METHOD AND SYSTEM FOR ESTIMATING CLUTCH PARAMETERS

A method of controlling a component of a powertrain of a vehicle is provided. The method comprises calculating an estimated clutch surface friction coefficient as a function of an initial clutch surface friction coefficient, a temperature of the clutch, and a rotational speed difference between a driving part and a driven part of the clutch; and adjusting a command signal to the component of the powertrain based upon the estimated clutch surface friction coefficient. A method of controlling a component of a powertrain of a vehicle comprises: estimating a clutch touchpoint xct of a clutch controlled by a clutch actuation system including a ballramp system, based on the variables of the system to determine the translation of the ball for which the clutch will transmit torque; and adjusting a command signal to the component of the powertrain based upon the estimated clutch touchpoint xct of the clutch.

TECHNICAL FIELD

The present disclosure relates to vehicle transmission systems. More particularly, the present disclosure relates to a transfer case and a clutch actuation system thereof.

BACKGROUND OF THE DISCLOSURE

Vehicle drivetrains, in particular vehicle drivetrains for a four-wheel drive capable vehicle, typically include a powertrain operable to generate rotary power, such as drive torque, which is transmitted via a transfer case to a primary driveline and a secondary driveline. The powertrain may include a prime mover, such as an engine or an electric traction motor, and a transmission. The prime mover is configured to rotate an input shaft, which is selectively operable via the transfer case to convert the rotary motion of the input shaft into rotary motion of the vehicle axles.

The transfer case typically includes the input shaft, and further includes a rear output shaft and a front output shaft, for driving the rear axle and the front axle, which may be part of a primary and secondary driveline. The transfer case may include a clutch pack for a friction clutch mechanism, with a rotary to linear conversion mechanism, such as a ballramp unit, ballscrew unit, camming devices, pivotable devices, or the like, configured to control the magnitude of a clutch engagement force applied to the clutch pack. The clutch pack is operable to control the transfer of torque between shafts that are selectively coupled via the clutch pack.

The clutch engagement force may have a minimum engagement force in which a minimal amount of drive torque is transferred between the shafts. The clutch assembly may also have a released mode for the friction clutch in which no drive torque is transferred. The clutch assembly may further include a maximum clutch engagement force.

To control the transfer of torque between shafts, it is desirable to know the minimum and maximum clutch engagement forces, which may be dependent on the rotary to linear conversion mechanism.

One value in controlling the engagement of the clutch assembly to transmit torque is the clutch “kiss point.” The kiss point is the value of the control variable in a clutch system where the friction clutch will begin to transmit torque. The kiss point may also be considered to be related to the minimum engagement force. However, it can be difficult to accurately determine the kiss point of a clutch system without substantial experimentation, which can be costly, due to the high number of variables associated with the components of a clutch system.

Physical characteristics of a clutch in a vehicle powertrain are important parameters for modeling and understanding vehicle performance and operation. One such physical characteristic is the surface friction coefficient, which affects the amount of torque transmitted through the clutch. Improved estimates of the clutch surface friction coefficient can lead to improvements in vehicle powertrain control.

Accordingly, improvements can be made in the determination of the clutch kiss point and the surface friction coefficient.

SUMMARY

In accordance with an aspect of the disclosure, a method of controlling a component of a powertrain of a vehicle comprises: calculating an estimated clutch surface friction coefficient as a function of an initial clutch surface friction coefficient, a temperature of the clutch, and a rotational speed difference between a driving part and a driven part of the clutch; and adjusting a command signal to the component of the powertrain based upon the estimated clutch surface friction coefficient. The component of the powertrain is one of a clutch actuator configured to actuate the clutch or a prime mover configured to supply an input torque to the driving part of the clutch.

In accordance with an aspect of the disclosure, a method of controlling a component of a powertrain of a vehicle is provided. The method comprises: estimating a clutch touchpoint xctof a clutch controlled by a clutch actuation system including an electric motor having a first shaft, a reduction gear coupled to the first shaft, a second shaft coupled to the reduction gear, and a cam system coupled to the first shaft; and adjusting a command signal to the component of the powertrain based upon the estimated clutch touchpoint xctof the clutch, where the component of the powertrain is one of the clutch actuation system or a prime mover configured to supply an input torque to a driving part of the clutch. The cam system includes a ball configured to translate in an axial direction and to impart a clutch engagement force on a clutch pack, wherein rotation of the second shaft causes an axial translation of the ball; and the clutch touchpoint xctcorresponds to the axial translation of the ball where the clutch pack first transmits torque. The step of estimating the clutch touchpoint xctof the clutch includes determining the clutch touchpoint xctas a function of: a conversion rate correlating the axial translation of the ball to a rotation angle of a plate defining a ramp and configured to rotate about an axis to cause the axial translation of the ball, a total friction force on the ball, an angle between the ramp and a plane of the plate perpendicular to the axis, an axial stiffness of a clutch spring acting upon the clutch, a reduction gear ratio of the reduction gear, an equivalent gear ratio between the second shaft and the plate, a mechanical efficiency between the first shaft and the second shaft, a mechanical efficiency between the second shaft and the plate, a mechanical efficiency between the plate and the ball, and an orbital radius of the ball.

DESCRIPTION OF THE ENABLING EMBODIMENT

Referring initially toFIG. 1, a transfer case10is illustrated schematically, and includes a clutch actuation system12. The clutch actuation system12illustrated schematically is based on a transfer-case type clutch actuation system. It will be appreciated that the clutch actuation system12may be one part of the overall transfer case system, which is not shown in detail.

The clutch actuation system12is an electromechanical system, and includes an electrical portion14and a mechanical portion16. The electrical portion14and the mechanical portion16operate together to control the clutch actuation system12.

The electrical portion14includes an electric motor18, and the mechanical portion16includes a reduction gear20and a cam system22. The cam system22may include a cam24, a lever26, and a plate28. The electric motor18includes a rotor30that is rotated in response to an electric current applied to the motor18. The rotor30is coupled to the reduction gear20via a first shaft32, such that actuation of the motor18and rotation of the rotor30causes rotation of the reduction gear20. The reduction gear20is further coupled to the cam24of the cam system22via a second shaft34. Thus, rotation of the reduction gear20will cause rotation of the second shaft34and the cam24coupled thereto.

The transfer case10further includes a plurality of rotatable shafts that are part of the powertrain and drivetrain system of the vehicle. As shown schematically inFIG. 1, an input shaft or third shaft36is coupled to one side of a clutch pack38, which may also be called a clutch38. A rear shaft40is coupled to the opposite side of the clutch pack38. A chain41couples the rear shaft40to a front shaft42.

The cam system22may further include one or more balls44that are part of a ballramp system46. Actuation of the cam system22will cause the balls44to travel as part of the ballramp system46, thereby causing linear/axial movement of the cam system22, which will impart a clutch engagement force on the clutch pack38. With the clutch pack38engaged and transmitting torque, rotation of the third shaft36will cause rotation of the rear shaft40and the front shaft42. More specifically, the plate28defines a ramp48that interacts with the one or more balls44to cause the one or more balls44to translate, or to move, in an axial direction parallel to an axis of rotation of the plate28, as the plate28is rotated. The one or more balls44are disposed between the ramp48of the plate28and the clutch pack38, so this translation of the one or more balls44applies pressure to the clutch pack38which results in the clutch engagement force. Torque is selectively transmitted by the clutch pack38between the third shaft36and the rear shaft40when the clutch pack38is subjected to the clutch engagement force. It will be appreciated that other arrangements of the shafts may also be used, and that the clutch pack38may be coupled to different types of shafts for selectively transferring torque between shafts.

To operate the clutch actuation system12, the motor18may be actuated by an electric current (i) to the motor18, which will cause rotation or angular displacement of the first shaft32. Rotation or angular displacement of the first shaft32will cause rotation and angular displacement of the second shaft34, according to the ratio of the reduction gear20. Rotation or angular displacement of the second shaft34will cause movement of the cam system22and, ultimately, engagement of the clutch pack38.

The kiss point or touchpoint of the clutch actuation system12can be estimated as follows.

1. Adaptive Normalized Gradient Approach

Two cases are considered for the adaptive normalized gradient approach: linear spring case and nonlinear spring case.

Case 1: Estimation Algorithm based on Linear Clutch Spring

The equation that describes the electrical portion16can be represented by the following:

where i is the applied current in the motor18; θ1is the angular position of the first shaft32; v is the voltage supplied to the electric motor18; parameters R, L and Kerepresent the resistance, the inductance and the electromotive force constant, respectively.

The mechanical aspects of the motor18can be modelled by the following equation:

where Jmis the electric motor inertia; Kmis the motor torque constant; b1is the damping of first shaft32; and Tl1is the torque load from the first shaft32.

The reduction gear can be simply represented by the following equation if the gear lash is ignored:

where iris the reduction gear ratio; {dot over (θ)}1is the angular velocity of the first shaft32; and {dot over (θ)}2is the angular velocity of second shaft34.

The cam shaft-lever-ball subsystem of the cam system22converts the rotation angle of the second shaft34to the ball44displacement Xb. The conversion relationship between the cam angle to the following stroke is typically nonlinear, but in the 4-wheel-drive normal working range, the relationship is quite linear. Thus, the relationship between them can be expressed by:

where s is the stroke of the cam24, θ2is the angular position of second shaft34, and kcamand acamare constants. The cam24rotates the plate28on the third shaft36through the lever arm26and the rotation angle θ3of the plate28can be modelled as:

The ball ramp relationship, which is the relationship between the displacement of the ball44displacement and the rotation angle θ3of the plate28, is also a linear function, and can be modeled as following:

where p0is the conversion rate and xbis the total displacement of the ball44.

Combining all equations above, the total displacement of the ball44can be expressed as:

Although the clutch touchpoint is initially designed as a constant xc0, the total touchpoint varies over time. Consider the touchpoint variation as x0, the total touchpoint displacement xctnow becomes:

The relationship between the clutch displacement and the clutch force can be expressed as:

where FNis the clutch normal force; and is an axial stiffness of a clutch spring within the clutch38.

The load torque comes from the contact of the ball44and the clutch surface. The force that drives the ball44to rotate along the ramp48of the plate28is the force that will introduce the load torque to the third shaft36, and it can be represented by:

where Fbis the tangential force on the ball44in a plate plane extending perpendicular to the axis about which the plate28rotates; and β is the angle between the ramp48and the plate plane of the plate28.

In one aspect, there are three balls44and three ramps48distributed at regular intervals on the plate28(i.e. the ramps48are each spaced apart by 120 degrees). Thus, the load torque on the third shaft36can be obtained by:

where rbis the radius of the ball's orbit; Tl3is the load torque exerted on the third shaft36, ηpis the mechanical efficiency from the plate to the ball, and Ffis the total friction force on the ball44. The total friction force Ffis modeled as the general friction:

where FCis the Coulomb friction; Fsis the Stiction friction; Feis External force; Fvis the viscous friction coefficient; v is the movement velocity of the ball44; vsis the Stribeck velocity; and v0is threshold velocity.

Combining all the equations, the load torque on the third shaft36will be

Note that the torque relationship between the first shaft to the second shaft and between the second shaft to the third shaft can be represented below, respectively.

where ηris the mechanical efficiency coefficient from the first shaft32to the second shaft34, isis the equivalent gear ratio between the second shaft34and the plate28resulting from the action of the cam system22to rotate the plate28; and ηsis the mechanical efficiency coefficient between the second shaft34and the plate28resulting from the action of the cam system22to rotate the plate28.

Considering the torque ratio in the mechanical connection from the third shaft36to the first shaft32, when the clutch38is engaged, the load torque on the first shaft32is:

This completes the clutch actuation system12modeling.

With the clutch actuation system12being modeled, a model-based adaptive estimation algorithm has been established for estimating the clutch touchpoint.

For the preparation of developing the adaptive estimation algorithm, choose the states as

the state space representation of the system becomes:

A more compact form of the system can be read as:

and the term d is the unknown input due to the touchpoint.

In this case, the transfer function representation of the system is in the form of:

In preparation for the adaptive estimation of the unknown term d, using the hybrid notation containing both time domain and frequency domain signal, rearrange the above equation.

Rewrite it as:

where γ′(t)=y(t)−Gu(s)u(t),d=θ and φ(t)=Gd(s)*1. This is the linear parametric model for the adaptive estimation. If we choose the normalized gradient method, the adaptive law can be designed as:

where γ and k are designing adaptive parameters.

Once the unknown term dis estimated and converged, the clutch touchpoint xctcan be obtained from equation (16):

Accordingly, in view of the above, the clutch touchpoint xctcan be estimated and determined based on the modeling of the clutch actuation system12and the above-described adaptive estimation process.

Case 2: Estimation Algorithm based on Nonlinear Clutch Spring

In equation (9), the clutch spring stiffness is assumed to be linear. However, in practical, the spring stiffness may be nonlinear, especially when the clutch works under overtaken condition. Therefore, in this case, the estimation algorithm based on nonlinear spring stiffness is developed. Consider the nonlinear spring stiffness takes the following form.

where kc1is the linear portion coefficient of the spring stiffness; and kc2is the nonlinear portion coefficient of the spring stiffness.

Comparing with the linear spring case, the change is mainly in the load torque on shaft3(i.e. the third shaft36) described by equation (13). Therefore, the load torque on the first shaft32will be changed accordingly. With certain manipulation, the load torque on the first shaft32can be expressed as:

Note that K′ is the same as K in the linear case and term d′ now contains the nonlinear cubic unknown term. The adaptive estimation algorithm as the linear spring case can still be used, however, the estimated unknown term now becomes d′, instead of d. The third order nonlinear equation needs to be solved to obtain the touchpoint xct.

In the adaptive normalized Least-Squares estimation algorithm, only the linear spring case is considered. The algorithm is developed based on the equations (16) and (21). Specifically, the Least-Squares estimation algorithm is design as the following form.

where κ is the design parameter, P(k) is the ‘gain’ matrix.

To validate the above adaptive estimation analysis, actual vehicle testing data was obtained and touchpoint estimation results are presented for both linear and nonlinear spring cases. The results of vehicle testing data are shown inFIGS. 2 and 3. In the vehicle testing, actual measurements were made to obtain actual measured data for input voltage of the motor18, the rotating position of the cam24about the second shaft34, and the velocity of the ball44. This measurement data is shown inFIGS. 2 and 3for the two verification cases.

In addition to the measurement data of the voltage, cam position, and ball velocity, the estimation of the clutch touchpoint xctfor both linear clutch spring and nonlinear clutch spring according to the above algorithm are shown, based on the known variables of the system on which the actual verification was performed. Note that for the linear case as shown inFIG. 2, the touchpoint estimation results only valid between 21-23s, which is actually during clutch slip. However, in the nonlinear case, with the consideration of the nonlinear clutch spring stiffness, the touchpoint estimation result is valid between 20-23s, which compared with the linear case, has improved almost 1 second for effective estimation duration with acceptable estimation errors (maximum error is 1.6%). This improvement is important since the total clutch engaging period is only 4 seconds. And note that during the improved duration the clutch operates under overtaken condition. Therefore, by considering the nonlinear spring stiffness, the estimation can be extended to the clutch overtaken and slip conditions.

Furthermore, the accuracy and robustness of the algorithms can be evaluated by checkingFIG. 4, where the touchpoint estimation results of a linear spring case is presented in graph90, and the touchpoint estimation results of a nonlinear spring case is presented in graph92. As shown inFIG. 4, with both linear and nonlinear models, the estimation is accurate since the maximum estimation error is small, around 1.6% for linear case, and 1% for nonlinear case. However, the robustness of both cases appears to be unsatisfactory. In other words, both the linear and nonlinear models produce results with more variation than results from using non-model-based approaches.

Therefore, the adaptive normalized Least-Squares estimation algorithm is proposed to improve robustness.FIG. 5shows the estimation results in two graphs94,96having a common time axis. Specifically, graph94shows the touchpoint estimation results using the adaptive normalized Least-Squares estimation algorithm, and graph96shows clutch temperature over the same timeline as is used in graph94. The estimation results using the adaptive normalized Least-Squares estimation algorithm have a small mean error (0.8%), which shows that the estimation result is accurate. The estimation results using the adaptive normalized Least-Squares estimation algorithm also have a small standard deviation (0.0074), which shows that the Least-Squares estimation algorithm is more robust than current methods, such as non-model-based approaches which employ table lookups and heavy calibration. In addition, one important feature of the Least-Square estimation algorithm is that the estimated touchpoint displacement xctdecreases as the clutch oil temperature increases, which corresponds to the practical change due to the fact that there is thermal expansion in clutch disks.

A system and method for estimating a surface friction coefficient μcof a clutch in a vehicle powertrain is also provided. The clutch is configured to selectively couple a driven part to be rotated by a driving part. The subject clutch may be any clutch used in a vehicle powertrain, such as a clutch in a transfer case configured to selectively decouple a motor or engine from driving one or more wheels of a vehicle. The clutch may be any other type of clutch in a vehicle powertrain. For example, the clutch may be used to selectively control transfer of torque in a manual or automatic transmission vehicle. The clutch may be used within a conventional automatic transmission or a dual-clutch transmission. In some embodiments, the clutch may selectively transmit torque between an engine or motor and a transmission. In some embodiments, the clutch may selectively transmit torque between the transmission and one or more wheels of the vehicle. The clutch may have any physical arrangement, including one or more clutch surfaces, which may be operated under either dry conditions or wet conditions, submerged in a liquid.

Based on the estimated clutch surface friction coefficient, a parameterized clutch surface friction coefficient model is also proposed so that the clutch surface friction coefficient can be estimated in real-time. An important aspect to estimate clutch surface friction coefficient is to obtain the torque transmitted through the clutch. The clutch torque estimation is performed under various clutch operation conditions and relies on a vehicle speed estimation, and effective tire radius estimation. A way of estimating the vehicle speed is proposed based on the vehicle body dynamics. The advantage of the proposed speed estimation method is that the algorithm is based on the constraint of total tire force. A novel way of calculating the effective tire radius is described. Particularly, a nominal effective tire radius estimation method is proposed using the tire pressure information, and considering the acceleration effect of the vehicle, the effective tire radius is compensated with a quadratic term of vehicle acceleration. The above proposed way of estimating speed and effective tire radius resulting a good estimation of clutch torque when the clutch works in the overtaken condition. For clutch operation in a slip condition, a further slip speed compensation for the front tires is proposed, and the estimation results closely match the measured clutch torque.

FIG. 6shows a schematic block diagram of a system100for modeling clutch surface friction coefficient μcand estimating clutch torque T in accordance with the present disclosure. Specifically, the system100includes a clutch torque model112configured to generate an estimated clutch torque Tcas a function of clutch level or actuation position, clutch touchpoint xct, and the clutch surface friction coefficient μc. The system100also includes a parameterized model114configured to determine the clutch surface friction coefficient μcin real-time and as a function of an initial clutch surface friction coefficient, clutch temperature, and a rotational speed difference between clutch driving and driven plates. The parameterized model114may use a recursive least square algorithm to model the clutch surface friction coefficient μc. The real-time clutch surface friction coefficient μc0may be calculated by a surface friction coefficient model118based upon the clutch touchpoint xctand an estimated clutch torque Tc. The clutch touchpoint xctis estimated by a clutch touchpoint estimation model116. The estimated clutch torque Tc. may be determined by a clutch torque estimation model120under different clutch operating conditions using one or more vehicle operating values, such as speed, acceleration, effective tire radius, etc.

Any or all of the models112,114,116,118,120in the system100may be implemented using software, hardware, or a combination of hardware and software. Any or all of the models112,114,116,118,120in the system100may be implemented using general-purpose computing devices, such as a microprocessor or microcontroller running a program stored in a non-transient memory. Alternatively or additionally, any or all of the112,114,116,118,120in the system100may be implemented using special-purpose computing devices, such as an application-specific integrated circuit (ASIC) and/or a field-programmable gate array (FPGA).

Clutch Surface Friction Coefficient Estimation

Torque transmitted through a clutch is typically used to estimate the clutch surface friction coefficient. A known relationship between the clutch torque and the friction coefficient is:

where Tcis the clutch torque; μcis the clutch surface friction coefficient; ncis the total effective number of engaging clutch surfaces; FNis the normal force between clutch pack; and rceffis the effective radius of the clutch.

The clutch normal force FNconsidering clutch touchpoint distance is usually a piecewise linear function that can be expressed as:

where xpis the actuated position of the clutch, and xctis the clutch touchpoint displacement.

The clutch effective radius rceffis approximated by equation (29), below, which the parameter relationship is shown with reference to an example clutch130inFIG. 7.

where rcois the clutch outer radius; and rciis the clutch inner radius.

Therefore, combining equations (27)-(29), the clutch surface friction coefficient μccan be estimated by equation (30), below:

The first task is to estimate the torque transmitted by the clutch while the vehicle is operating, which will be introduced in the following sections.

Clutch Torque Estimation

Clutch Torque Estimation under Clutch Overtaken Condition

Consider the vehicle body dynamics, and refer to the free body diagram of a vehicle140shown inFIG. 8, the force balance can be expressed as following according to the Newton Second Law:

where m is the vehicle mass; v is vehicle longitudinal speed; F is the total longitudinal force respectively; Fais the air drag force; Ffroand Frroare the front and rear tire rolling resistance respectively; and θ is the road grade angle.

FIG. 8shows a free body diagram of a vehicle140in accordance with the present disclosure. The air drag force Fa acting on the vehicle140can be approximated using equation (32), below:

where Cais the air drag coefficient; pais air density; and Aais the vehicle front section area.

The front and rear tire rolling resistance force Ffro, and Frro, respectively, can be combined to a total tire resistance force, and is usually modeled as a function of vehicle speed, using equation (33), below:

Note that the measured acceleration ax usually contains the information of road grade, and can be represented by equation (34), below:

where axis the measured acceleration. Combining equations (31)-(34), the total longitudinal force Ff+Fris given by equation (9), below:

From this perspective, the longitudinal tire force F is a function of measured vehicle acceleration, which can be measured accurately, and vehicle speed.

The total longitudinal force can also be related with the tire speed and vehicle speed using the relation of equation (36), below:

where Cfand Crare the front and rear longitudinal stiffness, respectively.

Based on equations (35) and (36), equation (37), below, gives an estimate of the vehicle speed based on the vehicle acceleration.

Compensated Effective Tire Radius Model

The effective tire radius is calculated using the following equations.

where refis the front effective tire radius; rwfis the undeformed tire radius; and Zfis the deformation displacement of the front tires.FIG. 9is a side view diagram of a tire showing the tire radius parameters.

The tire deformation Zfis obtained by the tire normal force using the following equation:

where Fzfrepresents front tire normal force; and kftrepresents front tire vertical stiffness.

Tire normal force is obtained by Newton's Law using equation (14), below:

where Lfand Lrare the distance between front axle to center of gravity and rear axle to center of gravity.

Tire vertical stiffness is related with tire inflation pressure and tire parameters by equation (41), below:

where afand bfare coefficients that varies for different tires and need to be calibrated; pftrepresents front tire inflation pressure; AR is the aspect ratio of tires; SNis the section width of tires; and DRis the tire rim diameter.

The compensated effective tire radius takes the form of equation (42), below:

Front Tire Dynamics

FIG. 10shows a free body diagram of a front tire150f. In the free body diagram of the tire, consider the Newton's Law, the following equation can be obtained as equation (43):

where Jfis the front wheel inertia; wfis the front wheel speed; Tfis the front propeller shaft torque; ifdis the front differential ratio; Ffis the front wheel longitudinal force; and rfis the tire effective radius.

If ignoring the mechanical efficiency loss from the clutch to the front propeller shaft, the transmitted clutch torque Tcequals to the front propeller shaft torque Tf, i.e., Tc=Tf.

Torque Estimation Results

This section shows validation of the proposed method for estimating torque. Note that we can concentrate on the acceleration and coasting down duration data.FIG. 11shows a graph200with plots210,220,230,240of acceleration, tire radius, vehicle speed, and clutch torque, respectively, over a common time scale of 0-25s. Specifically, graph200shows estimation results under a clutch overtaken condition. First plot210includes a line212showing vehicle longitudinal acceleration in meters per second-squared (m/s2). Second plot220includes a first line222showing original or baseline front tire radius rfof a front tire150f, and a second line222showing compensated front tire radius rf, or the effective front tire radius refcas calculated using the effective tire radius model of the present disclosure, with values in meters (m). In other words, the compensated front tire radius rfplotted by line222shows the tire radius is changing according to the vehicle longitudinal acceleration.

Third plot230includes a first line232showing a measured vehicle speed Vspd, and a second line232showing estimated vehicle speed Vspd, as calculated using the effective tire radius refcof the present disclosure with values in meters per second (m/s). The estimated vehicle speed is compared to the measured vehicle speed, which is calculated based on the measured wheel rotating speed. As shown in the third plot230the estimated speed Vspdis very close to the measured speed Vspd. Fourth plot240shows different values of clutch torque Tcin Newton-meters (Nm). The fourth plot240includes a first line242showing measured clutch torque Tc, and a second line244showing non-compensated clutch torque Tcand a third line246showing compensated clutch torque Tccalculated in accordance with the present disclosure. The measured clutch torque Tcmay be determined, for example, using a dynamometer. The measured clutch torque Tcmay not be available to an onboard controller in the vehicle under normal operation. The compensated clutch torque Tcclosely tracks the measured clutch torque Tc, whereas the non-compensated clutch torque Tcdeviates significantly from the measured clutch torque Tc.

The estimated front torque is shown in the fourth plot240ofFIG. 11, where it can be seen that during both acceleration and coasting down, with effective tire radius compensation, the estimated result matches perfectly with the actual measured torque. Note that we can ignore the duration other than acceleration and coast down.

Clutch Torque Estimation Model under Clutch Slip Condition

Modified Model for Vehicle Speed Estimation

Under clutch slip condition, the rotational speed difference between clutch driving and driven parts is defined as Δrpm, and is calculated by equation (44), below:

where wfand wrare average front and rear tire rotational speed, respectively; ifdand irdare front and rear differential ratio, respectively.

Therefore, the slip speed in the front tires transmitted from clutch slip can be calculated by equation (45), below:

The actual front tires linear speed with slip speed compensation under clutch slip condition is defined by equation (46), below:

where vfcis the compensated front tires speed. The front tire force in equation (36) is then replaced by:

where Ffcis the compensated front tire force.

The speed estimation formula (37) is converted to the following form under clutch slip condition.

where vcis the compensated vehicle speed.

FIG. 12shows a graph250with plots260,270of vehicle speed and clutch torque over a common time scale. Specifically,FIG. 7shows the clutch torque estimation under clutch slip condition. Plot260includes a first line262of estimated vehicle speed Vspdand a second line264of measured vehicle speed Vspd, with values in meters per second (m/s). The estimated vehicle speed Vspdis calculated using a method of the present disclosure, with speed compensation under the clutch slipping condition. The estimated vehicle speed is compared to the measured vehicle speed, which is calculated based on the measured wheel rotating speed. As shown in the plot260the estimated vehicle speed Vspdwith slip speed compensation is still very close to the measured speed. Plot270shows different values of clutch torque Tcin Newton-meters (Nm). Plot270includes a first line272showing measured clutch torque Tc, and a second line274showing non-compensated clutch torque Tcand a third line276showing compensated clutch torque Tccalculated in accordance with the present disclosure. The compensated clutch torque Tcshows improved estimation performance to match the measured clutch torque Tccompared with the clutch torque Tcwithout compensation.

Parameterized Clutch Surface Friction Coefficient Model

Parameterized Model Development

Once the clutch surface friction coefficient is obtained through equation (30), to get the clutch surface friction coefficient in real time, a parameterized clutch surface friction coefficient model can be established relating it with the clutch surface friction material, clutch operating temperature and the clutch slip speed. The mathematical description can be expressed as:

where μ0is the initial clutch surface friction coefficient determined by the clutch material; Tois the clutch operating temperature;rpm is the clutch slip speed between the driving part and driven part; and the coefficients a and b are to be determined.

The model can be further arranged to the following linear parametric form:

where y=μc is the model output; θ*=[μ0a b] is the unknown coefficients vector to be estimated; and

is the known regression vector.

Letting θ be an estimate of θ*, the following output error parametric form in discrete time with sampling time T can be obtained:

where ε(k)=y(k)−θ(k)ϕ(k) is the output error; and {tilde over (θ)}(k)=θ(k)−θ* is the parameter error.

An adaptive estimation algorithm based on the normalized gradient method can be used to estimate θ.

where m2(k)=τ+ϕT(k)ϕ(k) is designed to guarantee the boundedness of the estimation algorithm, and τ>0 is a designing parameter that determines the estimation convergence rate. F is another design parameter satisfying 0<Γ<2I to guarantee the convergence of the output error, where I is an identity matrix with appropriate dimension;θandθare calibrated lower and upper bound for θ, respectively.

Enabling Conditions Specification

Note that the parameterized model will only update the friction coefficient model when the vehicle is operating under certain conditions. These conditions are chosen based on the model accuracy. This will not impact the overall estimation due to the fact that the friction coefficient changes slowly with time. This implies the friction coefficient surface will only be updated when modeling is accurate and represents the actual physics of the system. The following conditions are specified to ensure the accuracy of the updated adaptive friction surface.

Conclusion of Clutch Surface Friction Coefficient Estimation Model

In conclusion, first, the clutch surface friction coefficient estimation model is established; second, the clutch torque is estimated under various clutch operation conditions and the estimation shows the validity of the proposed estimation scheme; finally, a parameterized model of clutch surface friction coefficient for real-time estimation using the adaptive estimation algorithm is proposed.

In accordance with an aspect of the disclosure and as shown in the flow chart onFIG. 13, a first method300of controlling a component of a powertrain of a vehicle is provided. The provided first method300may provide for smoother and/or more efficient operation of the vehicle powertrain. For example, the provided first method300may allow a clutch to be operated with an actuation force that causes the clutch to produce a desired output torque that is more precise than is possible with conventional methods. The provided first method300may allow a smoother operation of the clutch38and/or a smoother operation of the vehicle powertrain as a whole, when compared with conventional methods.

The first method300includes a first step302of calculating an estimated clutch surface friction coefficient μcas a function of an initial clutch surface friction coefficient μ0, a temperature Toof the clutch38, and a rotational speed differencerpm between a driving part and a driven part of the clutch38.

In some embodiments, a parameterized model is used to calculate the estimated clutch surface friction coefficient μc. In some embodiments, the first method300includes estimating the clutch surface friction coefficient μcin real time during operation of the vehicle. In some embodiments, the estimated clutch surface friction coefficient μcis calculated only when a given set of vehicle operating parameters are within corresponding predetermined conditions. For example, the estimated clutch surface friction coefficient μcmay be calculated only when the clutch is to be engaged or disengaged, or when an input to the clutch is driven above a predetermined speed and/or above a predetermined torque.

The estimated clutch surface friction coefficient μcmay be calculated in the first step302according to the equation μc=μ0+aTo+bΔrpm, where μcis the estimated clutch surface friction coefficient, go is the initial clutch surface friction coefficient determined by the clutch material; Tois the clutch operating temperature, Δrpm is the rotational speed between the driving part and driven part, and a and b are coefficients to be determined. In some embodiments, calculating the estimated clutch surface friction coefficient μcfurther comprises determining values of the coefficients a and b using an adaptive estimation model.

The first method300proceeds with a second step304of adjusting a command signal to the component of the powertrain based upon the estimated clutch surface friction coefficient μc. The command signal may be generated by a controller, such as a powertrain control module (PCM), to control operation of the component of the powertrain. The component of the powertrain may be a clutch actuator configured to actuate the clutch. For example, adjusting the operation of the component of the powertrain may include adjusting a command signal, such as a position command or a torque command, supplied to the clutch actuator. The clutch actuator may include the electric motor18, although other actuators may be used, such as a hydraulic cylinder. Alternatively or additionally, the component of the powertrain may be a prime mover, such as an electric motor or an internal combustion engine configured to supply an input torque to the driving part of the clutch. For example, adjusting the command signal to the component of the powertrain may include adjusting a torque command, an applied voltage, or a throttle position of the prime mover. This second step304may include adjusting other components of the powertrain, such as a gear selection or a gear ratio setting in a transmission or other gearbox.

In some embodiments, the first method300further comprises estimating the clutch touchpoint displacement xctusing a clutch touchpoint estimation model116at step306.

In some embodiments, the first method300further comprises estimating a clutch torque Tctransmitted by the clutch38using the estimated clutch surface friction coefficient μcat step308. For example, the clutch torque Tctransmitted by the clutch38may be estimated with the clutch in an overtaken condition. Alternatively or additionally, the clutch torque Tctransmitted by the clutch38may be estimated with the clutch38in a slip condition. The estimated clutch torque Tctransmitted by the clutch38may be used for adjusting the command signal to the component of the powertrain, similarly to how the command signal is adjusted based upon the estimated clutch surface friction coefficient μcat step304.

In some embodiments, step308of estimating the clutch torque Tctransmitted by the clutch38further comprises the first sub-step308A of determining an effective tire radius re of a tire of the vehicle. The effective tire radius may include a tire deformation as a function of a normal force acting upon the tire and as a function of a vertical stiffness of the tire. For example, a compensated effective tire radius may be calculated in accordance with

where reis the effective tire radius; rwis the undeformed tire radius; and z is the deformation displacement of the tire.

Step308of estimating the clutch torque Tctransmitted by the clutch38may further include the second sub-step308B of calculating a velocity of the vehicle as a function of a measured rotational speed of the tire and the effective tire radius re. Step308of estimating the clutch torque Tctransmitted by the clutch38may further include the third sub-step308C of calculating the clutch torque based Tcupon the velocity of the vehicle.

Step308of estimating the clutch torque Tctransmitted by the clutch38may further include calculating an estimated clutch torque Tcas a function of the estimated clutch surface friction coefficient μcand a normal force FNbetween the engaging clutch surfaces in the clutch38; and calculating the normal force FNbetween the engaging clutch surfaces in the clutch38as a function of clutch displacement position and a clutch nominal touchpoint displacement. For example, the estimated clutch torque Tcmay be calculated in accordance with Tc=,μcncFNrceffwhere Tcis the estimated clutch torque, μcis the estimated clutch surface friction coefficient, ncis a total effective number of engaging clutch surfaces in the clutch38, FNis the normal force between the engaging clutch surfaces in the clutch38, and rceffis an effective radius of the engaging clutch surfaces in the clutch38.

In some embodiments, the clutch effective radius rceffmay be approximated as

where rcois the clutch outer radius; and rciis the clutch inner radius.

In some embodiments, the normal force between the engaging clutch surfaces in the clutch may be determined as

where FNis the normal force between the engaging clutch surfaces, xpis an actuated position of the clutch; kcis a clutch spring axial stiffness; and xctis the clutch touchpoint displacement.

In some embodiments, the parameterized model uses an adaptive estimation algorithm to estimate a vector of unknown coefficients relating the clutch operating temperature and the rotational speed difference between clutch driving and driven parts to the estimated clutch surface friction coefficient. In some embodiments, the adaptive estimation algorithm may include a recursive least square algorithm, although other algorithms may be used.

In some embodiments, the adaptive estimation algorithm includes calculating

where θ is the vector of unknown coefficients relating the clutch operating temperature and the rotational speed difference between clutch driving and driven parts to the estimated clutch surface friction coefficient, m2(k)=τ+ϕT(k)ϕ(k) is designed to guarantee the boundedness of the estimation algorithm, and τ>0 is a designing parameter that determines the estimation convergence rate. Γ is another design parameter satisfying 0<Γ<2I to guarantee the convergence of the output error, where I is an identity matrix with appropriate dimension;θandθare calibrated lower and upper bound for θ, respectively.

In accordance with an aspect of the disclosure, and as shown in the flow chart ofFIG. 14, a second method400of controlling a component of a powertrain of a vehicle is provided. The provided second method400may provide for smoother and/or more efficient operation of the vehicle powertrain. For example, the second method400may allow a clutch38to be operated with an actuation force that causes the clutch to produce a desired output torque that is more precise than is possible with conventional methods. The second method400may allow a smoother operation of the clutch38and/or a smoother operation of the vehicle powertrain as a whole, when compared with conventional methods.

The second method400includes a first step402of estimating a clutch touchpoint xctof a clutch38controlled by a clutch actuation system12. The clutch actuation system12includes an electric motor18having a first shaft32, a reduction gear20coupled to the first shaft32, a second shaft34coupled to the reduction gear20, and a cam system22coupled to the first shaft32. The cam system22includes a ball44configured to translate in an axial direction and to impart a clutch engagement force on a clutch pack38, which may also be called the clutch38. Rotation of the second shaft34causes axial translation of the ball44. The clutch touchpoint xctcorresponds to the axial translation of the ball44where the clutch pack38first transmits torque.

Estimating the clutch touchpoint xctof the clutch38includes determining the clutch touchpoint xctas a function of: a conversion rate correlating the axial translation of the ball44to a rotation angle of a plate28defining a ramp48and configured to rotate about an axis to cause the axial translation of the ball44, a total friction force on the ball44, an angle between the ramp48and a plane of the plate28perpendicular to the axis, an axial stiffness of a clutch spring acting upon the clutch38, a reduction gear ratio of the reduction gear20, an equivalent gear ratio between the second shaft34and the plate28, a mechanical efficiency between the first shaft32and the second shaft34, a mechanical efficiency between the second shaft34and the plate28, a mechanical efficiency between the plate28and the ball44, and an orbital radius of the ball44.

More specifically, the clutch touchpoint xctmay include estimating and converging an unknown term d in order to determine the clutch touchpoint xctbased on the equation

where kp, acam, and apare constants, p0represents the conversion rate correlating the axial translation of the ball44to the rotation angle of the plate28, Ffrepresents the total friction force on the ball44, β represents the angle between the ramp48and the plane of the plate28perpendicular to the axis, kcrepresents the axial stiffness of the clutch spring acting upon the clutch, irrepresents the reduction gear ratio of the reduction gear20, isrepresents the equivalent gear ratio between the second shaft34and the plate28, ηrrepresents the mechanical efficiency between the first shaft and the second shaft, ηsrepresents the mechanical efficiency between the second shaft34and the plate28, ηprepresents the mechanical efficiency between the plate28and the ball44, rbrepresents the orbital radius of the ball44, and d represents the unknown term.

In some embodiments, the second method400includes estimating the clutch touchpoint xctin real time during operation of the vehicle. In some embodiments, estimating the clutch touchpoint xctof the clutch38includes accounting for a non-linear stiffness of the clutch spring. In some embodiments, estimating the clutch touchpoint xctof the clutch38includes performing a recursive least square algorithm.

In some embodiments, the second method400includes estimating the clutch touchpoint xctby estimating and converging an unknown term d and calculating the clutch touchpoint xctaccording to the equation

In some embodiments, the second method400also includes recording measurable variables of the clutch actuation system12, and wherein, when the clutch pack38is engaged, load torque on the first shaft32is modeled according to equation:

The second method400proceeds with a second step404of adjusting a command signal to the component of the powertrain based upon the estimated clutch touchpoint xct. The command signal may be generated by a controller, such as a powertrain control module (PCM), to control operation of the component of the powertrain. The component of the powertrain may be a clutch actuator configured to actuate the clutch. For example, adjusting the command signal to the component of the powertrain may include adjusting a position command or a torque command supplied to the clutch actuator. The clutch actuator may include the electric motor18, although other actuators may be used, such as a hydraulic cylinder. Alternatively or additionally, the component of the powertrain may be a prime mover, such as an electric motor or an internal combustion engine configured to supply an input torque to the driving part of the clutch. For example, adjusting the command signal to the component of the powertrain may include adjusting a torque command, an applied voltage, or a throttle position of the prime mover. This second step404may include adjusting other components of the powertrain, such as a gear selection or a gear ratio setting in a transmission or other gearbox.

Obviously, many modifications and variations of the present invention are possible in light of the above teachings and may be practiced otherwise than as specifically described while within the scope of the appended claims. These antecedent recitations should be interpreted to cover any combination in which the inventive novelty exercises its utility.