception of gearshift environments; hence the following figures in theand the mechanical data [5]. For example, a time- text illustrate many cases. Thus, synchronizationsynchronization integral has been introduced durations and synchronizing force maximum values[21, 9], corresponding to the sum of loads during can change from one figure to another, dependingthe synchronization phase. on the case in question.

New advances in synchronizers as well as increased3.1 Presentation of working phasestransmitted power and actuating load control give

rise to new technical problems that in turn must be In order to illustrate part positions during gearaddressed. For example, a high experimental force changing, only the splines of the sleeve, the ring,peak is sometimes seen after the synchronization and the gear are shown (Fig. 3). Note that an innerphase. This peak is called the second bump. The view of the sleeve is given in order to facilitateamplitude of this second bump of axial force cannot visualization. In fact, the real position of the sleeveclearly be explained and is then difficult to simulate. splines in relation to the meshing of the other mech-The occurrence of the second bump and its size seem anical parts is reversed. The following descriptionsto be random phenomena. It is also assumed that of phases are based on experimental visualizationsthis force is responsible for the cracking noise during made with a high-speed videocamera during specificgear changing. Furthermore, some other phenomena gearbox tests not reported here.are not clearly explicable, such as the wear of thecoupling spline chamfers of the synchro ring. These 3.1.1 First free fly (Phase 1)poorly understood phenomena make it difficult to

Free fly means that the sleeve moves forward axiallyoptimize synchronizer performance. Consequently,without significant mechanical resistance (Fig. 4).this study reviews all the process and mechanicalDuring this phase, the sleeve also displaces themodels in greater detail. It begins with a descriptioncentring mechanisms that push the synchro ringof the successive phases of synchronizer behaviour.towards the cone of the gear. The axial velocity ofThen, simulation models are presented and, finally,the sleeve is high, the required axial force is low,the stick-slip phenomenon in synchronizers and

second bump are studied in detail. and both are constant. The equations describing the


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Fig. 2 Definition of working phases during the gear-changing process

Fig. 3 Presentation of the main parts of splines

Fig. 4 Variation of the spline position during the first free fly (Phase 1)

force and angular velocity variations are given in on the sleeve increases. The force is transmitted fromthe sleeve to the balls of the centring mechanisms,Appendix 2, Section 2.4.then to the side of the synchro ring. The equilibriumof the balls is ensured by springs. When the trans-3.1.2 Start of the speed synchronization (Phase 2)mitted force reaches a given level, it cannot be

The spline position at the start of speed synchron- balanced by the springs and the balls of the centringization corresponds to the final position of the pre- mechanisms withdraw into their housings. The

sleeve moves forward slightly and the sleeve splinesvious phase (Fig. 4). The axial pushing force applied


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enter into contact with the splines of the synchro 3.1.4 Turning the synchro ring (Phase 4)ring. The axial force is transmitted directly from

If the angular velocity difference reaches zero,the sleeve to the synchro ring. As the synchro ring

the friction phenomenon stops. The synchro ringapproaches the gear cone, it compresses the oil

previously heated by the dissipated friction energytrapped between the synchro ring and the gear

loses the heat and its diameter decreases. It soonconical surfaces. With the decrease from the normal

becomes stuck on the gear cone. The resistant forcedistance between the conical surfaces, the oil film

component on the spline chamfers disappears. Thepressure increases. Thus, a rapid increase of axial

sleeve starts to move axially (Fig. 5). At the same time,force is needed to achieve gear changing. In order to

a decreasing axial force is imposed. The displace-break the hydrodynamic oil film and minimize force

ment of the sleeve turns the synchro ring and theincrease, grooves are made in the conical surface of

gear while the chamfers remain in contact. Thethe synchro ring. In this study, only radial groove

axial velocity of the sleeve increases from zero toeffects are discussed. The grooves help to break the

maximum. The axial force falls to a minimumoil film and remove the oil. During this phase,

value. As before, the equations describing the forcethe axial velocity of the sleeve decreases to zero. The

and angular velocity variations are well known andequations describing the force and angular velocity

displayed in Appendix 2, Section 2.3.variations involved are well known and displayed inAppendix 2, Section 2.1.

3.1.5 Second free fly (Phase 5)

3.1.3 Angular velocity synchronization (Phase 3) The synchro ring stops turning when the splinechamfers separate. The sleeve moves forward axially

The spline position of each mechanical elementuntil approaching the spline chamfers of the gear

during angular velocity synchronization corresponds(Fig. 6). The axial velocity of the sleeve is maximal

to the final position of the first phase (Fig. 4). Afterwhile the required axial force becomes minimal.

most of the oil has been evacuated, mixed lubri-During this phase, the sleeve meshes with the synchro

cation takes place between the conical surfaces.ring. The angular velocity of the gear is assumed

An increasing axial force is applied and then main-to be equal to that of the sleeve. The equations

tained practically at a constant high level of 500–describing the force and angular velocity variations

700 Newtons. The mixed friction consumes theare also well known and displayed in Appendix 2,

kinetic mechanical energy difference, and the angularSection 2.4.

velocity difference between the sleeve and the geardecreases towards zero. While an angular velocity

3.1.6 Start of the second bump (Phase 6)difference exists, the equilibrium of axial andtangential forces applied on the spline chamfers When the spline chamfers of the sleeve and that of

the gear approach each other (Fig. 7), a thin film ofprevents continuation of the gear-changing process.This phase usually lasts for approximately half of oil is formed again between the chamfer surfaces.

The compression of the oil film requires an increasethe gear-changing time. The equations describingthe force and angular velocity variations are also well of axial force in order to maintain the axial velocity

of the sleeve. Normally, this increase is not enoughknown and displayed in Appendix 2, Section 2.2.

Fig. 5 Variation of the spline position during turning of the synchro ring (Phase 4)


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Fig. 6 Variation of the spline position during the second free fly (Phase 5)

Fig. 7 Variation of the spline position during the start of the second bump (Phase 6)

to maintain the axial velocity and the sleeve slows at a constant velocity, a narrower turn angle requiresmore force to accelerate and turn the gear in adown while the oil film is broken, as can be seen in

[11]. Then, the axial force increases strongly as the shorter time. This phase constitutes the second andmajor part of the second bump phenomenon. Theoil is discharged and the metallic chamfer surface

becomes compressed. This axial force increase stops turning force is completely independent of the forceseparating the gear and the synchro ring. Thewhen the tangential force component from the force

equilibrium on the chamfers is high enough to turn equations describing the force and angular velocityvariations are given in Appendix 2, Section 2.6.the synchro ring previously stuck on the cone. The

synchro ring then becomes free, and the sleeve cancontinue the axial displacement. The consecutive 3.1.8 Final free fly (Phase 8)increase of the axial force is the first component of

After turning the gear, the sleeve moves forwardthe phenomenon called double bump. Here also, theaxially and meshes the splines of the gear. The axialequations describing the force and angular velocityvelocity of the sleeve reaches a maximum value andvariations are displayed in Appendix 2, Section 2.5.the axial force becomes minimal. The equationsdescribing the force and angular velocity variations3.1.7 Turning the gear (Phase 7)are also given in Appendix 2, Section 2.4.

After separation of the synchro ring and the gearcone, the sleeve turns the gear when it moves

3.2 Models for synchronizer behaviourforward with low axial velocity (Fig. 8). Clearly,

simulationthe axial force required for turning depends on therelative position of the sleeve splines and the gear A simulation using a numerical model was per-

formed in order to describe synchronizer behaviour.splines. This relative initial position is obtained atthe end of synchronization. If the turning angle is The model consists of eight units, each of which

describes the previously mentioned phases. Eachwide, the force required is low. If the angle is narrow,the force amplitude can reach a high level. As the unit contains iteration loops that calculate the

interactions between the mechanical parts and takeaxial displacement of the sleeve is assumed to occur


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Fig. 8 Variation of the spline position when turning the gear (Phase 7)

into account the variations of the main parameters. force is still present, the synchro ring cannot movedown on the cone. The mean synchronizing diameterThe models used in the numerical simulation are

described below. decreases, surface pressure increases, and the synchroring remains stuck on the gear cone (Fig. 9). Thismodel is described in [15]. Separation of the synchro3.2.1 A model of power losses in the gearboxring from the gear cone needs a second bump force

In a gearbox, power losses come mainly from threepeak (see Section 4.2.1).

sources. Firstly, power losses in roller bearings arecalculated with the Palmgren formula referred to in

3.2.3 The elastic deformation model of the synchro[23] and [24]. Classical hydrodynamic formulae are

ringused in the case of hydrodynamic plain bearings [23].Secondly, power losses due to the friction of seals Due to machining tolerances, the conicity angles

of the synchro ring cone and gear cone canused to isolate the oil are calculated with empiricalformula given in [24]. Thirdly, oil-churning power differ. A conicity angle error is defined (Appendix 2,

Section 2.1). In this study, only positive values arelosses are calculated with formulae developed by [25]and [24] for given ranges of oil immersion and oil considered as defined in Fig. 10. As the synchro

ring is far less rigid than the gear cone, the syn-temperature. Clearly, a gearbox contains many bear-ings, gears, and isolation seals and, consequently, chronization force produces considerable displace-

ment and tends to rotate cross-sections of thepower losses are non-negligible [26]. During gearchanging, the clutch is supposed to be disengaged; synchro ring, reducing Da towards zero (Fig. 10). This

phenomenon is analytically described in [15] andthus, friction on the clutch plate does not influencethe gear-changing process. visualized through finite element simulations in [27].

Conicity angle difference values from Da=0.05° toDa=0.25° were calculated from measured gear cone3.2.2 The heating model of the synchro ringand synchro ring conicity angles [27, 28]. Note that

During synchronization, friction occurs between thethese values change owing to continuous wear of

conical surfaces of the synchro ring and the gearcone. The friction converts kinetic energy into heat.One part of the dissipated heat is absorbed by thegear, the other part is absorbed by the synchro ring.It is assumed that the thermal mass (the mass of thepart multiplied by the thermal capacity) of the gearis much higher than that of the synchro ring. Thus,the increase of the gear bulk temperature is notsignificant. However, the synchro ring bulk tempera-ture increases (Dt=4–9 °C) and results in thermalexpansion. Thus, the cone radius of the synchro ringincreases. Meanwhile, the axial synchronization forceis still present and pushes the synchro ring higherand higher on the gear cone. Clearly, heat production Fig. 9 Displacement of the synchro ring issued from

thermal dilatationsstops at the end of synchronization. As the axial


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separation less than 10−5 mm). Contact damping cc

can also be introduced (5Ω105 Ns/m [23] for a surfaceseparation less than 10−5 mm) coming from the oilfilm. A geometrical model describing the approachof the sleeve chamfer and the gear chamfer surfaceis given in Fig. 11 [23]. Equations describing theprocess are given in Appendix 2, Section 2.5.

3.2.5 A gear-turning model

After separation of the synchro ring from the gearcone, the sleeve has to turn the gear. The equationproposed to describe the turning force can be foundFig. 10 Model of deformation for the synchro ringin Appendix 2, Section 2.6. During turning, the axialvelocity of the sleeve increases from the value result-the conical surfaces. Conicity angle error provokes aing at the end of the previous phase to the maxi-quick axial force increase at the start of the synchron-mum value. As axial and tangential velocities areization phase [16]. On the other side, synchro ringconnected on the spline chamfers, axial accelerationdeformation caused by axial force in the presence ofcan be computed from the tangential acceleration.conicity angle error results in sticking of the synchro

ring on the gear cone. Thus, separation of thesynchro ring from the gear cone also needs a second 3.2.6 A model of stick-slipbump force peak. Heating and elastic deformation

The stick-slip phenomenon appears when a mass iseffects are supposed to be independent of each other

placed on a surface and moved there by a com-in the computation model, and their effects are

bination of stiffness and damping (Fig. 12). Variousadded for computation of the second bump force

phenomena can be observed that depend first on(see Section 4.2.)

mass, surface friction, and sliding velocity on thecontact surface and, secondly, on elasticity and

3.2.4 A model for the start of the second bumpdamping loads parallel to the sliding velocity. Ifthe normal force is low and the sliding velocityAs the sleeve approaches the gear spline chamfers,

an oil film is created between the chamfer surfaces. is high, simple sliding is observed. If the normalforce increases and the sliding velocity decreases,Contact elasticity coming from oil-film compression

can be introduced [11, 10] and an increase of contact harmonic oscillations are observed. Finally, when thenormal force is high and the sliding velocity is low,stiffness k

cas a result of surface asperity compression

can also be introduced (106–5Ω107 N/m for a surface harmonic oscillation phases are interrupted by linear

Fig. 11 Spline chamfer contact geometry


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(Fig. 14). As both normal forces and sliding velocitieschange considerably during the gear-changing pro-cess, it is assumed that stick-slip oscillations will varystrongly, and all three previous forms of amplitudeoscillations will occur.

3.3 A brief survey of the numerical simulationFig. 12 Model of the stick-slip

software and validation

The numerical simulation model was developed ondisplacement phases. The latter phenomenon isa Delphi informatics’ environment (Pascal language)called stick-slip (Fig. 13). An equation describing theusing a simple modular structure. Each moduleprocess is given in Appendix 2, Section 2.7.corresponds to one of the previously mentionedIt is assumed that stick-slip phenomena appearworking phases. The modular structure enables tobetween contact surfaces in the synchronizer. Thestudy each working phase on a desired descriptivefirst contact surface is the side surface of the sleevelevel of mechanical behaviour to be studied, and thisspline. Here, the normal force is the local tangentiallevel as a function of local conditions to be modified.force, and the sliding velocity is the axial velocityIn each module, iteration loops allow the variationof the sleeve (Fig. 14). The second contact surface isof parameters describing the behaviour of the partsthe gear cone. Here, the normal force comes fromto be calculated. The main modules and iterationthe axial force and the sliding velocity is given by theloops are presented in Fig. 15.angular velocity difference of the two cone surfaces

The governing parameters are either the axialvelocity, or the axial force applied on the sleeve.Only one of them is applied for a specific numericalsimulation, depending on the studied working phaseand the actual geometric position of the parts. Thesoftware has more than 60 input parameters thatensure highly flexible use and permit adaptationsto various boundary conditions. Furthermore, thesoftware takes into consideration the effect of gear-box architectures: the number and type of bearingsas well as lubricant type, oil quantity, temperature,and inertia of mechanical parts.

The numerical values of parameters transmittedfrom one phase to another are the sleeve axialposition, synchronized angular velocity, and theFig. 13 Variations of oscillation amplitude depending

on exiting velocity vb

axial force applied on the sleeve. When computing

Fig. 14 The contact surfaces concerned: a) the sleeve spline side, b) the cone of the gear


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Fig. 15 Structure of the simulation software

Phase 1, the sleeve axial velocity is considered to Phase 5 is computed in the same way as Phase 1.The sleeve has to move axially in order to mesh thebe constant. The axial force is computed from the

equation given in Appendix 2, Section 2.4. Phase 1 synchro ring (Fig. 6).In Phase 6, the sleeve approaches the gear splinesends when the normal distance between the conical

surfaces of the synchro ring and the gear cone (Fig. 7). The relative position between the sleevespline side chamfers and gear spline side chamfersbecomes small enough for the application of hydro-

dynamics laws. is an input data. Sleeve axial velocity decreaseswhen the contact force increases on the spline sideIn Phase 2, the relationships of both the decreasing

axial velocity and the increasing axial force (Fig. 28) chamfers. When axial velocity falls below a givenlimit, an axial force increase is needed to maintainare given. Synchronized gear angular velocity is com-

puted from hydrodynamics equations (Appendix 2, the contact. At the same time, the sticking force ofthe synchro ring on the gear cone is computed fromSection 2.1). The phase ends when the axial force

becomes big enough to break the oil film. conicity angle error (input data) and synchro ringthermal expansion owing to accumulated heat. WhenIn Phase 3, the axial force increases based on the

preceding phase conditions. Synchronized angular the tangential component of the axial force appliedon the spline chamfers is high enough (Fig. 29),velocity is computed from mixed lubrication

equations (Appendix 2, Section 2.2). Heat produced the synchro ring is set free and the phase is over(Appendix 2, Section 2.5).from the dry friction part of the mixed lubrication is

also computed, in addition to the distributions of In Phase 7, the sleeve turns the gear. The necessaryturning angle (Fig. 8) comes from the spline relativeheat into the synchro ring and gear. Oil viscosity

variation between the conical surfaces as a result of position, given as input data. The equation forturning is given in Appendix 2, Section 2.6. As theheat dissipation is taken into consideration. Phase 3

ends when the synchronized angular velocity equals axial velocity is given, the turning force amplitudedepends on the turning angle. Because of turning,the synchronizing angular velocity.

For computing Phase 4, the relationships of both the synchronized angular velocity is different fromthe synchronizing one. The phase ends when gearaxial force decrease and sleeve axial velocity increase

are given. The equation for turning is given in turning is finished.Phase 8 is again a free fly phase when the sleeveAppendix 2, Section 2.3. Because of mechanical part

turning, the synchronized angular velocity differs meshes gear splines. It is computed like the previousfree fly phases.from the synchronizing one. The phase ends when

the synchro ring is turned with an angle issued from Power losses are computed in each step of com-putation and refreshed values are introduced inthe spline geometry (Fig. 5).


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motion equations. Occurrence of stick-slip is observed test bench was used. The numerical simulationand measurement data display similar character-in each non-free fly phase. If limit conditions are

reached, axial or tangential stick-slip equations are istics to the literature in three main zones (Fig. 16).The first zone is that of the constant axial forcecomputed and the position of mechanical parts is

modified. applied on the synchro ring. The calculated axialforce equals the mean experimental 240 N forceThe synchromesh behaviour, for a JH five-speed

car gearbox (Fig. 31) was simulated. Based on gear- during this period. The measured data display axialforce oscillations, which are not considered in thebox architecture, synchronized inertias were com-

puted for each speed. Power losses issued from simulation. On the one hand, this variation can beattributed to the fact that small contact zones existrolling bearings and from the oil-churning of the

gears were computed depending on the instant between the synchro ring and the gear cone insteadof the whole apparent contact surface. As the twoangular velocity of each part. The numerical results

confirm the variation of the gear-changing time parts are in rotation with different angular velocities,and both have eccentricities, friction conditionsas a function of engaged speed (Fig. 32), engaged

inertia and changing axial force (Fig. A6) (Appendix 2, can vary during angular velocity synchronization.Therefore, force variations can appear.Section 2.8).

The numerical results for synchronisation behaviour The second cause of force variation can beattributed to the stick-slip phenomenon and will bewere also compared to measured data published in

the literature [18] using the same initial conditions. discussed later. A 700 N second bump of axial forceis then calculated (Fig. 16), corresponding also to theSynchro ring and cone parameters, and command

parameters were set as described [18]. For numerical amplitude of the measured second bump load [18].Furthermore, the measured angular velocity presentssimulation, the inertia and power loss model of the

Fig. 16 Data for validating the simulation software. The numerical test-bench environment withsynchro and command parameters from [18]


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a desynchronization period after reaching the syn- way, oscillation is present in the axial force that isapplied on the synchro ring by the sleeve.chronization point that corresponds to the turning

phase of the ring [18]. This desynchronization isequal to 35 r/min; a similar value is obtained by 4.1.1 Three small bumps on the axial force plateaunumerical simulation (Fig. 16). Then, two small peaks

With appropriate stick-slip parameters (hR=0.063

can be observed on the measured angular velocitykgm2, c

Q=1 Nms/rd, k

Q=500 Nm/rd, m

m=0.1, m

v=0.2,

curve. The first peak is the smallest and is assumedv

m=45 rd/s, Da=0), the simulated axial force (Fig. 16)

to be as a result of the turning of the ring, while theand the measured axial force [18] have similar shapes

second higher peak corresponds to the turning ofand the oscillation amplitudes have similar orders of

the gear. The same amplitudes are also obtainedmagnitude. In this case, low torsional elasticity is

from the numerical simulation.used and the sliding velocity limit is very high. Insuch a configuration, the bumps on the axial forceplateau can be reproduced, because the sliding

4 PRESENTATION OF RESULTS AND velocity limit when stick-slip appears is reached in anDISCUSSION early moment of angular velocity synchronization.

As the angular velocity difference between theThe numerical simulation software enables the study synchro ring and synchronized gear cone decreasesof eight working phases of synchronizer behaviour. quickly, and torsional stiffness is relatively low, thereThe following discussion is restricted to the role of is no time for the formation of classical stick phases.the stick-slip phenomena and to the second bump The simulated axial force (Fig. 17) oscillates aroundobservation. a mean value of 500 N with an amplitude of 10 N,

which represents a variation of 2 per cent. The meanvalue and the amplitude of the measured force have4.1 The role of stick-slip phenomenathe same magnitude.

Harmonic axial force oscillations with small ampli-tudes are observed in various phases [Fig. 2, see

4.1.2 No bump on the axial force plateau butalso Fig. 23(b)], and they do not have a considerable

oscillations at the endeffect on the gear-changing process with the givenboundary conditions. The applied elasticity, damp- Using sliding parameters similar to those published in

[30, 31] (hR=0.063 kgm2, c

Q=1 Nms/rd, k

Q=250 000ing, and mass data come from the literature [18, 29].

On the contrary, stick-slip phenomena are assumed Nm/rd, mm=0.1, m

v=0.2, v

m=9 rd/s, Da=0), the

simulation result obtained is a flat plateau [32].mainly to take place between two contact zones ofthe synchronizer: at the sleeve spline side contact Harmonic oscillations appear only at the end of the

synchronization process, a short time before the finalsurface and at the conical surfaces. Numerical simu-lation results allow discussion as to whether stick- synchronization (Fig. 18). The oscillating frequency

is high and the axial force amplitude is about 12 N,slip on the spline-side surfaces can exist. Numericalsimulations confirm significant stick-slip effects on considered as negligible for governing the angular

velocity of the gear. With this first set of parameters,conical surfaces, also. Various types of behaviour canbe obtained as a function of the involved stick-slip stick-slip oscillations appear only just before the

synchroni ation, and have no effect on the end ofparameters while using the same changing forceand sleeve velocity command. The main parameters the synchroni ation.

However, by modifying the friction coefficientsinfluencing stick-slip phenomena are torsionalinertia, elasticity and damping, dynamic and static on the conical surfaces and the spline chamfers

( fs=0.04, f

2=0.1; h

R=0.063 kgm2, c

Q=1 Nms/rd,friction coefficients, and critical sliding velocity

when harmonic oscillations appear. Only orders of kQ=314 000 Nm/rd, m

m=0.1, m

v=0.2, v

m=4rd/s,

Da=0), examples can be found where stick phasesmagnitude of the parameters were used. The studyof parameters makes it possible to distinguish the occur before synchronization (Fig. 19). This can

happen when the friction conditions on the conefollowing cases.When stick-slip appears, firstly oscillating move- and dynamical behaviour of the transmission during

gear-changing are not adapted. During the stickment is superposed on the decelerating motionof the synchronized gear. Instant force equilibrium phenomenon, the synchro ring and gear turn together.

The sleeve interprets this as if there were no inter-between the synchro ring and gear cone follows themovement oscillation. Thus, oscillation in the instant diction and thus moves forward axially (Fig. 20).

Then, harmonic oscillation occurs. The sleeve stopsforce equilibrium on the synchro ring appears. In this


d000001604 08-05-06 22:20:18 Rev 14.05



Fig. 17 Results from simulating the plateau with three bumps. The numerical test-bench environ-ment, synchro, and command parameters from measurements; stick-slip parametersfrom section 4.1.1.

Fig. 18 No bumps on the plateau. The numerical test-bench environment, synchro, andcommand parameters from measurements; stick-slip parameters from section 4.1.2.

because the interdiction force appears again. Next, the second bump results from the separation of thesynchro ring and the gear cone, and lasts a very shortanother stick phenomenon follows and the sleevetime. The force peak in the second part of the secondmoves forward again.bump results from the turning of the gear and lastsIf the sleeve reaches the end of the synchrolonger. As the overall duration of the bump is lessring gear chamfer well before the theoretical syn-than 2×10−2 s (Fig. 16), these two successive phaseschronization time, synchronization is performedare difficult to distinguish from test measurementsinstantaneously by shocks and the gearbox emits aand visualizations. However, a distinction must berattled synchronizer noise. At the same time, bothmade: the first part is influenced mainly by synchrosleeve and synchro ring splines suffer heavy wearring material, cone and spline chamfer frictiondamage.characteristics, and surface conicity error [28], whilethe second part depends on spline chamfer friction

4.2 Discussion of the second bump phenomenoncharacteristics and the relative spline position of the

It was assumed that the second bump phenomenon synchro ring and the gear. In order to decreaseis in fact constituted by two force peaks with different the second bump peak, different parameters have to

be considered in both cases.origins. The axial force peak in the first part of


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Fig. 19 Stick at the end of the synchronization phase (numerical test-bench environment,synchro, and command parameters from measurements)

Fig. 20 Forces on the sleeve during synchronization with stick-slip

4.2.1 The separation force peak sum of two force components. The first part ofthe tangential force is the force needed to counter-

At the end of the speed synchronization, the synchro balance the pressure that the synchro ring exercisesring is pushed against the gear cone but it is in a on the gear cone when stuck on it. This pressurethermal expansion state and deformed geometric comes from two sources: from synchro ring defor-position. The difference of angular velocity then mation because of conicity angle difference, andstops with a concomitant disappearance of friction. from deformation because of synchro ring thermalThe synchro ring cools down quickly and remains expansion. The conicity angle difference vanishes bystuck on the gear cone as the axial force is still pre- the end of the synchronization, as the synchro ringsent and does not allow the synchro ring to lower. is deformed by axial force and takes the conicityThe sleeve moves forward axially until reaching the angle of the gear cone.splines of the gear. Then, the sleeve must slow down, The synchro ring initial bulk temperature isbecause it cannot turn the gear without separating assumed to be similar to the gearbox oil temperature:the gear from the synchro ring. An increase of axial t=80 °C. During synchronization, the conical sur-force is needed, so that the tangential component of face temperature can increase until t=120 °C. Thisthe force equilibrium can overcome the static friction latter value is confirmed by both measurements [27]resistance of the synchro ring and turn the ring on and simulations [25, 28]. Part of the heat producedthe gear cone. during friction is absorbed by the synchro ring

The axial force needed for the separation is and its bulk temperature increases with Dt=4–9 °C.obtained from the tangential force calculation (see Under temperature increase, the synchro ring

expands, its mean radius increases, and the synchroFig. 23 later). The separating tangential force is the


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ring moves upwards on the gear cone surface. This changing force will act on the gear and sleeve splinechamfers.situation is maintained while differential motion

and circumferential friction exist between conicalsurfaces. When the differential motion ends with

4.2.2 The turning force peakreaching the angular velocity synchronization, thesynchro ring loses the accumulated heat and its Immediately after the separation of the synchro ring

from the gear cone, the sleeve starts to turn the gearmean radius decreases. As the axial force is stillpresent, the synchro ring cannot move down on the in order to mesh it. The turning angle is determined

by the relative position of the sleeve splines andgear cone and remain stuck.The equations of the deformation model [15, 22] the gear splines at the end of the synchronization.

During turning, the sleeve is assumed to move(Fig. 9) and the thermal expansion model [15, 22](Fig. 10) give these pressure values. The second part forward first with constant axial acceleration, starting

from the axial velocity inherited from the previousof the tangential force comes from contact forceexisting between the sleeve and gear spline chamfers phase. At the same time, it is assumed that the turn-

ing force accelerates the gear with a constant angular(Fig. 11). Equations of the geometry and the contactmodel (Appendix 2, Section 2.5), [23, 22] give this acceleration. After the sleeve has reached the maxi-

mum axial velocity, the axial acceleration stops.force value.There is a second chamfer of angle xmanufactured As the angular acceleration is linked to the axial

acceleration, it stops at the same time. Gear splineon the spline sides of the sleeve (Fig. 21). When thesleeve is meshed with the gear splines, this chamfer tangential velocity will have exactly the value needed

to leave space for the approaching sleeve. The axialhelps to maintain the sleeve in a meshed position.During gear changing, when the separating force is force decreases, as it only has to compensate for the

gearbox power losses.applied, a good choice of second chamfer angle candecrease the axial force needed to pass beyond the Assuming this, the effect of the turning angle on

the turning force needed for acceleration can besame tangential resistant force [see Fig. 23(a) later].In order to decrease axial force, the second chamfer described as follows: the higher the absolute value

of the turning angle, the smaller is the turning forceangle x must be greater than the friction angle r2

between the sleeve spline and gear spline chamfers required. When turning starts, the axial velocity ofthe sleeve is low. It has to be accelerated to reach the(Fig. 29).

The variation of the conicity angle error seems to nominal axial velocity. As the spline chamfers are incontact, axial and angular velocities are connected.have a significant influence on this force peak and

the stiffness of the synchro ring also seems to have Firstly, an axial force increase causes the sleeve axialvelocity to increase and thus the gear angular velocityan influence on the phenomenon. The static friction

coefficient on the conical surfaces and the mech- increases. The forces are high due to the high inertiaaccelerated in a very short time. Secondly, whenanical and thermal properties of the ring material are

other important parameters. the sleeve reaches the maximum axial velocity, theaxial and angular accelerations become zero. Then aAfter separation of the gear cone and synchro ring

cone, friction on the gear cone is neglected, as axial lower axial force is applied to maintain the constantangular velocity of the gear and to compensate powerforce on the synchro ring coming from only centring

mechanisms is supposed to be small. The main axial losses. Thus, axial force is relatively high at the

Fig. 21 Geometric position and photo of the splines


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beginning of turning and is lower when acceleration turning. Thus, a higher turning force is needed tomaintain constant angular acceleration. A lowerhas ended. As the turning angle is a random quantity,

even in the case of strictly identical working force must then be maintained in order to completeturning with a higher constant angular velocity thanconditions, it is different for each gear change.

Numerical simulations win a test-bench numerical the synchronized one (Fig. 23, right side).The measured data can be used to observe gearenvironment show that synchro ring material has

a very small effect on variation in turning force angular velocity variation. Observations and simu-lation are compared in Fig. 23 [33]. Test-bench(Fig. 22). As assumed, bronze and sintered steel

synchro rings behave similarly in this phase (friction measured results [Fig. 23(b)] and numerical simu-lation results [Fig. 23(c)] in a test-bench numericalcoefficients: 0.08 for bronze, 0.1 for sintered material).

Considering the spline chamfer geometry, a global environment are of similar shape but with slightlydifferent numerical values in both turning cases.symmetry can be observed in the variation of the

turning force as a function of the turning angle Differences between measured and simulated peak-to-valley angular velocity are supposed to come(Fig. 22). Close to the turning angle Q=0 (where no

large turning is needed), two force peaks of equal from effects of the synchronized inertia, smoothingsharp angular velocity variations. The inertia effectsize should be present owing to the symmetry of the

spline geometry. However, they are of different size. is stronger in the Q>0 turning case (Fig. 23, rightside) than in the Q<0 turning case (Fig. 23, left side).This could be attributed to the effect of the oriented

power losses that always occur in the direction This effect has not yet been included in thesimulation. The duration of peak-to-valley angularopposing the angular velocity.

If the gear has to be turned in the opposite velocity variation is 0.075 s in the Q<0 turning casemeasurements [Fig. 23(b) left side] and 0.04 s indirection to the mean angular velocity (Q<0), it has

to be slowed down instantaneously (Fig. 22). The the numerical simulations [Fig. 23(c), left side]. Theduration of peak-to valley angular velocity variationturning force can be lower, because the power losses

aid gear-turning (angular acceleration). When the is 0.03 s in the Q>0 turning case measurements[Fig. 23(b), right side], and 0.01 s in the numericalangular acceleration has stopped, the gear follows

turning with a lower constant angular velocity than simulations [Fig. 23(c), right side].From the theoretical point of view, geometricthe synchronized one, under the effect of power

losses (Fig. 23, left side). Consequently, no supple- positions exist where turning is impossible owing tothe sharp end of the chamfers. In such cases, gearmentary axial force is needed to finish the turning.

If the gear has to be turned with Q>0, it has to be changing is theoretically impossible. However, inpractice, turning is possible because the chamfersaccelerated instantaneously (Fig. 22). Gearbox power

losses decrease the angular acceleration of gear are blunted, though very high axial force is required.

Fig. 22 Turning force distribution versus turning angle


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Fig. 23 Synchronized angular velocity variation in two directions

The measured data show that either very high second classes of values and an upper force limit is defined.Peaks higher than the limit are included in the higherbump force peaks are present, or a long delay

before the second bump. Clearly, these phenomena class of the diagram, regardless of their size. Thismethod is confirmed by the presence of maximumdecrease shift feel comfort, but the probability of

such cases is low. force limits in the measured signals for one side. Onthe other side, it is assumed that simulated very highAnother theoretical position is encountered when

sleeve splines are exactly opposite the gear splines. peak force values cannot be realistic. The gear-changing mechanism has intrinsic inertia and damp-In such cases turning is not needed, as the theoretical

turning force is zero. In the measured data, the ing and gear changing has a non-zero duration.Consequently, extreme high peaks are damped orsecond bump peaks do not appear at all, or else they

are very small. Changing is done quickly and shift filtered and do not appear in the measurements;hence, they are considered as maximum peak valuescomfort is good. Unfortunately, the probability of

such cases is also low because of spline geometry in the simulation.In the case of the test-bench numerical environ-and medium-size second bump force peaks are

usually observed. ment, the behaviour of one synchronizer is simu-lated. The synchronizer can be set to threeAn analysis of measured second bump data con-

firms the previous description. From a study of the geometrical positions: successively, position P1,neutral, and position P2 (Fig. 1). As in real test bench,occurrences, a peak force occurrence diagram can be

drawn. The measured data are obtained by sampling power losses are different for positions P1 and P2.Synchronizer data come from measurements on reallong duration tests. Peak values are gathered into


d000001604 08-05-06 22:20:18 Rev 14.05



synchronizers. It is supposed that every relative in the simulated case. Simulations fit well with themeasured data in this case.spline position j can be realized with the same

probability. If the quantity of sampled measured data A study of measured data and numerical simu-lations was also performed for changing P2P1is great enough, approximately every relative spline

position is presented; thus, measured and simulated (Fig. 25). Here, the measured peak occurrencespectrum is similar to that of the previous case. Thedata can be compared.

When simulating gear changing from position main difference is the larger number of elements inthe class 0 N. After tuning the parameters, simulationP1 to position P2 (P1P2) using a bronze synchro

ring, it can be seen that peaks occur mainly in two with the following values approaches the measureddata: jµ[0.15; 0.8], and the friction coefficient on theforce classes: class 0 N and class 550 N (Fig. 24). The

measured data appear to have a maximal force limit spline chamfers is f=0.2. As in the previous case,the measured and simulated peak force spectra areof 550 N, which can be attributed to the fact that the

maximum imposed axial force is 550 N. similar. The sum of the occurrences in the two upperclasses is 56 per cent in the experimental case andNumerical simulations were performed in order to

investigate this phenomenon. Second bump peaks 49 per cent in the simulated case. The occurrence ofthe lower class is the same in both cases. Here also,were simulated, with j varying from 0.05 to 0.95, in

order to study the effect of the relative spline chamfer simulations fit well with the measured data in thiscase.position to the turning force during the second

bump peak. An occurrence spectrum similar to the Next, the sintered synchro ring is considered.Experimental force peaks are distributed mainlymeasured spectrum was obtained. After tuning the

parameters, simulation with the following values in three zones: around class 0 N, class 300 N, andaround the maximum class (Fig. 26). For P1P2 gearapproaches the measured data: jµ[0.2; 0.8], and the

friction coefficient on the spline chamfers is f=0.25. changing, after tuning the parameters, simulationwith the following values approaches the measuredFriction coefficient values of these magnitude and

even higher classically were found in the literature data: jµ[0.2; 0.95], and the friction coefficient on thespline chamfers is f=0.15.[34]. By comparing the peak force spectra (Fig. 24) it

can be seen that both have similar shapes. Moreover, Measured and simulated peak force spectra aresimilar. The lower three classes give 14 per cent ofthe sum of occurrences in the two upper classes is

68 per cent in the experimental case and 64 per cent total peaks in the experimental case and 16 per cent

Fig. 24 Second bump peak values and occurrence, bronze synchro ring, gear changing P1P2


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Fig. 25 Second bump peak values and occurrence, bronze synchro ring, gear changing P2P1

Fig. 26 Second bump peak values and occurrence, sintered synchro ring, gear changing P1P2

in the simulated case. The upper three classes give For P2P1 gear changing, the measured forcepeaks are again concentrated in three zones: around36 per cent in the experimental case versus 36 per

cent in the simulated case. The mean classes are 0 N, around 200 N, and in the maximal class (Fig. 27).Note that the maximal force limit is relatively low,slightly different: 300 N in the experimental case and

350 N in the simulated case. The simulations also fit only 450 N. After tuning the parameters, simulationwith the following values approaches the measuredwell with the measured data in this case.


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Fig. 27 Second bump peak values and occurrence, sintered synchro ring, gear changing P2P1

data: jµ[0.05; 0.95], and the friction coefficient on It is interesting to note that high force peaks do notappear in extreme relative position conditions (j#0the spline chamfers is f=0.08.

The experimental and simulated peak force or j#1). Peaks are high when the position is almostideal to mesh the sleeve and gear without turningspectra are similar. The lower two classes give 23 per

cent of total peaks in the experimental case and (j#0.5). In such cases, sleeve splines have very little28 per cent in the simulated case. The upper two time to turn the gear. As the gear inertia is high, aclasses give 14 per cent in the experimental case strong force is needed, applied via a small contactversus 30 per cent in the simulated case. The mean surface next to the starting edge of the chamfer.classes are different: 200 N in the experimental When the decreasing contact surface becomes zero,case and 300 N in the simulated case. Here, the simu- the turning force disappears suddenly, provokinglated spectrum approaches the experimental data strong dynamical excitation. This could be avoidedspectrum, but some differences exist in the position by placing a connecting radius in this zone insteadof the mean force class and in the higher force of the sharp theoretical chamfer edge.peak values. When acting upon gear-changing factors without

It can be established that four main parameters changing spline chamfer geometry, the best resultinfluence the spectrum zones. These are the para- that can be obtained with this type of synchronizermeters modified during tuning. is a decrease of the mean force level. Other improve-

ments need changes of chamfer geometry, such aspronounced radii instead of chamfer edges, or modi-1. j

mininfluences the sample in the class of 0 N.

fications of the plane chamfer surface. Even in theseIf jmin

increases, the sample in the class decreases.cases, the second bump force peak distribution will2. j

maxinfluences the sample in the mean force class.

contain high force peaks, but their occurrence willIf jmax

increases, the mean force class will have abe less.lower position in the spectrum.

Further improvement of gear changing can come3. f influences the distribution in the classes. If thefrom an exact knowledge of the axial position of thefriction coefficient on the spline chamfers is high,

more items are situated in the higher classes. sleeve and the tangential position of the spline. Thiswould permit modification of the sleeve axial speed4. b

gearacts as f. If the chamfer angle is high, more

items are gathered in the higher classes. in order to obtain optimal spline chamfer contact


d000001604 08-05-06 22:20:18 Rev 14.05



between the sleeve and gear, and minimize or avoid to the spectrum resulting from the measured data,the role played by the relative position of the splinethe occurrence of risky geometric configuration.chamfer in the formation of the turning force can bestudied. Finally, they established that simulated andmeasured force spectra are very similar.

5 CONCLUSION

The gear-changing process was studied, and eightmain phases of synchronizer behaviour were defined.

ACKNOWLEDGEMENTSThe phases were delimited by using measured datafrom gear changing. These phases were described

This work was carried out thanks to a grant from theusing classical tribological, mechanics, and thermo-

Hungarian Ministry of Education and the Frenchdynamics theories. Existing models were used and

Government. The authors would also like to thankadapted to a synchronizer. New models were pro-

the Federal Mogul Company (Sintered Products) forposed when such models did not exist. These

helpful discussions during the preliminary experi-models were organized and interconnected in order

mental approach.to describe the gear-changing process and thebehaviour of the synchronizer. The models wereincluded in a numerical simulation software.

The comparison of measured data with simulationREFERENCESresults allowed a study of stick-slip phenomena in

the synchronizer during gear-changing. Stick-slip1 Socin, R. J. and Walters, L. K. Manual transmissionis considered to occur either in an axial or in a

synchronizers. SAE paper 68008, 1968.tangential direction. Axial stick-slip, when the sleeve2 Lanzerath, G. and Patzer, H. Synchronizer blockermoves axially, produces small amplitude oscillations

ring with organic lining. SAE paper 860384, 1986.and does not influence the gear-changing process. 3 McCord, L. GYLON friction material for trans-Tangential stick-slip occurs when the ring rubs against mission synchronizers. SAE paper 860382, 1986.the gear cone and also produces small-amplitude 4 Ohtomo, M. Synchronizer rings made of resin andoscillations. However, it occurs in a sensitive working iron alloy for pin-type blocking synchronizers used

in heavy vehicles. JSAE Review, 1989, 10(4), 71–74.phase and may be responsible for gear-changing5 Sykes, L. M. The Jaguar XJ220 triple-cone syn-noise and cracking, because the ring meshes before

chronizer – A case study. SAE paper 940737, 1994.reaching synchronicity. More detailed study of this6 Koga, H. and Anzai, K. Development of manualphenomenon, supported by experimental results,

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Part D: J. Automobile Engineering, 1997, 214, 55–65.can avoid this kind of gear-changing noise.8 Murata, S., Mori, Y., Doi, T., Takada, T., andA study of the second bump phenomenon was also

Nogichi, Y. Synchronizer and shift system optimiz-undertaken. The second bump is considered asation for improved manual transmission shiftability.two successive independent phenomena from whichSAE paper 891998, 1989.models with geometric parameters resulting from

9 D’Orazio, A., Caudano, M., Uberti, M., andmeasured sycnhro ring and gear cone geometry Urbinati, M. Multicone synchronizer dynamiccould be proposed. The study of the synchro ring modeling and experimental bench test rig toand the gear cone stuck together at the end of improve manual transmission shiftability. In Pro-

ceedings of the JSME International Conference onthe synchronization phase gave the first element ofMotion and Power Transmissions, Fukuoka, Japan,second bump. This force peak zone is influenced by15–17 November 2001, pp. 649–656.the material properties of the synchro ring, conicity

10 Kim, J., Sung, D., Seok, C., Kim, H., Song, H.,angle error, and friction coefficient variation on theLim, C., and Kim, J. Development of shift feelingcones. Gear rotation then constitutes the second partsimulator for a manual transmission. SAE paper

of the second bump force peak. The study of spline 2002-01-2202, 2002.chamfer geometry, taking real working conditions 11 Hoshino, H. Simulation on synchronisationinto account, gave wide axial force peak spectra mechanism of transmission gearbox. International

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12 Satoh, K., Shintani, M., Akai, S., and Hiraiwa, K. 28 Lovas, L., Play, D., Marialigeti, J., and Rigal, J.-F.Modelling dynamical processes in the synchron-Development of a new synchronizer with the leverisation process of manual gearboxes (in Hungarian).mechanism. JSAE Review, 2003, 24(1), 93–97.Gep, 2003, LIV(2003/10-11), 103–109.13 Nellums, R. A. Low force ‘Boost’ concept for

29 Kwittner, G., Back, O., and Schreiber, U. Simulationbaulk ring synchronizers. VDI Berichte, 1998, (1393),des Schaltvorgangs synchronisierter Kfz-Getriebe. In215–227.Laschet, A. Systemanalyse in der Kfz-Antriebstechnik,14 Ore, T. G., Nellums, R. A., and Skotnicki, G.II, 2003, pp. 239–250 (Expert Verlag, Renningen).Improved synchronizers for truck transmissions.

30 Hwang, D. H. and Zum Gahr, K. H. TransitionSAE paper 952602, 1995.from static to kinetic friction of unlubricated or oil15 Ghaem, H. Contribution a l’etude des materiaux delubricated steel/steel, steel/ceramic and ceramic/synchronisation. PhD Thesis, University Paris VI,ceramic pairs. Wear, 2003, 255, 365–375.1994.

31 Thomsen, J. J. and Fidlin, A. Analytical approxi-16 Paffoni, B., Progri, R., Gras, R., and Blouet, J.mations for stick-slip vibration amplitudes. Int. J.The hydrodynamic phase of gearbox synchromeshNon-Linear Mech., 2003, 38, 389–403.operation: the influence of radial and circum-

32 Lovas, L., Play, D., Marialigeti, J., and Rigal, J.-F.ferential grooves. Proc. IMechE, Part J: J. EngineeringInternal excitation and effects in gear changingTribology, 1997, 211, 107–116.process of manual automotive gearboxes. In17 Roper, H. and Yang, J. Die Qualitat des Schaltkraft-‘Gepeszet 2004’ Proceedings of the Fourth Inter-verlaufs beim Gangwechsel manuell geschalteternational Conference on Mechanical EngineeringGetriebe. VDI Berichte, 1998, (1393), 321–354.(Eds Penninger, A., Kullmann, L., and Voros, G.),18 Hohn, B. R. and Pinnekamp, B. HochschaltkratzenBudapest University of Technology and Economics,bei kalten Pkw-Schaltgetrieben. VDI Berichte, 1995,Budapest, 27–28 May 2004, Vol. II, pp. 573–577.(1175), 435–451.

33 Lovas, L., Play, D., Marialigeti, J., and Rigal, J.-F.19 Goto, Y., Yagi, Y., Morimoto, Y., and Kawasaki, M.Modelling indexing phase of Borg-Warner gearboxShift feel in manual transmissions – an analysis ofsynchromesh mechanism. In Proceedings of theunsmooth shifting and gear clashing. JSAE Review,International Conference on Power Transmissions1988, 9(4), 52–55.’03, 2003, Vol. 3, pp. 105–110.20 Shinbata, K. and Nakamura, N. Achievement of

34 Dunkin, J. E. and Kim, D. E. Measurement of statictheoretical quantitative evaluation method andfriction coefficient between flat surfaces. Wear, 1996,effective countermeasures for manual transmission193, 186–192.nibble. SAE paper 91524, 1991.

35 Lovas, L., Play, D., Marialigeti, J., and Rigal, J.-F.21 Moir, G. B. An investigation into objectiveAn improved method for calculating friction inmeasures of gear-shift quality. Proc. IMechE, Part D:conical clutches. VSDIA 2002 8th Mini ConferenceJ Automobile Engineering, 1995, 209, 273–279.on Vehicle System Dynamics, Identification and22 Lovas, L. Etude des relations entre le fonctionne-Anomalies, Budapest, 11–13 November 2002.ment et la fabrication des synchronisateurs des

36 Lovas, L., Play, D., Marialigeti, J., and Rigal, J.-F.boıtes de vitesses manuelles. PhD Thesis, INSA-Modelling the friction process in the synchron-Lyon, 2004.isation process of manual gearboxes (in Hungarian).23 Derrien, D. Oscillations transitoires dans lesGep, 2002, LIII(2002/6-7), pp. 73–78.chaınes cinematiques automobiles. PhD Thesis,

37 Paffoni, B., Progri, R., and Gras, R. The mixed phaseEcole Centrale de Nantes, 1999.of gearbox synchromesh operation. Proc. IMechE,24 Roulet, B. Modelisation de l’evolution de laPart J: J. Engineering Tribology, 2000, 214, 157–165.dissipation de puissance et du comportement

thermique d’une boıte de vitesses manuelle. PhDThesis, University Paris VI, 1995.

25 Boness, R. J. Churning losses of discs and gearsrunning partially submerged in oil. Proceedings of APPENDIX 1the 1989 International Power Transmission andGearing Conference, Chicago, pp. 355–359. Notation

26 Lovas, L., Play, D., Marialigeti, J., and Rigal, J.-F.Modelling the synchronisation behaviour of manual c damping coefficientcar gearbox synchromesh mechanisms. In Scientific c

cdamping coefficient in spline side chamfer

Bulletin of North University of Baia Mare, Series C, contactVol. XVII, Fascicle: Mechanics, Tribology, Tech- c

Qtorsional damping coefficient

nology of Machine Manufacturing, Part II: Papers ofdB axial displacement of the sleeve duringthe 5th International Multidisciplinary Conference,

Phase 623–24 May 2003, Baia Mare, Romania.dPF tangential displacement of the gear during27 Spreckels, M. Einfluss der Temperaturverteilung auf

Phase 6das tribologische Verhalten von Synchronisier-ungen. PhD Thesis, University of Hannover, 2001. f friction coefficient


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vB

angular velocity of the sleevef2

friction coefficient between the spline andv

Rsynchronized angular velocity of the gearsynchro ring chamfers

vR0

initial angular velocity of the gearf3

friction coefficient between the spline andgear chamfers

F forceF

axaxial force APPENDIX 2

Ffr

friction forceF

fr2friction force between the sleeve and 2.1 Equations describing the start ofsynchro ring synchronization

Ffr3

friction force between the spline and gearThis phase is described using hydrodynamicschamfersequations. The variation of the axial force needed toF

tgtangential force

collapse the oil filmFturn

turning force during Phase 7h normal distance between two surfacesh

daxial length of a spline chamfer Fax=KNR16pmvax sin2ar1C b

h(t)D3 (1)k elasticity coefficientk

celasticity coefficient in spline chamfer where m is the dynamic viscosity of the oil [Pas], b iscontact the half-length of the cone generatrix [m]

kQ

torsional elasticity coefficientL

dhalf-width of a spline

KNR=w3h

2(a+w)b2 sin a(2 sin a+cos a tan Da)m mass

N normal force to a surfaceN

1normal force between the sleeve and gear ×

h+tan Da

(h+2 tan Da)2(2)

spline chamfersN

2normal force between the sleeve and for radial grooves, where a is the half-width of asynchro ring groove on a conical surface (m), w is the half-width

p spline pitch of a surface portion between grooves on a conicalr

1gear cone mean radius surface

r2

spline mean radiust time Da=(asin chroring−agear cone) (3)T torque

is the conicity angle error. The variation of thev velocityangular velocity of the synchronized gear isv

axaxial velocity of the sleeve

vtg

tangential velocity of the gearvR=vB−C(vB−vR0) h(t)

h1 DY (4)x axial displacement

a conicity angleY=KCR

4pbr31hRnaxv sin a

(5)Da conicity angle errorb spline chamfer angle

where h1

is the initial distance between the conicalbgear

spline chamfer angle of the gearsurfaces at the beginning of the oil film compression,e

Rgear angular acceleration

naxv

is the axial speed at the end of viscous frictionQR

gear turning angle during Phase 7periodh

Rsynchronized inertia

k constantKCR=

w

a+w(6)j random spline relative position variable

r2

friction angle between the spline andsynchro ring chamfers for radial grooves. For more details, see [15, 3, 22].

r3

friction angle between the spline and gearchamfers

2.2 Equations describing synchronizationt temperatureDt temperature varation This phase is also described with the equations ofx spline second chamfer angle the mixed lubrication. The command signal is the

axial force, varying as described in the Fig. 28. Thev angular velocity


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Supposing that oil viscosity varies linearly with thetemperature within a given temperature interval

m=amT+b

m(7)

where am

and bm

are constant. It is described inthe literature, that maximum temperatures on theconical surfaces are around 120 °C [27]. Knowing thatthe working temperature of a gearbox is around80 °C, an oil temperature increase of 40 °C can beFig. 28 Variation of the axial forceassumed during the synchronization phase betweenthe conical surfaces. In a first approximation, a lineartemperature increase law can be admitted for thevariation of the synchronized angular velocity isshort duration of synchronization:

vR(t)=ek1t2+k2tCK+√pAQ22 −Q14 k2

k3/21 B ek22/4k1 T=cTt (18)

where cT#200 °C/s is constant.

Replacing this in the equation of the oil viscosity×erfA√k1t+ k22√k1BD− Q12k1

(7)between conical surfaces gives

where m=amcTt+b

m=At+B (19)

Equation (19) gives the origin of constants A and B.In these equations, Da=0 is assumed, as the

K=

vRv+hRg3Ag2+g1GFaxv+[(Fax,max−Faxv)/tm ]AhRg3+tvBHB

eg3tv/hR angular velocity difference vanishes by the end of

the synchronization phase owing to synchro ring(8)

deformation (Fig. 10). Full development of theequations is described in [16, 36, 37, 22].The following expressions are constant during com-

putation of one solution for vR

(t)2.3 Equations describing the turning of the

synchro ringk1=g∞3

2hRA (9)

This phase is described by solid mechanics laws. Thevariation of the axial force isk2=

g∞3hR

B (10)

Fax=fs+tgb

1−fstgbTlosses+hReR

r2(20)

Q1=g∞2hR

A+g1Fax,max−Faxv

tm(11)

where fs

is the friction coefficient on spline chamfersurfaces, T

lossesis the torque of power losses.

Q2=g∞2hR

B+g1Faxv (12)The variation of the synchronized angular velocity

is

g∞3=fs−fv

S2−S1f∞

r1sin aC1+ 1

3A br1B2 sin2 aD (13) vR=vR0+eRt (21)

where vR0

is the angular velocity of the gear at theg∞2=−g∞3vC (14)

start of the phase.

g∞1= fs+g∞3f∞

S1 (15) 2.4 Equation describing the free fly

Each free fly phase is described by solid mechanicswherelaws. The necessary axial force is also constant and

f∞=4pr21b sin a (16) it results from friction on the side chamfers of sleevesplines owing to torque power lossesS

1is the Stribeck’s number at the end of the mixed

friction [22, 37], S2

is the Stribeck’s number at theFax=

fsTlossesr2

(22)start of the mixed friction [22, 37].Here, constants A and B come from the equation

of oil viscosity variation during synchroniation The angular velocity of the gear is the same as thatof the sleeve.(Phase 3), between the conical surfaces [22].


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2.5 Equations describing start of the second Here, a negative sign means that the sleeve isslowed down by the chamfer contact force. A positivebumpsign means that a supplementary axial force is

This phase is described by solid mechanics laws. Theapplied in order to maintain the original axial

normal distance between the spline chamfer surfacesvelocity of the sleeve. This supplementary force

(Fig. 11) is given by the following equations [3, 22]:increases the second bump peak. The original axial

for the rear side of the gear chamfervelocity increases the axial force needed in thefollowing phase. For more information, see [22].h1=

√[(1−j)p−Ld+dPF ]2+(hd−dB)2

2.6 Equations for turning the gear×cosCb−arctanA hd−dB

(1−j)p−Ld+dPFBD (23)

This phase is also described by classical mechanicsFor the front side of the gear chamfer laws. The axial force needed for turning is

h2=√(jp−Ld−dPF )2+(hd−dB)2

Fax=AmaxeRr2 tan b+hReRmTlosses

r2 B f3+tan b

1−f3 tan b×cosCb−arctanA hd−dB

jp−Ld−dPFBD (24)(31)

where Here, the negative sign means that turning is in theopposite direction to that of the angular velocitydB=vaxt (25)of the gear. This slows down the gear and requires

is the axial displacement of the sleevelower axial force. The positive sign means that the

dPF=(vR−vC)r2t (26) turning direction is that of the angular velocity. Thisaccelerates the gear, and needs higher axial force.is the tangential displacement of the gear, p is theWhen angular acceleration e

Rbecomes zero, the axialpitch of the splines, j is the random coefficient of

force has to compensate only the torque of gearboxthe relative position of the synchro ring and gearpower losses.chamfers.

In this phase, the forces are in equilibrium on the2.7 Equation describing the stick-slip motionspline chamfers. The equilibrium equations are given

as follows. The equation of motion for the system is thefollowingTangential direction

Ftgr2=(N cos b−f3N sin b)r2=hReR (27)m

d2xdt2+c

dx

dt+kx+f (vr)F=0 (32)

where Ftg

is the tangential force, f3

is the frictioncoefficient on the chamfer surfaces where m is the mass, x is the displacement of the

mass, F is the normal force on the surface, f (vr) is

N=kch+ccdh

dt(28) the friction coefficient depending on the relative

sliding velocity, c is the damping coefficient, k is theis the normal force on the chamfer surface elasticity coefficient.

Note that the value of the excitation velocity vb

isAxial directionconstant (Fig. 12). Various oscillations are as a result

Fax+F∞ax=N sin b+f3N cos b−N2 sin x+f2N2 cos x of Coulomb friction taking place between the twomoving surfaces. The friction coefficient between(29)the mass and the sliding surface is modelled by the

where F∞ax

is the axial force needed to compensate following equation (Fig. 29)friction losses during sleeve movement, x is the

f (vr)=sign(vr) fs−k1vr+k3v3r (33)second chamfer angle (Fig. 20).From the above equation, the axial force for where v

r=dx/dt−v

bis the relative sliding velocity

separation is

Fax=N sin b±maax (30) k1=3

2

fs−fmvm

(34)

where m is the mass of parts of gear-changingmechanism, including the sleeve, a

axis the axial

k3=1

2

fs−fmv3m

(35)acceleration of the parts of gear-changing mechanism.


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2.8 Simulation results of a transaxle car gearbox

Gear-changing simulations of a five-speed JH cartransaxle gearbox (Fig. 30).

The following figures show certain results. Whensimulating the effect of a given parameter, only thisparameter changes; all the other parameters are keptconstant. Fig. 31 shows that changing time increases

Fig. 29 Friction coefficient function model with initial angular velocity inertia.Tables 1 and 2 illustrate that changing time is pro-

The parameters of the friction coefficient function portional to synchronized inertia. The higher theare: f

sbeing the static friction coefficient; f

m, the inertia, the longer the changing time. The tables also

minimum friction coefficient; and vm

, the relative show that for a given inertia, downshifting requiressliding velocity at the moment of the friction more time than upshifting. This is attributed to thecoefficient minimum. effect of energy dissipation. In the case studied,

Stick-slip phenomenon can also appear in rotating energy dissipation slows down the turning gear andmotion. Equation (32) can be changed and applied power losses can be evaluated. When upshifting, it

decreases the changing time as this slowing downfor rotating motion.

Fig. 30 General drawing of the five-speed Renault JH gearbox

Table 1 Changing time versus changing inertia during gear upshift

Gear speed changing 01 12 23 34 45Synchronized inertia [kgm2] 0.061 237 0.018 798 0.009 451 0.005 736 0.005 412Changing time [s] 0.4 498 0.2 495 0.1 998 0.1 739 0.1 709

Table 2 Changing time versus changing inertia during gear downshift

Changing 54 43 32 21Synchronized inertia [kgm2] 0.005 736 0.009 451 0.018 798 0.061 237Changing time [s] 0.1 804 0.2 071 0.2 581 0.4 896


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Fig. 31 Changing time variation versus angular velocity difference variation, upshift 12

Fig. 32 Changing time versus changing force during gear upshift 12

effect is superposed to the effect coming from the Figure 32 shows that the changing time decreaseswhen the changing force increases. Note that thechanging force. When downshifting, the slowing down

effect increases the time needed for accelerating relation is not linear.gears. Thus, downshift needs more time.


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