AU697532B1

AU697532B1 - Oleopneumatic anti-roll or anti-hunting suspension apparatus

Info

Publication number: AU697532B1
Application number: AU77447/98A
Authority: AU
Inventors: Philippe Boichot; Fabienne Bondon
Original assignee: GEC Alsthom Transport SA
Current assignee: Alstom Transport SA
Priority date: 1997-07-24
Filing date: 1998-07-23
Publication date: 1998-10-08
Anticipated expiration: 2018-07-23
Also published as: TW504473B; NO983413D0; EP0893321A1; NO983413L; JPH1191558A; BR9802573A; CA2242700A1

Description

AUSTRALIA

Patents Act COMPLETE SPECIFICATION

(ORIGINAL)

Class Int. Class Application Number: Lodged: Complete Specification Lodged: Accepted: Published: Priority Related Art: Name of Applicant: GEC Alsthom Transport SA S Actual Inventor(s): tI, Philippe Boichot I, a Fabienne Bondon Address for Service: PHILLIPS ORMONDE FITZPATRICK Patent and Trade Mark Attorneys 367 Collins Street Melbourne 3000 AUSTRALIA S.Invention Title: OLEOPNEUMATIC ANTI-ROLL OR ANTI-HUNTING SUSPENSION APPARATUS Our Ref 537036 S POF Code: 110174/202864 The following statement is a full description of this invention, including the best method of performing it known to applicant(s): -1la OLEOPNEUMATIC ANTI-ROLL OR ANTI-HUNTING SUSPENSION

APPARATUS

The present invention relates to oleopneumatic suspension apparatus. It is particularly applicable to damping roll, or to damping yaw-type hunting or to longitudinal damping in a road vehicle or in a rail vehicle.

Karnop's Patent US 5 024 302 relates to a controlled shock-absorber whose damping characteristic is controllable by means of electrically-controlled valves.

The function of the accumulator in that shockabsorber is to perform volume compensation and to maintain a pressure that is substantially constant in the chamber which is relieved via one or other of the check valves.

The controlled shock-absorber described in Patent US 5 024 302 does not have an anti-roll or anti-hunting stiffness function.

Combining two shock-absorbers is not taught.

AUTOMOTIVE PRODUCTS Ltd's Utility Certificate FR 2 252 228 relates to improvements concerning suspensions for vehicles.

As appears from that document, the object of the apparatus disclosed in that prior art document is to implement a vehicle suspension such that, during changes in dynamic load, resulting from a tendency to roll when going round bends, and from a tendency to pitch due to weight being transferred from front to back when accelerating or from back to front when slowing down, the suspension varies the quantity of liquid contained in cavities of liquid-filled structures via which the weight of the vehicle is transmitted to the wheels, so as to maintain the vehicle horizontal.

An analysis of that vehicle suspension as described in Document FR 2 252 228 is given at the beginning of the description below.

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2 As shown by this analysis, the vehicle suspension described in Document FR 2 252 228 clearly provides antiroll torque but suffers from the following major drawbacks.

Its vertical stiffness and its roll stiffness are coupled together because of the differences in section in the actuators.

Its vertical stiffness ind its roll stiffness are determined by the accumulator preloading pressure.

The flow-restriction constrictions provide a damping function both when the fluid in the high chambers is compressed and also when it is expanded.

In the event of rapid expansion, the high chamber can suffer cavitation.

When the suspension described in FR 2 252 228 is applied mutatis mutandis to damping hunting, it suffers from drawbacks similar to those that it suffers when it is applied to damping roll.

An object of the invention is therefore to design a single secondary suspension apparatus for damping roll or hunting, that does not suffer from the drawbacks of known apparatus, and that incorporates the following functions: providing anti-roll or anti-hunting righting torque with it being possible to adjust the anti-roll stiffness or the anti-hunting stiffness without disassembling the oleopneumatic suspension apparatus; providing vertical damping or longitudinal damping, with it being possible to adjust the viscance without disassembling the suspension apparatus; and providing roll damping or hunting damping, with adjustment being possible without disassembling the c suspension apparatus, aind with it being possible to increase this damping without increasing the vertical damping or the longitudinal damping.

To this end, the invention provides oleopneumatic i suspension apparatus for a vehicle, the apparatus connecting a vehicle body to wheels of the vehicle, and 3 1] comprising first and second shock-absorbers Al and Al' connecting the wheels to the vehicle body, each shockabsorber comprising: an actuator provided with a cylinder in which a nonperforated piston provided with a rod is slidably mounted, said piston, defining an expansion first chamber and a compression second chamber, said cylinder being filled with a fluid; and a compression first check valve CL1, CL1', an expansion second check valve CL2, CL2', a compression first hydraulic valve V2, V2', an expansion second hydraulic valve Vl, Vl', and a preloaded oleopneumatic accumulator constituted by a chamber, said compression check valve CL1, CL1' and said expansion hydraulic valve Vl, Vl' being mounted in parallel, said compression check valve CL1 and said expansion hydraulic valve Vl being disposed between the expansion chamber and an intermediate point A, said compression check valve CL1' and said expansion hydraulic valve VI' being disposed between said expansion chamber and an intermediate point said expansion check valve CL2, CL2' and said compression hydraulic valve V2, V2' being mounted in parallel, said expansion check valve CL2 and said compression hydraulic valve V2 being disposed between the compression chamber and said intermediate point said expansion check valve CL2' and said compression hydraulic valve V2' being disposed between the compression chamber and said intermediate point A; said apparatus being characterized in that it further comprises: a check valve CL3, CL3' and a hydraulic valve V3, V3' mounted in parallel, said check valve CL3 and said hydraulic valve V3 being disposed between said intermediate point A and said chamber of the accumulator, said check valve CL3' and said hydraulic valve V3' being disposed between said intermediate point A' and said chamber of the accumulator.

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4' Ii 4 7 14 4 CC An advantage of the suspension apparatus of the invention is that it provides an anti-roll or an antihunting stiffness function.

Since the accumulators 3, 3' are preloaded identically, they induce pneumatic stiffness which, via the hydraulic circuit and the lever arm, results in roll or hunting righting torque that is ideally linear and of the following form: Mpneum VO, S, a) 0 c (roll righting) Mpneum VO, S, a) ac (hunting righting) the meanings of these variables being given at the end of the description.

The absence of difference in section (St 0) in the actuators induces no vertical or longitudinal stiffness or preloading for the apparatus.

By modifying the preloading PO of the accumulators, it is possible to modify the value of Ke or K,.

Another advantage of the suspension tpparatus of the invention is that it provides a vertical or longitudinal damping function.

The check valve and hydraulic valve sets CL1/V1, CL2/V2, and CL1'/VI', CL2'/V2' make it possible to adjust the vertical damping characteristic Fdamz, F'damz or the longitudinal damping characteristic Fdamx, F'damx 25 generated by the apparatus.

The hydraulic valves may be passive elements that open progressively as a function of the pressure difference, or they may be elements whose flow sections are controlled by an external system.

When the fluid in the chamber 1 is compressed, the check valve CL1 is closed, and the hydraulic valve VI makes it possible to adjust the headloss from the chamber 1 towards the point A.

With the fluid in the chamber 2 being expanded, the check valve CL2 is open and it bypasses the hydraulic valve V2, and headloss between the point A' and the chamber 2 is at a minimum.

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This mode of operation is characteristic of the apparatus and makes it different from the apparatus described in Document FR 2 252 228.

The operation is symmetrical when the fluid in chamber 2 is compressed.

The use of relief check valves avoids any risk of cavitation in the chambers in which the fluid is expanded.

The apparatus of the invention makes it possible to control the damping characteristic over a wide range.

The apparatus of the invention makes it possible for adjustment to be performed independently in compression and in expansion, pressure regulation always being performed at the chamber in which the fluid is compressed.

The check valves avoid any problems related to the dynamics of hydraulic valves.

Unlike in conventional two-tube damping, the hydraulic valves and the check valves are adjusted without removing the piston.

Another advantage of the suspension apparatus of the invention is that it provides a roll-damping function or a hunting-damping function.

The check valve and hydraulic valve sets CL3/V3 and CL3'/V3' make it possible to impart additional headloss PB-P3' and PA-P3 related, as appropriate, to the angular velocity of roll for generating roll-damping torque Mdam8, or to the angular velocity of hunting to generate hunting damping torque Mdama.

Such roll damping or hunting damping induces no additional contribution to vertical damping or to longitudinal damping.

This property is related to the fact that the actuators are symmetrical, and this makes the apparatus of the invention different from the apparatus described in Document FR 2 252 228.

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rII I An important advantage of the roll-damping apparatus of the invention is that is enables roll damping to be increased without modifying vertical damping.

It is thus possible, where appropriate, to increase roll damping without modifying vertical damping, or to increase hunting damping without modifying longitudinal damping.

Another advantage of the suspension apparatus of the invention is that it can be controlled.

The hydraulic valves VI, V2; VI', V2'; and V3, V3' may be passive components, e.g. valves that open progressively as a function of the pressure differential.

The hydraulic valves may also be controlled externally to vary their flow section.

The orifices in the hydraulic valves VI, V2 may, for example, correspond to two 2/2 valves or to the two flow sections of a 4/2 valve. The same applies for the valves VI', V2', and V3, V3'.

By controlling the flow sections of the orifices of 20 the hydraulic valves VI, V2, and Vl', V2', it is possible, where appropriate, to control the vertical Sdamping forces Fdamz, F'damz or he longitudinal damping forces Fdamx, F'damx.

The apparatus of the invention thus makes it possible to perform semi-active control over vertical c* ,mode and over roll mode. Vertical damping and roll damping can be completely decoupled.

Vertical damping and roll damping are thus controlled, guaranteeing angular stiffness in roll.

The apparatus of the invention also makes it S, possible to perform semi-active control over longitudinal mode and over hunting mode. Longitudinal damping and hunting damping can be completely decoupled.

Longitudinal damping and hunting damping are thus controlled, guaranteeing angular stiffness in hunting.

The structure and the implementation of the apparatus of the invention are thus different from those j V7 t

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C S C S of the apparatus described in Documents FR 2 252 228 and US 5 024 302.

Other objects, characteristics, and advantages of the invention appear on reading the following description given merely by way of example, and with reference to the accompanying drawings, in which: Figure 1 is a diagram of the suspension apparatus of the invention as applied to roll damping; and Figure 2 is a diagram of the suspension apparatus of the invention as applied to hunting and longitudinal damping.

The following description relates to an analysis of the vehicle suspension described in Document FR 2 252 228. Reference is made to the list of variables given at the end of the description.

If Pa is atmospheric pressure, then, in terms of force for each actuator: F (P2-Pa)S2 (Pl-Pa)Sl (P2-P3')S2 (P1-P3)S1 (P3'-Pa)S2 (P3-Pa)Sl Likewise: F' (P2'-P3)S2 (P1'-P3')S1 (P3-Pa)S2 (P3'-Pa)S1 I) If the FR 2 252 228 suspension is considered in anti-roll operation, then: F Fdamz Fpneum and F' F'damz F'pneum where Fdamz (P2-P3')S2 (P1-P3)S1 Fpneum (P3'-Pa)S2 (P3-Pa)S1 F'damz (P2'-P3)S2 (P1'-P3')S1 F'pneum (P3-Pa)S2 (P3'-Pa)Sl where each of F and F' comprises: a damping term (Fdamz, F'damz) related to the headloss in the circuit; the headloss itself is related to the flow rate in the constrictions which are functions of the displacement rate of the actuators, hence the term "damping force"; and 8 a pneumatic stiffness term (Fpneum, F'pneum) related to the pressure variation (P3'-P3) of the accumulators; the pressure of each of the accumulators is a function of the volume of gas contained therein; assuming that the volume of fluid in the hydraulic circuit is constant, on the grounds that the oil is incompressible compared with the gas, it can be shown that this variation in volume is related to the displacement of the pistons. The forces Fpneum and F'pneum are thus functions of piston displacement, hence the term "pneumatic stiffness".

With St S2 S1 S (S2 Sl)/2 i Then, for the vehicle body, in terms of vertical resultant and of roll moment at 0 (Mo): R F F' (Fdamz+F'damz) [(P3-Pa) St MO (F'damz Fdamz)a 2Sa (P3-P3') The following damping terms are obtained: Rdam (Fdamz F'damz) Modam (F'damz Fdamz)a The following vertical stiffness term is obtained with preloading: Rpneum [(P3-Pa) (P3'-Pa)]St Rpneum 2(PO-Pa)St Kz(PO, VO, St)zc The stiffness Kz is a function of the preloading and of the volume and of the difference in section of each of the actuators.

The following roll righting torque is obtained: Mpneum 2Sa(P3-P3') Bp Mpneum -Ke(PO,VO,S,a)ec The angular stiffness K 9 is a function of the preloading and of the volume of each of the accumulators (PO, VO), of the sum of the thrust sections and of the lever arm When the actuators are displaced simultaneously, the volume of gas in each of the accumulators remains identical, and the pressures in the accumulators remain identical, and there is no righting torque. When the pistons are displaced in opposite directions (roll), the volume of gas in one accumulator decreases, while the volume of the gas in the other accumulator increases, thereby creating a pressure difference between the accumulators, resulting in righting torque.

That apparatus clearly provides anti-roll righting torque. However: the accumulator is presented as being a resilient element for supporting the vehicle body (this function is indeed performed because of the asymmetry of the thrust sections of the actuators); the use of the accumulator to provide angular stiffness in roll is suggested in the general text, but it is not claimed; the emphasis is laid on the effects of roll damping and of vertical damping; and the differences in the sections of the actuators couple together the vertical stiffness and the angular stiffness in roll. Those two stiffnesses are determined by the preloading pressure of the accumulator. That is a drawback of that apparatus.

II) If the FR 2 252 228 suspension is considered in anti-hunting operation, then: F Fdamx Fpneum and F' F'damx F'pneum where Fdamx (P2-P3')S2 (PI-P3)S1 Fpneum (P3'-Pa)S2 (P3-Pa)Sl F'damx (P2'-P3)S2 (P1'-P3')S1 F'pneum (P3-Pa)S2 (P3'-Pa)S1 where each of F and F' comprises: a damping term (Fdamx, F'damx) related to the headloss in the circuit; the headloss itself is related to the flow rate in the constrictions which are functions of the displacement rate of the actuators, hence the term "damping force"; and a pneumatic stiffness term (Fpneum, F'pneum) related to the pressure variation (P3'-P3) of the accumulators;

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the pressure of each of the accumulators is a function of the volume of gas contained therein; assuming that the volume of fluid in the hydraulic circuit is constant, on the grounds that the oil is incompressible compared wi-h the gas, it can be shown that this variation in volume is related to the displa.cement of the pistons. The forces Fpneum and F'pneum ire thus functions of piston displacement, hence the term "pneumatic stiffness".

With St S2 S1 S (S2 S1)/2 Then, for the vehicle body, in terms of vertical resultant and of hunting moment at O R F F' (Fdamx+F'damx) [(P3-Pa) St MO (F'damx Fdamx)a 2Sa (P3-P3') The following damping terms are obtained: Rdam (Ydamx F'damx) Modan (F'damx Fdamx)a The following vertical stiffness terr. is obtained with preloading: Rpneum [(P3-Pa) (P3'-Pa)]St Rpneum 2(PO-Pa)St Kx(PO, VO, St)rc The stiffness Kx is a function of the preloading and of the volume and of the difference in section of each of the actuators.

The following hunting righting torque is obtained: Mpneum 2Sa(E3-P3') Mpneum -K,(PO,V0,S,a)ac The angular stiffness K, is a function of the preloading and of the volume of each of the accumulators (PO, VO), of the sum of the thrust sections and of the lever arm When the actuators are displaced simultaneously, the volume of gas in each of the accumulators remains identical, and the pressures in the accumulators remain identical, and there is no righting torque. When the pistons are displaced in opposite directions (hunting), the volume of gas in one accumulator decreases, while che volume of the gas in the i ii ~-t tee.

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Ii 4 wniA 111 other accumulator increases, thereby creating a pressure difference between the accumulators, resulting in righting torque.

That apparatus clearly provides anti-hunting righting torque. However: the accumulrtor is presented as being a resilient element for supporting the vehicle body (this function is indeed performed because of the asymmetry of the tlrust sections of the actuators); the use of the accumulator to provide angular stiffness in hunting is suggested in the general text, but it is not claimed; the emphasis is laid on the effects of hunting damping and of longitudinal damping; and the differences in the sections of the actuators couple together the longitudinal stiffness and the angular stiffness in hunting. Those two stiffnesses are determined by the preloading pressure of the accumulator.

That is a drawback of that apparatus.

Figure 1 is a diagram showirg the principle of the roll-damping apparatus of the invention.

The roll-damping apparatus comprises a first shockabsorber Al and a second shock-absorber Al'.

Each shock-absorber comprises a cylinder 11, 11' in which a non-perforated piston 12, provided with rod 13, 13' is slidably mounted, the resulting assembly constituting an actuator 114, 114'.

The rod 13, 13' passes through the piston 12, 12'.

The piston 12, 12' delimits a first chamber 1, 1' referred to as a "compression chamber", and a second chamber 2, 2' referred to as the "expansion chamber".

The cylinder 11, 11' is filled with a fluid 16, 16', e.g. hydraulic oil.

The shock-absorber is further provided with a first check valve CL1, CL' referred to as a "compression zheck valve", and with a second check valve CL2, CL2' referred to as an "expansion check valve".

-t 12 A first hydraulic valve V2, V2' referred to as a "compression hydraulic valve", and a second hydrauli valve VI, Vl' referred to as an "expansion hydraulic valve" may be controlled electrically.

The semi-active shock-absorber further comprises a pre-loaded oleopneumatic accumulator 3, 3' constituLed by a chamber.

Such an oleopneumatic accumulator 3, 3' forms a fixed volume containing an inert gas under pressure and hydraulic oil to which the gas communicates its pressure.

The two fluids arce generally separated physically by a diaphragm or by a bladder.

The function of the accumulator is firstly to absorb the volume of oil corresponding to the volume of the rod when the shock-absorber is fully compressed, and secondly to guarantee at least a minimum pressure in the hydraulic circuit.

The compression check valve CL1, CL1' and the expansion hydraulic valve Vl, Vl' are mounted in parallel.

The compression check valve CL1 and the expansion hydraulic valve V1 are disposed between the expansion chamber 1 and an intermediate point A.

The compression check valve CL1' and the expansion hydraulic valve Vl' are disposed between the expansion chamber 1' and an intermediate point A'.

The expansion check valve CL2, CLT2' and the compression hydraulic valve V2, V2' aie mounted in parallel.

The expansion check valve CL2 and the compression hydraulic valve V2 are disposed between the compression chamber 2 and the intermediate point A'.

The expansion check valve CL2' and the compression hydraulic valve V2' are disposed between the compression chamber 2' and the intermediate point A.

A check valve CL3, CL3' and a hydraulic valve V3, V3' are mounted in parallel.

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Cr t 1 The check valve CL3 and the hydraulic valve V3 are disposed between the intermediate point A and the chamber of the accumulator 3.

The check valve CL3' and the hydraulic valve V3' are disposed between the intermediate point A' and the i chamber of the accumulator 3' The direccions of the check valves are as shown in Figure 1.

The actuators 114, 114' are disposed vertically in a transverse plane and, when they are used in a rail context, between a bogie 14 of the rail vehicle and the body 15 thereof.

One of the ends of each of the actuators 114, 114' is secured to the bogie 14 of the rail vehicle, and the other end of each of the actuators 114, 114' is secured to the body 15 of the vehicle.

The following description relates to an analysis of the roll-damping apparatus of the invention, the analysis being performed on the same basis as the analysis of Document FR 2 252 228 in the particular case when St 0, S1 S2 S.

The pressures at the intermediate points A and A' are included.

After calculation, the following are obtained: F [(P2-PB)-(P1-PA)]S S(P3'-P3)S F' (P3-P3')S With: 1 30 Fdamz [(P2-PB) (P1-PA)]S F'damz [P2'-PA) (P1'-PB)]S Fdame [(PA-P3) (PB-P3')]S Then: R F F' Fdamz F'damz MO (F'damz-F'damz)a 2Fdamea 2(P3-P3')Sa i The following roll righting torque is obtained: 17 Mpneum 2(P3-P3')Sa Mpneum -K 9 (PO,VO,S,a)ec The angular stiffness K 9 is a function of the preloading and of the volume of each of the accumulators (PO, VO), of the sum of the thrust sections and of the lever arm When the actuators are displaced simultaneously, the volume of gas in each of the accumulators remains identical, and the pressures in the accumulators remain identical, and there is no righting torque. When the pistons are displaced in opposite directions (roll), the volume of gas in one accumulator decreases, while the volume of the gas in the other accumulator increases, thereby creating a pressure difference between the accumulators, resulting in righting torque.

The fcllowing vertical damping force is obtained: Rdam Fdamz F'damz Fdamz and F'damz also induce damping torque: Mdam (F'damz-Fdamz)a As shown by the expressions Famz and F'amz as a function of the headloss, these forces are determined by the check valve/hydraulic valve sets (CL1/V1, CL2/V2, CL1'/VI', CL2'/V2').

The following roll-damping torque is obtained: 25 Mdam9 2Fdamea 2[(PA-P3) (PB-P3')]Sa This torque has no effect on the vertical damping.

It is determined by the headlosses (PA-P3) and (PB-P3'), and thus by the check valve/hydraulic valve sets (CL3/V3, CL3'/V3').

30 PA-P3 is related to the fluid flow rate QA3 from A towards the chamber of the accumulator 3. Assuming constant flow rate: QA3 Sz-Sz' S(zc-aSc)-S(zc+aec) -2S a ec Thus PA-P3 is related to Oc, and similarly PB-P3' is 35 related to QB3, 2S ec and therefore to ec, hence the term "roll damping" is justified.

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Figure 2 is a diagram showing the principle of the hunting-damping and longitudinal-damping apparatus of the invention.

In Figure 2, elements that are analogous to the elements shown in Figure 1 are designated by identical references.

In this anti-hunting apparatus, the actuators 114, 114' are disposed longitudinally, preferably in the same plane, and, when they are used in a rail context, between a bogie 14 of the rail vehicle and the body 15 thereof.

The following description relates to an analysis of the oleopneumatic hunting-damping and longitudinaldamping apparatus of the invention, the analysis being performed on the same basis as the analysis of Document FR 2 252 228 in the particular case when St 0, Sl S2 S.

The pressures at the intermediate points A and A' are included.

After calculation, the following are obtained: F [(P2-PB)-(P1-PA)]S (P3'-P3)S F' (P3-P3')S With: Fdamx [(P2-PB) (P1-PA)]S F'damx [P2'-PA) (P1'-PB)]S Fdame [(PA-P3) (PB-P3')]S Then: R F F' Fdamx F'damx MO (F'damx-F'damx)a 2Fdamua 2(P3-P3')Sa cr The following hunting righting torque is obtained: l t Mpneum 2(P3-P3')Sa Mpneum -K,(PO,V0,Sa)cc 35 The angular stiffness K, is a function of the preloading and of the volume of each of the accumulators (PO, VO), of the sum of the thrust sections and of 11 16 the lever arm When the actuators are displaced simultaneously, the volume of gas in each of the accumulators remains identical, and the pressures in the accumulators remain identical, and there is no righting torque. When the pistons are displaced in opposite directions (hunting), the volume of gas in one accumulator decreases, while the volume of the gas in the other accumulator increases, thereby creating a pressure difference between the accumulators, resulting in righting torque.

The following longitudinal damping force is obtained: Rdam Fdamx F'damx Fdamx and F'damx also induce damping torque: Mdam (F'damx-Fdamx)a.

As shown by the expressions Famx and F'amx as a function of the headloss, these forces are determined by the check valve/hydraulic valve sets (CL1/V1, CL2/V2, CL1'/V1', CL2'/V2').

The following hunting-damping torque is obtained: Mdama 2FdamQa 2[(PA-P3) (PB-P3')]Sa This torque has no effect on the longitudinal damping. It is determined by the headlosses (PA-P3) and and thus by the check valve/hydraulic valve S: 25 sets (CL3/V3, CL3'/V3').

;Pa-P3 is related to the fluid flow rate QA3 from A towards the chamber of the accumulator 3. Assuming constant flow rate: 3 QA3 Sx-Sx' S(xc-ac)-S(xc+ac) -2S a ac Thus PA-P3 is related to ac, and similarly PB-P3' is related to QB3' 2S ac and therefore to ac, hence the term "hunting damping" is justified.

List of variables used: F, F' actuator force on the vehicle body r 35 a 1/2 of the distance between the fastening i points at which the actuators are fastened to the vehicle body (lever arm) z, z' vertical displacement between the vehicle body and the bogie at the actuator fastening point zc vertical vehicle body displacement at the point 0 of the vehicle body, fixed bogie ec roll between the vehicle body and the bogie (radians); y transverse displacement of the vehicle body at the center of gravity a vehicle body hunting (radians); x, x' longitudinal displacement between the vehicle body and the bogie at the actuator fastening point xc longitudinal vehicle body displacement at the point 0 of the vehicle body, fixed bogie ac hunting between the vehicle body and the bogie (radians); S1 section of the actuator at the rod (asymmetrical actuator) (m 2 S2 section of the actuator at the end-wall (asymmetrical actuator) (m 2 St difference in the thrust section of the actuator (m 2 St S2 S1 rod section if the actuator is asymmetrical (m 2 and St 0 if the actuator is symmetrical; S actuator section (symmetrical actuator) (m 2 S (Sl S2)/2 if the actuator is asymmetrical; 30 Vl, V2, V3, V3', V1', V2': headloss regulation system, in which: opening is progressive as a function of pressure (passive system); opening is externally controlled an electrically controlled system); (Vi, V2) or (V3, V3') or V2') may correspond to the two orifices of the same valve; r :r S 88 cc 88 *85 8 88 8 t 8c C 8 C I 1 ,r

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CL1, CL2, CL3, CL4: check valves; vO, PO initial volume and pressure of the accumulators 3 and 3' (suspension at rest); and V forward speed of the vehicle

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