A method for high efficiency torque splitting between a front axle and a rear axle of a motor vehicle with an electric powertrain

Abstract

There is described a method for splitting torque between a front axle ( FA) and a rear axle (RA) of a vehicle (V) with an electric powertrain comprising at least one electric traction motor (Ml, M4) operatively associated with the front axle (FA) of the vehicle (V) and at least one electric traction motor (M2, M3) operatively associated with the rear axle (RA), the method comprising: - defining a reference torque split ratio (SF Nom ) as a function of a total target torque (TTgtTot), of a speed (VehicleSpeed) of the vehicle (V), of a limit electric power that can be absorbed by the electric traction motors in propulsion (PLimPrp) and a limit of electric power that can be delivered by the electric traction motors in regeneration (PLimRgn), - defining a corrected torque split ratio (SFCorr) as a function of said reference torque split ratio (SFNom), as a function of a torque splitting between a left wheel and a right wheel of each axle, and as a function of limit values of the torque deliverable (Xlim_mot_prp, Ylim_mot_prp, Zlim_mot_prp, Wlim_mot_prp) or the torque absorbable (Xlim_mot_rgn, Ylim_mot_rgn, Zlim_mot_rgn, Wlim_mot_rgn) by each electric traction motor of each axle, - controlling the torque delivered or absorbed by each traction electric motor of each axle as a function of said corrected torque split ratio (SFCorr).

Description

[0001] "A method for high efficiency torque splitting between a front axle and a rear axle of a motor vehicle with an electric powertrain"

[0002] ★★★★

[0003] TEXT OF THE DESCRIPTION

[0004] Field of the Invention

[0005] The present invention refers to vehicles having an electric powertrain, specifically of the type comprising at least one electric motor operatively associated with a front axle of the vehicle, and at least one electric motor operatively associated with a rear axle of the vehicle.

[0006] Prior Art

[0007] The torque split in the vehicles with an electric powertrain of the type comprising at least one electric motor operatively associated with a front axle of the vehicle and at least one electric motor operatively associated with a rear axle of the vehicle is generally performed only as a function of operating conditions - for example limits of electric power absorbed by the electric motors for the vehicle propulsion and / or limits of electric power delivered by the electric motors in the regeneration mode - and as a function of the dynamic balance of the vehicle - for example a torque split ratio between the front axle and the rear axle, and sometimes an asymmetrical distribution of the torque between a right wheel and a left wheel of the same axle. Although this is perfectly suitable for the purposes of operating management and dynamics of the vehicle, there is no further mediation of the control aiming at an increase in travel ranges or generally in efficiency requirements of the powertrain.

[0008] Object of the Invention

[0009] The invention aims at solving the technical problem described in the foregoing. Specifically, the invention aims at providing a method for splitting torque between a front axle and a rear axle of a motor vehicle with an electric powertrain which, while meeting all the management targets envisaged for the powertrain, will lead to a highly efficient operation of the same powertrain .

[0010] Summary of the Invention

[0011] The object of the invention is achieved by means of a method having the features set forth in the annexed claims, which form an integral part of the technical disclosure provided herein in relation to the invention.

[0012] Brief Description of the Figures

[0013] The invention will now be described with reference to the annexed Figures, which are provided by way of non-limiting example only and wherein:

[0014] - Figure 1 shows a flow diagram representative of a method according to the invention,

[0015] - Figure 2 shows a functional block diagram representative of a method according to the invention, - Figures 3 to 6 show various configurations of an electric powertrain for implementing the method according to the invention,

[0016] - Figure 7 and Figure 8 show first characteristic diagrams relating to the implementation of the method according to the invention,

[0017] - Figure 9 and Figure 10 show second characteristic diagrams relating to the implementation of the method according to the invention,

[0018] - Figure 11 is a functional block diagram representative of a step of the method according to the invention,

[0019] - Figure 12 is a functional block diagram representative of a further step of the method according to the invention, and

[0020] - Figure 13 is a functional block diagram representative of a still further step of the method according to the invention.

[0021] Detailed Description

[0022] Referring to Figure 1 and Figure 2, the invention defines a method for splitting torque between a front axle FA and a rear axle RA of a vehicle with an electric powertrain comprising at least one electric traction motor operatively associated with the front axle FA of the vehicle and at least one electric traction motor operatively associated with the rear axle RA. Referring to Figures 3 to 6, the method is generally applicable to vehicles with a powertrain corresponding to any one of the arrangements shown therein, specifically:

[0023] Figure 3

[0024] - a first electric traction motor Ml, operatively associated with a front right wheel FR of the vehicle V; the references and respectively denote a torque delivered by the motor Ml in propulsion and a torque absorbed by the motor Ml in regeneration,

[0025] - a second electric traction motor M2, operatively associated with a rear right wheel RR of the vehicle V; the references and respectively denote a torque delivered by the motor M2 in propulsion and a torque delivered by the motor M2 in regeneration,

[0026] - a third electric traction motor M3, operatively associated with a rear left wheel of the vehicle V; the references and respectively denote a torque delivered by the motor M3 in propulsion and a torque absorbed by the motor M3 in regeneration,

[0027] - a fourth electric traction motor M4, operatively associated with a front left wheel FL of the vehicle V; the references and respectively denote a torque delivered by the motor M4 in propulsion and a torque absorbed by the motor M4 in regeneration.

[0028] Figure 4

[0029] - a first electric traction motor M1, operatively associated with the front axle FA (by means of a differential); the references and respectively denote a torque delivered by the motor Ml in propulsion and a torque absorbed by the motor Ml in regeneration;

[0030] - a second electric traction motor M2, operatively associated with a rear right wheel RR of the vehicle V; the references and respectively denote a torque delivered by the motor M2 in propulsion and a torque absorbed by the motor M2 in regeneration;

[0031] - a third electric traction motor M3, operatively associated with a rear left wheel RL of the vehicle V; the references and respectively denote a torque delivered by the motor M3 in propulsion and a torque absorbed by the motor M3 in regeneration.

[0032] Figure 5

[0033] - a first electric traction motor Ml, operatively associated with a front right wheel FR of the vehicle V; the references and respectively denote a torque delivered by the motor Ml in propulsion and a torque absorbed by the motor Ml in regeneration;

[0034] - a second electric traction motor M2, operatively associated with the rear axle RA (e.g. by means of a differential); the references and respectively denote a torque delivered by the motor M2 in propulsion and a torque absorbed by the motor M2 in regeneration;

[0035] - a third electric traction motor M4, operatively associated with a front left wheel FL of the vehicle V; the references and respectively denote a torque delivered by the motor M4 in propulsion and a torque absorbed by the motor M4 in regeneration.

[0036] Figure 6

[0037] - a first electric traction motor Ml, operatively associated with the front axle FA (by means of a differential); the references zpropand zrgnrespectively denote a torque delivered by the motor Ml in propulsion and a torque absorbed by the motor Ml in regeneration;

[0038] - a second electric traction motor M2, operatively associated with the rear axle RA (e.g. by means of a differential); the references and respectively denote a torque delivered by the motor M2 in propulsion and a torque absorbed by the motor M2 in regeneration.

[0039] The method is schematically shown as a flow diagram in Figure 1 and as a functional diagram in Figure 2, and in both instances it is associated with reference number 1. The general description of the method according to the invention refers to the most general case shown in Figure 3, but it is to be understood that it is applicable to any of the powertrain arrangements shown, by simply removing the values or the relationships pertaining to the electric motors which are absent with respect to the diagram of Figure 3.

[0040] Generally speaking, the method according to the invention comprises:

[0041] - defining a reference torque split ratio (block 2) as a function of a total target torque (or barycentric torque) of a speed of the vehicle, of a limit electric power that can be absorbed by the electric traction motors in propulsion and of a limit electric power that can be delivered by the electric traction motors in regeneration

[0042] - defining a corrected torque split ratio (block 6) as a function of the reference torque split ratio , as a function of limit values of deliverable torque absorbable torque each electric traction motor Ml, M2, M3, M4 of each axle, and if necessary (depending on the configuration of the powertrain) also as a function of a torque difference between a left wheel and a right wheel of each axle 2ΔTVRP,2ΔTVRR,2ΔTVFP,2ΔTVFR(the first letter in the subscript ofΔTV denotes the axle - R for the rear axle, F for the front axle - and the second letter denotes the operating mode, in propulsion P or in regeneration R), (block 4),

[0043] - controlling the torque delivered ^r absorbed by each traction electric motor Ml, M2, M3, M4 of each axle as a function of the corrected torque split ratio SFCorr.

[0044] Preferably (block 8), the method according to the invention may further comprise limiting (block 8) a rate of temporal variation of the torque split ratio in a transition from the reference torque split ratio SFNomto the corrected torque split ratio SFCorr.

[0045] Figures 7, 8, 9 and 10 exemplify characteristic diagrams which are used for determining the ratio SFNom. In detail, the diagrams of Figures 7 and 8 - associated with the references 20 and 21 - correspond to representations of the curves of the efficiency value of the electric motors equipping the vehicle V as a function of the barycentric torque and of the travelling speed of the vehicle. As an exception to the premise set forth in the foregoing, for mere simplicity of illustration Figures 7 and 8 show a set of curves which may be applied to the configuration with three motors of Figure 4; however, it is to be understood that maps of this kind are available for any configuration of powertrains as per Figures 3 to 6.

[0046] The information conveyed by the set of curves of Figures 7 to 8 is a distribution of maximum efficiency domains of the powertrain as a function of the distribution of the barycentric torque request among one or more of the motors of the powertrain. In other words, in vehicles having the configuration shown in Figures 3 to 6, the request of the nominal barycentric torque may be satisfied by using one or more motors, in a way perfectly visible to the driver. In the case of the configuration with three motors in Figure 4, with low barycentric torques the maximum efficiency operating condition (domain "FA only") corresponds to meeting the barycentric torque request by the motor Ml only, on the front axle. This is due to the fact that operating both motors M2, M3 with a torque equalling half a torque which is already low in itself corresponds to operating the motors in conditions of low efficiency. As the request of barycentric torque increases, the maximum efficiency domain moves from "FA only" to "RA only", and therefore the barycentric torque is delivered by the two motors M2, M3, each operating at torque values which may be compared to the values of the motor Ml in the domain "FA only". As the barycentric torque further increases, the maximum efficiency operating point is necessarily in a domain "RA+FA", wherein both axles ae involved in the propulsion, and thus all the motors Ml, M2, M3 are working to satisfy the barycentric torque request. As regards regeneration, the same description applies, albeit using reversed signs for the torques. In both diagrams of Figures 7 and 8, the part of the plane with high barycentric torques and high speeds has a hyperbolic perimeter, which corresponds to the power limit in propulsion and in regeneration envisaged for the electric motors of the powertrain. In other words, the diagrams of Figures 7 and 8 show a nominal torque split ratio which corresponds to a maximum efficiency operation, i.e. the reference split ratio SFNom.

[0047] Figures 9 and 10 - associated with the references 22, 23 - exemplify the evolution of the maximum barycentric torque as the vehicle speed varies, with parametrisation with respect to the power limit (the parameter is associated with an arrow, which indicates the rising direction thereof; it is the limit power in propulsion or the limit power in regeneration • The speed of the vehicle is indicated elsewhere, with the reference .

[0048] Referring to Figure 11, the diagrams of Figures 9 and 10 are used for determining the upper limit (Hi) and the lower limit (Lo) of the value of the total barycentric torque (which corresponds to the nominal torque request imparted by the driver). The upper limit value - maximum barycentric torque in propulsion - and the lower limit value - maximum barycentric torque in regeneration - are determined by means of the diagrams of Figures 9 and 10 by using, as input data, the speed of the vehicle (both in propulsion and in regeneration) , and the limit value of power in propulsion for the operation in the propulsion mode, and the limit value of power in regeneration, • By using the value with upper and lower limits as an input item of data, together with the speed of the vehicle , in a map SF_MAP which summarises the sets of curves 20, 21 of Figures 7 and 8, it is possible to determine the reference torque split ratio . From an operational point of view, SFNomis defined as a torque split ratio expressed as a function of the torque on the front axle (either in propulsion or in regeneration), thus

[0049] Wherein : is the torque on the front axle is the torque on the rear axle

[0050] With reference to Figure 12, it describes the logic structure of the blocks 4 and 6 in combination, i.e. the sequence for calculating the corrected split ratio Defining the corrected torque split ratio comprises, in sequence:

[0051] - defining (block 60) a first reference torque for the front axle FA, as a function of the reference torque split ratio and of the total target torque, or total barycentric torque, ; the block 60 is a multiplier and therefore, due to the definition of provided in the foregoing (torque on the front axle / total torque), the block 60 calculates the torque through the product of by , which therefore represents the torque on the front axle in nominal conditions;

[0052] - defining (block 61) a first torque correction applicable to the first reference torque as a function of the limit values of the torque in propulsion and in regeneration for the front axle FA, and obtaining a first corrected torque for the front axle; the limit values (upper limit Hi at block 61) and (lower limit value Lo at block 61) may vary as a function of the component in consideration (i.e. of the configuration of the individual axle) and as a function of possible constraints of asymmetrical torque distribution on the axle (torque vectoring), the latter instance being considered only if the axle is equipped with two electric traction motors, one for each wheel;

[0053] - defining (block 62) a second reference torque for the rear axle RA by a difference between the total target torque and the first corrected torque for the front axle; the torque represents the torque which the rear axle should express in order to meet the target torque and the limitation imposed at block 61 to the front axle;

[0054] - defining (block 63) a second torque correction applicable to the second reference torque as a function of limit values of the torque in propulsion (upper limit Hi at block 63) and in regeneration (lower limit Lo at block 63) for the rear axle RA, and obtaining a second corrected torque for the rear axle RA; the limit values (upper limit Hi at block 63) and (lower limit Lo at block 63) may vary as a function of the component in consideration (i.e. of the configuration of the individual axle) and as a function of possible constraints of asymmetrical torque distribution on the axle (torque vectoring), the latter instance being applicable only if the axle is equipped with two electric traction motors, one for each wheel;

[0055] - obtaining (block 64) a second corrected torque for the front axle FA by a difference between the total target torque and the second corrected torque for the rear axle RA; the torque represents the torque which the front axle FA should express in order to meet the total target torque and the limitation imposed to the rear axle at block 63;

[0056] - defining (block 65) a third torque correction applicable to the second corrected torque as a function of the limit values of the torque in propulsion (upper limit Hi at block 65) and in regeneration (lower limit Lo at block 65) for the front axle FA, and obtaining a third corrected torque for the front axle FA,

[0057] - defining (block 67) the corrected torque split ratio as the ratio of the third corrected torque for the front axle FA to a sum of the third corrected torque for the front axle FA and of the first corrected torque for the rear axle RA.

[0058] In a vehicle having a configuration as per Figure 3, said limit values of the propulsion torque and of the regeneration torque for the front axle FA are determined as follows wherein : is a limit value of the propulsion torque for the fourth electric motor (M4) is a limit value of the propulsion torque for the first electric motor (Ml) 2ΔTVFPis a predetermined propulsion torque difference between the propulsion torque of the first electric motor Ml and the propulsion torque of the fourth electric motor M4, and represents the term of torque vectoring in propulsion, is a limit value of the regeneration torque for the fourth electric motor (M4) is a limit value of the regeneration torque for said first electric motor (Ml) 2ΔTVFRis a predetermined regeneration torque difference between the regeneration torque of the first electric motor Ml and the regeneration torque of the fourth electric motor M4, and represents the term of torque vectoring in regeneration.

[0059] Substantially, the torque limits are defined based on the most stringent torque situation on the individual wheel, chosen between the limit of the component (the terms without the part of torque vectoring) and the limit deriving from the torque vectoring (the terms with the part of torque vectoring).

[0060] Similarly, in the case of a powertrain according to Figure 3, the limit values of the propulsion torque and of the regeneration torque for the rear axle RA are determined as wherein : is a limit value of the propulsion torque for the third electric motor M3 is a limit value of the propulsion torque for the second electric motor (M2) 2ΔTVRPis a predetermined propulsion torque difference between the propulsion torque of the third electric motor and the propulsion torque of the second electric motor, and it represents the term of torque vectoring in propulsion, is a limit value of the regeneration torque for the third electric motor (M3) is a limit value of the regeneration torque for the second electric motor (M2) 2ΔTVRRis a predetermined regeneration torque difference between the regeneration torque of the third electric motor M3 and the regeneration torque of the second electric motor M2, and it represents the term of torque vectoring in regeneration.

[0061] In the case of a vehicle with a powertrain according to the diagram of Figure 4, the limit values of the propulsion torque and of the regeneration torque for the rear axle are determined exactly as in the case of the powertrain of Figure 3, i.e. as

[0062] On the contrary, for the front axle FA, the term of torque vectoring being absent due to the presence of only one electric motor, the following holds

[0063] It will be observed that the expressions provided in the foregoing for the front axle FA are true for both axles - of course, with reference to the respective torques - in the powertrain configuration of Figure 6, since the term of torque vectoring due to the presence of two electric traction motors on the same axle is absent, given the presence of only one electric traction motor for each axle FA, RA. It must be borne in mind that, if the mechanical connection system between the single motor of an axle (for example the motors Ml, M2) for the powertrain in figure 6 and the axle in consideration (FA, RA) is adapted to implement an asymmetrical torque distribution downstream of the electric motor (for example a torque vectoring differential or a limited slip differential), the action of asymmetrical torque distribution is not involved in the expressions for calculating the values of limit torque in propulsion and in regeneration as a term of torque vectoring, since this is an action which does not pertain to the electric powertrain. If necessary, the characteristics of the mechanical connection system may be included in the terms which express the torque limits of the component (especially if the use of such a mechanical system impacts on the limit torque deliverable or absorbable by the electric motor).

[0064] Referring to Figure 13, the diagram shown represents a logical sequence in order to limit a rate of temporal variation of the torque split ratio in a transition from the reference torque split ratio SFNomto the corrected torque split ratio SFCorr. Globally, this corresponds to the block 8 of the diagrams in Figures 1 and 2. In order to limit the temporal rate, from a map 80 the value is extracted of a maximum torque gradient (or maximum rate of temporal variation of the torque) as a function of the vehicle speed. The map 80 is parametrized as a function of increasing values of target torque and the maximum torque gradient generally increases as the vehicle speed increases and as the torque increases. The value of the maximum torque gradient is then multiplied (block 81) by a reference time interval thereby obtaining the maximum tolerable torque increase in the same reference time interval. Then, at block 82, the maximum tolerable torque increase divided by the torque yields the absolute value of the upper limit and of the lower limit of the gradient (rate of temporal variation) of the torque split ratio, thereby enabling controlling - and mitigating - the variations of the torque split ratio in the transition from .to Corr(block R_LIM, the output is a torque split ratio limited in the rate of temporal variation . This enables preventing the driver from perceiving the torque transition between the axles which is inherent in the transition from to

[0065] Thanks to the method according to the invention, it is possible to always operate in conditions of maximum efficiency and maximum safety with regard to overloads of the components of the powertrain, while simultaneously increasing the travel range and the reliability of the vehicle.

[0066] Of course, the implementation details and the embodiments may amply vary with respect to what has been described and illustrated, without departing from the extent of the present invention as defined in the annexed claims.

Claims

CLAIMS1. A method for splitting torque between a front axle (FA) and a rear axle (RA) of a vehicle (V) with an electric powertrain comprising at least one electric traction motor (Ml, M4) operatively associated with the front axle (FA) of the vehicle (V) and at least one electric traction motor (M2, M3) operatively associated with the rear axle (RA), the method comprising:- defining a reference torque split ratioas a function of a total target torque, of a speed of the vehicle (V), of a limit electricpower that can be absorbed by the electric traction motors in propulsion and a limit of electricpower that can be delivered by the electric traction motors in regeneration- defining a corrected torque split ratioas a function of said reference torque split ratio , and as a function of limit values of deliverabletorque or absorbabletorqueof each electric traction motor of each axle,- controlling the torque delivered or absorbed by each traction electric motor of each axle according to said corrected torque split ratio .

2. The method according to Claim 1, comprising defining said corrected torque split ratioalso as a function of a torque difference between a left wheel and a right wheel of at least one of the axles (FA, RA).

3. The method according to claim 1 or Claim 2, further comprising limiting a rate of temporal variation of the torque split ratio in a transition from said reference torque split ratio to said correctedtorque split ratio .

4. The method according to claim 3, wherein said limiting a rate of temporal variation comprises limitingthe rate of temporal variation below and above.

5. The method according to any one of the preceding claims, wherein said defining a corrected torque split ratiocomprises:- defining (60) a first reference torquefor the front axle (FA) as a function of said reference torque split ratioNomand said total target torquedefining (61) a first torque correction applicable to said first reference torqueas a function of propulsionand regeneration torque limit values for the front axle (FA),and obtaining a first corrected torquefor the front axle (FA)- defining (62) a second reference torquefor the rear axle (RA) by difference between said total target torque and said first corrected torquefor the front axle (FA),defining (63) a second torque correction applicable to said second target torqueas a function of propulsion and regenerationtorque limit values for the rear axle (RA), and obtaining a second corrected torquefor the rear axle (RA),- obtaining (64) a second corrected torque forthe front axle (FA) by a difference between said total target torqueand said second corrected torque for the rear axle (RA), defining (65) a third torque correction applicable to said second corrected torqueas a function of propulsion and regenerationtorque limit values for the front axle (FA),and obtaining a third corrected torquefor the front axle- defining said corrected torque split ratioas the ratio between said third corrected torquefor the front axle (FA) and a sum of said third corrected torquefor the front axle (FA) and said first corrected torque for the rear axle (RA).

6. The method according to Claim 1 or Claim 2, wherein the vehicle comprises:- a first electric traction motor (Ml) operatively associated with a right front wheel (FR) of the vehicle (V),- a second electric traction motor (M2) operatively associated with a right rear wheel (RR) of the vehicle (V),- a third electric traction motor (M3) operatively associated with a left rear wheel (RL) of the vehicle (V),- a fourth electric traction motor (M4) operatively associated with a left front wheel (FL) of the vehicle (V), wherein said propulsion and regeneration torque limit values for the front axle (FA) are determined aswherein: is a propulsion torque limit value for saidfourth electric motor (M4), is a propulsion torque limit value for saidfirst electric motor (Ml), 2ΔTVFPis a predetermined propulsion torque difference between the propulsion torque of the fourth electric motor (M4) and the propulsion torque of the first electric motor (Ml), is a regeneration torque limit value forsaid fourth electric motor (M4),is a regeneration torque limit value forsaid first electric motor (Ml), 2ΔTVFRis a predetermined regeneration torque difference between the regeneration torque of the fourth electric motor (M4) and the regeneration torque of the first electric motor (Ml).

7. The method according to claim 6, wherein said limit values of propulsion torque and regeneration torque for the rear axle (RA) are determined aswherein : is a propulsion torque limit value for saidthird electric motor (M3) is a propulsion torque limit valuefor said second electric motor (M2) 2ΔTVRPis a predetermined propulsion torque difference between the propulsion torque of the third electric motor and the propulsion torque of the second electric motor is a regeneration torque limit value forsaid third electric motor (M3) is a regeneration torque limit value forsaid second electric motor (M2) 2ΔTVRRis a predetermined regeneration torque difference between the regeneration torque of the third electric motor (M3) and the regeneration torque of the second electric motor (M2).

8. The method according to claim 1 or Claim 2, wherein the vehicle comprises:- a first electric traction motor (Ml) operatively associated with a front axle (FA) of the vehicle (V),- a second electric traction motor (M2) operativelyassociated with a right rear wheel (RR) of the vehicle (V),- a third electric traction motor (M3) operatively associated with a left rear wheel (RL) of the vehicle (V), wherein said propulsion and regeneration torque limit values for the rear axle are determined aswherein: is a propulsion torque limit value for saidthird electric motor (M3) is a propulsion torque limit value for saidsecond electric motor (M2) 2ΔTVRPis a predetermined propulsion torque difference between the propulsion torque of the third electric motor and the propulsion torque of the second electric motoris a regeneration torque limit value for said third electric motor (M3)is a regeneration torque limit value for said second electric motor (M2) 2ΔTVRRis a predetermined regeneration torque difference between the regeneration torque of the third electric motor (M3) and the regeneration torque of the second electric motor (M2).

9. The method according to claim 8, wherein the limit values of propulsion torque andregeneration torque for the front axle (FA) aredetermined as wherein:is a propulsion torque limit value for saidfirst electric motor (Ml), is a regeneration torque limit value forsaid first electric motor (Ml).

10. The method of Claim 4, wherein said limiting a temporal rate of variation of the torque split ratio comprises :- determining a value of a maximum rate of temporal variation of torque as a function of the vehicle speed ,- multiplying (81) said maximum rate of temporal variation of torque by a reference time intervalthereby obtaining a maximum tolerable torque increase in the reference time interval, - dividing (82) said maximum tolerable torque interval by said total target torque, thereby obtaining an absolute value of a lower limit and of an upper limit of said rate of temporal variation of torque

Images