Real-time determination of tire normal forces

A device includes a plurality of tires and a suspension system as subcomponents. The suspension system includes at least one suspension sensor configured to provide suspension data (S). A controller is operatively connected to the suspension sensor. The controller has a processor and tangible, non-transitory memory on which is recorded instructions for executing a method for determining respective tire normal forces (Fzi(t), i=1 . . . 4) for one or more of the plurality of tires, based at least partially on the suspension data (S). The tire normal force (Fz) is the net force acting on each tire (or wheel) in the vertical direction. The tire normal force acting on each tire may be determined without using the specific model of the tire, road information, wheel or tire sensors.

TECHNICAL FIELD

The disclosure relates generally to determination of tire normal forces in a device, without the use of any tire or wheel sensors.

BACKGROUND

Tire normal forces play significant roles in the dynamics of a device having tires. The tire normal forces may be determined with the use of tire sensors.

SUMMARY

A device includes a plurality of tires and a suspension system. The device may be a vehicle, a robot, a farm implement, sports-related equipment or any other type of apparatus. The suspension system includes at least one suspension sensor configured to provide suspension data (S). A controller is operatively connected to the suspension sensor. The controller has a processor and tangible, non-transitory memory on which is recorded instructions for executing a method for determining respective real-time tire normal forces (e.g. Fzi(t), i=1 . . . 4) for one or more of the plurality of tires, based at least partially on the suspension data (S). The tire normal force is the net force acting on each tire (or wheel, used interchangeably) in the vertical direction. The tire normal force acting on each tire is determined without requiring tire sensors, the specific model of the tire or road information. At least one suspension sensor may include a strain gage or a thin-film strain gage.

Execution of the instructions by the processor causes the controller to determine a transformation matrix (T) based on a plurality of predefined parameters. The controller is configured to obtain the respective real-time tire normal forces (e.g. Fzi(t), i=1 . . . 4) by multiplying the suspension data (S) with the transformation matrix (T). The suspension data (S) may include respective real-time suspension forces (Si(t), i=1 . . . 4) for each of the plurality of tires. The respective tire normal forces are operative to adjust the operation or control of the device, i.e., the operation of the device may be adjusted based on the magnitude or value of the respective tire normal forces.

The predefined parameters include: a first distance (a) from a front axle of the device to a center of gravity of the device; a second distance (b) from a rear axle of the device to the center of gravity of the device; and a track width (d) between respective first and second centerlines of two laterally-spaced tires. The plurality of tires includes two laterally-spaced tires, such that the two laterally-spaced tires are both on one of the front axle and the rear axle. The predefined parameters further include: a roll moment of inertia (Ixx); a pitch moment of inertia (Iyy); a sprung mass (M) of the device; and respective masses (mi) of each of the plurality of tires.

The transformation matrix (T) may include a first row having first, second, third and fourth coefficients (T11, T12, T13, T14) based at least partially on a first mass (mi) of the first tire, the first distance (a), the second distance (b), the track width (d), the roll moment of inertia (Ixx), the pitch moment of inertia (Iyy) and the sprung mass (M).

The transformation matrix (T) may include a second row having fifth, sixth, seventh and eighth coefficients (T21, T22, T23, T24) based at least partially on a second mass (m2) of the second tire, the first distance (a), the second distance (b), the track width (d), the roll moment of inertia (Ixx), the pitch moment of inertia (Iyy) and the sprung mass (M).

The transformation matrix (T) may include a third row having ninth, tenth, eleventh and twelfth coefficients (T31, T32, T33, T34) based at least partially on a third mass (m3) of a third tire, the first distance (a), the second distance (b), the track width (d), the roll moment of inertia (Ixx), the pitch moment of inertia (Iyy) and the sprung mass (M).

The transformation matrix (T) may include a fourth row having thirteenth, fourteenth, fifteenth and sixteenth coefficients (T41, T42, T43, T44) based at least partially on a fourth mass (m4) of a fourth tire, the first distance (a), the second distance (b), the track width (d), the roll moment of inertia (Ixx), the pitch moment of inertia (Iyy) and the sprung mass (M).

DETAILED DESCRIPTION

Referring to the Figures, wherein like reference numbers refer to the same or similar components throughout the several views,FIG. 1is a schematic fragmentary plan view of a device10having a plurality of tires14. The device10may be a vehicle12. However, it is to be understood that the device10may be a robot, a farm implement, sports-related equipment or any other type of apparatus. In the embodiment shown, the plurality of tires14include first, second, third and fourth tires16L,16R,18L,18R, respectively. However, it is to be understood that the device10may include any number of tires.

FIG. 2is a schematic fragmentary side view of the device10, showing the first and third tires16L,18L. Referring toFIG. 2, the device10includes a suspension system20operatively connected to the plurality of tires14. The suspension system20may include springs22, shock absorbers or dampers24and various other components (not shown) operatively connected to a body26. The suspension system20includes at least one suspension sensor28(see sensors28A, B, C inFIG. 2). Referring toFIG. 2, a controller30is operatively connected to the suspension sensor28and various other components of the device10.

Referring toFIG. 2, the controller30has a processor32and tangible, non-transitory memory34on which is recorded instructions for executing a method100, described below with reference toFIGS. 1-3, for determining respective real-time tire normal forces (Fzi(t), i=1 . . . 4) for one or more of the plurality of tires14, based at least partially on the suspension data (S) obtained by the suspension sensor28. The suspension data (S) includes respective real-time suspension forces (Si(t), i=1 . . . 4) for each of the plurality of tires14, on a device10with 4 tires.

The tire normal force is the net force acting on each tire (or wheel, used interchangeably) in the vertical direction z. Referring toFIG. 2, the respective centers of gravity40,42for the first and third tires16L,18L are shown. Each of the plurality of tires14has a tire normal force (Fz) and a suspension force (Si) acting on it. Referring toFIG. 2, the first tire16L is acted upon by a tire normal force (F1), shown by arrow44, and a suspension force (S1), shown by arrow46. Referring toFIG. 2, the third tire18L is acted upon by a tire normal force (F3), shown by arrow48, and a suspension force (S3), shown by arrow50.

The method100ofFIG. 3may be employed in any device10that requires tire normal force (Fz) estimation. Using method100, the tire normal force may be determined without requiring tire model information, road information, wheel or tire sensors. Thus, execution of the instructions by the processor32improves the functioning of the device10by allowing the determination of tire normal forces in realtime using suspension sensors28, without requiring the use of tire or wheel sensors.

Referring toFIG. 2, the suspension sensor28may be installed in various positions, as shown by sensors28A,28B and28C. Variations in installation of the suspension sensor28may depend upon the design of the device10and affect only transition from measured signals to suspension forces, see eqn. (1). However, mathematical structure of the transformation matrix (T) remains the same. Referring toFIG. 2, the suspension sensor28may include strain gage52(such as a a thin-film strain gage) operatively connected to the controller30. The strain gage52is configured to vary its electrical resistance with the variation of strain elements at the surface of installation. Strain variations are caused by suspension forces that may be identified through strains by using linear elasticity laws in the controller block30. This resistance change of the strain gage52may be measured using a Wheatstone bridge54, as understood by those skilled in the art. The strain may be defined as the relative displacement of the entire suspension part20or any local segment of spring, shock absorber, or any component of the suspension mount. The controller30accounts for the type of strain definition and type sensor installation through its ‘strain to force’ conversion relationship; see equation (1) below. The strain gage52may detect a combined force created by both spring and shock absorber together (as shown by sensor28C). It is to be understood that the device10may employ any type of suspension sensor28known to those skilled in the art.

The controller30may be an integral portion of, or a separate module operatively connected to, other control modules of the device10. The device10may take many different forms and include multiple and/or alternate components and facilities. While an example device10is shown in the Figures, the components illustrated in the Figures are not intended to be limiting. Indeed, additional or alternative components and/or implementations may be used.

Referring now toFIG. 3, a flowchart of the method100stored on and executable by the controller30ofFIG. 1is shown. Method100need not be applied in the specific order recited herein. Furthermore, it is to be understood that some blocks may be added or eliminated. Referring toFIG. 3, method100may begin with block102where the controller30is programmed to obtain suspension data (S) via the at least one suspension sensor28. The suspension data (S) may include respective real-time suspension forces (Si(t), i=1 . . . 4) for each of the plurality of tires14. The suspension sensor28and suspension data (S) may be calibrated in a test lab with a set of calibration factors, shown below as [α, β, γ, δ]. In equation (1) below, Sirepresents the suspension force and εirepresents the readings from the suspension sensor28. Dependence for equation (1) may be linear or nonlinear based on the type of suspension sensors28.

In block104ofFIG. 3, the controller30is programmed or configured to determine a transformation matrix (T) based on a plurality of predefined parameters for the device10. Referring toFIG. 1, the predefined parameters include: a first distance60(a) from a front axle62of the device10to a center of gravity64of the device10; a second distance66(b) from a rear axle68of the device10to the center of gravity64of the device10; and a track width70(d). Referring toFIG. 1, the track width70(d), or side-side lateral width of the device10, may be defined as the distance between first and second centerlines74L,74R (or76L,76R) of two laterally-spaced tires16L,16R (or18L,18R) of the plurality of tires14, such that the two laterally-spaced tires are on either the front axle62(first and second tires16L,16R) or the rear axle68(third and fourth tires18L,18R).

The predefined parameters further include: a roll moment of inertia (Ixx); a pitch moment of inertia (Iyy); a sprung mass72(M) of the device10(seeFIG. 2); and respective masses (mi) of each of the plurality of tires14. The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body determines the torque needed for a desired angular acceleration about a rotational axis, such as the y-axis for pitch movement78(θ) (front to rear motion of the device10shown inFIG. 2) or the x-axis for roll movement80(φ) (side to side motion of the device10shown inFIG. 2). The moment of inertia depends on a body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation.

The predefined parameters may vary in real-time or may be constant for each device10. For example, the first distance60(a), second distance66(b) and track width70(d) may be predetermined constants for the device10. The roll moment of inertia (Ixx) and pitch moment of inertia (Iyy) may be predefined with respective initial values for a given device10and calibrated in real time afterwards. The sprung mass72(M) and respective masses (mi) of the tires may be predefined through a nominal, initial value and may then be calibrated in real time afterwards. One or more mass sensors86may be employed to calibrate or scale the initial values of the sprung mass72(M) and respective masses (mi) of each of the plurality of tires14.

Referring toFIG. 2, in a device10with a suspension system20, the sprung mass72(M) is the portion of the total mass of the device10that is supported above the suspension system20. The sprung mass72(M) typically includes the body26and the internal components (not shown) of the device10such as passengers, cargo, etc. The sprung mass72(M) does not include the mass of the components suspended below the suspension system20. In contrast, the unsprung mass is the mass of the suspension system20, wheel axles/bearings/hubs, tires and other components directly connected to the suspension system20, rather than supported by the suspension system20. The device10may include a roll sensor82and a pitch sensor84.

As noted above, in block104ofFIG. 3, the controller30is programmed or configured to determine a transformation matrix (T) based on a plurality of predefined parameters. In a device10with n tires, the transformation matrix (T) may include n rows and n columns. In the embodiment shown, the device10includes four tires16L,16R,18L,18R; thus the transformation matrix (T) is a four-by-four matrix as shown below in equation (2):

The transformation matrix (T) includes a first row having first, second, third and fourth coefficients (T11, T12, T13, T14) that are based at least partially on a first mass (m1) of a first tire (such as16L inFIG. 1), the first distance60(a), the second distance66(b), the track width70(d), the roll moment of inertia (Ixx), the pitch moment of inertia (Iyy) and the sprung mass (M). It is to be understood that the order of the tires may be changed, thus any one of the plurality of tires14may be termed the “first tire.” Referring to the set of equations (3) below, the first, second, third and fourth coefficients (T11, T12, T13, T14) may be defined as:
T11=1+m1*(d2/Ixx+a2/Iyy+1/M);
T12=m1*[−(d2/Ixx)+a2/Iyy+1/M];
T13=m1*[−(a*b/Iyy)+1/M+(d2/Ixx)];
T14=m1*[−(a*b/Iyy)+1/M−(d2/Ixx)].  (3)

The transformation matrix (T) includes a second row having fifth, sixth, seventh and eighth coefficients (T21, T22, T23, T24) that are based at least partially on a second mass (m2) of a second tire (such as16R inFIG. 1), the first distance60(a), the second distance66(b), the track width70(d), the roll moment of inertia (Ixx), the pitch moment of inertia (Iyy) and the sprung mass (M). Referring to the set of equations (4) below, the fifth, sixth, seventh and eighth coefficients (T21, T22, T23, T24) may be defined as:
T21=m2*[−(d2/Ixx)+a2/Iyy+1/M];
T22=1+m2*(d2/Ixx+a2/Iyy+1/M);
T23=m2*[−(a*b/Iyy)+1/M−(d2/Ixx)];
T24=m2*[−(a*b/Iyy)+1/M+(d2/Ixx)].  (4)

The transformation matrix (T) includes a third row having ninth, tenth, eleventh and twelfth coefficients (T31, T32, T33, T34) that are based at least partially on a third mass (m3) of a third tire (such as18L inFIG. 1), the first distance60(a), the second distance66(b), the track width70(d), the roll moment of inertia (Ixx), the pitch moment of inertia (Iyy) and the sprung mass (M). Referring to the set of equations (5) below, the ninth, tenth, eleventh and twelfth coefficients (T31, T32, T33, T34) may be defined as:
T31=m3*[−(a*b/Iyy)+1/M+d2/Ixx];
T32=m3*[−(a*b/Iyy)+1/M−d2/Ixx];
T33=1+m3*(b2/Iyy+1/M+d2/Ixx);
T34=m3*(b2/Iyy+1/M−d2/Ixx).  (5)

The transformation matrix (T) includes a fourth row having thirteenth, fourteenth, fifteenth and sixteenth coefficients (T41, T42, T43, T44) that are based at least partially on a fourth mass (m4) of a fourth tire (such as18R inFIG. 1), the first distance60(a), the second distance66(b), the track width70(d), the roll moment of inertia (Ixx), the pitch moment of inertia (Iyy) and the sprung mass (M). Referring to the set of equations (6) below, the thirteenth, fourteenth, fifteenth and sixteenth coefficients (T41, T42, T43, T44) may be defined as:
T41=m4[−(a*b/Iyy)+1/M−d2/Ixx];
T42=m4*[−(a*b/Iyy)+1/M+d2/Ixx];
T43=m4*(b2/Iyy+1/M−d2/Ixx); and
T44=1+m4*(b2/Iyy+1/M+d2/Ixx).  (6)

In block106ofFIG. 3, the controller30is programmed or configured to obtain the tire normal force (Fz) for each of the plurality of tires14by multiplying the suspension data (S) with the transformation matrix (T), as indicated below in equation (7).

Execution of the instructions by the processor improves the functioning of the device10by allowing the determination of tire normal forces, without requiring installation of tire sensors or road information. Tire normal forces may play significant roles in the dynamics of the device10and may be employed as inputs for various control algorithms, further improving the functioning of the device10.

Referring toFIGS. 1 and 4, the processor32and tangible, non-transitory memory34of the controller30may include recorded instructions for executing an example method200for obtaining the transformation matrix (T). Method200is one example and other methods may be employed for obtaining the transformation matrix (T). Method200includes blocks202,204and206, shown inFIG. 4.

In block202, the controller30is programmed or configured to obtain a first set of equations (8) describing the vertical wheel dynamics of the device10and a second set of equations (9) describing the suspension forces (Si=Si(t), i=1, . . . , 4), referred to herein as sprung- and unsprung mass dynamic equations, respectively. Here, ksf, csf, and ksr, and csrare front and rear stiffness and viscosity coefficients of the suspension system20of the device10, respectively; Zc describes the vertical motion of the sprung mass (M); and (zi, i=1, . . . , 4) are the vertical displacements of wheel/tire centers14, the over dot indicates time derivative, and the other parameters are the same as previously described.
Mc=S1+S2+S3+S4
Iyy=−aS1−aS2+bS3+bS4
Ixx=d/2(S1−S2+S3−S4)  (8)
S1(t)=−csf(c−a+(d/2)−1)−ksf(Zc−aθ+(d/2)φ−z1)
S2(t)=−csf(c−a−(d/2)−2)−ksf(Zc−aθ−(d/2)φ−z2)
S3(t)=−csr(c+b+(d/2)−3)−ksr(Zc+bθ+(d/2)φ−z3)
S4(t)=−csr(c+b−(d/2)−4)−ksr(Zc+bθ−(d/2)φ−z4)  (9)

In block204, the controller30is programmed or configured to obtain the Laplace transforms (converting from ‘z’ space to ‘p’ space) of the first and second set of equations, shown below as equations (10) and (11), respectively. Here, each tilde variable indicates the corresponding Laplace image as a function of p.

In block206ofFIG. 4, the transformation matrix (T) may be obtained by using the equations (7), (10) and (11) above, and equation (12) below. The transformation matrix (T) may be calibrated using known values of suspension forces (Si=Si(t), i=1, . . . , 4) and tire normal forces (Fzi(t), i=1 . . . 4) for the device10.
mi=−Si+Fzi(12)

As noted above, the controller30ofFIG. 1may include a computing device that employs an operating system or processor32and memory34for storing and executing computer-executable instructions. Computer-executable instructions may be compiled or interpreted from computer programs created using a variety of programming languages and/or technologies, including, without limitation, and either alone or in combination, Java™, C, C++, Visual Basic, Java Script, Perl, etc. In general, a processor52(e.g., a microprocessor) receives instructions, e.g., from a memory, a computer-readable medium, etc., and executes these instructions, thereby performing one or more processes, including one or more of the processes described herein. Such instructions and other data may be stored and transmitted using a variety of computer-readable media.

Look-up tables, databases, data repositories or other data stores described herein may include various kinds of mechanisms for storing, accessing, and retrieving various kinds of data, including a hierarchical database, a set of files in a file system, an application database in a proprietary format, a relational database management system (RDBMS), etc. Each such data store may be included within a computing device employing a computer operating system such as one of those mentioned above, and may be accessed via a network in any one or more of a variety of manners. A file system may be accessible from a computer operating system, and may include files stored in various formats. An RDBMS may employ the Structured Query Language (SQL) in addition to a language for creating, storing, editing, and executing stored procedures, such as the PL/SQL language mentioned above.