Abstract:
A brake rotor providing reduced brake pad radial taper wear by providing brake rotor friction surface indent patterns. For example, the indent patterns are the form of radial-biased grooves or linearly arranged cross-drill hole sets, patterned in a configuration that balances brake pad wear, thereby reducing brake pad radial taper wear in a manner tuned specifically for a given type of brake caliper and brake pad material, wherein the reduction in brake pad radial taper wear is accomplished with virtually no penalty to brake pad life.

Description:
TECHNICAL FIELD 
     The present invention relates, in general, to vehicle disk brake systems and in particular to the rotor friction surfaces thereof. More particularly, the present invention relates to indent patterns in the rotor friction surfaces which are tuned to produce even brake pad wear, and attendantly improve the brake feel of the brake system. 
     BACKGROUND OF THE INVENTION 
     Motor vehicle disk brake systems utilize, at each wheel, a brake rotor connected to an axle hub of a rotatable axle of the motor vehicle, and an opposing set of selectively movable brake pads connected to a non-rotating brake caliper which carries a set of brake pads. The brake rotor includes opposing brake pad engagement surfaces, or rotor cheeks, wherein when braking is to occur, the braking system causes the caliper to press the brake pads upon respective brake pad engagement surfaces of the rotor cheek. Frictional interaction between the rotating rotor cheeks and non-rotating brake pads causes braking of the motor vehicle to transpire, the rate of braking depending upon the pressure of the brake pads against the rotor cheeks. 
     In the automotive art, modern hydraulic braking systems typically include an operator or driver interface, such as a brake pedal. As the driver applies force to this pedal, this force is transmitted by means of control arms and other related devices to the master cylinder. The master cylinder accepts mechanical force as input and produces hydraulic pressure, in the form of pressurized brake fluid, as an output. This pressure is conveyed by means of pressurized brake fluid through lines and valves of the motor vehicle to interface with each brake corner, found near each wheel of the motor vehicle. 
       FIG. 1A  schematically depicts a brake corner  10 , known in the art, configured for the usage of a sliding caliper (i.e., piston(s) at one side of the caliper). A brake line  12  conveys hydraulic brake fluid into the brake corner  10 . This permits the application of force from the master cylinder (not shown) through pressurization of the hydraulic brake fluid, thereby creating a means of hydraulic control of the hydraulically active components of the brake caliper  20 . The hydraulic brake fluid passes into a caliper actuator cylinder  22  and makes contact with a caliper actuator piston  24 . The inboard side of the brake caliper  20   a  is hydraulically active in a sliding caliper configuration, whereas the outboard side of the brake caliper  20   b  is hydraulically inactive. A brake pad  32   a ,  32   b , is respectively affixed at each side of the brake caliper  20 , so that when the hydraulic brake fluid in the brake line  12  supplying the brake corner  10  is pressurized, the brake caliper  20  causes the brake pads to squeeze upon the rotor friction surfaces (i.e., rotor cheeks)  30   a  of the brake rotor  30 , thereby inducing braking of the vehicle. The rotor cheeks  30   a , are each located on a respective rotor plate  34   a ,  34   b , mutually separated by vanes  36 . 
       FIG. 1B  schematically depicts a brake corner  10 ′, known in the art, configured for the usage of a fixed caliper (i.e., piston(s) at each side of the caliper). In this case, each side of the brake caliper  20 ′ is hydraulically active and contains a caliper actuator cylinder  22   a ,  22   b  which in turn contains a caliper actuator piston  24   a ,  24   b . A brake pad  32   a ′,  32   b ′, is respectively affixed at both sides of the brake caliper  20 ′ so that when the hydraulic brake fluid is pressurized in the master cylinder, the pressure is transmitted via the hydraulic brake fluid to the caliper actuator pistons  24   a ,  24   b , causing the brake caliper  20 ′ to engage the brake pads to squeeze upon the cheeks  30   a ′ of the brake rotor  30 ′, inducing braking of the vehicle. The rotor cheeks  30   a ′, are each located on a respective rotor plate  34   a ′,  34   b ′, mutually separated by vanes  36 ′. 
     Historically, engineering of the human interface with a braking system has been a subjective endeavor. With the advent of a Brake Feel Index (BFI) as reported in SAE technical paper 940331 “Objective Characterization of Vehicle Brake Feel” by D. G. Ebert and R. A. Kaatz (1994), a method was developed to correlate objective engineering parameters to these subjective assessments. In the case of BFI, such aspects as pedal application force, pedal travel and pedal preload are compared to desired target values which correlate to a particular type of response desired and the deviation from these target values is reflected in a lower index value. In disk brake systems, one of the primary causes of undesirable brake pedal feel has been brake pad radial taper wear. 
     Brake pad (or brake lining) radial taper wear develops with brake usage, wherein the taper angle tends to increase with more aggressive, higher energy brake usage conditions. Brake pad radial taper wear is driven by flexure of the caliper housing under hydraulic pressure, causing a radial pressure gradient over the friction surface by differences in sliding speed over the friction surfaces and by distortion of brake corner components under braking and/or thermal loads, including knuckle abutment distortion and brake rotor coning. Sliding caliper applications will tend to develop most of their radial taper wear on the outboard side, and fixed caliper applications will tend to develop more equalized inboard to outboard radial taper wear, wherein the radial taper wear in fixed caliper applications is usually less pronounced than that of the outboard side of sliding caliper applications. 
     The primary impact that radial taper wear has on the driver is brake torque variation, which can be perceived as brake pulsing, particularly in high energy applications. Other consequences produced on brake feel by radial taper wear include, but are not limited, to excessive pedal travel and excessive pedal force required in high energy brake applications. It is possible to partially mitigate the effects promoting radial taper wear by optimizing the pad shape, i.e., using a fan shaped pad. However, in many applications it is impractical to impossible to fully stop radial taper wear via pad shape. 
     Also known in the art is the practice of modifying the brake rotor surface mechanically by cutting grooves into the surface of the rotors, or by drilling holes (i.e., cross-drill holes) forming patterns of holes in a particular configuration. These modifications have been used to increase the friction between the frictional surfaces of the rotor and the brake pad to enhance the removal of heat from the frictional surfaces for purpose of prolonging life of the brake pad material, or to facilitate the clearing of debris which may build up over time between the brake frictional surfaces. Another application of placing grooves in the head is to reduce vibration during braking, wherein the grooves are used to provide a means through which the stresses on the brake pad are balanced while not impairing its coefficient of friction. 
     Accordingly, what remains needed in the art is a means to enhance the surface characteristics of the friction surfaces of disk braking systems to reduce the radial taper wear behavior of the brake pad surfaces, through a balancing or evening out of the brake pad surface wear. 
     SUMMARY OF THE INVENTION 
     The present invention enhances the surface wear characteristics of brake pad friction surfaces of rotors of disk brake systems to reduce the radial taper wear of the brake pad (or brake lining) friction surfaces. Additionally, the present invention provides an adjustment of these enhanced surface wear characteristics tailored to match the type of calipers used in the braking system. 
     The present invention balances (i.e., evens) brake pad radial taper wear by providing brake rotor friction surface indent patterns, for example in the form of radial-biased grooves or linearly arranged cross-drill hole sets, patterned in a configuration that balances brake pad wear, thereby reducing brake pad radial taper wear in a manner tuned specifically for a given type of brake caliper and brake pad material. 
     The benefit of the present invention to the driver of the vehicle is improved brake feel in high energy driving conditions, in the form of lower pedal force and pedal travel. In some applications, the invention will also reduce the characteristic brake torque variation or brake pedal pulsation associated with high energy driving conditions. This is accomplished with virtually no penalty to brake pad life, versus the current state of the art, as discussed above, which involves cross-drilling or grooving on both sides of the rotor, for reasons other than to control radial taper wear, extending into most of the swept friction areas of the rotor cheeks, and accompanied by a significant penalty in the reduction of brake pad life. 
     The different types of calipers, as indicated by  FIGS. 1A and 1B , impart different forces upon the friction surface of the brake pads. As discussed in the background of invention, these forces produce different wear characteristics for different calipers. The present invention employs the brake rotor friction surface indent patterns to increase brake pad wear in the areas less affected by the application of the calipers. This enhanced wear in these areas will, in effect, equalize the wear produced in the areas of the brake pad surface to the wear produced in areas strongly affected by the operation of the calipers, which, in turn, will promote a more radially even wear in the brake pad surface based on the knowledge that grooving or cross-drilling of the brake rotor friction surfaces tends to increase brake pad surface wear thereover. 
     In a preferred embodiment of the present invention for use in a sliding caliper application (i.e.,  FIG. 1A ), brake rotor friction surface indent patterns according to the present invention are formed in the rotor outboard friction surface. Additionally, the brake rotor friction surface indent patterns may also be added to the rotor inboard friction surface in the event the sliding caliper creates substantial radial taper wear (i.e., the radial taper wear is non-negligible) on the friction surface of the facing inboard brake pad; otherwise if radial taper wear of the facing inboard brake pad is insubstantial (i.e., the radial taper wear is negligible), then no brake rotor surface indent patterns need be present at the inboard friction surface. 
     Firstly with regard to the outboard friction surface, the brake rotor friction surface indent patterns are preferably in the form of grooving or cross-drilling patterns formed in the rotor outboard friction surface of the outboard side rotor cheek, originating preferably near the radial inner edge of the rotor cheek, generally outside of the swept friction surface, and extending in a radial direction toward the rotor outer edge. These indent patterns only partially cover the swept friction surface. The radial length of the grooves or of the cross-drill hole sets and the distribution (i.e., number, spacing and placement) of grooves or the cross-drill hole sets is adjusted (i.e., tuned) to the requirements of the caliper and brake pad material in the application. The grooves or the linear placement of the cross-drill hole sets may be oriented at a sweep angle with respect to the rotor radial direction in a manner such that the force of the interaction between the grooves or hole sets and the brake pads will impart a moment on the brake pads in a direction that will tend to alleviate radial taper wear. 
     Secondly with regard to the inboard friction surface, the brake rotor friction surface indent patterns, if used, are preferably in the form of grooving or cross-drilling patterns formed in the rotor inboard friction surface of the inboard side rotor cheek, originating preferably near the radial outer edge of the rotor cheek, generally outside of the swept friction surface, and extending in a radial direction towards the rotor center. These indent patterns only partially cover the swept friction surface. The radial length of the grooves or of the cross-drill hole sets and the distribution (i.e., number, spacing and placement) of grooves or cross-drill hole sets is adjusted to the requirements of the caliper and brake pad material in the application. The grooves or the linear disposition of the cross-drill hole sets may be placed at a sweep angle with respect to the rotor radial direction in a manner such that the force of the interaction between the grooves or cross-drill hole sets and the brake pads will impart a moment on the brake pads in a direction that will tend to alleviate radial taper wear. 
     In a preferred embodiment of the present invention for use in a fixed caliper application (i.e.,  FIG. 1B ), brake rotor friction surface indent patterns are formed in the rotor inboard and outboard friction surfaces of the inboard and outboard rotor cheeks, respectively. 
     The brake rotor friction surface indent patterns are preferably in the form of grooving or cross-drilling patterns formed in the inboard and outboard friction surfaces of the inboard and outboard side rotor cheeks, originating preferably near the inside the radial inner edge of the rotor, generally outside of the swept friction surface swept friction surface, and extending in a radial direction towards the rotor radial outer edge partially, but not completely, over the swept friction surface. The radial length of the grooves or of the cross-drill hole sets and the distribution (i.e., number, spacing and placement) of grooves or cross-drill hole sets are adjusted to the requirements of the caliper and brake pad material in the application. The grooves or the linear disposition of the cross-drill hole sets may be placed at a sweep angle with respect to the rotor radial direction in a manner such that the force of the interaction between the grooves or the cross-drill hole sets and the brake pads will impart a moment on the pads in a direction that will tend to alleviate radial taper wear. 
     The radial length of the brake rotor surface indent patterns may be equal, or differing, wherein if differing, a preferred arrangement is for the brake rotor indent patterns to be arranged circumferentially around the rotor cheek in the form of serially repeating groups, the radial height of each brake rotor surface indent pattern radial of each group being progressively different in the sense each group starts with a shortest radial height, to progressively longer radial heights to a longest radial height, then to progressively shorter radial heights to the shortest radial height. 
     With respect to the sweep angle, this is an angle with respect to a radiant of the rotor, generally being preferably between 0 degrees and about 70 degrees, wherein where the sweep angle is greater than zero degrees, the radially innermost portion of the indent patterns is leading with respect to the rotation direction of the rotor when the motor vehicle is moving in a forward direction. 
     Accordingly, it is an object of the present invention to provide brake rotor friction surface indent patterns in the rotor cheeks of disk brake systems to improve the radial taper wear behavior of the brake pad friction surfaces, wherein these indent patterns are adjusted to match the different performance requirements of different applications so as to mitigate the radial taper wear characteristics associated with particular caliper applications. 
     This and additional objects, features and advantages of the present invention will become clearer from the following specification of a preferred embodiment. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a cross-sectional view of a prior art disk brake system employing a sliding caliper configuration. 
         FIG. 1B  is a cross-sectional view of a prior art disk brake system employing a fixed caliper configuration. 
         FIG. 2A  is a plan view of the inboard side of a modified rotor according to the present invention having, if needed to reduce radial taper wear, brake rotor friction surface indent patterns in the form of uniform length grooves originating from near the radial outer edge of the rotor configured for a sliding caliper application. 
         FIG. 2B  is a cross-sectional view seen along the line  2 B- 2 B of  FIG. 2A , showing the cross-section of a groove. 
         FIG. 2C  is a plan view of the inboard side of a modified rotor for use in a sliding caliper application where radial taper wear is not a problem, whereby no brake rotor friction indent patterns are provided. 
         FIG. 2D  is a plan view of the outboard side of a modified rotor for use with the rotor of  FIGS. 2A and 2C  for use in a sliding caliper application, having brake rotor friction surface indent patterns in the form of uniform length grooves originating from near the radial inner edge of the rotor;  FIG. 2D  is also a plan view of the inboard and outboard sides of a modified rotor according to the present invention having brake rotor friction surface indent patterns in the form of uniform length grooves configured for a fixed caliper application. 
         FIG. 3A  is a plan view of the inboard side of a modified rotor according to the present invention having, if needed to reduce radial taper wear, brake rotor friction surface indent patterns in the form of uniform length cross-drill hole sets originating from near the radial outer edge of the rotor configured for a sliding caliper application. 
         FIG. 3B  is a cross-sectional view seen along the line  3 B- 3 B of  FIG. 3A , showing the cross-section of a cross-drill hole. 
         FIG. 3C  is a plan view of the inboard side of a modified rotor for use in a sliding caliper application where radial taper wear is not a problem, whereby no brake rotor friction indent patterns are provided. 
         FIG. 3D  is a plan view of the outboard side of a modified rotor for use with the rotor of  FIGS. 3A and 3C  for use in a sliding caliper application, having brake rotor friction surface indent patterns in the form of uniform length cross-drill hole sets originating from near the radial inner edge of the rotor;  FIG. 3D  is also a plan view of the inboard and outboard sides of a modified rotor according to the present invention having brake rotor friction surface indent patterns in the form of uniform length cross-drill hole sets configured for a fixed caliper application. 
         FIG. 4A  is a plan view of the inboard side of a modified rotor according to the present invention having, if needed to reduce radial taper wear, brake rotor friction surface indent patterns in the form of non-uniform length grooves originating from near the radial outer edge of the rotor configured for a sliding caliper application. 
         FIG. 4B  is a plan view of the inboard side of a modified rotor for use in a sliding caliper application where radial taper wear is not a problem, whereby no brake rotor friction indent patterns are provided. 
         FIG. 4C  is a plan view of the outboard side of a modified rotor for use with the rotor of  FIGS. 4A and 4B  for use in a sliding caliper application, having brake rotor friction surfaces indent patterns in the form of non-uniform length grooves originating from near the radial inner edge of the rotor;  FIG. 4C  is also a plan view of the inboard and outboard sides of a modified rotor according to the present invention having brake rotor friction surface indent patterns in the form of non-uniform length grooves configured for a fixed caliper application. 
         FIG. 5A  is a plan view of the inboard side of a modified rotor according to the present invention having, if needed to reduce radial taper wear, brake rotor friction surface indent patterns in the form of non-uniform length cross-drill hole sets originating from near the radial outer edge of the rotor configured for a sliding caliper application. 
         FIG. 5B  is a plan view of the inboard side of a modified rotor for use in a sliding caliper application where radial taper wear is not a problem, whereby no brake rotor friction indent patterns are provided. 
         FIG. 5C  is a plan view of the outboard side of a modified rotor for use with the rotor of  FIGS. 5A and 5B  for use in a sliding caliper application, having brake rotor friction surface indent patterns in the form of non-uniform length cross-drill hole sets originating from near the radial inner edge of the rotor;  FIG. 5C  is also a plan view of the inboard and outboard sides of a modified rotor according to the present invention having brake rotor friction surface indent patterns in the form of non-uniform length cross-drill hole sets configured for a fixed caliper application. 
         FIG. 6A  is a schematic drawing of the bias wear profile of a brake pad with a prior art rotor. 
         FIG. 6B  is a schematic drawing of the bias wear profile of a brake pad with a modified rotor surface according to the present invention. 
         FIG. 7A  is a schematic drawing of a brake pad average edge position in accordance with the present invention. 
         FIG. 7B  is a schematic drawing illustrating a brake pad radial pressure distribution bias. 
         FIG. 8  is a graph of wear moment versus groove length for the caliper moment of wear and for the groove plus groove sweep angle moment of wear for grooves having a sweep angle of 0 degrees and 45 degrees. 
         FIG. 9  is an algorithm for carrying out a method for optimizing a brake rotor surface with indent patterns in accordance with the present invention. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring now to the Drawing,  FIGS. 2A through 5C  depict examples of disk brake systems which contain rotors with brake rotor friction surface indent patterns which are tuned, according to the present invention, to the choice of brake pad material and caliper configuration so as to promote even wear of the brake pad and thereby reduce radial taper wear of the brake pad and improve the brake feel consequences that would otherwise be associated with radial taper wear. The following description of the preferred embodiment is merely exemplary in nature and is not intended to limit the invention, its applications, or its uses. 
       FIG. 2A  shows the inboard side  100   a  of a modified brake rotor  100  according to the present invention. In this modification for use with a sliding caliper application in which radial taper wear is substantial thereat, the brake rotor friction surface indent patterns  102  are in the form of grooves  104  in the friction surface of the rotor cheek  106  at the inboard side  100   a  of the rotor  100 . Each groove  104  is of the same radial height (or radial length) L 1G , set at a sweep angle of φ 1  with respect to the radiant R 1  of the rotor. Each groove  104  originates near (i.e., about 6 mm inside from) the radial outer edge  108  of the rotor cheek, preferably outside of the swept friction surface, and each groove is separated in this example from its neighboring groove by an angular separation A 1  of 12 degrees. The radial height L 1G  is less than the radial height H 1R  of the rotor friction surface  106 , as described below with respect to  FIGS. 6A through 8 . The rotation arrow RA 1  shows the rotor rotation when the vehicle is moving forward. The foregoing being exemplary, the number of grooves may be more or less, and the sweep angle of each groove may be the same or be selectively different. 
       FIG. 2B  is a cross-sectional view of the same rotor  100 , showing a groove  104  formed in the rotor friction surface  106 , wherein the groove has a depth D 1  of for example 0.5 mm and a width W 1  of for example 1.58 mm, and wherein for example the radial height L 1G  may be 25 mm, wherein the rotor friction surface radial height H 1R  may be 64 mm. 
       FIG. 2C  shows the inboard side  100   a ′ of a modified brake rotor  100 ′ in which radial taper wear is insubstantial such that no brake rotor friction surface indent patterns are needed at the rotor cheek  106 ″ at the inboard side  100   a ′ of the rotor  100 ′. The rotation arrow RA 1  shows the rotor rotation when the vehicle is moving forward. 
       FIG. 2D  shows the outboard side  100   b  of the modified brake rotor  100 ,  100 ′ for use in a sliding caliper application in conjunction with the inboard side  100   a ,  100   a ′ of, respectively, either  FIGS. 2A  or  2 C. Although the description below pertains to rotors  100 ,  100 ′ it is to be understood that  FIG. 2D  also pertains to the inboard and outboard sides of a brake rotor for use in a fixed caliper application. 
     Brake rotor friction surface indent patterns  102 ′ are in the form of grooves  104 ′ in the friction surface of the rotor cheek  106 ′ at the outboard side  100   b  of the rotor  100 ,  100 ′. Each groove  104 ′ is of the same length L′ 1G , set at a sweep angle of φ 1 ′ with respect to the radiant R′ 1  of the rotor. Each groove  104  originates near (i.e., about 6 mm inside from) the radial inner edge  108 ′ of the rotor cheek, preferably outside of the swept friction surface, and each groove  104 ′ is separated in this example from its neighboring groove by an angular separation A 1 ′ of 12 degrees. The length, depth and width of the grooves  104 ′ may be as those of the inboard side described above, or otherwise, wherein the radial height L′ 1G  is less than the radial height H′ 1R  of the rotor friction surface  106 ′, as described below with respect to  FIGS. 6A through 8 . The rotation arrow RA 1  shows the rotor rotation when the vehicle is moving forward. The foregoing being exemplary, the number of grooves may be more or less, and the sweep angle of each groove may be the same or be selectively different. 
       FIG. 3A  shows the inboard side  300   a  of a modified brake rotor  300  according to the present invention. In this modification for use with a sliding caliper application in which radial taper wear is substantial thereat, brake rotor friction surface indent patterns  302  are in the form of a plurality of cross-drill hole sets  304  consisting of a plurality of linearly arranged individual cross-drill holes  304   a  which are formed in the friction surface of the rotor cheek  306  at the inboard side  300   a  of the rotor  300 . Each cross-drill hole set  304  is of the same radial height (or radial length) L 3G , set at a sweep angle of φ 3  with respect to the with respect to the radiant R 3  of the rotor. Each cross-drill hole set  304  originates generally about 6 mm inside from the radial outer edge  308  of the rotor cheek, preferably outside of the swept friction surface, and each cross-drill hole set is separated in this example from its neighboring cross-drill hole set by an angular separation A 3  of 12 degrees. The radial height L 3G  is less than the radial height H 3R  of the rotor friction surface  306 , as per the below description with respect to  FIGS. 6A through 8 . The rotation arrow RA 3  shows the rotor rotation when the vehicle is moving forward. The foregoing being exemplary, the number of hole sets may be more or less, and the sweep angle of each hole set may be the same or be selectively different. 
       FIG. 3B  is a cross-sectional view of the same rotor  300  showing the cross-section of an individual drill hole  304   a , wherein the hole extends through the rotor plate  300   ap  on which the rotor cheek  306  is disposed and a cross-sectional diameter W 3  of for example 3.0 mm, the holes being linearly aligned and mutually separated between 10 and 15 mm on center, wherein the radial height L 3G  of the cross-drill hole set may be 25 mm, and wherein the rotor friction surface radial height H 3R  may be 64 mm. 
       FIG. 3C  shows the inboard side  300   a ′ of the modified brake rotor  300 ′ in which radial taper wear is insubstantial such that no brake rotor friction surface indent patterns are needed at the rotor cheek  306 ″ at the inboard side  300   a ′ of the rotor  300 ′. The rotation arrow RA 3  shows the rotor rotation when the vehicle is moving forward. 
       FIG. 3D  shows the outboard side  100   b  of the modified brake rotor  300 ,  300 ′ for use in a sliding caliper application in conjunction with the inboard side  300   a ,  300   a ′ of, respectively, either  FIGS. 3A  or  3 C. Although the description below pertains to rotors  300 ,  300 ′ it is to be understood that  FIG. 3D  also pertains to the inboard and outboard sides of a brake rotor for use in a fixed caliper application. 
     Brake rotor friction surface indent patterns  302 ′ are in the form of a plurality of cross-drill hole sets  304 ′ consisting of a plurality of linearly arranged individual cross-drill holes  304   a ′ which are formed in the friction surface of the rotor cheek  306 ′ of the outboard side  300   b  of the rotor  300 . Each cross-drill hole set  304 ′ is of the same radial height (or radial length) L′ G3 , set at a sweep angle of φ′ 3  with respect to the radiant R′ 3  of the rotor. Each cross-drill hole set  304 ′ originates generally about 6 mm inside from the radial inner edge  308 ′ of the rotor cheek, preferably outside of the swept friction surface, and each cross-drill hole set is separated in this example from its neighboring cross-drill hole set by an angular separation A′ 3  of 12 degrees. The length, depth and width of the cross-drill hole sets  304 ′ may be as those of the inboard side described above, or otherwise, wherein the radial height L′ 3G  is less than the radial height H′ 3R  of the rotor friction surface  306 ′, as per the below description with respect to  FIGS. 6A through 8 . The rotation arrow RA 3  shows the rotor rotation when the vehicle is moving forward. The foregoing being exemplary, the number of hole sets may be more or less, and the sweep angle of each hole set may be the same or be selectively different. 
       FIG. 4A  shows the inboard side  400   a  of a modified brake rotor  400  according to the present invention. In this modification for use with a sliding caliper application in which radial taper wear is substantial thereat, brake rotor friction surface indent patterns  402  are in the form of six periodically repeating groove groups  410   a  through  410   f , each groove group including grooves  404   a  through  404   e  (labeled at groove group  410   a ), disposed circumferentially around, and formed in, the friction surface of the rotor cheek  406  of the inboard side  400   a  of the rotor  400 . While the depth and width of the grooves may be, for example, as described above, or otherwise, each groove  404   a  through  404   e  of each groove group is of a progressively non-uniform (differing) radial height (or radial length) L 41G  through L 45G , (labeled at groove group  410   b ), and is set at a sweep angle of φ 4  with respect to the radiant R 4  of the rotor. Each groove  404  originates near (i.e., about 6 mm inside from) the radial outer edge  408  of the rotor cheek, preferably outside of the swept friction surface, and each groove is separated in this example from its neighboring groove by an angular separation A 4  of 12 degrees. The radial height L 41G  through L 45G  is less than the radial height H 4R  of the rotor friction surface  406 , as per the below description with respect to  FIGS. 6A through 8 . The rotation arrow RA 4  shows the rotor rotation when the vehicle is moving forward. The foregoing being exemplary, the number of grooves and/or groove groups may be more or less, and the sweep angle of each groove may be the same or be selectively different. 
       FIG. 4B  shows the inboard side  400   a ′ of the modified brake rotor  400 ′ in which radial taper wear is insubstantial such that no brake rotor friction surface indent patterns are needed at the rotor cheek  406 ″ at the inboard side  400   a ′ of the rotor  400 ′. The rotation arrow RA 4  shows the rotor rotation when the vehicle is moving forward. 
       FIG. 4C  shows the outboard side  400   b  of a modified brake rotor  400 ,  400 ′ for use in a sliding caliper application in conjunction with the inboard side  400   a ,  400   a ′ of, respectively, either  FIGS. 4A  or  4 B. Although the description below pertains to rotors  400 ,  400 ′ it is to be understood that  FIG. 4C  also pertains to the inboard and outboard sides of a brake rotor for use in a fixed caliper application. 
     The brake rotor friction surface indent patterns  402 ′ are in the form of six periodically repeating groove groups  410   a ′ through  410   f ′, each groove group including grooves  404   a ′ through  404   e ′ (labeled at groove group  410   a ′), disposed circumferentially around, and formed in, the friction surface of the rotor cheek  406 ′ of the inboard side  400   b  of the rotor  400 . While the depth and width of the grooves may be, for example, as described above, or otherwise, each groove  404   a ′ through  404   e ′ of each groove group is of a progressively non-uniform (differing) radial height (or radial length) L′ 41G  through L′ 45G , (labeled at groove group  410   b ′), and is set at a sweep angle of φ′ 4  with respect to the radiant R′ 4  of the rotor. Each groove  404 ′ originates near (i.e., about 6 mm inside from) the radial inner edge  408 ′ of the rotor cheek, preferably outside of the swept friction surface, and each groove is separated in this example from its neighboring groove by an angular separation A′ 4  of 12 degrees. The radial height L′ 41G  through L′ 45G  is less than the radial height H′ 4R  of the rotor friction surface  406 ′, as per the below description with respect to  FIGS. 6A through 8 . The rotation arrow RA 4  shows the rotor rotation when the vehicle is moving forward. The foregoing being exemplary, the number of grooves and/or groove groups may be more or less, and the sweep angle of each groove may be the same or be selectively different. 
     By way merely to exposit a comparative, non-limiting example, the sweep angle φ 4 , φ′ 4  is 20 degrees, and the progressive radial heights may be as follows: groove L 41G , L′ 41G  is a “short” radial height of 21.7 mm, adjacent groove L 42G , L′ 42G  is a “medium” radial height of 31.7 mm, adjacent groove L 43G , L′ 43G  is a “long” radial height of 41.7 mm, adjacent groove L 44G , L′ 44G  is the “medium” radial height of 31.7 mm, and adjacent groove L 45G , L′ 45G  is the “short” radial height of 21.7 mm. 
       FIG. 5A  shows the inboard side  500   a  of a modified brake rotor  500  according to the present invention. In this modification for use with a sliding caliper application in which radial taper wear is substantial thereat, the brake rotor friction surface indent pattern  502  is in the form of six periodically repeating cross-drill hole set groups  510   a  through  510   f , each cross-drill hole set group including cross-drill hole sets  504   a  through  504   e  (labeled at hole set group  510   a ), disposed circumferentially around, and formed in, the friction surface of the rotor cheek  506  of the inboard side  500   a  of the rotor  500 . While the depth and cross-sectional diameter of the holes  504  may be, for example, as described above, or otherwise, each cross-drill hole set  504   a  through  504   e  of each cross-drill hole set group is of a progressively non-uniform (differing) radial height (or radial length) L 51G  through L 55G  (labeled at hole set group  510   b ), and is set at a sweep angle of φ 5  with respect to the radiant R 5  of the rotor. Each cross-drill hole set  504  originates generally about 6 mm from the radial outer edge  508  of the rotor cheek, preferably outside of the swept friction surface, and each cross-drill hole set is separated in this example from its neighboring cross-drill hole set by an angular separation A 5  of 12 degrees. The radial height L 51G  through L 55G  is less than the radial height H 5R  of the rotor friction surface  506 , as per the below description with respect to  FIGS. 6A through 8 . The rotation arrow RA 5  shows the rotor rotation when the vehicle is moving forward. The foregoing being exemplary, the number of cross-drill hole sets and/or cross-drill hole set groups may be more or less, and the sweep angle of each cross-drill hole set may be the same or be selectively different. 
       FIG. 5B  shows the inboard side  500   a ′ of a modified brake rotor  500 ′ in which radial taper wear is insubstantial such that no brake rotor friction surface indent patterns are needed at the rotor cheek  506 ″ at the inboard side  500   a ′ of the rotor  500 ′. The rotation arrow RA 5  shows the rotor rotation when the vehicle is moving forward. 
       FIG. 5C  shows the outboard side  500   b  of a modified brake rotor  500 ,  500 ′ for use in a sliding caliper application in conjunction with the inboard side  500   a ,  500   a ′ of, respectively, either  FIGS. 5A  or  5 B. Although the description below pertains to rotors  500 ,  500 ′ it is to be understood that  FIG. 5C  also pertains to the inboard and outboard sides of a brake rotor for use in a fixed caliper application. 
     The brake rotor friction surface indent patterns  502 ′ are in the form of six periodically repeating cross-drill hole set groups  510   a ′ through  510   f ′, each cross-drill hole set group including cross-drill hole sets  504   a ′ through  504   e ′ (labeled at hole set group  510   a ′), disposed circumferentially around, and formed in, the friction surface of the rotor cheek  506 ′ of the outboard side  500   b  of the rotor  500 . While the depth and cross-sectional diameter of the holes  504 ′ may be, for example, as described above, or otherwise, each cross-drill hole set  504   a ′ through  504   e ′ of each cross-drill hole set group is of a progressively non-uniform (differing) radial height (or radial length) L′ 51G  through L′ 55G  (labeled at hole group  510   b ′), and is set at a sweep angle of φ′ 5  with respect to the radiant R′ 5  of the rotor. Each cross-drill hole set  504 ′ originates generally about 6 mm from the radial inner edge  508 ′ of the rotor cheek, preferably outside of the swept friction surface, and each cross-drill hole set is separated in this example from its neighboring cross-drill hole set by an angular separation A′ 5  of 12 degrees. The radial height L′ 51G  through L′ 55G  is less than the radial height H′ 5R  of the rotor friction surface  506 ′, as per the below description with respect to  FIGS. 6A through 8 . The rotation arrow RA 5  shows the rotor rotation when the vehicle is moving forward. The foregoing being exemplary, the number of cross-drill hole sets and/or cross-drill hole set groups may be more or less, and the sweep angle of each cross-drill hole set may be the same or be selectively different. 
     By way merely to exposit a comparative, non-limiting example, the sweep angle φ 5 , φ′ 5  is 20 degrees, and the progressive radial heights may be as follows: cross-drill hole set L 51G , L′ 51G  is a “short” radial height of 21.7 mm, adjacent cross-drill hole set L 52G , L′ 52G  is a “medium” radial height of 31.7 mm, adjacent cross-drill hole set L 53G , L′ 53G  is a “long” radial height of 41.7 mm, adjacent cross-drill hole set L 54G , L′ 54G  is the “medium” radial height of 31.7 mm, and adjacent cross-drill hole set L 55G , L′ 55G  is the “short” radial height of 21.7 mm. 
     Following is a discussion of how the brake rotor friction surface indent patterns affect radial taper wear. 
     The mechanism of radial taper well is well known in the art. The design of most sliding caliper brake systems involves significant radial taper wear on the outboard brake pad, and a lesser degree of taper wear on the inboard brake pad; whereas, the design of most fixed caliper brake systems involves radial taper wear generally equivalent on the inboard and outboard sides of the brake rotor, wherein the radial taper wear in fixed caliper applications is generally less than that of the outboard side in sliding caliper applications. Therefore, with regard in particular to the outboard side radial taper wear in sliding caliper applications, the outboard bias in brake pad taper wear is driven in large part by caliper stiffness decreasing significantly in the portion of the caliper opposite the caliper actuator cylinder versus the piston cylinder to connector interface. Comparatively high positive radial taper wear on the outboard side of the brake pads tends to rotate the caliper actuator around the vehicle fore-aft axis in an attempt to conform to the brake pads. This movement will bias the piston to inboard pad contact towards the radial inward direction which promotes negative taper wear on the inboard brake pads. 
     Referring to  FIGS. 6A through 8 , optimization of the brake rotor friction surface indent patterns will be discussed with particular reference by way of example to the grooving and it will be understood that discussion similarly applies to cross-drilling. 
     Referring firstly to  FIG. 6A , illustrated is a radial taper wear profile  200  of a brake pad in a disc brake system with a prior art rotor configured for a sliding caliper. The profile  200  reflects the assumption that radial taper wear occurs linearly over the area of the brake pad friction surface. The radial height of the brake pad H is used as a dimensional reference for the analysis of the radial taper wear. At the edge of the pad, the maximal wear W T  of the friction surface represents the maximal taper wear as would occur in a prior art rotor. The quantity W E,T  represents the equivalent wear of the radial taper wear profile along the friction surface of the brake pad (analogous to the equivalent force representing a force distribution). The angle θ represents the wear angle associated with radial taper wear. A dimension “a” is a calculated value whereby the average edge position is determined. 
     From the assumption of linearity of taper wear over the area of the frictional surface and the data presented, one may calculate the groove radial height L G  and the groove sweep angle φ necessary to produce the maximal reduction in radial taper wear, wherein the parameters of the profile  200  are used to compute the parameters in the grooving (or cross-drilling) pattern according to the present invention. 
     Referring next to  FIG. 6B , the wear profile  220  for a brake pad is shown, reflecting the wear pattern of the brake pad over grooves according to the present invention. The wear profile  220  reflects the assumption that the radial taper wear of the brake pad will generally conform to a step profile. The maximal wear of the friction surface due to the grooves is W G . The wear of the friction surface at the edge thereof due to the grooves is W E,G . The required radial height of the groove is L G  (and its half length is L G/2 ). 
     The results from the assumptions are that the radial taper wear profile  200  from the prior art and the radial taper wear profile  220  according to the present invention allow for computations particularly associated with the grooving (and cross drilling) according to the present invention. 
     The parameter “a”, as defined above, is computed from calculating the moment of wear of the radial taper wear around the brake pad radial inner edge according to the equation: 
                         W     E   ,   T       ·   a     =       ∫   0   R     ⁢       x   ·     tan   ⁡     (   θ   )       ·   x     ⁢           ⁢     ⅆ   x           ,           (   1   )               
where W E,T  is the equivalent wear of the radial taper wear profile (analogous to an equivalent force of a force distribution), R is the radius of the brake rotor and θ is the wear angle, which allows us to calculate the parameter “a” as:
 
                     a   =       2   ⁢   H     3       ,           (   2   )               
where H is the radial height of the taper wear pattern, i.e., the radial height of the brake pad. The radial height of the groove is computed by solving for the dimension L G  that yields the closest equivalent moment of wear with the rectangular groove pattern wear bias pattern. The resultant equation is:
 
                         W     E   ,   T       ·   a     =           H   2     ·     W   T       3     =       W   G     ·     L   G     ·     (     H   -       L   G     2       )     ·     L   G           ,           (   3   )               
where W T  and W G  are defined above. Solving this equation for L G  yields the following quadratic solution:
 
                     L   G     =         W   G     ·   H     +           W   G   2     ·   H     -       2   ·     H   2     ·     W   T       3                   (   4   )               
which has a real solution only when:
 
     
       
         
           
             
               
                 
                   
                     W 
                     G 
                   
                   ≥ 
                   
                     
                       
                         
                           2 
                           · 
                           
                             W 
                             T 
                           
                         
                         3 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Turning now to  FIGS. 7A and 7B , the effects of forces and moments from employing a rotor groove sweep angle φ are illustrated.  FIG. 7A  is a diagram  230  which illustrates the vector decomposition of the reaction force F R  caused by using a sweep angle φ in the grooves of the brake rotor friction surface. F R  is the frictional force on the brake pad that is generated by the groove pattern. F R,J  is the projection of the force F R  along the direction of the normal to the radial edge of the rotor. F R,I  is the projection of the force F R  perpendicular to F R,J .  FIG. 7B  is a diagram  240  which shows the influence these forces have on the radial pressure distribution bias RPDB on the brake pad. The thickness of the pad between the friction face and the center of the backing plate is defined by T. 
     The sweep angle φ of the grooves (or cross-drill hole sets) of the brake rotor friction surface gives rise to a force between the grooves (or cross-drill hole sets) and the brake pad which will tend to push the brake pad friction surface in a radially upward direction. This, combined with the above mentioned reaction force F R  causes a moment M on the pad that will tend to draw the radial inner edge of the pad in towards the rotor, thus further counteracting the forces causing radial taper wear. 
     The equivalent moment of wear M imposed by employing brake rotor friction surface indent patterns according to the present invention and a sweep angle φ is given by: 
                   M   =           H   2     ·     W   GI       3     =       H   2     ·     F   R     ·     sin   ⁡     (   φ   )       ·   T               (   6   )               
where F R  is the friction force on a pad multiplied by an estimate of the percentage of the total friction force on the brake pad that is generated over the groove pattern or the cross-drill hole set pattern on the friction surface of the brake rotor, and where H, W GI , and T are as defined above. Note that the effect of the groove sweep angle on the radial force distribution is related to the brake friction force level. Accordingly, the groove (or cross-drill hole set) pattern radial length and the groove (or cross-drill hole set) pattern sweep angle can therefore be optimized for a given set of operating conditions.
 
     The above equations were programmed into a spreadsheet, and the solver feature was used to find the value of L G  for a proposed groove sweep angle that resulted in an exact or closest match possible between the moment of wear driven by the caliper, and the net (sum) moment of wear driven by the groove pattern and groove sweep angle, summarized in Table 1. Table 1 and  FIG. 8  show the results for a proposed twin piston sliding caliper application. 
     
       
         
               
               
             
               
               
             
           
               
                   
                 TABLE I 
               
               
                   
                   
               
               
                   
                 Value 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Inputs 
                   
               
               
                 Piston Diameter 
                 42 mm 
               
               
                 No. of Pistons 
                 2 
               
               
                 Apparent Friction 
                 0.40 
               
               
                 Percent Force on Grooves 
                 10% 
               
               
                 Hydraulic Pressure 
                 5,000 kPa 
               
               
                 Pad Radial Height 
                 59 mm 
               
               
                 Pad Thickness 
                 8 mm 
               
               
                 Groove Sweep Angle 
                 45 deg 
               
               
                 Wear Increase with Grooves 
                 1 mm 
               
               
                 Radial Taper Wear without Grooves 
                 20 microns/mm 
               
               
                 Calculated Parameters 
               
               
                 Critical Groove Wear 
                 0.89 mm 
               
               
                 Friction Force (1 pad) 
                 5,542 N 
               
               
                 Upward Force from Grooves 
                 392 N 
               
               
                 Moment on Pads from Grooves 
                 3 Nm 
               
               
                 Radial Force Gradient due to Groove Sweep Angle 
                 0.00090 
               
               
                 Equiv. Angle of Rad. Force Gradient 
                 0.052 deg 
               
               
                 Edge Wear Dimension due to Groove Sweep Angle 
                 0.053 mm 
               
               
                 Moment of Wear due to Groove Sweep Angle 
                 62 mm 3   
               
               
                 Taper Wear 
                 1.18 mm 
               
               
                 Equiv. Caliper Radial Moment of Wear 
                 1,369 mm 3   
               
               
                 Equiv. Groove Moment of Wear 
                 1,307 mm 3   
               
               
                 Groove + Groove Sweep Angle Equiv. Moment of Wear 
                 1,369 mm 3   
               
               
                 Ideal Groove Length, L G   
                 29.6 mm 
               
               
                   
               
             
          
         
       
     
     Referring now to  FIG. 8 , depicted is a graph  250  of wear moment versus groove length measured from the radial inner edge of the rotor cheek, wherein plot  252  represents the caliper moment of wear, Plot  254  represents groove plus groove sweep angle of zero degrees, and plot  256  represents groove plus groove sweep angle moment of wear with a sweep angle of 45 degrees. It is seen that with a groove sweep angle of 45 degrees and a braking force distribution of 10% supported by the grooves, the estimated groove pattern radial height to achieve an even radial wear of the brake pad drops from 31.7 mm (plot  254 ) to 29.6 mm (plot  256 ). In this regard, the term “braking force distribution of 10% supported by the grooves” means that of the friction generated in the interface, 10 percent of it stems from interaction between the pad and the edges of the grooves, and 90 percent of it from the ‘normal’ pad to rotor friction interaction elsewhere in the interface. This distribution is appropriate for high energy/high temperature driving conditions where the pad can actually extrude slightly into interference with the grooves. 
     Referring now to  FIG. 9 , an algorithm  260  for carrying out a method for optimizing the brake rotor surface indent patterns will be discussed. 
     At Block  262 , a rectangular radial taper wear profile of a brake pad is determined, as for example in the manner exemplified by  200  in  FIG. 6A  and the accompanying discussion recounted above. Next, at Block  264  an optimal radial height of the indent patterns is determined, as for example via the above discussion with respect to  FIGS. 6A and 6B  and equations (1) through (5), as based upon a closest equivalent moment of wear with respect to the rectangular radial taper wear profile of Block  262 . Next, at Block  266  an optimal sweep angle of the indent patterns is determined, as for example via the above discussion with respect to  FIGS. 7A and 7B  and equation (6), wherein the sweep angle is an angle measured with respect to a radiant of the rotor (generally being between 0 degrees and about 70 degrees), wherein where the sweep angle is greater than zero degrees, the radially innermost portion of the indent patterns is leading with respect to the rotation direction of the rotor when the motor vehicle is moving in a forward direction. Then at Block  268 , a distribution of the indent patterns is selected based upon empirical estimation. At Block  270 , a brake rotor is fabricated which is predetermined to suit a particular brake corner application, and the determined plurality of indent patterns from Blocks  262  to  268  is formed in the selected rotor cheek thereof. At Decision Block  272 , the rotor cheek is tested to determine whether the indent patterns provide an optimal minimization of radial taper wear, per the brake corner application. If the answer to the inquiry is no, then Blocks  268  to  272  are repeated until optimization is achieved, whereupon the answer to the inquiry at Decision Block  272  will be yes, and the rotor side is then optimized at Block  274 . The other side of the brake rotor is then optimized with indent patterns (if necessary) by a repeat of algorithm  260 , whereupon the brake rotor is optimized for minimization of radial taper wear. 
     An evaluation of various brake rotors was performed, including a conventional brake rotor and brake rotors having indent patterns according to the present invention, per the following example. 
     EXAMPLE 
     Three brake rotors were tested in a dynamometer simulating a brake corner to evaluate radial taper wear characteristics. A first rotor had no brake rotor friction surface indent patterns, and served as a baseline. A second rotor had a brake rotor friction surface indent pattern on the outboard side in the form of 6 groups of 5 grooves per group, the radial heights being characterized as being “short”, “medium”, “long”, “medium”, and “short”, wherein the “short” was 21.7 mm, the “medium” was 31.7 mm, and the “long” was 41.7 mm, as shown by way of example at  FIG. 4C . And a third rotor having a brake rotor friction surface indent pattern in the form of equal length grooves, equally spaced and numbering 30, the length being 31.7 mm, generally as shown by way of example at  FIG. 2D . 
     The test equipment was as follows. The caliper was manufactured by ADVICS Mfg. Ohio, Inc. of Lebanon, Ohio of cast iron sliding caliper with dual pistons (disposed at one side thereof) with a total area of 2,877.4 mm 2 . The rotors were vented cast iron having a mass of 11.28 kg, an outer diameter of 345 mm, a cheek inner diameter of 203 mm, a rotor width of 30 mm, and a brake rotor plate width of 9.75 mm (outer) and 9.0 mm (inner). The brake pad lining was manufactured by Federal Mogul, product lining edge code HP1000/2. The inboard and outboard brake pads each had (puck only) length of 145.5 mm, width of 57 mm, a height of 9.3 mm, and a mass of 0.598 kg. The backing plate was steel with a thickness of 6.5 mm. The aspect ratio (L/W) was 2.55. The surface area was 8,293.5 cm 2 , and the volume was 7,671,487.5 mm 3 . 
     The following results were obtained. 
     Both the second and third (grooved) rotors showed lower warm burnished apparent friction than the first (baseline) rotor. This is consistent with performance observed on cross-drilled rotors, as reported in “The effect of Rotor Crossdrilling on Brake Performance” by D. Antanaitis and A. Rifici, SAE Technical paper 2006-01-0691 (2006). It does not result in an appreciable change in pedal feel in this condition. The second (unequal length grooved) rotor showed the lowest apparent friction in this case, consistent with it having the highest coverage of the friction surface. 
     Both of the second and third (grooved) rotors showed higher apparent friction during the fade sequences than the first (baseline) rotor, 0.24 for the second and third rotors, versus 0.22 for the first rotor, a 9 percent improvement for the second and third rotors versus the first rotor. This is a result of the lower radial taper wear and increased mechanical efficiency of the caliper, and the added pad to rotor interaction mechanism on the outboard fade afforded by the grooving patterns. 
     Both of the second and third (grooved) rotors exhibited lower radial taper wear than the first (baseline) rotor, 13.0 microns/mm for the second (differing groove length) rotor and 15.4 microns/mm for the third (equal groove length) rotor versus 22.6 microns/mm for the first (baseline) rotor. This is due to the groove pattern causing a ‘moment of wear’ opposite that of the moment of wear caused by caliper deflection and increasing friction surface sliding speed. 
     Both of the second and third (grooved) rotors achieved lower apparent piston travel during the fade sequences than the first (baseline) rotor. This is a result of lower outboard pad radial taper wear. 
     The conclusion is that both the second (unequal length grooved) rotor and the third (equal length grooved) rotor provide lower output in the new burnished condition, higher output in the fade condition, and lower apparent piston travel. The second (unequal length grooved) rotor was the most effective, and had the added benefit of reducing brake torque variation on the order of 50 percent during the fade sections. Both the second and third rotors reduced radial taper wear, with little effect on brake pad lining wear rates. 
     Accordingly, it is most preferred to utilize brake rotor friction indent patterns which are arranged in repeating groups, wherein each brake rotor friction indent pattern of each group is of progressively non-uniform (differing) radial height, as for example as shown at  FIGS. 4A ,  4 C,  5 A and  5 C. 
     To those skilled in the art to which this invention appertains, the above described preferred embodiments may be subject to change or modification. Such change or modification can be carried out without departing from the scope of the invention, which is intended to be limited only by the scope of the appended claims.