Patent Publication Number: US-6668635-B2

Title: Method of improving steering performance robustness utilizing dimensional non-uniformity in tire/wheel

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application relates to applications entitled METHOD OF IMPROVING STEERING PERFORMANCE ROBUSTNESS UTILIZING MASS NON-UNIFORMITY IN TIRE/WHEEL, Attorney&#39;s Docket No. DN2000058USA; and METHOD OF IMPROVING STEERING PERFORMANCE ROBUSTNESS UTILIZING STIFFNESS NON-UNIFORMITY IN TIRE/WHEEL, Attorney&#39;s Docket No. DN2000246USA; both having a filing date concurrent with that of the present application. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     This invention relates to methods of improving the steering performance of vehicles, particularly passenger vehicles having pneumatic tires. 
     BACKGROUND OF THE INVENTION 
     The term “steering performance” (or simply “steering”) refers to a vehicle driver&#39;s feeling that a vehicle&#39;s steering (and/or “handling”) is responsive to movement of the steering wheel. The better the steering performance, the better the driver&#39;s “feeling” of having control over the vehicle&#39;s steering. Because it relates to a “feeling” on the part of a driver, steering performance is essentially a subjective evaluation of a vehicle&#39;s steering. Steering performance can change over time, mainly deteriorating as components in the vehicle steering system wear, age, or suffer damage. Steering system components include the steering wheel, the tires and wheels, and everything in between such as the steering box, any power assist components, and linkages and joints. Steering performance can also vary with operating conditions, including, for example, road texture, vehicle speed, steering wheel settings, minor tire inflation pressure changes, and tire/wheel uniformity changes (e.g., balance). 
     Worsening steering performance is generically referred to as “steering performance loss” (SP-Loss), or “give-up”. A steering system or component which is resistant to steering performance loss is “robust” or can be said to possess “steering performance robustness”. Similarly, any component change which appears to delay or prevent SP-Loss in a vehicle steering system can be said to improve steering performance robustness. Also, it has to be mentioned that SP-Loss is more noticeable on vehicles which have, in general, a very good and crisp steering. Finally, it has been noted that steering component changes which improve steering performance robustness usually also enhance the driver&#39;s perception of steering performance. The inverse may not be true, i.e., a component change which enhances steering performance initially may not be robust and therefore quickly deteriorates to yield a net steering performance loss. 
     Steering performance loss is mostly a concern in passenger vehicles with pneumatic tires and power assisted steering (power steering), although the phenomenon has also been observed in passenger vehicles without power steering. Although a trained driver can determine steering performance at virtually any vehicle speed, the steering performance (and therefore a change in performance, e.g., SP-Loss) is most noticeable above a certain vehicle speed threshold. Even though SP-Loss is generally a change over time, it can be practically instantaneous. 
     Certain vehicles appear to be more susceptible to SP-Loss, and it has been noted (especially on these vehicles) that steering performance is affected by differences in tire construction, or even by changes from one tire to another of the same tire construction. (The common industry term “tire construction” includes all elements of a tire&#39;s design—including, for example, tire/carcass shape, tread pattern, number and type of plies, materials and manufacturing methods used, etc.) It is well known that tire uniformity (e.g., balance) varies from tire to tire, and that an unbalanced tire causes vibrations which are felt in the steering, therefore tire uniformity is almost universally controlled in tire and wheel design, during tire and wheel manufacturing, and after forming a tire/wheel assembly. It is generally assumed that improved tire/wheel uniformity will improve steering performance and hopefully will also help with steering performance robustness. As noted above, this is not always the case, and thus a great deal of research has been directed toward additional solutions to SP-Loss, such as various tire design changes. 
     Regardless of tire construction/design, the tire and vehicle industry generally strives for the best possible tire uniformity and, by extension, uniformity of the tire/wheel assembly whenever a tire is mounted on a wheel for use on a vehicle. This is a multi-part optimization process whereby the tire manufacturer strives for optimum tire uniformity, the wheel manufacturer strives for optimum wheel uniformity, and then the vehicle operator has the tire/wheel assembly tested and corrected for “balance”. 
     Tire uniformity and tire/wheel balance are well known topics in the tire industry. A brief description of certain relevant portions of these topics will now be presented. 
     Uniformity and Balance 
     Tire manufacturers generally perform quality checks on tires at various points during the manufacturing process. Tire uniformity is an important, performance-related check typically performed on a tire uniformity machine (TUM) which is well-known in the art and will not be described in detail herein. Tire uniformity machines most commonly rotate a tire mounted on a known-to-be-uniform or “true running” wheel, and measure variations in forces on the wheel axis (or on a load wheel) and/or measure variations in tire outer surface positions. Typical force variation measurements include radial force variation (RFV) which is indicative, for example, of static imbalance or radial runout; and lateral force variation (LFV) which is indicative, for example, of couple imbalance, lateral runout, or tire radial runout skewness. Tire surface measurements are directly indicative of runout conditions and conicity. Another measurement, generally done on a sampling basis on special laboratory grade, high speed TUMs, is tangential force variation (TFV), or fore-aft force variation which is experienced at the surface of contact between a tire and a road surface in a direction both tangential to the tire tread and perpendicular to the tire axis of rotation. 
     In terms of effect on a vehicle and its tires, all of the types of force variations can cause vibrations dependent upon the magnitude of the force variation (modified by vehicle characteristics such as wheel suspension mass/stiffness/damping conditions). The lateral force variation (and/or couple imbalance) primarily cause vibrations due to a wobbling motion of the tire, with the axis of rotation for the oscillation being vertical or horizontal, parallel to the tire&#39;s circumferential plane, and approximately centered within the tire/wheel volume. In contrast, radial and tangential force variation and/or static imbalance mainly cause vibrations due to movement in vertical and fore-aft directions (although some lateral movements exist, they are distributed symmetrically about the equatorial plane and involve only a small percentage of the total tire/wheel assembly mass). 
     Static and Couple Imbalances 
     Generally speaking, when a tire/wheel assembly is “balanced”, the modern practice is to test, and correct if necessary, both the static and the couple balance of the assembly. This balancing is generally performed using special-purpose equipment. For couple balancing, the equipment generally rotates the tire/wheel assembly at a relatively high speed, and the tire is not in contact with any surface (compare to the road-wheel used in TUM testing). 
     Static imbalance arises in a rotational system such as a tire and wheel assembly when the mass of the rotating tire/wheel assembly is non-uniformly distributed about the axis of rotation in such a way that the sum of the centrifugal force vectors arising from each moving part of the rotating system is non-zero. The term “static,” when used in reference to rotational balance, refers to the fact that rotational motion is not needed to identify, locate and correct the rotational imbalance. That is, a wheel that has a static imbalance will, at certain stationary angular orientations about the horizontal axis of rotation, exert a torque vector about the axis of rotation, due to gravity forces. An optimally balanced tire/wheel system will produce no such torque vector about the axis of rotation. Of course, it must be acknowledged that no rotational system can have “perfect” static balance, but that adequate or optimal static balance can be achieved in real-world rotational systems such as tire/wheel assemblies and aircraft propellers and the high-rotational-speed components of gas turbine and steam turbine engines. One precise way to describe and define ideal static balance is to say that a rotating system is in static balance if all of the centrifugal force vectors (which act perpendicularly to the axis of rotation) have a sum that is zero. 
     In contrast to static imbalance, couple imbalance can, for all practical purposes, be detected only during rotational motion and therefore requires dynamic balancing machines. That is, a rotational system such as a tire/wheel assembly can appear to have perfect static balance, and yet, during rotation, vibrations associated with imbalance forces will arise, due to couple imbalance. 
     A dynamic balancing machine can be used to detect and correct both couple imbalance and static imbalance, and therefore a tire/wheel assembly that is characterized as “dynamically balanced” is generally understood to be both statically and couple balanced. The definition given above for static balance—namely, that all of the centrifugal force vectors have a sum that is zero—can be supplemented to provide a corresponding definition of dynamic balance: i.e., dynamic balance of a rotational system exists when the sum of all the centrifugal force vectors is zero (static balance), and the sum of the moments of these centrifugal force vectors about any axis that is perpendicular to the axis of rotation is zero (couple balance). 
     One example of a statically balanced but dynamically unbalanced tire/wheel assembly would be one in which one sidewall of a tire is non-uniform in such a way that some angular portion of the sidewall is either lighter or heavier than the other portions of the sidewall while, at the same time, the other sidewall has exactly the same mass-distribution properties but is oriented about the axis of rotation in such a way that the respective non-uniformities of each sidewall are oriented angularly apart from one another with respect to the tire/wheel&#39;s axis of rotation. In such a tire/wheel assembly, the centrifugal force vectors would thus have a non-zero resulting moment and would tend to rotate the tire about an axis that is perpendicular to both the axis of rotation and the direction of these centrifugal force vectors. However, with regard to static balance, the centrifugal force vectors for such a tire as a whole could have a sum that is zero if the locations of excess mass associated with the respective sidewalls in the above example are located angularly apart from one another. For example, if two equal excess masses “M” are located one at a point in each sidewall, then dynamic imbalance with static balance (i.e. pure couple imbalance) will occur if mass M in the first sidewall is located 180 degrees around from mass M in the second sidewall, and both masses M are located at the same radius. (In the irregular sidewall example given above for dynamic imbalance, if only one of the sidewalls is unbalanced, the tire/wheel assembly will have both a static and a couple imbalance.) 
     Other Non-Uniformities 
     In addition to static and couple mass imbalances, rotational vibrations can arise from other non-uniformities in tire/wheel assemblies. For example, a tire might have a tread or sidewall(s) that has greater or lesser flexibility (stiffness) within one angular portion compared to other portions of the tread or sidewalls. Such a tire/wheel assembly might have “perfect,” i.e., as close to perfect as is practical, couple and static balance, but when it is operated upon a vehicle, the portion of the tread or sidewall that is either softer or stiffer will interact with the road surface in ways that will give rise to vibrations comparable to (similar in some regards, but somewhat more complex than) those of a tire/wheel assembly that is unbalanced. 
     For example, if a portion of the tread is more or less flexible than the other portions of the tread, and the tire is otherwise uniform in its properties across its lateral dimension, a resulting vibration may be comparable to that arising from a static imbalance. Or, if the stiffness properties of the tire are not uniform from side to side and along the tire circumference, then the resultant rotational vibrations might mimic the effects of a couple imbalance. 
     Similarly, tires with radial or lateral runout will interact with the road surface in ways that will give rise to vibrations comparable to those of a tire/wheel assembly that is unbalanced, statically or dynamically. 
     BRIEF SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide methods of improving vehicle steering performance and steering performance robustness (reducing the risk of steering performance loss), as defined in one or more of the appended claims. 
     According to the invention, a method of improving steering performance robustness in a vehicle having a plurality of tire/wheel assemblies, including a number of front tire/wheel assemblies and a number of rear tire/wheel assemblies, each tire/wheel assembly comprising a tire mounted on a wheel, comprises imparting a controlled amount of dimensional non-uniformity to at least one of the tire/wheel assemblies, preferably one or more of the front tire/wheel assemblies. Preferably all of the plurality of tire/wheel assemblies are statically and dynamically balanced. 
     According to an embodiment of the inventive method, the dimensional non-uniformity is imparted to the tire of the at least one tire/wheel assembly, preferably distributed meridionally symmetrically about the equatorial plane of the tire, and then the tire with the dimensional non-uniformity is corrected as needed to assure minimum lateral force variation. The dimensional non-uniformity can be imparted by imparting a different thickness to at least one tire component in at least one sector of the tire, thereby adding mass non-uniformity to the dimensional non-uniformity for a synergistic beneficial effect. Alternatively, the dimensional non-uniformity is imparted by manufacturing the tire such that the tire&#39;s ply cords vary in length around the circumference of the tire, using a tire manufacturing method which includes, for example, inclining bead setters in the tire mold, preferably by approximately 0.5 degrees to approximately 3 degrees. Alternatively, the dimensional non-uniformity is imparted by varying a tread pattern for the tire. Alternatively, the dimensional non-uniformity is radial runout of the tire comprising at least one radial runout peak. 
     According to an embodiment of the inventive method, the dimensional non-uniformity in the at least one tire/wheel assembly is imparted as at least one radial runout peak, preferably approximately 0.1 mm to approximately 0.8 mm. 
     According to an embodiment of the inventive method, the dimensional non-uniformity is imparted by placing one or more shims between the wheel&#39;s bead seats and the tire&#39;s beads in the at least one tire/wheel assembly. 
     According to an embodiment of the inventive method, the dimensional non-uniformity in the at least one tire/wheel assembly is imparted to the wheel of the at least one tire/wheel assembly, preferably symmetrically about the equatorial plane of the wheel, and the wheel with the dimensional non-uniformity is corrected as needed to assure minimum lateral force variation in the tire/wheel assembly utilizing the wheel. For example, the dimensional non-uniformity can be an eccentric wheel, or can be radial runout of the wheel comprising at least one radial runout peak. 
     According to the invention, a method of improving steering performance robustness in a vehicle having a plurality of tire/wheel assemblies, each tire/wheel assembly comprising a tire mounted on a wheel, comprises minimizing lateral force variations, wobbling moment variations, couple imbalance, lateral run-out, tread snaking and radial run-out skewness, for all of the plurality of tire/wheel assemblies. Preferably, all of the plurality of tire/wheel assemblies are statically and dynamically balanced. 
     Other objects, features and advantages of the invention will become apparent in light of the following description thereof. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Reference will be made in detail to preferred embodiments of the invention, examples of which are illustrated in the accompanying drawing figures. The figures are intended to be illustrative, not limiting. Although the invention is generally described in the context of these preferred embodiments, it should be understood that it is not intended to limit the spirit and scope of the invention to these particular embodiments. 
     Certain elements in selected ones of the drawings may be illustrated not-to-scale, for illustrative clarity. The cross-sectional views, if any, presented herein may be in the form of “slices”, or “near-sighted” cross-sectional views, omitting certain background lines which would otherwise be visible in a true cross-sectional view, for illustrative clarity. 
     Elements of the figures can be numbered such that similar (including identical) elements may be referred to with similar numbers in a single drawing. For example, each of a plurality of elements  199  may be referred to individually as  199   a ,  199   b ,  199   c , etc. Or related but modified elements may have the same number but are distinguished by primes. For example,  109 ,  109 ′, and  109 ″ are three different elements which are similar or related in some way, but have significant modifications e.g., a tire  109  having a static imbalance versus a different tire  109 ′ of the same design, but having a couple imbalance. Such relationships, if any, between similar elements in the same or different figures will become apparent throughout the specification, including, if applicable, in the claims and abstract. 
     The structure, operation, and advantages of the present preferred embodiment of the invention will become further apparent upon consideration of the following description taken in conjunction with the accompanying drawings, wherein: 
     FIG. 1A is a schematic diagram of a rotating system having static imbalance, according to the prior art; 
     FIG. 1B is a schematic diagram of a dynamically balanced rotating system (static and couple balance), according to the prior art; 
     FIG. 1C is a schematic diagram of a rotating system with couple imbalance, according to the prior art; 
     FIG. 1D is a cross sectional schematic view of a wheel having pure static imbalance without any couple imbalance, according to the prior art; 
     FIG. 1E is a cross sectional schematic view of a wheel having pure couple imbalance without any static imbalance, according to the prior art; 
     FIG. 2A is a schematic diagram illustrating a circular motion that is induced by a static imbalance about the rotational axis of a rotating system, according to the prior art; 
     FIG. 2B is a schematic diagram illustrating a motion that is induced by a couple imbalance about the rotational axis of a rotating system, according to the prior art; 
     FIG. 3A is a graph illustrating a subjective rating of steering performance of a vehicle as a function of the use of a single, rear-mounted tire/wheel assembly having a residual static imbalance, according to the invention; 
     FIG. 3B is a schematic diagram showing the location of a single statically unbalanced rear tire/wheel assembly, according to the invention; 
     FIG. 4A is a graph illustrating a subjective rating of steering performance of a vehicle as a function of the use of a single, front-mounted tire/wheel assembly having a residual static imbalance, according to the invention; 
     FIG. 4B is a schematic diagram showing the location of a single statically unbalanced front tire/wheel assembly, according to the invention; 
     FIG. 5A is a graph illustrating a subjective rating of steering performance of a vehicle as a function of the use of four tire/wheel assemblies, each of which has a residual static imbalance, according to the invention; 
     FIG. 5B is a schematic diagram showing the locations of four statically unbalanced tire/wheel assemblies, according to the invention; 
     FIG. 5C is a graph illustrating a subjective rating of steering performance of a vehicle as a function of the use of a single, front-mounted tire/wheel assembly having a couple imbalance, according to the invention; 
     FIG. 5D is a schematic diagram showing the location of a single couple-unbalanced front tire/wheel assembly, according to the invention; 
     FIG. 6A is a graph illustrating a subjective rating of steering performance of a vehicle as a function of the use of a single, front-mounted tire/wheel assembly having a mixed static and couple imbalance, according to the invention; 
     FIG. 6B is a schematic diagram showing the location of a front-mounted tire/wheel assembly with a mixed static and couple imbalance, according to the invention; 
     FIG. 6C is a graph illustrating a subjective rating of steering performance for two different tire constructions tested on a vehicle as a function of the Steering Robustness Level (SRL), according to the invention; 
     FIG. 6D is a schematic illustration of a tire with a symmetric second order mass non-uniformity configuration, according to the invention; 
     FIG. 6E is a schematic illustration of a tire with an asymmetric second order mass non-uniformity configuration, according to the invention; 
     FIG. 7A is a schematic diagram of a tire/wheel assembly with a mass non-uniformity and a balance weight, according to an embodiment of the invention; 
     FIG. 7B is the tire/wheel assembly of FIG. 7A shown rolling on a road surface, according to the invention; 
     FIG. 7C is a graph illustrating predicted vertical and fore-aft forces caused at the axis of rotation by the mass non-uniformities of the tire/wheel assembly of FIG. 7B, according to the invention; 
     FIG. 7D is a graph illustrating fore-aft moments associated with the fore-aft forces illustrated in FIG. 7C, according to the invention; 
     FIG. 7E is a schematic diagram of the tire/wheel assembly of FIG. 7B illustrating vertical force vectors corresponding to vertical force peaks illustrated in FIG. 7C, according to the invention; 
     FIG. 7F is a schematic diagram of the tire/wheel assembly of FIG. 7B illustrating fore-aft force vectors corresponding to fore-aft force peaks illustrated in FIG. 7C, and moment vectors corresponding to moment peaks illustrated in FIG. 7D, according to the invention; 
     FIG. 8A is a circumferential cross section of a sector of a tire illustrating splice methods for incorporating non-uniformities, according to the invention; 
     FIG. 8B is a circumferential cross section of a sector of a tire illustrating fabric methods for incorporating non-uniformities, according to the invention. 
     FIG. 9A is a side view of a schematic representation of a tire having a form of dimensional non-uniformity, according to the invention; 
     FIG. 9B is a side view of a schematic representation of a tire having another form of dimensional non-uniformity, according to the invention; 
     FIG. 9C is a side view of a schematic representation of a wheel having a form of dimensional non-uniformity, according to the invention; and 
     FIGS. 10A and 10B are graphs illustrating a subjective feeling of steering performance as a function of the use of a single, front-mounted tire/wheel assembly having varying amounts of imbalance mass added, according to the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Definitions 
     The following terms may be used throughout the descriptions presented herein and should generally be given the following meaning unless contradicted or elaborated upon by other descriptions set forth herein. 
     “Axial” refers to a direction parallel to the axis of rotation of the tire. 
     “Balance” refers to a distribution of mass around a tire or tire/wheel assembly. 
     “Circumferential” refers to circular lines or directions extending along the perimeter of the surface of the annular tread perpendicular to the axial direction, and can also refer to the direction of sets of adjacent circular curves whose radii define the axial curvature of the tread, as viewed in cross section. 
     “Conicity” is an average lateral force resulting from, for example, a conical shaped tire. In general, conicity is a non-uniformity resulting from a dimensional, stiffness or mass property that is distributed asymmetrically along a tire&#39;s meridional contour, thereby causing a lateral (i.e. steering) force in a constant lateral direction, independent of the direction of tire rotation. It can be caused, for example, by off-center tire components. 
     “Couple Imbalance” refers to an imbalance that tends to rotate the tire about an axis that is perpendicular to the axis of rotation, thereby generally resulting in tire/wheel assembly wobble. 
     “Dimensional non-uniformities” refers to non-uniformities in tire dimensions wherein the non-uniformities are measurable when the tire is at rest. 
     “Dynamic Balancing” refers to a method of balancing a tire/wheel assembly while rotating the assembly. 
     “Dynamic non-uniformities” refers to non-uniformities that are manifested when the tire is rotating. 
     “Equatorial plane” refers to a plane perpendicular to the tire&#39;s axis of rotation and passing through the center of its tread, or to a plane containing the circumferential centerline of the tread. 
     “Footprint” refers to a contact patch or area of contact of a tire tread with a flat surface (the ground, a road) under normal load and pressure. Footprints can change with speed. 
     “Hop” refers to a vertical oscillatory motion of a wheel between the road surface and the spring mass. 
     “Inflation” refers to the tire cold inflation pressure required for specific loads and speed conditions. 
     “Imbalance” (equivalently “unbalance”) refers to a condition which is not balanced. 
     “Lateral” refers to a direction parallel to the axial direction, and usually refers to forces acting on the tire tread in a lateral (axial) direction. 
     “Lateral force variation” is a dynamic non-uniformity referring to the tire&#39;s lateral (axial) force being non-uniform around its circumference, thereby causing lateral vibration (e.g., wobbling) during driving. It is typically generated by a non-uniform dimensional, stiffness or mass distribution both along the meridional contour and along the tire circumference. 
     “Meridian” and “Meridional” refer to a tire cross-section cut along a plane that includes the tire axis. 
     “Offset” refers to the lateral distance from the center of a rim (midway between the flanges) to the wheel-mounting surface of the rim. 
     “On-center feel” refers to the subjective feeling of the absence or presence of free play in a vehicle&#39;s steering wheel before noticeable steering response occurs. 
     “Oversteer” refers to a condition where the rear tires have a greater slip angle than the front tires, causing the vehicle to turn in a smaller radius than desired by the driver. 
     “Parallel hop” refers to a form of wheel hop in which a pair of wheels hop in phase with one another. 
     “Pneumatic tire” is a laminated mechanical device of generally toroidal shape (usually an open-torus) having two beads, two sidewalls and a tread and made of rubber, chemicals, fabric and steel or other materials, and typically inflated with air under pressure. 
     “Radial force variation” is a dynamic non-uniformity referring to the tire&#39;s radial force being non-uniform around the tire&#39;s circumference, thereby causing vertical and fore-aft vibration during driving. It is typically generated by a non-uniform dimensional, stiffness or mass distribution along the tire&#39;s circumference. 
     “Radial runout” is a dimensional dynamic non-uniformity representing a variation in tire radius around the circumference of a rotating tire. 
     “Residual Static Imbalance” or RSI refers to the intentional introduction of a static imbalance in a tire or tire/wheel assembly, wherein the RSI is of adequate magnitude to have beneficial influences upon steering performance, by generating fore-aft and/or vertical force variations at the wheel axis, without at the same time being of sufficient magnitude to be noticeable to the vehicle&#39;s occupants as vibrations. 
     “Runout” refers to a variation in the reading of a rotating object dimensional indicator. It generally refers to the difference between maximum and minimum readings (peak to peak), as applied to: 
     a. Radial wheel runout—The difference between the maximum and minimum measurements of the wheel bead seat radii measured perpendicular to the spin axis. Values can be different for each side (flange). 
     b. Lateral wheel runout—The difference between the maximum and minimum measurements parallel to the axis of rotation on the inside vertical portion of a rim flange. Values can be different for each side (flange). 
     c. Radial tire runout—The difference between the maximum and minimum measurements on the tread surface and in a plane perpendicular to the axis of rotation while the tire is mounted on a true running wheel. The runout value can depend on the axial location of the measuring point on the tread surface. 
     d. Lateral tire runout—The difference between the maximum and minimum measurements parallel to the axis of rotation at a given point of the tire surface (e.g. at the widest point of each sidewall, exclusive of decoration), while the tire is mounted on a true running wheel. 
     e. Radial runout skewness—Can be applied to wheels or tires and refers to radial runouts of the two sides (wheel flanges or tire shoulders) that are out of phase or asymmetric about the equatorial plane. 
     “Shimmy” refers to a rapid sidewise (lateral) vibration of the front wheels, and can be caused by worn kingpins or other parts of a vehicle&#39;s steering mechanism, as well as by tires with couple imbalance. 
     “Sidewall” refers to that portion of a tire between the tread and the bead. 
     “Slip Angle” refers to an angle between the vehicle&#39;s direction of travel and the direction in which the front wheels are pointing. 
     “Static Imbalance” refers to a condition such that when a tire/wheel assembly is turned on a horizontal, very low friction, free axle, it will always come to rest (become static) at a given rotational position. 
     “Steering Robustness” refers to the ability of a tire/wheel/vehicle system to maintain a high steering performance, despite unfavorable and/or variable test conditions. A “Steering Robustness Level” (SRL) is the concept used to describe and measure the steering robustness. 
     “Steering Robustness Level” or SRL refers to a combination (additive function) of all the positive and negative contributions to steering performance (static imbalance, couple imbalance and all other relevant factors). A split can be made between “intrinsic” and “extrinsic” contributions to SRL to cover for example, intrinsic contributions related to tire characteristics, including built-in non-uniformities, and extrinsic contributions related to vehicle/road/test conditions, test condition variations, tire manufacturing variations, etc. 
     “Tangential force variation” refers to the nonuniform rotation of the tire&#39;s outer surface relative to the rotation of the tire&#39;s bead area. It produces a fore-aft or “push-pull” force variation which is generated at the surface of contact between tire and road surface in a direction both tangential to the tire tread and perpendicular to the tire axis of rotation. 
     “Tire Balancing” refers to adding external weights around a tire/wheel assembly to compensate for static and/or couple imbalance of the tire and wheel as an assembled unit. 
     “Traction” refers to the friction force between a tire and a surface on which it is moving. 
     “Tramp”refers to a form of wheel hop in which a pair of wheels hop in opposite phase. 
     “True Running Wheel” (or “True Wheel”) refers to a wheel which rotates (“runs”) without exhibiting any forms of runout or imbalance. 
     “Understeer” refers to a condition where the front tires have a larger slip-angle than the rear tires, making the vehicle tend to turn less sharply than the wheels are pointed. The vehicle must be held into the turn. 
     “Uniformity” refers to a measure of the ability of a tire or a wheel to run smoothly and vibration free. Typically measured with a tire uniformity machine. Measurements include, for example, radial/lateral/tangential force variation, radial/lateral runout, and static/couple balance. 
     “Wheel” refers to a generally cylindrical, typically metallic, disc-like mechanical support for supporting a typically pneumatic tire and mounting to a vehicle axle. A wheel has two axially spaced-apart flanges (or annular lips), each flange adapted to securely receive a respective one of the two beads of the mounted tire. 
     “Wheel Alignment” refers to an adjustment of wheel position to ensure proper orientation of wheels (and tires) to the vehicle chassis and to each other. 
     “Wheel Balance Weight” refers to a small weight mounted (clamped or adhered) to a wheel (often to an outside portion of a flange of the wheel) to correct an unbalanced tire and/or wheel condition. 
     “Wheel Geometry” refers to an axis about which a wheel assembly rotates. Conditions such as bent wheels, worn bushings and improper alignment affect wheel geometry. 
     “Wobbling moment variation” refers to a variation in the moments about a fore-aft horizontal axis (camber or overturning moment) or about a vertical axis (steer or self-aligning moment) and, as lateral force variation, is generated by a non-uniform dimensional, stiffness or mass distribution both along the meridional contour and along the tire circumference. 
     Introduction 
     While researching the effects of tire and wheel characteristics on steering performance, the inventors have determined that, contrary to assumptions of the prior art, certain types and magnitudes of tire/wheel vibration can have an ameliorating effect on steering performance and steering performance robustness, and can therefore avoid the steering performance loss (SP-Loss) problem described in the background hereinabove. The invention therefore concerns application of this discovery as methods for improving steering performance robustness, i.e., long-term prevention of SP-Loss. 
     Many vehicles have a tendency to undergo steering performance loss. This tendency depends, for example, on the design and condition of the vehicle, the road and driving conditions, as well as the tire/wheel characteristics. SP-Loss may manifest itself in the following possible ways: performance variations in steering precision and on-center feel while driving (the less severe case), a sudden performance drop in steering precision and on-center feel while driving (the most obvious case to detect), or a poor performance in steering precision and on-center feel right from the test start (the most severe case). When SP-Loss sets in, the vehicle response seems not properly in phase with torque feedback from the steering wheel. Our research indicates that SP-Loss does not seem to be related to changes in tire force and moment characteristics, but rather seems to arise within the vehicle&#39;s steering system and linkages that connect the driver&#39;s steering wheel to the tires and wheels that actually steer the vehicle. 
     As will be described in more detail hereinbelow, it has been determined that tire/wheel vibrations due to lateral force variations (LFV, e.g., couple imbalance) generally have a detrimental effect on steering performance and steering performance robustness, can easily lead to SP-Loss, and therefore should be minimized if not eliminated. On the other hand, vibrations due to radial force variations (RFV) and/or tangential force variations (TFV) caused, for example, by static imbalance or by mass non-uniformities concentrated in the tread area (including tread rubber, belts and carcass layers underlying it) and positioned symmetrically about the equatorial plane may have a beneficial effect on steering performance and steering performance robustness, and these beneficial effects can be obtained even when the radial/tangential force variations are at a low enough magnitude so as to be un-noticeable by the vehicle&#39;s driver or occupants, and also have a negligible impact on tire wear. 
     Various theories have been proposed to explain how certain vibrations could trigger or prevent SP-Loss. Also, the causes of steering performance loss are theoretical and manifold. Of most immediate interest are the theoretical effects of static vs. couple imbalance of tire/wheel assemblies, or more generally, the effects of RFV/TFV versus LFV. The general characteristics of each type of imbalance/non-uniformity can be differentiated from one another in one particular respect that has at least a superficial plausible relationship to the steering performance loss problem: RFV/TFV (e.g., pure static imbalance) gives rise to vibrations that act upon the tire&#39;s axis of rotation in a way that applies forces that are more or less perpendicular to the axis of the tire/wheel assembly, while LFV (e.g., couple imbalance) produces vibrations that tend to force the axis of rotation to rotate about a point on the axis near where it intersects the tire&#39;s equatorial plane. Due to the design of the vehicles and of their components (steering system, suspension system, brake system, etc.), it is plausible that lateral hub vibrations will propagate differently and have different effects than radial or fore-aft vibrations. On the other hand, vibrations are known to affect the friction and stick/slip behavior at the interface between involved components: a dynamic friction is, for example, lower than a static friction. Friction changes in a complex system such as a steering system, taken as a whole, will logically affect the reactivity of that system and the subjective perception of its reactions. 
     Tangential, radial, and lateral force variations in rotating tire/wheel assemblies are known to have a wide variety of causes. The most obvious cause, and also the simplest to vary in a controlled way for research testing, is imbalance of the tire/wheel assembly. Adding balance weights to wheel rims is a well-known method for “balancing” a tire/wheel assembly, thereby canceling out a part of the radial and lateral force variations, to the extent that they can be measured by existing tire balancing equipment, in non-loaded spinning conditions. (As will be discussed in more detail hereinbelow, this method generally can not fully compensate for the effect of all tire characteristics, such as abrupt force and moment peaks caused by localized tire non-uniformities.) Thus the concepts underlying the methods of the present invention for improving steering performance robustness will first be developed using the simplified concepts involving tire/wheel balance. 
     Static and Couple Imbalances 
     In the theoretical, “perfectly” balanced rotating system, the centrifugal force vectors, which act perpendicularly to the axis of rotation, have a sum that is zero. Such perfection (in most any endeavor) can be approached, but is typically never achieved. 
     FIG. 1A shows a rotating system  10  comprising a rotating shaft  12  to which is attached a mass m at the end of an arm  14  having a length r which is also taken, in FIG. 1A, as the radial distance of the center of mass m from the axis of rotation  16  of the shaft  12 . The plane EP is the equatorial plane within which the mass m revolves in a circular trajectory having a radius r. (The equatorial plane EP is shown as having a circular outer limit purely for purposes of illustrating that the plane exists.) The point P represents a point whereat the axis of rotation  16  intersects the equatorial plane EP. The mass m exerts a radially outward-directed centrifugal force vector F whose magnitude, from Newton&#39;s Second Law of Motion, is the multiplicative product of m and r and the square of the shaft&#39;s rotational speed (in units of radians per second). Such a rotational system has an obvious imbalance. 
     Assuming, in reference to FIG. 1A, that the equatorial plane EP represents the equatorial plane of a tire/wheel assembly, then the location of the mass m within the equatorial plane would result in a static imbalance of the system shown, but would not result in a couple imbalance. By contrast, were the mass m to be located outside of the equatorial plane EP, i.e., to either side of the equatorial plane, the imbalance would be of both the static and the couple types. This will become more evident upon examination of the FIGS. 1B and 1C. 
     FIG. 1B shows a rotating system  10 ′ having two masses, m 1  and m 2  at the ends of arms  15  and  17 , having respective lengths r 1 , and r 2 . The two masses m 1  and m 2  and their respective arms and  17  are shown to be disposed in radial opposition to one another about the rotational (spin) axis  16  and to be within the equatorial plane EP. During rotation of the shaft  12 , the respective centrifugal force vectors F 1  and F 2  will be oppositely directed from one another. If F 1  and F 2  are of equal magnitude, then the rotating system shown in FIG. 1B will be in perfect dynamic balance (i.e., both static balance and couple balance). Note that even if F 1  and F 2  are equal, the respective masses, m 1  and m 2  and their respective distances, r 1  and r 2 , from the axis of rotation  16  need not be respectively equal to one another. Note further that if the two masses m 1  and m 2  and their respective arms  15  and  17  are moved outside of the equatorial plane EP, static balance will be maintained, even if the two masses are not maintained in the same plane, as long as they are 180 degrees apart around the rotational axis  16 . In other words, static balance will be achieved and maintained as long as all centrifugal force vectors, acting perpendicularly to the axis of rotation, have a sum that is substantially zero. 
     In the rotating system  10 ″ shown in FIG. 1C, the same two masses m 1  and m 2  are shown disposed opposite one another, as in FIG. 1B, but in separate respective planes, e.g. on opposite sides of the equatorial plane EP. For the purpose of the remainder of this description of couple imbalance, it is important to know that the plane in which m 1  is revolving about the axis  16  needs not be equally far from the equatorial plane EP as the plane in which m 2  is rotating. However, for the sake of simplicity in this discussion, the assumption of equal distances of the equatorial plane EP from the respective planes of rotation of the respective masses might be useful. The rotating system shown in FIG. 1C will exhibit couple imbalance, even if the respective centrifugal forces F 1  and F 2  are of equal magnitude (in which case the system will have static balance). If the forces F 1  and F 2  have different magnitudes, then the rotating system  10 ″ shown in FIG. 1C will have both static and couple imbalances. 
     With continued reference to FIG. 1C, one having ordinary skill in the art to which the present invention most nearly pertains will recognize that the respective forces F 1  and F 2  each will produce a torsional moment with respect to the point P, and the torsional moment(s) will cause the axis to tend to rotate in a complex pattern described more fully below. 
     FIGS. 1D and 1E illustrate tire/wheel assembly balancing cases where, for example, due to wheel design, two balance weights are not or cannot be located at the same axial distance from the equatorial plane and/or at the same radial distance from the axis of rotation, thereby forcing a geometrical asymmetry. In these cases, pure static imbalance or pure couple imbalance can still be achieved, providing the two balance weights have a different mass, in such a way that the geometrical asymmetry is compensated for. FIG. 1D illustrates a cross sectional schematic view of a wheel  11  which rotates about an axis of rotation  16 , and has an equatorial plane EP. A pure static imbalance without couple imbalance, can be achieved for the wheel  11  (and a tire, not shown, mounted on it) by installing, at substantially the same rotational angle about the axis of rotation  16 , two balance weights m 1  and m 2  having different masses such that their mass ratio m 1 /m 2  is substantially inversely proportional to the ratio l 1 /l 2  of their respective axial distances l 1  and l 2  from the equatorial plane EP, and also inversely proportional to the ratio r 1 /r 2  of their respective radial distances r 1  and r 2  from the axis of rotation  16 . Expressed as an equation: m 1 /m 2 =(l 2 l 1 )*(r 2 /r 1 ). Given these conditions, respective resultant centrifugal force vectors F 1  and F 2  will be substantially inversely proportional to the ratio of their respective distances from the axis of rotation (F 1 /F 2 =l 2 /l 1 ), and therefore the resulting moment (e.g., F 1 *l 1 −F 2 *l 2 ) about any axis that is perpendicular to the axis of rotation will substantially be zero (couple balance). 
     FIG. 1E illustrates a cross sectional schematic view of a wheel  11 ′ which rotates about an axis of rotation  16 , and has an equatorial plane EP. In contrast with the wheel  11  of FIG. 1D, a pure couple imbalance without static imbalance, can be achieved for the wheel  11 ′ (and a tire, not shown, mounted on it) by installing, 180 degrees apart about the axis of rotation  16 , two balance weights m 3  and m 4  having different masses such that their mass ratio m 3 /m 4  is substantially inversely proportional to the ratio r 3 /r 4  of their respective radial distances r 3  and r 4  from the axis of rotation  16 . Expressed as an equation: m 3 /m 4 =r 4 r 3 . Given these conditions, respective resultant centrifugal force vectors F 3  and F 4  will be substantially equal and in opposite directions, which guarantees a perfect static balance, but, due their axial offsets, l 3  and l 4 , respectively, will create a non-zero resulting moment (e.g., F 3 *l 3 +F 4 *l 4 ) about an axis that is perpendicular to the axis of rotation  16  (wobbling moment). 
     Referring to FIG. 2A, there is shown an axis of rotation  16  passing through a point P which, as in the preceding FIGS. 1A,  1 B and  1 C, lies in the equatorial plane EP (which is not shown in FIGS. 2A and 2B) of a tire/wheel assembly. The axis  16  is the ideal axis of rotation of a perfectly balanced rotating system. FIG. 2A demonstrates the effect of a pure static imbalance (mass not shown) upon the rotational axis  16 . Specifically, a pure static imbalance will produce forces that will tend to cause an orbiting movement of the axis  16 , as shown by the dashed line  16   a , which tends toward a circular motion about the ideal axis of rotation  16 . The circular motion of the orbiting axis  16   a  is shown by the arrows  18 . FIG. 2A illustrates an idealized representation of the effect of a pure static imbalance upon the axis of rotation  16  of rotating systems  10 ,  10 ′ of the types shown in FIGS. 1A and 1B, respectively. 
     Referring to FIG. 2B, there is shown an ideal axis of rotation  16  passing through a point P which, as in the preceding FIGS. 1A,  1 B and  1 C, lies in the equatorial plane EP (which is not shown in FIGS. 2A and 2B) of a tire/wheel assembly. FIG. 2B demonstrates the effect of a pure couple imbalance (masses not shown) upon the rotational axis  16 . Specifically, a pure couple imbalance will produce torques that will tend to cause a nutating (wobbling) movement of the axis  16 , as shown by the dashed line  16   b , which will have a tendency toward a wobbling motion about the point P. The motion of the wobbling axis  16   b  is shown by the two oppositely oriented arrows  19  and  21 . FIG. 2B is an idealized representation of the effect of a pure couple imbalance upon the axis of rotation  16  of a rotating system  10 ″ of the type shown in FIG.  1 C. 
     With respect to pneumatic tires for automotive vehicles, couple and static imbalances interact in ways that tend to move the tire&#39;s axis of rotation  16  in complex ways. The tendency of the axis of rotation  16  to be affected in the ways shown in FIGS. 2A and 2B may also be affected by mechanical and inertial constraints that are a function of the vehicle design. These constraints vary with the frequency of the imbalance excitation (vehicle speed dependant) and the constraints can be moderately weak at the resonance frequencies of the system. Depending upon the frequency, the constraints can be different in the vertical and the fore-aft directions. It should be noted that the movement of the rotational axis  16   a , as depicted in FIG. 2A for the case of pure static imbalance, is entirely in directions perpendicular to the ideal axis  16 , and therefore has no axial (lateral) component. 
     Steering Performance as a Function of Tire/Wheel Imbalance 
     FIGS. 3A,  4 A,  5 A,  5 C and  6 A illustrate test results showing the effects of tire/wheel imbalance upon the phenomenon of steering performance loss (SP-Loss). These tests were conducted using balance weights applied to the wheel flanges of tire/wheel assemblies, and the tire/wheel assemblies were mounted on a test vehicle known to be particularly susceptible to steering performance loss. For the tests detailed hereinbelow, it can be seen that in most cases (i.e., all except for the test illustrated by FIG. 5C) the test vehicle exhibited poor (“not okay”) steering performance with balanced tire/wheel assemblies (zero imbalance mass). As explained hereinabove, the results of these imbalance tests can be generalized to indicate the effects of tire and wheel non-uniformities. The amount of steering performance loss associated with each of the imbalance scenarios shown in the above-referenced FIGS.  3 A, 4 A,  5 A,  5 C, and  6 A is derived from and rated by the subjective reports of steering performance by vehicle test drivers. The numerals  3 ,  5  and  7  on the vertical axis in each of the graphs of the referenced FIGS. 3A,  4 A,  5 A,  5 C, and  6 A are steering performance rating numbers which represent increasing steering performance. In general, a rating of 6 or higher is “OK”, and 5 or lower is “NOK” (not okay). The horizontal axes of the FIGS. 3A,  4 A,  5 A,  5 C, and  6 A represent the mass (in grams) of balance weights which were added on each flange in order to induce a desired magnitude and type of imbalance (e.g., pure static, or pure couple imbalance). Before adding the test weights, all of the tire/wheel assemblies on the test vehicle were statically and dynamically balanced to eliminate, as much as possible, any pre-existing static and couple imbalance; true running wheels and excellent uniformity tires were employed; and to avoid adding any couple imbalance to tests of added static imbalance, the test weights were added to both flanges of the wheel. For example, a 5 gram imbalance mass shown on the test result charts means two 5 gram balance weights, one added on each wheel flange (i.e., on opposite sides of the tire/wheel equatorial plane). For FIGS. 3A,  4 A, and  5 A, illustrating tests of pure static imbalance, the two balance weights were added at the same rotational angle on each flange. When a static imbalance is imposed on an otherwise balanced tire/wheel assembly, it is referred to as a residual static imbalance (RSI). In the context of the present invention, RSI will generally preferably mean a residual static imbalance which is sufficient to have a positive effect on steering performance. 
     Referring to FIG. 3B, a test vehicle was outfitted with a single rear-mounted tire/wheel assembly  22  having static imbalance imposed upon the wheel by a set of flange-mounted balancing weights  24  (thus “static imbalance weights”) arranged so as to induce a static imbalance in the tire/wheel assembly. (The two circles shown in the locations of each wheel correspond to the flanges of the wheels to which the imbalance weights, shown by dots, were affixed.) FIG. 3A shows the test driver&#39;s subjective evaluation of steering performance as a function of the amount of mass (in grams) used to provide a static imbalance in the single rear-mounted tire/wheel assembly  22 . In summary, FIG. 3A demonstrates that a single rear-mounted tire/wheel assembly having a controlled amount (e.g., more than 5 grams on each flange) of RSI incorporated therein has a beneficial effect upon a given vehicle&#39;s steering performance. Generally, the more RSI incorporated into the tire/wheel assembly, the better the effect on steering performance as well as on steering performance robustness. However, an upper limit for RSI of 20 grams on each flange (i.e. 40 grams in total) was empirically determined as being the maximum RSI that could be incorporated, at least in relationship with that specific test vehicle  20 , without producing vehicle vibrations that were noticeable by the vehicle&#39;s driver or passengers. 
     FIGS. 4A and 4B show the effect on steering performance resulting from mounting a single front-mounted tire/wheel assembly  26  having a set of flange-mounted balancing weights  24   a  (compare  24 , FIG. 3B) arranged so as to impose residual static imbalance (RSI) on the single tire/wheel assembly  26  on a test vehicle  20   a  (compare  20 , FIG.  3 B). The test drivers&#39; subjective feel for steering performance, as indicated in the vertical axis of FIG. 4A, indicates that RSI in a single front-mounted tire/wheel assembly  26  of as little as 5 grams on each flange can significantly improve steering performance. Comparing FIGS. 4A and 3A, it is apparent that when a single one of four tire/wheel assemblies incorporating RSI is a front tire/wheel assembly  26 , rather than a rear tire/wheel assembly  24 , the beneficial effects upon steering performance were generally more effective. 
     FIGS. 5A and 5B show the effect on steering performance resulting from adding RSI to all four wheels  28  of a test vehicle  20   b . The test driver&#39;s subjective feel for steering performance, as indicated in the vertical axis of FIG. 5A, indicates that introducing RSI in all four tire/wheel assemblies  28  has an even more beneficial effect than in the previous two tests (compare FIGS.  4 A and  3 A). 
     FIGS. 5C and 5D show the effect on steering performance resulting from introducing a pure couple imbalance (no static imbalance) on a single front-mounted tire/wheel assembly  29  on a test vehicle  20   c . Note that, unlike the other tests illustrated by FIGS. 3A,  4 A,  5 A, and  6 A, this test vehicle  20   c  exhibited a high steering performance rating with zero imbalance. As shown in FIG. 5D, balance weights which were added to introduce couple imbalance were mounted on opposite flanges, 180 degrees apart to assure the addition of a pure couple imbalance. FIG. 5C indicates that the test vehicle  20   c  had excellent steering performance with little or no imbalance, but a couple imbalance generated by 10 grams or more on each flange of a single front-mounted tire/wheel assembly  29  can produce poor steering performance. The steering performance did not recover from the NOK rating level (4.0) even out to as much as 40 grams per flange of added couple imbalance (results above 20 grams per flange not shown in FIG.  5 C). 
     FIGS. 6A and 6B show the effect on steering performance resulting from introducing an imperfect static imbalance (dynamic imbalance having a static component plus a moderate couple component) on a single front-mounted tire/wheel assembly  30  on a test vehicle  20   d . FIG. 6A shows that the single assembly  30 , with a mixed static and couple imbalance, has a mostly detrimental effect on steering performance. Although a 5 gram per flange mixed imbalance appears to help steering performance, a higher amount of imbalance mass does not help, and may even aggravate steering performance. Other tests, such as the test illustrated by FIGS. 5C and 5D, have shown that a vehicle/tire/wheel combination having excellent steering performance with balanced tires/wheel assemblies, can exhibit steering performance loss when sufficient couple imbalance is added. 
     In summary, improved steering performance and steering performance robustness is best effected by minimizing couple imbalance and by simultaneously implementing a suitable amount of residual static imbalance in the vehicle&#39;s tire/wheel assemblies, preferably all of them. It is also important to note that this concept works across very different vehicles: vehicles with hydraulic or electric power steering or with a basic mechanical steering system, vehicles with front, rear or all wheel drive, etc. Furthermore, since theory indicates that the steering performance effects are due to beneficial radial/tangential force variation and detrimental lateral force variation, this conclusion can be extended to read that improved steering performance and steering performance robustness is best effected by minimizing lateral force variations and by simultaneously implementing a suitable amount of radial and/or tangential force variation in one or more of the vehicle&#39;s tire/wheel assemblies, preferably all of them. 
     Principle of Additivity and Concept of Steering Robustness Level (SRL) 
     As illustrated in FIGS. 3A-5A, static imbalance has a positive but non-linear effect on steering performance: depending upon the level of static imbalance that is already achieved, the addition of an additional 5 grams per flange of static imbalance causes a big improvement, a small improvement, or no improvement at all, in steering performance. As illustrated in FIG. 5C, couple imbalance has a negative and non-linear effect on steering performance: depending upon the level of couple imbalance that is already achieved, the addition of an additional 5 grams per flange of couple imbalance causes a big drop, a small drop, or no drop at all, in steering performance. Moreover, it must be noted that if the curve describing the effect of couple imbalance is mirrored vertically, we basically obtain a curve that is similar to the curves describing the effect of static imbalance. Furthermore, a lot of other factors having a positive or a negative effect on steering performance have been identified, and they also seem to affect steering performance in a non-linear way. The effects of all the factors tend to add to or subtract from each other (additive behavior). Steering Robustness Level (SRL) represents the additive combination of all the beneficial and detrimental factors from any origin (vehicle/road/driving conditions, tire/wheel assembly characteristics, etc.). FIG. 6C shows representative SRL curves  61  and  62  which plot steering performance rating on the vertical axis versus Steering Robustness Level on the horizontal axis. The SRL curves  61  and  62  illustrate the (positive and non-linear) effect of SRL on steering performance. If beneficial contributions are much stronger than detrimental contributions, the SRL can achieve a high enough level to allow the vehicle to operate in the right hand, plateau, portion of the SRL curve  61 ,  62 , with a high steering performance rating (OK or better steering performance). If negative contributions are much stronger than positive contributions, the SRL will be at a low level, causing the vehicle to tend to operate in the left hand portion of the SRL curve  61 ,  62 , with a low steering performance (NOK or worse, indicating severe steering performance loss). In the intermediate situation where positive and negative contributions are similar, the vehicle will tend to operate in the mid part of the SRL curve  61 ,  62  and exhibit possibly large steering performance variations and low test repeatability, due to small uncontrolled SRL variations during the test(s). From a tire manufacturer&#39;s point of view, the Steering Robustness Level can be split into tire-based SRL (intrinsic) and test-based SRL (extrinsic). As an example, the SRL curves  61  and  62  illustrate the result of using various levels of static or couple imbalance, or any other extrinsic SRL variations, to compare two tires manufactured with two different tire constructions (arbitrarily labeled “A” and “B”). The SRL curve  61  for the tire with tire construction A shows that the tire construction A has a higher intrinsic steering performance robustness than the tire with tire construction B (plotted as SRL curve  62 ), because the tire construction A SRL curve  61  features a wider plateau at a high steering performance rating, which means that it is able to maintain a higher steering performance under more severe test conditions, in terms of extrinsic Steering Robustness Level. The same approach can be used to compare the steering performance robustness of different vehicles, different roads, different test conditions, etc. 
     Steering Performance as a Function of Tire Imbalance 
     In addition to the tests described hereinabove where imbalance was produced by adding weights to wheel flanges, further tests were conducted to determine the effect of tire mass non-uniformities on steering performance and steering performance robustness. Tire non-uniformities were simulated and controlled by means of various-sized lead weights glued at various locations on one or more of the tires on a test vehicle. These tests were conducted on a test vehicle known to be particularly susceptible to steering performance loss in combination with tires having a tire construction known to display good and robust steering characteristics. The tests revealed that for the tire sidewall, shoulder area or bead area, 1.5 to 3 grams of couple imbalance are sufficient to induce a substantial degradation of steering performance. Attaching a lead weight inside a tire close to its circumferential centerline has no negative effect on steering performance. Also, attaching imbalance weights symmetrically on both sides of the tire, either in the sidewall, the shoulder area or the bead area, has no negative, but a positive effect on steering performance. This is in line with the test results detailed hereinabove concerning the addition of static imbalance by mounting balance weights symmetrically on opposing wheel flanges, although the vibrations generated by tire mass non-uniformities are somewhat more complex than the vibrations generated by wheel mass non-uniformities. Any weight addition on the tire that was asymmetric with respect to the equatorial plane (e.g., one lead weight glued on each shoulder or sidewall but oriented at different rotational angular locations, or even one lead weight glued only on one shoulder or sidewall) was detrimental to the vehicle steering performance and triggered steering performance loss. This is in line with the test results detailed hereinabove concerning the addition of couple imbalance, although the vibrations generated by tire mass non-uniformities are somewhat more complex than the vibrations generated by wheel mass non-uniformities. 
     The importance of symmetry about the equatorial plane was further highlighted by an experiment wherein two, three, or four balance weights of equal masses were attached to each sidewall of a tire with known good steering performance, all at the same radial location, and with evenly spaced rotational angular locations about the axis of rotation on each sidewall. A steering performance comparison was made between tire configurations having weights at the same rotational angular locations on both sidewalls (in phase) versus at different (out of phase) rotational angular locations on each sidewall (a 90, 60 or 45 degree phase difference, respectively, for configurations with two, three, or four balance weights per sidewall). In-phase, i.e., symmetric weight distributions about the equatorial plane gave good, un-reduced steering performance ratings, and asymmetric (out of phase) configurations gave lower steering performance ratings. FIGS. 6D and 6E illustrate, respectively, a symmetric and an asymmetric configuration, in the case of two balance weights on each shoulder of a tire. (The latter can be termed a second order tire mass non-uniformity.) 
     Referring to FIG. 6D, there is shown in schematic format a tire  65  having two shoulders  66 : a left shoulder  66   a  and a right shoulder  66   b . For illustrative sake, the tire  65 , by itself, is assumed to be perfectly uniform. On the left shoulder  66   a  are attached two balance weights  68   a  and  68   c , positioned 180 degrees apart. On the right shoulder  66   b  are attached two balance weights  68   b  and  68   d , also positioned 180 degrees apart. It can be seen that if, for example, all of the balance weights  68  ( 68   a ,  68   b ,  68   c ,  68   d ) are equal in mass, then there will be no static imbalance imposed by the balance weights  68  positioned as shown. Since the balance weights  68   b ,  68   d  are positioned on the right shoulder  66   b  in phase with the balance weights  68   a ,  68   c  on the left shoulder  66   a , i.e., at the same rotational angles, there will be no couple imbalance as long as the balance weights  68   a  and  68   b  are of equal mass and also the balance weights  68   c  and  68   d  are of equal mass (i.e., there is a symmetric weight distribution about the equatorial plane of the tire  65 ). Furthermore, if the balance weights  68   a  and  68   b  are of equal mass, and also the balance weights  68   c  and  68   d  are of equal mass, but the (equal) masses of the balance weights  68   a  and  68   b  are suitably different from the (equal) masses of the balance weights  68   c  and  68   d , then a static imbalance without couple imbalance would be introduced to the tire  65 . The tire  65  can be said to have a symmetric second order mass non-uniformity (with or even without static imbalance), and higher order symmetric weight distributions such as this have a beneficial effect on Steering Robustness Level (SRL), by causing tangential and/or radial force variation when the tire  65  is rotated, especially when rotated under load on a supporting surface (e.g., a road). 
     Referring to FIG. 6E, there is shown in schematic format a tire  65 ′ having two shoulders  66 ′: a left shoulder  66   a ′ and a right shoulder  66   b ′. For illustrative sake, the tire  65 ′, by itself, is assumed to be perfectly uniform. On the left shoulder  66   a ′ are attached two balance weights  68   a ′ and  68   c ′, positioned 180 degrees apart. On the right shoulder  66   b ′ are attached two balance weights  68   b ′ and  68   d ′, also positioned 180 degrees apart. It can be seen that if, for example, all of the balance weights  68 ′ ( 68   a ′,  68   b ′,  68   c ′,  68   d ′) are equal in mass, then there will be no static imbalance imposed by the balance weights  68 ′ positioned as shown. Although the balance weights  68   b ′,  68   d ′ are positioned on the right shoulder  66   b ′ out of phase (asymmetrically) with the balance weights  68   a ′,  68   c ′ on the left shoulder  66   a ′, i.e., not at the same rotational angles, there will be no couple imbalance, at least if all masses are equal. The tire  65 ′ can be said to have an asymmetric second order mass non-uniformity (with or even without couple imbalance), and higher order asymmetric weight distributions such as this have a detrimental effect on SRL, by causing lateral force variations (e.g., wobbling moment variations at wheel axis) when the tire  65 ′ is rotated under load on a supporting surface. 
     Non-Uniformities in Tires and Wheels 
     A variety of non-uniformities in tire and wheel construction can be utilized to implement the methods of the present patent for improving steering performance robustness. Beneficial non-uniformities, i.e., those producing radial and/or tangential force variations but not lateral force variations, fall into three general categories: mass non-uniformity, dimensional non-uniformity, and stiffness non-uniformity. Detrimental non-uniformities, i.e., those producing lateral force variations, also fall into the same three general categories. 
     Mass non-uniformity includes, for example, static imbalance (beneficial) and couple imbalance (detrimental), and can occur in the tire and/or in the wheel. Beneficial mass non-uniformity can be designed into the tire or wheel; random occurrences of detrimental and beneficial mass non-uniformities in the tire and/or in the wheel can be controlled to be within empirically-determined limits using, for example, tire uniformity machines and tire/wheel balancing equipment; and/or suitable excess mass can be intentionally added-on to tires or wheels. 
     Dimensional non-uniformity includes, for example, radial runout (beneficial) and detrimental non-uniformities such as lateral runout, tread snaking (lateral tread distortion), tire skewness (asymmetric radial run-out with shoulders in counter-phase), wheel skewness, and non-uniform (tapered) wheel offset. Dimensional non-uniformities can be purposely implemented and/or controlled during the design and manufacturing of tires and/or wheels. 
     Stiffness non-uniformity includes, for example, tire tread, belt, and/or sidewall stiffness which varies with the rotational angle around the tire. The stiffness non-uniformity can be beneficial as long as it is symmetric along every meridional section of the tire, e.g., equal stiffness in both sidewalls of a given meridional section. Stiffness non-uniformities can be purposely implemented and/or controlled during the design and manufacturing of tires. 
     Since the effects of mass, dimensional and stiffness non-uniformity are essentially additive, it is desirable to use more than one method simultaneously in order to achieve a required steering performance and steering robustness level. This enables one to utilize smaller magnitudes of individual non-uniformities to achieve a certain steering performance while at the same time not exceeding acceptable vehicle vibration levels. 
     The main concept of the present invention is to introduce a controlled amount of dimensional non-uniformity into a tire, thereby generating fore-aft and vertical force variations excited by the tire when operated on a vehicle. The effect is similar to that of a mass non-uniformity, which will be discussed first. 
     Mass Non-uniformities 
     In the tests described hereinabove, mass non-uniformities were introduced by means of balance weights added to the wheel. In practice, this would be an unreliable way to implement the desired RSI because it takes vehicle performance out of the control of the manufacturers and relies instead on the vehicle operator (and by proxy their chosen mechanics) to implement the RSI necessary for proper vehicle performance. Furthermore, purposely implementing an imbalance is counter to the common knowledge and therefore likely to be resisted. Thus there is an advantage to implementing beneficial mass non-uniformity (e.g., RSI) in the tire, such as by design of the tire or by control of the manufacturing process. A further advantage of a tire solution will become evident in the following discussion. 
     An article in  Tire Science and Technology  by Stutts et al. entitled “Fore-Aft Forces in Tire-Wheel Assemblies Generated by Unbalances and the Influence of Balancing” (TSTCA, Vol. 19, No. 3, July-September, 1991, pp. 142-162), observes that “during drum tests [road-wheel tests of tire-wheel assemblies, e.g., on a TUM]. . . beyond certain speeds, the horizontal force variations or so-called fore-aft forces were larger than the force variations in the vertical direction.” The article goes on to postulate and then prove a theory explaining this phenomenon. In particular, the article shows that unbalanced mass in or near the tread portion of the tire can produce this result, and furthermore shows that the effect remains to a certain extent even if the tire/wheel assembly is balanced at the wheel rim (flange). For an explanation of this effect, refer to FIGS. 7A and 7B. As explained hereinabove, the centrifugal force due to a rotating mass is proportional to the mass and to the radius of the location of the mass. Tires are generally balanced when they are freely rotating, as in FIG. 7A, where a tire  70  mounted on a wheel  73  is rotating about an axis of rotation  71 . The tire  70  has a mass non-uniformity comprising an excess mass  74  having a mass M t  and located near the outer circumference of the tire  70  (e.g., in the tread) at a radius R t  from the axis  71 . To balance the excess mass  74 , a balance weight  72  having a mass M w  is attached to the rim or flange of the wheel  73  which is at a fixed radius R w . For simplicity of illustration, only two dimensions are shown and discussed. It should be understood that to avoid couple imbalance (lateral force variation), the masses M t  and M w  must be appropriately distributed laterally relative to the equatorial plane of the tire/wheel assembly. For the tire mass M t , a meridional symmetry condition must be strictly respected, wherein the mass non-uniformity M t  is symmetrically distributed laterally relative to the equatorial plane of the tire/wheel assembly. For the wheel-mounted mass M w , the mass needs not be distributed symmetrically about the equatorial plane, provided no couple imbalance is generated. For example, in the case of wheels that do not allow attaching balance weights symmetrically with respect to the equatorial plane, the mass M w  can be understood as a set of two balance weights having unequal masses m 1 , m 2  (such that m 1 +m 2 =M w ), mounted in such a way that the lack of geometrical symmetry is compensated for, while keeping zero couple imbalance, i.e., m 1 /m 2 =(l 2 /l 1 )*(r 2 /r 1 ), as described hereinabove with reference to FIG.  1 D. The mass of the balance weight M w  is selected according to the equation M t R t =M w R w , thereby counterbalancing centrifugal forces to produce a net centrifugal force of zero (assuming that the balance weight(s)  72  is located 180 degrees around from the excess mass  74 ). Referring now to FIG. 7B, when the balanced tire  70  is rolling in contact with a road surface  76 , the radius of the excess mass  74  will be reduced from R t  to R t ′ whenever the tread portion where the excess mass  74  is located comes into contact with the road  76 . Whenever this happens, the inertial forces (e.g., centrifugal force) due to the excess mass  74  are temporarily cancelled, and the balance weight  72  on the rim becomes an imbalance because its centrifugal force M w R w  is still present. Thus a periodic force variation is generated in the rolling tire  70 , whether or not it is balanced, providing the excess tire mass  74  is primarily located in the tread region of the tire. 
     Further analysis shows that a localized mass non-uniformity (excess mass) on a tire has some other specific effects that also cannot be compensated for by adding balance weights on the wheel flanges. Masses produce inertia forces when they follow non-linear trajectories and/or if they have a non-constant speed (i.e., undergoing acceleration/deceleration). In the case of a mass in a rotating vehicle tire, the correct way to measure or compute these inertia forces is relative to a coordinate system (frame of reference) attached to a level surface upon which the tire/vehicle is moving (e.g., a smooth, level road). Such a coordinate system can be considered as an inertial reference system, if we neglect the movements of the earth. It is, however, convenient to consider the inertia forces in a “spinning wheel” frame of reference relative to an observer attached to the axis of rotation at the center of the tire/wheel assembly and spinning with it, rather than relative to an observer fixed to the road. In the spinning wheel frame of reference centrifugal forces are very convenient, because they can be very simply measured or predicted with respect to the spinning wheel, but they reflect the true inertia forces only if the mass non-uniformity follows plane circular (constant radius) trajectories about the axis of rotation (which is substantially the case for wheel balance weights); and also the speed must remain constant. In the case of non-circular trajectories about the axis of rotation, as, for example, would be the case for weights attached to a tire tread or sidewall area while in loaded/rolling condition, the calculation of centrifugal force is not sufficient to calculate the true inertia forces, and correction terms need to be added to the calculation (e.g., terms of angular acceleration, Coriolis acceleration, and relative radial and lateral accelerations). In simple words, any speed or curvature changes along the trajectory of the mass non-uniformity cause inertia forces (similar to the effects felt by a passenger sitting in a vehicle following a curvy and/or hilly road). 
     FIGS. 7C and 7D (with reference to FIGS. 7A,  7 B,  7 E, and  7 F) are graphs illustrating predicted forces and moments caused on the environment of a tire  70  by an exemplary 6 gram mass  74 , M t  attached close to the tread surface at the equatorial plane of a perfectly uniform tire  70  mounted on a wheel  73 , which is mounted on a vehicle (not shown), wherein the tire/wheel assembly  70 / 73  is loaded and rolling at 120 km/h on a level road surface  76 , using the simplifying assumption that the trajectory of the tire mass non-uniformity  74  is constant with time. The term ‘environment’ is meant to include the wheel  73  axis of rotation  71 , the tire  70 , and the road  76 . The way the forces caused by tire/wheel assembly  70 / 73  mass non-uniformities are transmitted to and distributed respectively to a wheel axis  71  and a road  76  depend on the dynamic properties of the tire  70  mounted on the wheel  73  and of the suspension of the vehicle upon which the tire/wheel assembly  70 / 73  is mounted. We will, however, use the predictions illustrated in the graphs of FIGS. 7C and 7D to illustrate qualitatively what happens at the wheel axis  71 . The idealized “perfectly uniform tire  70 ” is assumed to be perfectly balanced, with no static or couple imbalance, after the excess mass  74  is added to the tire  70  (by adding, for example, a suitable mass M w  as balance weights  72  on the flanges of the wheel  73 ). In FIGS. 7C and 7D, the forces and moments are shown vertically versus the (time related) position of the excess mass  74  along the circumference of the tire  70 , with the circumferential position indicated in degrees of rotation (zero degrees being at the center of the footprint area). FIG. 7C illustrates vertical forces (curve  77 ) and fore-aft forces (curve  78 ). It can be seen that, for the major part of the trajectory of the excess mass  74 , away from the footprint area, the vertical and fore-aft forces are substantially zero, because the tire/wheel assembly  70 / 73  is well re-balanced. When approaching, passing through and leaving the footprint area, the vertical force curve  77  respectively shows high/low/high values (peaks), because the trajectory of the excess mass  74  features successively high/low/high curvature (for example, there is essentially zero curvature in the footprint area). The negative vertical force value in the mid footprint area represents the temporary imbalance that was described and explained hereinabove with reference to FIGS. 7A and 7B. The directions of the vertical force peaks are indicated by the arrows  75   a  in FIG.  7 E wherein a positive vertical force is directed downward (away from the axis of rotation  71 ). 
     The fore-aft force curve  78  in FIG. 7C shows a negative force peak as the excess mass  74  enters the footprint area (at a negative rotational angle), and shows a positive force peak as the excess mass  74  leaves the footprint area. The negative and positive fore-aft force peaks are due to respective deceleration and acceleration of the excess mass  74  (and tire tread portion to which it is attached) which normally occurs to tire tread upon respectively entering and leaving the footprint area. The deceleration and acceleration directions are indicated by the arrows  75   b  in FIG. 7F, and the forces due to the excess mass  74  and acting on the ‘environment’ (wheel  73  axis of rotation  71  and the road  76 ) are indicated by the arrows  75   f  in FIG. 7F, wherein a positive fore-aft force has a direction corresponding to the vehicle&#39;s direction of motion as indicated by the arrow  75   e . FIG. 7D illustrates (curve  79 ) the moment about the axis of rotation  73  that goes together with the fore-aft force shown by curve  78 . It can be seen that the moment curve  79  has a negative peak when the excess mass  74  enters the footprint area, and has a positive peak upon leaving. The moment directions are indicated by the arrows  75   c  in FIG. 7F, wherein a positive moment direction is in the same direction as the tire&#39;s direction of rotation as indicated by the arrow  75   d.    
     Methods of Incorporating Beneficial Mass Non-uniformity in Tire/Wheel Assemblies 
     A concept of the present invention takes advantage of the effects of mass non-uniformities described hereinabove, because the inventors desire to produce a controlled amount of fore-aft and radial force variation, and also desire to maintain these beneficial force variations while allowing anyone mounting a tire to normally balance his tire/wheel assemblies. Thus an inventive method for improving steering performance and steering performance robustness is to generate beneficial force variations by incorporating suitable amounts of excess mass  74  (i.e. a mass non-uniformity) into a tire  70  as close to the outer circumference (e.g., tread region) as possible. Since beneficial force variations may come from a static imbalance but not from a couple imbalance, the excess mass  74  added to the tire  70  must be distributed meridionally symmetric about the equatorial plane of the tire (i.e., the tire tread, belt package and carcass). 
     FIGS. 8A and 8B are circumferential cross sections of a sector of tires illustrating various methods for adding mass non-uniformities (e.g., excess mass  74 ) according to the invention (shading of cross sectioned areas eliminated for illustrative clarity). A quick and easy way to add the excess mass  74  to a tire is to simply apply a patch (not shown) to the inner surface (innerliner  86 ) of the tire  80 , preferably under the tread  82  region. An alternative would be to add an extra piece of fabric  89  (i.e., any suitable fabric including tread belt or carcass ply material) to the carcass  90  (preferably in the tread region) or to the tread belt  84  package or tread  82  rubber of a tire  80 ′. Referring to FIG. 8B, a sector of tire  80 ′ is shown with the tread  82 , one or more belts  84  (belt package), and a carcass  90  comprising one or more carcass plies  85 , a piece of fabric  89 , and an innerliner  86 , all shown in cross section. The inside surface (innerliner  86 ) of the carcass  90  is shown extending from the tread  82  region down to a bead  88  and an apex  87 , about which the carcass  90  wraps. The fabric  89  is a width W′ in a sector  81 ′ of the tire  80 ′, and is made of a material suitable for providing the desired excess mass  74 , while also having physical characteristics appropriate for tire usage such as bending and durability. The fabric  89  can reside entirely in the tread  82  region, or it can extend to the bead(s)  88  and wrap around the bead(s)  88  to end(s)  89   a , as shown in the portion  89   a  of FIG.  8 B. In order to prevent the introduction of any couple imbalance, the two fabric ends  89   a  are positioned symmetrically about the circumferential plane of the tire  80 ′. Thus, an equal mass of fabric  89  is positioned on either side of the circumferential plane of the tire  80 ′. The mass non-uniformity beneficial effect of the fabric  89  is only slightly influenced by which tire layer  82 ,  84 ,  85 ,  86  is selected for positioning of the fabric  89 , so normal tire design considerations can be factored into this selection process. As illustrated, the fabric  89  is positioned between the innermost carcass ply  85  and the innerliner  86 , but an essentially equivalent embodiment of the invention could, for example, place the fabric  89  between others of the layers  82 ,  84 ,  85 ,  86 , or even in the midst of a layer, such as embedded in the tread  82  rubber, or placed between belts  85 , or attached on the inside surface of the innerliner  86 , or on an outside surface of the tire, such as the sidewall (not shown) near the shoulder (not shown). 
     It should be noted that the added fabric piece embodiment just described includes within its scope the idea of adding a “patch” to the tire, since the “fabric” comprises all manner of materials compatible with tire construction (including metals), and applying the patch to an outside surface of one of the tire layers is equivalent to adding a fabric piece to that layer. 
     A more elegant way to add beneficial mass non-uniformity (e.g., excess mass  74 ) is to create a “heavy splice” (illustrated for the tire  80  in FIG.  8 A), thereby taking advantage of an existing mass non-uniformity in all tires: the splices of various tire layers where, for example, the ends  85   a ,  85   b  of the carcass plies  85  (one ply  85  shown) overlap in order to form a complete circle of the carcass plies  85 . Other splices include, for example, tread  82  material (merging along the meridional line  83 ), one or more tread belts  84  (one belt  84  shown with overlapping ends  84   a ,  84   b ), and innerliner  86  material (with overlapping ends  86   a ,  86   b ). Other splices in the bead  88  and in the sidewall/apex area close to the beads  88  can also be used to produce desired excess mass  74 , but are not preferred for reasons which will become clear in the following discussion (primarily because bead mass non-uniformities can be approximately counteracted by balance weights on the wheel). For example, the bead  88  has a splice or at least two overlapping ends  88   a ,  88   b . For example, an apex  87  has a splice where two ends merge in the shaded region  87   ab.    
     Typical tire construction methods attempt to distribute various splices around the circumference of the tire, but in the inventive embodiment of the tire  80 , for example, the splices of different tire layers are aligned so that they all occur approximately within the same meridional sector. The amount of mass non-uniformity introduced can be controlled by varying the number of splices which are within the same meridional sector  81 , and also by varying the amount of overlap of each splice (e.g., width W). In addition, changing to a thicker innerliner  86  material will further increase the mass non-uniformity due to the innerliner splice  86   a / 86   b . An advantage of using splices to create beneficial mass non-uniformity in a tire, is that properly-implemented splices are inherently meridionally symmetric. 
     An alternate approach consists of creating several “heavy splices” (2, 3, 4, etc . . . ) around the tire circumference, in order to generate more frequent fore-aft and radial force peaks. This method generates more frequent beneficial fore-aft and radial force peaks (i.e., tangential force variation and radial force variation, respectively). 
     Another embodiment of beneficial mass non-uniformity, similar to one or more heavy splices, is one or more sectors of a tire component having excess mass. For example, a length W of tread  82  material (e.g., at the end  82   a  of the tread) is made of a heavier material than the remainder of the tread  82 , or the tread pattern is adjusted to incorporate excess mass at one or more locations around the tread circumference (e.g., lateral bars or a wider tread portion jutting out from the tread shoulder). Alternatively, components such as the belts  84 , plies  85 , innerliner  86 , apex  87 , and beads  88  could be provided with heavier material in one or more sectors. Also, a sector having excess component mass could be advantageously superimposed on the sector  81  where one or more splices are located. 
     It should be noted that the term “excess mass” as used herein is intended to include not only an excess of mass in one or more circumferential locations; but also includes one or more circumferential locations having a lack of mass relative to the remainder of the circumferential locations. After all, a lack of mass in a first location relative to a second location equates to an excess of mass in the second location relative to the first location. 
     Given the inventive concept of adding controlled mass non-uniformities (one or more excess masses) to a tire/wheel assembly, and given the examples disclosed hereinabove, no doubt many other ways to incorporate the inventive excess mass(es) into tire/wheel assemblies will occur to the reader skilled in the relevant arts. All such means of incorporating the inventive excess mass(es) are intended to be within the scope of the present invention, including methods which combine beneficial mass non-uniformity with other beneficial forms of non-uniformities (in particular dimensional non-uniformity and stiffness non-uniformity). 
     It should be noted that, in order to be beneficial, the inventive excess mass(es) introduced in a tire must not produce any kind of lateral force variations such as are caused by asymmetry about the equatorial plane (e.g., couple imbalance). Therefore, when tires are manufactured with built-in beneficial mass non-uniformity, they are preferably tested for tire uniformity and corrected or rejected as needed to assure minimum lateral force variations, for example, forces caused by: overturning (i.e. camber) moment variation, couple imbalance, lateral run-out, tread snaking, radial run-out skewness, etc. For example, lateral force variations in tires should be less than 12 pounds peak-to-peak. This tire uniformity testing preferably occurs after the excess mass has been incorporated into the tire, but could be performed before the excess mass has been incorporated into the tire by means of a patch, for example. In the later case, the patch would have to be positioned well enough that any possible couple imbalance introduced by the patch could be overcome either by further factory testing and correction, or by post-production dynamic balancing of the tire mounted on a wheel. 
     Steering Performance Robustness Test Method 
     The inventors tested the mass-non-uniformity-in-the-tire concept with an inventive test method which was designed to not only test the instantaneous steering performance but to also indicate the steering performance robustness of the tested tire/wheel assembly. In other words, for each tested assembly the test is designed to answer questions such as: (a) What is the immediate steering performance? (b) How bad/noticeable is the resulting vibration? (c) How resistant is the assembly to steering performance loss in the long term (over the life of the tire)? (d) If the assembly exhibits immediate steering performance loss, how much correction is needed to provide acceptable steering performance. 
     The question (c) concerns robustness of steering performance and is predictive in nature. It is known that over the life of a tire, especially while mounted on a wheel and used on a vehicle, the uniformity of the tire/wheel assembly can change, even if it was initially very uniform (dimensionally and in terms of force variations). This is because of the visco-elastic nature of a tire and the fact that the tire ply doesn&#39;t always follow an equilibrium shape. Another important factor determining tire uniformity is how well the bead seats on the wheel rim, and how much this contact may change with service conditions such as heavy braking, heavy cornering, etc. Examples of other factors determining tire uniformity include: tread wear (both a change in wear distribution as well as local wear due to braking and many other factors), and “asymmetric flat-spotting” (when parking with tires in a steered position, or parking on a laterally inclined surface, or partly on the edge of a curb, a hot tire may deform in an asymmetric way). Also, tires as well as the rims can, due to improper service conditions such as hitting a curb or a pothole, undergo changes which can ultimately result in changes in the mass uniformity (e.g., balance), the stiffness uniformity, or the dimensional symmetry of a tire/wheel assembly about its equatorial plane. Moreover, vehicle condition varies during its life, and road/driving conditions are also variable in essence and have an effect on Steering Robustness Level (SRL). The question (d) also concerns steering robustness. In essence, the test method seeks to determine the nature of the intrinsic SRL factors, and where the SRL “plateau” lies relative to the SRL total of intrinsic and extrinsic factors existing for the tested combination of tire, wheel and vehicle. 
     As described hereinabove, the inventors have determined that increasing static imbalance has a positive effect on steering performance, while increasing couple imbalance has a negative effect on steering performance. Thus a test design which subjects a test tire/wheel assembly to a progression of balance conditions from large static imbalance (only), decreasing to no imbalance (i.e., a statically and dynamically balanced assembly), then increasing to large couple imbalance (only), provides a calibrated scale of operating conditions from favorable through neutral to unfavorable. The farther into the unfavorable range of operating conditions that a test tire/wheel/vehicle combination can operate while still having OK (acceptable) steering performance, then the more robust that test tire/wheel/vehicle combination is against steering performance loss. Stated in terms of the SRL concept discussed hereinabove with reference to FIG. 6C, the progression of balance conditions imposed by the inventive test method causes the extrinsic portion of the tire/wheel/vehicle combination&#39;s SRL to progress from positive through neutral to negative values, in order to determine the shape, magnitude and relative location of the SRL “plateau” for the SRL curve resulting from a sum of the intrinsic and extrinsic SRL portions characterizing the subject tire/wheel/vehicle combination. Thus the inventive test method includes within its scope not just a progression of balance conditions, but rather any progression of imposed conditions which cause the extrinsic SRL value to progress from positive through neutral to negative values. Of course the progression can go in the opposite direction, and depending on test results, may be limited to a portion of the overall range. In fact, testing can be done at selected extrinsic SRL values in any desired order. For example, if the testing at a high positive extrinsic SRL value produces poor steering performance, then the test may be aborted and the tire/wheel/vehicle combination may be declared inappropriate or un-usable. Or, for example, the progression of extrinsic SRL values may be halted as soon as a “not-okay” (NOK) steering performance result (or vibration level result) is obtained. 
     It should be noted that the inventive test method can be used to test the steering performance robustness of any tire construction (or even any tire/wheel/vehicle combination), regardless of how it has been changed. Although the test preferably uses wheel balance weight changes to produce various test conditions, these changes in mass uniformity of the tire/wheel assembly are not to be confused with intentional design changes of uniformity in, for example, the tire construction (e.g., tire design changes of mass, stiffness, and/or dimensional uniformity). 
     Dimensional Non-uniformities 
     Dimensional variations in tire and wheel components are known to cause force variations, and for that reason are generally avoided in tire and wheel manufacturing by careful design and manufacturing techniques, plus testing (e.g., on a TUM) and appropriate correction or rejection of the tire or wheel. The concept of the present invention is to purposely alter the design, production and testing methods in order to produce controlled amounts of specific types of dimensional variation in the tires and/or wheels, preferably in the form of radial runout. Several advantages are inherent in this approach to improving steering performance and steering performance robustness. If done in a way which minimizes lateral force variations(LFV) (which are detrimental), the dimensional variation will introduce (beneficial) tangential force variations (TFV) and/or radial force variations (RFV), which are substantially unaffected by tire/wheel balancing. Furthermore, dimensional non-uniformities such as radial runout generate beneficial TFV at slow vehicle speeds as well as at fast speeds, compared to the other types of non-uniformities, which primarily generate beneficial force variations at faster vehicle speeds. Also, dimensional non-uniformities appear to be extremely effective in improving steering performance robustness. In experimental tests, for example, a relatively small radial runout (0.4 mm eccentricity) was able to prevent steering performance loss (SP-Loss) for a relatively high amount of couple imbalance (e.g., 60 grams per flange). 
     Referring to FIG. 10A, results of a series of tests are shown by two curves  102  and  104  of steering performance plotted against the mass of balance weights added to each wheel flange of the left front tire/wheel assembly on the test vehicle. For both curves  102 ,  104  the same set of four tires was tested on a car known to be sensitive to SP-Loss. The four tires were TUM tested and selected because they all had excellent uniformity (i.e., the set of tires produced very low force variations of all types when tested), however, the tire construction of the selected tires was known to deliver generally very poor steering performance ratings on the test vehicle. Curve  102  (with diamond-shaped data points) shows the results of a steering performance test using these tires mounted on wheels which had been tested and selected because they had excellent dimensional uniformity (e.g., no lateral or radial runout) and excellent balance. The curve  102  data point at zero (0) grams of imbalance represents the test result when the four tire/wheel assemblies were statically and dynamically balanced (i.e., no imbalance). The steering performance rating of “4” is considered poor i.e., “NOK” (not okay). The data points on curve  102  at increasing imbalance masses represent the test results as static (not couple) imbalance was added to the tire/wheel assemblies. It can be seen that approximately 15 grams per flange of static imbalance was required to achieve a good i.e., “OK” level (over “5.5”) of steering performance, and required 20 or more grams per flange to achieve excellent ratings of over “7”. These curve  102  results show that this vehicle/tire/wheel combination has poor steering performance robustness. Curve  104  (with square-shaped data points) shows the results of a steering performance test using the same set of four tires, but mounted on a specially-prepared set of wheels designed to induce radial runout without lateral runout. The amount of radial runout in millimeters (mm) as measured on the four curve  104  test tire/wheel assemblies is shown in the following table: 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 TIRE POSITION 
                 RADIAL RUNOUT 
               
               
                   
                   
               
             
            
               
                   
                 Left Front 
                 0.30 mm 
               
               
                   
                 Right Front 
                 0.38 mm 
               
               
                   
                 Left Rear 
                 0.40 mm 
               
               
                   
                 Right Rear 
                 0.48 mm 
               
               
                   
                   
               
            
           
         
       
     
     The curve  104  data point at zero (0) grams of imbalance represents the test result when the four tire/wheel assemblies were statically and dynamically balanced (i.e., no imbalance). The steering performance rating of “7.8” is considered excellent, well into the “OK” (okay) range. The data points on curve  104  at increasing imbalance masses represent the test results as couple (not static) imbalance was added to the tire/wheel assemblies. It can be seen that the excellent steering performance was unaffected by even as much as 60 grams per flange of couple imbalance, indicating a very robust steering performance for the same tires which required static imbalance to achieve OK steering performance when there was no radial runout present. 
     A different test showed that the presence of radial runout in the tire has beneficial effect roughly equivalent to the beneficial effect of radial runout in the wheel, as described hereinabove. Referring to FIG. 10B, results of the different test are shown by a curve  106  and a point  107  illustrating steering performance plotted against the mass of balance weights added to each wheel flange of the left front tire/wheel assembly on the test vehicle —a car known to be sensitive to SP-Loss. In this test, a set of four wheels which had been tested and selected because they had excellent dimensional uniformity (e.g., no lateral or radial runout) and excellent balance was employed. When the set of test tires was mounted on these wheels, the radial runout of the tire/wheel assembly (caused by runout of the test tire) was measured as follows: 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 TIRE POSITION 
                 RADIAL RUNOUT 
               
               
                   
                   
               
             
            
               
                   
                 Left Front 
                 0.18 mm 
               
               
                   
                 Right Front 
                 0.42 mm 
               
               
                   
                 Left Rear 
                 0.22 mm 
               
               
                   
                 Right Rear 
                 0.16 mm 
               
               
                   
                   
               
            
           
         
       
     
     The curve  106  plots the results of testing these tire/wheel assemblies, and shows excellent steering performance when no static or couple imbalance is present. The maintenance of OK steering performance as increasing couple imbalance was added indicates good steering performance robustness. When only the tire of the right front tire/wheel assembly (which had 0.42 mm of radial runout) was replaced with another tire having negligible runout, the vehicle steering performance rating dropped to “NOK” when all tire/wheel assemblies were statically and dynamically balanced (plotted as point  107  in FIG.  10 B). Thus it is seen that, for example, 0.42 mm of radial runout in a front tire is sufficient to produce good steering performance robustness for the tested vehicle, tire, and wheel designs, and that an average of 0.20 mm of runout on the remaining three positions is not necessarily sufficient to produce OK steering performance (and robustness). 
     Methods of Incorporating Dimensional Non-uniformities in Tires 
     The controlled increase in TFV and/or RFV according to this invention can be brought about by any controllable method which causes one or more sectors (meridional sections) of the tire/wheel assembly to be dimensionally non-uniform compared to the remainder of the tire/wheel assembly. In order to be beneficial, the inventive dimensional non-uniformity must be meridionally symmetric and must minimize lateral force variations (keeping them as close to zero as possible). 
     Preferred embodiments of the inventive method generally comprise imparting radial runout as the preferred form of dimensional non-uniformity in the wheel and/or in the tire (thus in the tire/wheel assembly). The embodiments are designed to optimize the dimensional non-uniformity in order to produce the desired amount of TFV/RFV (which, in turn, is determined to be the amount of TFV/RFV needed to produce the desired steering performance and steering performance robustness). Incidental to the design of inventive embodiments is a certain amount of mass non-uniformity and/or stiffness non-uniformity that may accompany tire designs for implementing dimensional non-uniformity. For example, a thicker sector of tread material will impart mass non-uniformity along with the intended radial runout type of dimensional non-uniformity. For example, a variation in tread pattern (e.g., groove width) is a dimensional non-uniformity which can produce beneficial mass and/or stiffness non-uniformities. Since meridionally-symmetric mass and stiffness non-uniformities are also advantageous, and since the effects of non-uniformities are additive, the combination of mass non-uniformity and/or stiffness non-uniformity along with dimensional non-uniformity is desirable and advantageously utilized in the methods of the present invention. By simultaneously increasing multiple beneficial types of non-uniformities, beneficial steering performance effects can be realized with smaller individual non-uniformities. 
     FIGS. 9A,  9 B, and  9 C illustrate embodiments of the inventive method for improving vehicle steering performance and robustness by adding dimensional non-uniformity to a tire and/or a wheel. FIG. 9A is a schematic representation of a tire  91  having one or more sectors “S” (one sector S illustrated) wherein the radius of the radially outermost surface  93  of the tire  91  (e.g., the tread surface) is greater (run out) in the sector S compared to elsewhere around the tire circumference. Measured from the axis of rotation  94  of the tire  91 , the radius of the radially outermost surface  93  is a substantially constant value of “R” everywhere except in the asymmetric (non-uniform) sector S where a dashed line  93   a  illustrates a continuation of the surface  93  with radius R, and the solid line  93   b  represents the actual radially outermost surface of the tire  91  in the sector S. The surface  93   b  increases in radius to a maximum radius (a radial runout peak) which is an amount “RR” greater than the radius R of the rest of the tire  91 . Such a tire can be manufactured, for example, by adding extra tread rubber (extra thickness) in the sector S (thereby also causing a mass asymmetry), or by causing the carcass ply cords (not shown) to be longer in the sector S. Methods of achieving the latter embodiment include, for example, a radially outward bulge in at least a portion of a tire mold segment, or an offset in at least a portion of corresponding sidewall plates. A different way to achieve the embodiment illustrated by the tire  91 , would be to mount a tire (which may have zero runout) on a wheel  92  which has a bead seat circumference having a runout shape corresponding to the shape of the outermost surface  93 / 93   b  of the tire  91 . Such a wheel  92  would force the beads  95  to conform in shape, thus allowing the outermost surface  93  of the tire mounted on the wheel  92  to be distorted to the shape of the surface  93 / 93   b  shown for the tire  91 . This shape change of the wheel  92  could also be accomplished by means of one or more shims  96  placed between the wheel&#39;s bead seats and the beads  95  of the tire  91 . The shims  96  can, for example, be incorporated in the bead rubber of the tire  91 , or simply inserted between tire and wheel when the tire  91  is mounted on the wheel  92 . It should be understood that, for convenience of illustration, FIG. 9A shows features (e.g.,  93   b ) of a runout tire  91  together with features (e.g.,  96 ) of a runout wheel  92 , however the present invention preferably comprises these tire and wheel features in separate embodiments (although they could be combined). 
     FIG. 9B is a schematic representation of a tire  91 ′ which has runout of a maximum magnitude “RR” due to a radial offset of the (substantially circular) tire beads  95  relative to the (substantially circular) radially outermost surface  93  (generally the tread surface) of the tire  91 ′. The axis of rotation  94   a  of the tire  91 ′ is determined by the center of the beads  95  with a radius “RW” from the center  94   a  to the beads  95 , but the outermost surface  93  has a different circular center  94   b  and a radius “R” from the center  94   b  to the surface  93 . The circular center  94   b  is radially offset from the axis of rotation  94   a  by the runout amount of “RR”. The dashed line  93   b  shows a circle of radius R drawn about a center  94   a , and represents the imaginary position of the outermost surface of the tire  91 ′ if there were no runout present. Comparing the circles  93   a  and  93  shows that the radial runout peak of the tire  91 ′ has the same magnitude RR as the radial offset RR between the tire&#39;s axis of rotation  94   a  and the tire surface&#39;s circular center  94   b . Examples (not illustrated) of some of many ways to achieve this type of tire construction would be: purposely holding the beads radially offset by the amount RR from the center of the tire mold while the tire carcass is blown up into the mold, a radial offset of the drum which applies the tread and breaker package to the carcass, and/or an inclination of a few degrees (e.g., approximately 1 degree to 3 degrees) in the bead setters. It can be seen that such manufacturing methods would cause the ply cords (not shown) to continuously vary in length around the circumference of the tire  91 ′, being longest on the left side and shortest on the right side of the drawing in FIG.  9 B. It should be noted that an advantage of imparting dimensional non-uniformities by means of varying ply cord lengths is that “creep” of the carcass plies over time may actually increase the amount of dimensional non-uniformities in a way which improves steering performance and robustness over time. This improvement should help counteract any tendency that a tire/wheel assembly may have to develop increasing couple imbalance over time (which is detrimental to steering performance). 
     FIG. 9C is a schematic representation of a wheel  92 ′ (note the larder drawing scale compared to the tire/wheel assemblies of FIGS. 9A and 9B) which has runout of a maximum magnitude (peak) “RR” due to a radial offset of the (substantially circular) heel hub  99  relative to the (substantially circular) bead seats  98  of the wheel  92 ′. The axis of rotate n  94   a ′ of the wheel  92 ′ (and therefore of any circular tire mounted on the wheel  92 ′) is determined y the center of the wheel hub  99 (as determined by the positions of the mounting holes  97 ), but the wheel&#39;s bead seat  98  has a different circular center  94   b ′ and a radius “RW” from the center  9  ′ to the radially outermost surface of the bead seats  98 . The circular center  94   b ′ is radially offset from the axis of rotation  94   a ′ by the runout amount of“RR”. The dashed line  98   b  shows a circle of radius RW drawn about a center  94   a ′, and represents the imaginary position of the bead seats  98   a  if there were no runout present. Comparing the circles  98   a  and  98  shows that the (radial) runout of the wheel  92 ′ has the same magnitude RR as the radial offset RR between the wheel&#39;s axis of rotation  94   a ′ and the bead seats&#39; circular center  94   b ′. An example embodiment of the offset or eccentric wheel  92 ′ (i.e., having radial but not lateral runout) is the wheels utilized for the test described hereinabove and plotted as curve  104  in FIG.  10 A. For this embodiment, the mounting holes  97  were formed slightly off-center in the wheel hubs  99  to produce wheels  92 ′ having radial runout of approximately 0.3 mm to 0.5 mm (as measured on the tire/wheel assembly). These eccentric wheels  92 ′ proved very effective in providing steering performance robustness as illustrated by curve  104  in FIG.  10 A. 
     It should be understood that in all of this discussion hereinabove, the inventively imparted offsets, runouts and non-uniformities referred to are intended to have substantially radial components but not lateral or axial components since we intend to induce controlled radial/tangential force variation while minimizing all lateral force variations. As stated hereinabove, this includes maintaining meridional symmetry about the equatorial plane of the tire. 
     It should also be understood that, although the embodiments of radial runout discussed hereinabove only illustrate a single radial runout peak for a given tire or wheel, the scope of the invention should be considered to include any number of radial runout peaks around the circumference of a tire or wheel. 
     Given the inventive concept of adding dimensional non-uniformities (possibly in combination with other beneficial non-uniformities) to a tire and/or wheel, and given the exemplary embodiments disclosed hereinabove, no doubt many other ways to implement the inventive methods in tire/wheel assemblies will occur to the reader skilled in the relevant arts. All such means of incorporating the inventive beneficial non-uniformities are intended to be within the scope of the present invention, including methods which combine beneficial dimensional non-uniformity with other forms of beneficial non-uniformities (in particular beneficial mass non-uniformity and beneficial stiffness non-uniformity). 
     Although the invention has been illustrated and described in detail in the drawings and foregoing description, the same is to be considered as illustrative and not restrictive in character—it being understood that only preferred embodiments have been shown and described, and that all changes and modifications that come within the spirit of the invention are desired to be protected. Undoubtedly, many other “variations” on the “themes” set forth hereinabove will occur to one having ordinary skill in the art to which the present invention most nearly pertains, and such variations are intended to be within the scope of the invention, as disclosed herein.