Estimation of absolute wheel roll radii and estimation of vertical compression value

Abstract

Methods, apparatuses and computer program products for estimating absolute wheel roll radii and/or a vertical compression value of wheels of a vehicle are disclosed, wherein yaw rates of the vehicle, wheel speeds of first and second wheels, and optionally lateral acceleration of the vehicle are measured and used as a basis for the estimation.

Claims

1. A method of estimating absolute wheel roll radii of wheels of a vehicle, comprising: measuring at least two yaw rate signals, each indicative of a yaw rate of the vehicle; measuring at least two first wheel speed signals, each indicative of an angular velocity of a first wheel of the vehicle; measuring at least two second wheel speed signals, each indicative of an angular velocity of a second wheel of the vehicle; and determining a first absolute wheel roll radius of the first wheel and a second absolute wheel roll radius of a second wheel based on the at least two measured yaw rate signals, the at least two measured first wheel speed signals, and the at least two measured second wheel speed signals.

2. The method of claim 1, wherein the determining is further based on a relationship according to: ${\stackrel{.}{\Psi }}_m=\frac{r_l{\omega }_l-r_r{\omega }_r}{B}+K$ wherein {dot over (Ψ)}.sub.m denotes a yaw rate, r.sub.l denotes a first absolute wheel roll radius, r.sub.r denotes a second absolute wheel roll radius, ω.sub.l denotes a first wheel speed, ω.sub.r denotes a second wheel speed, B denotes an axle width, and K denotes an offset constant.

3. The method of claim 1, further comprising: measuring at least two lateral acceleration signals, each indicative of a lateral acceleration of the vehicle; wherein the determining is further based on a wheel compression value and the at least two measured lateral acceleration signals.

4. The method of claim 3, wherein the determining is further based on a relationship according to: ${\stackrel{.}{\Psi }}_m=\frac{\left(r_l-a_{y}C\right){\omega }_l-\left(r_r+a_{y}C\right){\omega }_r}{B}+K$ wherein {dot over (Ψ)}.sub.m denotes a yaw rate, r.sub.l denotes a first absolute wheel roll radius, r.sub.r denotes a second absolute wheel roll radius, ω.sub.l denotes a first wheel speed, ω.sub.r denotes a second wheel speed, B denotes an axle width, a.sub.y denotes a lateral acceleration of the vehicle, C denotes a wheel compression value and K donates an offset constant.

5. The method of claim 1, wherein the determining is performed without using a nominal wheel radius of a wheel of the vehicle.

6. The method of claim 1, wherein the determining comprises a statistical regression analysis, including at least one of (i) a recursive estimation such as a Kalman filter, or (ii) a batch analysis such as a least-squares-fit of a relationship between the at least two measured yaw rate signals, the at least two measured first wheel speed signals, and the at least two measured second wheel speed signals.

7. The method of claim 1, wherein the second absolute wheel roll radius is determined based on the determined first absolute wheel roll radius and a proportionality factor.

8. The method of claim 1, wherein at least one of: measuring the at least two yaw rate signals, measuring the at least two first wheel speed signals, or measuring the at least two second wheel speed signals is performed as a time series.

9. The method of claim 1, wherein the determining is carried out without using at least one of the following: a velocity signal, indicative of the velocity of the vehicle, or a GPS signal.

10. The method of claim 1, further comprising: receiving at least one accessory signal from an accessory sensor; wherein the determining is further based on the at least one accessory signal; and wherein the at least one accessory signal is indicative of at least one of the following: engine torque, specific axle/wheel torque, wheel slip, engine RPM, longitudinal acceleration, load of the vehicle, axle height, suspension pressure, ambient temperature, steering wheel angle, a tire type, an estimated friction potential, a normalized traction force on the wheel, a friction related value, a brake pressure, a tire temperature, a suspension height, a control flag register.

11. The method of claim 1, wherein the first wheel and the second wheel are rear wheels, or wherein the first wheel and the second wheel are front wheels.

12. A method of estimating a vertical compression value of a wheel of a vehicle, comprising: measuring a yaw rate signal, indicative of a yaw rate of the vehicle; measuring a first wheel speed signal, indicative of an angular velocity of a first wheel of the vehicle; measuring a second wheel speed signal, indicative of an angular velocity of a second wheel of the vehicle; measuring a lateral acceleration signal, indicative of a lateral acceleration of the vehicle; obtaining a first absolute wheel roll radius signal, indicative of an absolute wheel roll radius of the first wheel, and obtaining a second absolute wheel roll radius signal, indicative of an absolute wheel roll radius of the second wheel; and determining a vertical compression value of at least the first wheel based on the measured yaw rate signal, the measured first wheel speed signal and the measured second wheel speed signal, the measured lateral acceleration signal, the obtained first absolute wheel roll radius signal, and the obtained second absolute wheel roll radius of the second wheel.

13. The method of claim 12, wherein the first absolute wheel roll radius of the first wheel and second absolute wheel roll radius of the second wheel are estimated based on the measured yaw rate signals, the measured first wheel speed signal and the measured second wheel speed signal, the measured lateral acceleration signal, the obtained first absolute wheel roll radius signal, and the obtained second absolute wheel roll radius of the second wheel.

14. The method of claim 12, wherein the determining is further based on a relationship according to: ${\stackrel{.}{\Psi }}_m=\frac{\left(r_l-a_{y}C\right){\omega }_l-\left(r_r+a_{y}C\right){\omega }_r}{B}+K$ wherein {dot over (Ψ)}.sub.m denotes a yaw rate, r.sub.l denotes a first absolute wheel roll radius, r.sub.r denotes a second absolute wheel roll radius, ω.sub.l denotes a first wheel speed, ω.sub.r denotes a second wheel speed, B denotes an axle width, a.sub.y denotes a lateral acceleration of the vehicle, C denotes a wheel compression value and K donates an offset constant.

15. A computing device to estimate absolute wheel roll radii and or a vertical compression value of wheels of a vehicle, the computing device comprising: one or more processors; and a memory storing instructions that, when executed by the one or more processors, cause the computing device to: measure at least two yaw rate signals, each indicative of a yaw rate of the vehicle; measure at least two first wheel speed signals, each indicative of an angular velocity of a first wheel of the vehicle; measure at least two second wheel speed signals, each indicative of an angular velocity of a second wheel of the vehicle; and determine a first absolute wheel roll radius of the first wheel and a second absolute wheel roll radius of a second wheel based on the at least two measured yaw rate signals, the at least two measured first wheel speed signals, and the at least two measured second wheel speed signals.

Description

SHORT DESCRIPTION OF THE DRAWINGS

(1) The following detailed description refers to the appended drawings, wherein:

(2) FIG. 1 schematically illustrates side views of wheels wherein nominal roll radius and absolute roll radius differ.

(3) FIG. 2A schematically illustrates a top view of a vehicle during cornering, wherein methods according to embodiments may be applied.

(4) FIG. 2B schematically illustrates a further top view of a vehicle during cornering, wherein methods according to embodiments may be applied.

(5) FIG. 3 schematically illustrates a back view of a vehicle during lateral acceleration, wherein methods according to embodiments may be applied.

(6) FIG. 4 schematically illustrates a side view of a vehicle comprising an apparatus according to embodiments.

(7) FIG. 5 schematically illustrates an apparatus according to embodiments.

(8) FIGS. 6 to 8 illustrate flow diagrams of methods according to embodiments.

DETAILED DESCRIPTION OF EMBODIMENTS

(9) FIG. 1 schematically illustrates side views of wheels 12a and 12b, wherein the nominal roll radius 20r and the absolute roll radius 22r differ.

(10) In dashed lines, a geometry of a wheel 12a without load or deformation is illustrated as having a shape 20 with radius 20r and center 20c. In general, a wheel comprises a tire and a rim, on which the tire is mounted. Without load and deformation, a wheel has a circular outer circumference.

(11) The radius 20r of the wheel 12a can be referred to as “nominal radius” of the tire or of the wheel. In FIG. 1, the nominal radius 20r is illustrated by a dashed line directed vertically upwards from a geometric center 20c of wheel 12a.

(12) Usually, a wheel may have an outer circumference that differs form a circular shape due to static parameters, e.g., fabrication tolerances of tire and/or rim, even material distribution in the tire material, defects in the tire's tread, etc. as well as due to dynamic parameters, e.g., resulting from driving conditions like load, partial deflation, friction forces, acceleration/deceleration of a vehicle the wheel is mounted on, etc. Such a wheel 12b is also illustrated in FIG. 1.

(13) In continuous lines, a geometry of a wheel 12b is illustrated, which is has a form differing from that of wheel 12a. For illustration purposes, wheels 12a and 12b have been illustrated as having a common point of contact 24 with a road.

(14) The shape of wheel 12b differs from the shape 20 of wheel 12a, e.g., due to load, a partial deflation, friction forces, acceleration and/or any other reasons (as those already mentioned above). As a result, the wheel 12b has a shape 22, which may be non-circular, as shown, e.g. elliptical, with respect to a geometric center 12c of wheel 12b. In the following, shape 22 is referred to as non-circular just as an example without limiting shape 22 to such a form.

(15) An absolute roll radius 22r may be defined as the length between the center 22c of wheel 12b and a point of support 24, e.g. a point of contact with a road. Center 22c of wheel 12b may be, e.g., a center of gravity or a center of symmetry or a center of rotation for wheel 12b or any other reference point in relation to which an absolute roll radius 22r can be defined.

(16) In the illustrated case, the absolute roll radius 22r is smaller than the nominal radius 20r.

(17) The circular shape 20 and non-circular shape 22 are shown with a common point of contact 24 to the road. Due to the absolute roll radius 22r being smaller than the nominal radius 20r, the center 22c is located below center 20c.

(18) FIGS. 2A and 2B schematically illustrate top views of vehicles during cornering. In FIGS. 2A and 2b, the front of the vehicle is located at the top of the figures.

(19) In FIG. 2A, a vehicle 10 is shown, whose front wheels are inclined for a left-wards turn. A method according to the present invention may be applied to the driving condition of vehicle 10 in order to determine the absolute wheel roll radii of the rear wheels 12 and 14, connected by rear axle 16.

(20) A yaw rate {dot over (Ψ)}.sub.m is measured using a yaw rate sensor (not shown), a wheel speed of the rear left wheel 12 is measured using a wheel speed sensor and a wheel speed of the rear right wheel 14 is measured using a wheel speed sensor. The wheel speeds are given as angular velocities and are not equivalent to the vehicle speed.

(21) The measured values of yaw rate, rear left wheel speed and rear right wheel speed are considered to form a first set of measurements.

(22) The measurements of the first set may be performed simultaneously or at least in a synchronized manner such that the measurements of the first set can be related or associated to each other. This also applies to further sets of measurement, such as the second set referred to further below.

(23) The measured values of the first set are related via the relationship:

(24) ${\stackrel{.}{\Psi }}_m=\frac{r_l{\omega }_l-r_r{\omega }_r}{B}+K$
wherein {dot over (Ψ)}.sub.m denotes a yaw rate, r.sub.l denotes an absolute roll radius of the rear left wheel, denotes an absolute roll radius of the rear right wheel, ω.sub.l denotes a rear left wheel speed, ω.sub.r denotes a rear right wheel speed, B denotes the width of rear axle 16 (and is assumed to be known), and K donates an offset constant. For simplicity, in this embodiment, the sensors are assumed to have negligible errors and the offset constant K may be set to zero.

(25) Further, second measurements are performed, yielding a second set of values for yaw rate, rear left wheel speed and rear right wheel speed.

(26) The measured values of the second set are also related via the above relationship. Based on the two set of measurements and based on the above relationship, the absolute roll radii r.sub.l and r.sub.r of the rear left wheel 12 and of the rear right wheel 14, respectively, can be determined.

(27) For increased reliability, the number of sets of measurements may be increased and statistical analysis may be performed.

(28) A least-squares-fit batch analysis of a relationship between the measured signals may be performed.

(29) It should be noted that, in this embodiment, the determining does not make use of a nominal wheel radius or of a velocity of the vehicle (such as determined from a GPS signal).

(30) FIG. 2B illustrates a vehicle 10, wherein the method according to embodiments may be applied to the driving condition of vehicle 10 in order to determine the absolute wheel roll radii of the front wheels 12 and 14, connected by front axle 18. In the illustrated case, the front wheels 12 and 14 are the turning wheels of the vehicle.

(31) In order to take into account that the angular velocities may be not parallel or may not have an orthogonally directed offset between them, a further compensation factor is included in the determination as will be described below.

(32) An accessory signal indicative of a steering angle is received from an accessory sensor, such as a steering angle sensor, and the determining is based on the accessory signal. In particular, a steering angle may be used to compute the effective change of axle width due to the wheel angles. For instance, an effective axle width B′ may be computed as:
B′=B cos(∝)
wherein B is the actual axle width of the front axle 18, a denotes the steering angle measured with respect to straight driving.

(33) In other embodiments, in addition to those illustrated in FIGS. 2A and 2B, further arrangements may be taken into account, including a comparison of wheels located on a same side of the vehicle (e.g. front left wheel and rear left wheel) or a comparison of wheels located diagonally to each other (e.g. front left wheel and rear right wheel).

(34) As described with reference to FIG. 2B, lack of a orthogonally directed offset between the steering wheels with respect to the measured velocity can be at least partially corrected using a measured steering wheel angle allowing to estimate the lateral velocity (except for side slip) at the steering wheels. The lateral velocity at the non-steering wheels may be assumed to be zero (except for side slip). By using these lateral velocities and the wheel base as orthogonally directed offset, the methods as disclosed herein remain applicable.

(35) The rear and front wheels of a same side could be used in the same manner as the axle wheels with the additional signal steering wheel angle and potentially with an estimate of lateral velocities due to side slip for increased precision.

(36) For a comparison of diagonally located wheels, the method remains equally applicable. By using the steering angle the longitudinal velocity of the front wheel can be estimated and compared to the velocity of the rear wheel, which gives a good approximation (even without estimate of die slip) since the uncertainty of side slip is removed from the rear wheel and only exists on the front wheel and the side slip effect on the longitudinal velocity is smaller than on the lateral velocity.

(37) FIG. 3 schematically illustrates a back view of a vehicle during lateral acceleration, illustrated by the acceleration vector a.sub.y. In addition, gravity g acts on the vehicle 10 of mass m at its center of gravity G. The height of the center of gravity G is denoted with H. As a result, an upward-directed normal force and a sideward-directed friction force act on each wheel. In particular, a friction force f.sub.L and a normal force N.sub.L act on left wheel 12. Similarly, a friction force f.sub.R and a normal force N.sub.R act on right wheel 14. During lateral acceleration, these forces are not equal and generate a load difference, which leads to a difference in absolute roll radii at said wheels.

(38) A lateral acceleration of the vehicle (e.g. during cornering) may generate a load difference between the wheels.

(39) In the illustrated embodiment, the method comprises measuring a lateral acceleration signal, indicative of the lateral acceleration a.sub.y of the vehicle. The determining is based on a wheel compression value and the measured lateral acceleration signal.

(40) The vertical compression value C may also be denoted as a vertical compression ratio constant and may be defined as the proportionality constant between lateral acceleration and a further change in absolute roll radius

(41) In general, a vertical compression of the wheels Δr (i.e. a decrease in absolute roll radius) may be considered proportional to a vertical force F generating the compression with C′ being the nominal compression constant of each wheel:
Δr=C′×F

(42) For the illustrated case of a leftward lateral acceleration, the normal forces on said two wheels can be expressed as

(43) $N_L=\frac{\mathrm{mg}}{4}+\frac{a_y\mathrm{mH}}{2B}\mathrm{and}$$N_R=\frac{\mathrm{mg}}{4}-\frac{a_y\mathrm{mH}}{2B}$

(44) This leads to a relative normal force difference on the axle of

(45) $\frac{a_y\mathrm{mH}}{B},$
which gives rise to a further change in absolute roll radius

(46) 0$\Delta r=\pm C^{\prime }\times \frac{a_y\mathrm{mH}}{2B}=a_{y}C,$
with

(47) $C=\frac{{\mathrm{mHC}}^{\prime }}{2B},$
wherein m is the mass of the vehicle, H is the height of the center of gravity, B is the axle width and C′ is the nominal compression constant of each wheel's tire. If the wheels differ in their nominal compression constant, an effective compression constant may be used.

(48) Therefore, the relationship discussed with respect to the embodiments of FIG. 2A is adapted to recite the measured lateral acceleration and the compression value:

(49) ${\stackrel{.}{\Psi }}_m=\frac{\left(r_l-a_{y}C\right){\omega }_l-\left(r_r+a_{y}C\right){\omega }_r}{B}+K$
wherein {dot over (Ψ)}.sub.m denotes a yaw rate, r.sub.l denotes a left absolute wheel roll radius, r.sub.r denotes a right absolute wheel roll radius, ω.sub.l denotes a left wheel speed, ω.sub.r denotes a right wheel speed, B denotes the width of the axle connecting the left and right wheels, a.sub.y denotes a lateral acceleration of the vehicle, C denotes a wheel compression value and K donates an offset constant.

(50) In cases, where the wheel compression value may differ for the left and right wheel, the above relationship may recite a left wheel compression value C.sub.l in the left wheel term and a right wheel compression value C.sub.r in the right wheel term.

(51) The sign of a.sub.y in the above relationships may be adapted to the direction of acceleration.

(52) The above relationships recite a vertical wheel compression value. Generally, this value may be known or unknown. In the former case, the method of estimating absolute wheel roll radii of wheels may take into account an external vertical compression value, i.e. which is predetermined or received from another source. An example of a predetermined vertical compression value is a register entry in the onboard electronics regarding the mass m of the vehicle, height H of the center of gravity, the nominal wheel compression constant C and the axle width B, each of which as designated by the manufacturer.

(53) If the vertical compression value is not predetermined, it may be determined dynamically by another system of the vehicle and supplied as an input to the method of estimating absolute wheel roll radii as disclosed herein.

(54) Alternatively, if the vertical compression value is considered unknown, it may be estimated by the method itself. This approach requires a further, e.g. a third set of measurements of values of yaw rate, left wheel speed and right wheel speed and lateral acceleration. The above relationship in combination with three complete set of measurements allows to statistically determine an estimate for the three unknowns, namely left absolute wheel roll radius, right absolute wheel roll radius and vertical compression value. The determination of a vertical compression value by the method may be of great value. In particular, the current wheel compression constant can be deduced and used for further applications, such as indirect tire pressure monitoring systems.

(55) A vertical compression value estimated according to a method as disclosed herein may be used for various applications. For instance, in indirect tire pressure monitoring systems, it is preferred not to use relative roll radius estimates to detect load-change-induced pressure changes. In particular, a loaded wheel has a smaller roll radius as compared to an unloaded wheel. Differentiation between a highly loaded wheel and a wheel with deflated tire may not be unambiguous. Typically, an estimate of vehicle load may be used to remove load effects. For improved accuracy of not only the load estimate but also wheel or tire compression (due to this load), knowledge of a vertical compression value before the load change is desirable.

(56) FIG. 4 schematically illustrates a side view of a vehicle 10 comprising an apparatus 30 and a yaw rate sensor 36. The vehicle comprises four wheels, two of which are shown in this side view and one of which, the rear left wheel, is designated by reference numeral 12. Wheel 12 is equipped with a wheel speed sensor 32. The wheel speed sensor 32 may be a cogged wheel with optical or magnetic readout of the rotation speed of the cogs, as used for instance for anti-lock braking systems. Other wheel speed sensors may equally be used, provided that they emit signals indicative of an angular velocity of the wheel. In the illustrated case, rear right wheel (not shown) is also equipped with a wheel speed sensor (not shown).

(57) Yaw rate sensor 36 may be a gyroscope with at least one axis of rotation, namely yaw mode detection. Yaw mode gyroscopes are configured to detect rotations of the vehicle around a vertical axis. The illustrated yaw rate sensor is a gyroscope with three-axis detection, i.e. detection of rotations in yaw, roll and/or pitch mode. Without restriction, examples of gyroscopes include micromechanical ones operating based on Coriolis forces. Other examples yaw rate sensors may equally be used, provided that they emit signals indicative of a yaw rate of the vehicle. In some examples, the yaw rate sensor may be combined with an accelerometer, e.g. for detecting a lateral acceleration of the vehicle.

(58) Apparatus 30 is an apparatus to estimate absolute wheel roll radii. Apparatus 30 receives signals from the wheel speed sensors 32 and yaw rate sensor 36. Apparatus 30 comprises a processing part, the processing part configured to carry out the steps of a method as described with respect to the embodiments. Alternatively or additionally, Apparatus 30 may be to estimate vertical compression value of wheels 12 of vehicle 10.

(59) FIG. 5 schematically illustrates an apparatus 30 to estimate absolute wheel roll radii. Apparatus 30 comprises a processing part 31, the processing part 31 configured to carry out the steps of a method as described with respect to the embodiments.

(60) In addition, FIG. 5 illustrates a first wheel speed sensor 32 for measuring first wheel speed signals, indicative of an angular velocity of a first wheel of a vehicle and a second wheel speed sensor 34 for measuring second wheel speed signals, indicative of an angular velocity of a second wheel of the vehicle. Further, a yaw rate sensor 36 for measuring yaw rate signals indicative of a yaw rate of the vehicle is shown.

(61) The sensors 32, 34 and 36 are shown as not being comprised by the apparatus. However, in some embodiments, at least one of the sensors may be comprised by the apparatus. In some embodiments, the apparatus and at least one of the sensors may form a system to estimate absolute wheel roll radii.

(62) FIG. 6 illustrates a flow diagram of a method 60 of estimating absolute wheel roll radii of wheels of a vehicle. The method 60 comprises a step of first measurements 62. The first measurements 62 include measuring a yaw rate signal, indicative of a yaw rate of the vehicle, measuring a wheel speed signal, indicative of an angular velocity of a first wheel of the vehicle, as well as measuring a further wheel speed signal, indicative of an angular velocity of a second wheel of the vehicle. The first measurements 62 may be carried out in a synchronized manner, for example simultaneously or concurrently.

(63) The method 60 further comprises a step of second measurements 64. The second measurements 64 include measuring a further yaw rate signal, indicative of a further yaw rate of the vehicle, measuring a further wheel speed signal, indicative of a further angular velocity of the first wheel of the vehicle, as well as measuring a further wheel speed signal, indicative of a further angular velocity of the second wheel of the vehicle. The second measurements 64 may be carried out in a synchronized manner, for example simultaneously or concurrently.

(64) The step of first measurements 62 and the step of second measurements 64 may be directly consecutively or may be separated by a certain duration in time.

(65) The method 60 comprises a determination 66 of absolute wheel roll radii. Determination 66 is based on the first measurements 62 and second measurements 64.

(66) FIG. 7 illustrates a flow diagram of a method 70 of estimating a vertical compression value of a wheel of a vehicle. The method 70 comprises a measurement step 72. The measurements 72 include measuring a yaw rate signal, indicative of a yaw rate of the vehicle, measuring a wheel speed signal, indicative of an angular velocity of a first wheel of the vehicle, as well as measuring a further wheel speed signal, indicative of an angular velocity of a second wheel of the vehicle and measuring a lateral acceleration signal, indicative of a lateral acceleration of the vehicle. The first measurements 72 are carried out in a synchronized manner, for example simultaneously or concurrently.

(67) The method 70 also comprises a determination 74 of the vertical compression value. Determination 74 is based on the first measurements 72 and based on received absolute wheel roll radii. The absolute wheel roll radii are received as a first wheel roll radius signal, indicative of an absolute wheel roll radius of the first wheel, and a second absolute wheel roll radius signal, indicative of an absolute wheel roll radius of the second wheel.

(68) FIG. 8 illustrates a flow diagram of a method 80 of estimating absolute wheel roll radii and a vertical compression value of wheels of a vehicle.

(69) The method 80 comprises a first measurement step 81. The measurements 81 include measuring a yaw rate signal, indicative of a yaw rate of the vehicle, measuring a wheel speed signal, indicative of an angular velocity of a first wheel of the vehicle, as well as measuring a further wheel speed signal, indicative of an angular velocity of a second wheel of the vehicle and measuring a lateral acceleration signal, indicative of a lateral acceleration of the vehicle.

(70) In the second measurement step 82, the values of same set of quantities at a later point in time are collected. Similarly, the third measurement step 83 collects the values of the set of quantitates at still a further point in time.

(71) Based on the three set of measurements 81, 82 and 83, absolute roll radii are determined (reference numeral 86) and a vertical compression value is determined (reference numeral 88). Steps 86 and 88 are illustrated as being carried out simultaneously. However, as will be apparent to the skilled person, these steps may be carried out sequentially, simultaneously, independently or any combination thereof.