Abstract:
A method for minimizing the radial runout of a tire and rim assembly  10  having the steps of locating the position of maximum radial runout and measuring the amount of maximum radial runout; loosening the threaded fasteners  24  attaching the rim  20  and disk  22 ; and moving the disk  22  radially toward the location of the maximum radial runout a distance one-half the measured runout amount and then retightening the threaded fasteners is disclosed. The method minimizes first harmonic vibrations caused by the normal assembly of these components.

Description:
TECHNICAL FIELD 
     This invention relates to a method for correcting the radial runout of a tire and rim wheel assembly. More particularly, the method corrects ride vibration problems associated with large tires and rims specifically designed for off-road or agricultural use. The method corrects or minimizes the radial runout of farm tires and their two piece rim wheel assembly. 
     BACKGROUND ART 
     Large tires for tractors and the like vehicles are conventionally mounted on large two piece rims. The radially outer portion is an annular ring commonly referred to as the rim. The rim is adapted to hold the tire. The rim has a 5° bead seat, a pair of axially out flanges, and a drop center portion to facilitate mounting the tire over the flange portions. This annular ring further has a radially inner flange with a plurality of clearance holes to which the second portion of the rim is attached. 
     The second portion of the rim is a disk which has a central opening which preferably is tapered, this central opening engages the drive axle of the vehicle to which it is attached. The drive axle preferably is a tapered male end and when attached to the disk portion of the rim both parts have their respective axis of rotations substantially coincident. 
     Radially outward of the central opening is a plurality of holes which can be aligned with the openings of the rim and bolted to the rim by means of threaded fasteners. 
     These attachment holes in both the rim and the disk portion each have a clearance or relatively larger opening to accept the threaded fasteners. These dimensional tolerances permit the mounted tire and rim assembly to have their respective axis of rotation to be shifted relative to the common axis of the vehicle axle and wheel disk assembly. This ability to shift the relative position of the mounted tire and rim assembly relative to the disk portion can be positively beneficial in reducing tire and rim assembly vibration on tractors and the like vehicles. These vibration amplitudes are most disturbing on hard paved surfaces when the tractors are driven at relatively high speeds in excess of 30 km/h. 
     The prior art methods to correct this tire wheel assembly vibration characteristic involves numerous required steps of locating a maximum radial runout location, deflating the tire, breaking down the beads and rotating the tire to a distinct, precise location on the rim, reinflating the tire and remounting the tire rim assembly. This method of vibration reduction is commonly referred to as match mounting. When precisely accomplished the desired resultant vibration reduction can be achieved. The match mounting method is inherently time consuming, requires the tire beads to be detached from the rim, often times the fluid medium is a liquid which must be captured and reinjected into the tire, and after completing this procedure if not properly conducted the desired reduction in vibration will not result. 
     DISCLOSURE OF INVENTION 
     This invention relates to a method for minimizing the radial runout of a tire and rim assembly  10 , the rim  12  having an outer annular rim  20  and a disk  22  attached to the outer rim  20  by threaded fasteners  24 . The inventive method can be summarized by the following steps: 
     locating the position of maximum radial runout and measuring the amount of maximum radial runout; 
     loosening the threaded fasteners  24 ; 
     moving the disk  22  radially toward the location of the maximum radial runout a distance one-half the measured maximum runout amount, and then tightening the thread fasteners  24  thereby securely attaching the disk  22  to the tire  14  and outer rim  20  of the assembly. 
     The step of locating and measuring the maximum runout preferably can be accomplished by rotating the tire and rim assembly  10  about an axis of rotation. For example, the tractor like vehicle can be jacked up or placed on a lift whereby the normally inflated and unloaded tire  14  can be freely rotated. A runout measuring device  30  is used to locate the maximum runout location  2  preferably the runout device can be zeroed at that location  2  and rotated to read the runout at a location  4  approximately 180° from the maximum runout location  2 . This measured runout is considered for the purposes of this invention to be the amount of radial runout. The preferred device  30  preferably automatically indicates one-half the total amount of runout. This “one-half amount” is useful because it is the exact amount of adjustment that is required to zero the runout of the tire rim assembly  10 . These two locations  2 ,  4  are marked and in the most preferred method the operator then rotates the tire rim assembly  10  such that the location where rim disk  22  central opening  26  is contacting the axle  11  is oriented at the vertical or on top of the axle  11 , in other words at a 12:00 o&#39;clock orientation. The axle  11  and the disk  22  are both marked at that location  6 , prior to removing the tire and rim assembly. After removing the tire and rim assembly  10  the assembly  10  is positioned in a horizontal position, preferably over a support device  40 . Then, an apparatus  50  for precisely moving the disk  22  is inserted into the support device  40  and a pusher bar  52  on the apparatus  50  is placed in proximity to the opening  26  of the central disk  22  at a location aligned with the maximum radial runout mark  2  and the 180° location  4 . Each of the threaded fasteners  24  are loosened such that the disk  22  and the rim  20  are free to accept relative movement. Prior to moving the disk  22 , a device  60  for measuring the relative movement of the disk in relation to the tire  14  and rim  12  is placed in position aligned between the radial runout mark  2  and the 180° mark  4 . The displacement of the dial indicator arm is parallel to a line extending from  2 ,  4 . The dial indicator can be placed anywhere so long as the arm is parallel to the line  2 ,  4 . Preferably, measuring the device  60  includes a dial indicator  62  that can be set to the amount of displacement required which is precisely one-half the amount of the measured runout. The operator can then actuate the apparatus  50  which advances the pusher bar  52  which moves the disk  22  toward the location  2  of the maximum runout. At the point where the dial indicator  62  reads zero the disk  22  movement is stopped and the threaded fasteners  24  are retightened. The assembly  10  is then reattached to the axle  11  making sure that the axle  11  and disk  22  marks  6  are in the top vertical or 12:00 o&#39;clock position. At this point the tire rim assembly  10  will have been assembled minimizing the first harmonic radial runout. 
     Definitions 
     For ease of understanding this disclosure the following terms are disclosed: 
     “Aspect Ratio” means the ratio of the tire&#39;s section height to its section width. 
     “Axial” and “axially” means the lines or directions that are parallel to the axis of rotation of the tire. 
     “Bounce” or “Hop” means the vertical acceleration related to first Harmonic Radial Runout or Force Variation of each tire and rim assembly interacting with the other tire and rim assemblies of the vehicle. 
     “Circumferential” means lines or directions extending along the perimeter of the surface of the annular tire parallel to the equatorial plane EP and perpendicular to the axial direction. 
     “Design Rim” means a rim having a specified configuration and width. For the purposes of this specification, the design rim and design rim width are as specified by the industry standards in effect in the location in which the tire is made. For example, in the United States, the design rims are as specified by the Tire and Rim Association. In Europe, the rims are as specified in the European Tyre and Rim Technical Organization—Standards Manual and the term design rim means the same as the standard measurement rims. In Japan, the standard organization is The Japan Automobile Tire Manufacturer&#39;s Association. 
     “Equatorial Plane (EP)” means the plane perpendicular to the tire&#39;s axis of rotation and passing through the center of its tread. 
     “Footprint” means the contact patch or area of contact of the tire tread with a flat surface at zero speed and under normal load and pressure. 
     “Inner” means toward the inside of the tire and “outer” means toward its exterior. 
     “Literal Edge” means the axially outermost edge of the tread as defined by a plane parallel to the equatorial plane and intersecting the outer ends of the axially outermost traction lugs at the radial height of the inner tread surface. 
     “Leading” refers to a portion or part of the tread that contacts the ground first, with respect to a series of such parts or portions, during rotation of the tire in the direction of travel. 
     “Lope” means once per revolution fore &amp; aft acceleration/deceleration related to first harmonic radial runout or force variation of tire and rim assembly. 
     “Net-to-gross Ratio” means the ratio of the surface area of the normally loaded and normally inflated tire tread rubber that makes contact with a hard flat surface, divided by the area of the tread, including noncontacting portions such as grooves as measured around the entire circumference of the tire. 
     “Normal Inflation Pressure” means the specific design inflation pressure assigned by the appropriate standards organization for the service condition for the tire. 
     “Normal Load” means the load assigned by the appropriate standards organization for the service condition for the tire when inflated to the normal inflation pressure. 
     “Radial” and “radially” mean directions radially toward or away from the axis of rotation of the tire. 
     “Shake” means higher frequency lug induced vibration felt in cab or steering wheel or seen in movement of the exhaust stack (no particular acceleration). 
     “Shudder” means a lug induced vibration at low frequency, resulting in a vertical acceleration felt through the floor of the cab. 
     “Trailing” refers to a portion or part of the tread that contacts the ground last, with respect to a series of such parts or portions during rotation of the tire in the preferred direction of travel. 
     “Tramp” means side-to-side motion, or lateral acceleration, induced by first harmonic radial runout or force variation of each tire and rim assembly interacting with each other. 
     “Tread Arc Width” (TAW) means the width of an arc having its center located on the equatorial plane (EP) and which substantially coincides with the radially outermost surfaces of the various traction elements (lugs, blocks, buttons, ribs, etc.) across the lateral or axial width of the tread portions of a tire when the tire is mounted upon its designated rim and inflated to its specified inflation pressure but not subject to any load. 
     “Unit Tread Pressure” means the radial load borne per unit area (square centimeter or square inch) of the tread surface when that area is in the footprint of the normally inflated and normally loaded tire. 
     “Vibration Ratings” means the subjective ride terminology wherein “slight” means barely noticeable; “moderate” means noticeable but not objectionable; “severe” means objectionable. 
    
    
     BRIEF DESCRIPTION OF DRAWINGS 
     FIG. 1 shows a chart of the typical radial runout first harmonic with the tire and rim in their initial positions at 0°. 
     FIG. 2 shows the radial runout first harmonic for a perfect out-of-round condition where the tire rotates about an axis that is slightly off center. 
     FIG. 3 is a plan view of an exemplary tire and rim assembly  10 . 
     FIG. 4 is a cross-sectional view of the exemplary tire and rim assembly  10  of FIG. 3 taken along lines  4 — 4 . 
     FIG. 5 is a view of a preferred apparatus for locating and measuring the radial runout of the tire and rim assembly. 
     FIG. 6 is a view of the apparatus of FIG. 5 in contact with the outer surface of the tire  14 . 
     FIG. 7 is a view of a preferred apparatus for precisely moving the center disk relative to the tire and rim and the apparatus for measuring that movement. 
     FIG. 8 is a chart showing the resultant runout of the tire and rim assembly after moving the disk relative to the tire and rim. The resultant runout as shown as a solid line, the dashed lines representing the tire and outer rim and the disk runout. 
     FIGS. 9A,  9 B and  9 C depict three charts which show the approximate vertical displacement of the axle  10  at various tire inflation pressures for speeds of 32 km/m, 35 km/h and 42 km/h reading left to right the first bar being the tire wheel assembly prior to correcting the radial runout, the second bar representing a first harmonic corrective procedure, the third bar representing the simplified inventive method to correct the runout. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 shows the radial runout first harmonic measured in mm of a agricultural tire  14  and rim  12  assembly  10 . The bold line  1  showing the assembly&#39;s radial runout, the dashed line  3  showing the rim  12  radial runout and the dotted line  5  showing the tire radial runout. The initial position is at 0° and traverses the entire 360° around the assembly. For the purposes of this invention, the first harmonic represents the runout condition that is characterized by one high point and one low point. In other words, an out-of-round situation with one high point and one low point in each revolution. 
     Shown in FIG. 2, is the radial runout first harmonic for a perfect out-of-round condition where the tire rotates about an axis that is slightly off center. As shown in FIG. 2, the high point  2  being shifted off of the true oval center or circular center line  7  and the low point  4  being shifted radially inward of the true circular center line. 
     This first harmonic high point, low point condition of the tire and rim assembly  10  results in the tire  14  transmitting a harsh vibration to the driver of the vehicle. From past experience, the inventor has determined that the most important harmonic (for speeds up to 42 km/h) is the first harmonic. This first harmonic is felt as a once-per-revolution bounce or lope. If the bounce or lope is bad enough, serious driver jostling in the cab can occur. A vast majority of the ride and handling problems associated in agricultural tires results from this first harmonic radial runout condition. 
     As shown in FIGS. 3 and 4, an agricultural tire  14  is mounted to a rim  12 . The rim  12  has two primary components: a radially outer annular ring or rim  20  to which the tire  14  is mounted and a radially inner central disk  22 . The central disk  22  mounts over the axle  11  of the vehicle and is bolted by means of threaded fasteners  24  to the annular outer ring or rim  20  thereby making a completed assembly  10 . With further reference to the cross-sectional view of FIG. 4, it can be seen that the threaded fasteners  24  securely fasten the disk  22  to the rim  20 . This plurality of threaded fasteners  24  pass through clearance holes  28  in both the rim and disk. The clearance holes  28  must be of sufficient size to permit the rim  20  and disk  22  to be attached easily. These clearance holes  28  can provide a displacement of the disk  22  relative to the rim  20  by as much as 5 mm in any one direction. Historically, this displacement could cause a misalignment of the axis of rotation of the rim assembly  10  relative to the drive axle  11  of the vehicle. As will be discussed later, this detrimental effect can be used advantageously to compensate for the overall radial runout of the tire and rim assembly  10 . 
     For example, should the operator of a tractor or like agricultural vehicle find that his tire and rim assembly  10  is creating an objectionable or severe vibration. It may be possible to correct this situation using the following procedure. 
     The operator could jack the vehicle up so that the tire and rim assembly  10  is able to rotate freely about its axis. Then, by positioning a runout indicator device in proximity to the tire  14 , a measurement of the radial runout can be accomplished. This runout indicator device  30  as shown in FIG. 5 has a boot  32  which is attached to an indicator arm  33 . This boot  32  is specifically designed to follow the contour of the tread pattern at the equatorial plane of the tire  14  and traverses several of the tractor lugs  72  at one time. The operator simply places the boot gently against the curved contour of the tire tread  70 . The boot  32  should span several of the tire&#39;s tread lugs  72  at the center line or equatorial plane of the tread  70 . The operator adjusts the contour of the boot  32  such that the boot&#39;s radius of curvature is slightly larger than the radius of the tire  14 . The operator then positions the runout device  30  such as the dial indicator arm  33  is initially displaced approximately half of its total allowable travel. The operator then zeros the dial indicator  34 . He then slowly rotates through a complete 360° rotation making note of the location of the tire  14  where the dial indicator  34  registers the lowest value (the greatest negative value). He then rotates the tire and rim assembly  10  back to the location  4  corresponding to the lowest indicator value. He then rezeros the dial indicator. He slowly rotates the tire  14  through a 360° rotation making note of the location  2  and magnitude of the highest point on the tire  14 . He then makes a mark on the tire at this high point. The magnitude displaced is the total radial runout of the tire and rim assembly  10  relative to the hub or axle  11  center. This magnitude follows a one-to-one relationship with the displacement of the indicator. 
     However, the preferred device shown in FIG. 5 has a sloped indicator readout such that as the boot  32  is displaced the dial indicator  34  only moves one-half of the distance of the boot&#39;s displacement. This preferred device  30  will provide a simpler mechanism for the operator to make his measurements. The device magnitude displayed on the indicator using the apparatus shown in FIG. 5 results the magnitude being one-half the total radial runout of the tire and rim assembly  10  relative to the center of the axle  11 . This preferred, although not required, measurement reading permits the operator to directly use this measurement when he attempts to center the disk  22  relative to the outer rim  20  as will be discussed later. 
     The operator should then check the clearance between the axle  11  and the center disk  22  opening  26 . Typically, the axle  11  and the center disk  22  will be touching at some location  6 . The operator should mark on both the hub and the center disk this point of contact  6 . If there is no point  6  in contact, he should make a mark at a point  6  where the clearance is minimum. This will be important when reattaching the tire and rim assembly  10  back to the tractor. 
     The operator should then rotate the wheel so that the mark made on the disk  22  and axle  11  is in the vertical or top position when looking at the tire  14 . The operator should then lock the axle  11  in this position. He should then remove the tire and rim assembly  10  from the tractor by unbolting the axle hub  11  from the center disk  22 . As shown in FIG. 7, the operator should then place the tire over a portable support device  40  on a flat ground level surface. The tire  14  is rotated horizontally as needed so that the point  2  of largest runout is in line with the location in which a pusher bar  52  will be contacting the rim disk opening  26 . This may be achieved by the use of an alignment pin that is removably attached to the center of the portable support device  40 . The tire  14  is lowered until its entire weight is supported by the arms  42  of the support device  40 . The operator then removes any lifting chain or cable if used from the tire and rim assembly  10 . He removes the alignment pin and replaces it with the perforated center post  51  as shown in FIG.  7 . He then attaches a bottle jack  54  and its holder  55  to the center post  51  with a bolt  53  such that a pusher bar  52  extends at least 50 mm below the point of contact between the pusher bar  52  and the center disk  22 . Having accomplished this, the piston  57  of the bottle jack  54  should be radially aligned in the direction of the maximum runout location  2 . The operator then loosens the bolts  24  attaching the center disk  22  to the outer rim  20 . Once these bolts  24  have been loosened, it is very important that he does not accidentally disturb the placement of the center disk  22  relative to the outer rim  12  and tire  14 . He then attaches the dial indicator device  62  to the outer rim  12  using a magnetic base stand  64  as shown in FIG.  7 . The indicator  62  should be positioned horizontally so that its arm  65  is parallel with the piston of the bottle jack. He then attaches the second magnetic base stand  64  to the center disk  22  near to the point of contact between the disk  22  and the pusher bar  52 . He then positions the flat plate  66  attached to the magnetic base stand  64  so that it contacts and displaces the arm  65  of the dial indicator  62  by approximately 5 mm. The flat plate  66  should be locked in a vertical position perpendicular to the dial indicator arm  62 . 
     The operator should then move the rotating dial  68  of the indicator  62  until the arrow points to the precise value equal to minus or negative one-half of the total runout amount as previously discussed. The operator then makes sure that the bottle jack valve  58  is in the closed position. He attaches a crank handle  59  to the bottle jack  54  and advances the bottle jack piston  57  by repeatedly cycling the crank handle  59 . He continues indexing the piston  57  forward until there is a noticeable displacement registered on the dial indicator  62 . He continues to slowly index the piston  57  until the indicator dial reads 0. At this point the runout of the tire and rim assembly  10  has been compensated for. He notes that if at any time the indicator  62  fails to register movement of the disk  22  for more than three consecutive cycles of the crank handle  59  the system has reached its mechanical limit, i.e., the disk  22  and the outer rim  20  are physically touching. It is important that the operator stop indexing the piston  57  at this point for continued indexing could damage the devices  40 ,  50 . 
     The operator, having zeroed the assembly  10 , can then retighten the threaded fasteners  24  attaching the center disk  22  to the rim  20  starting with the bolts 180° form the contact point between the pusher bar  52  and the center disk opening  26 . The operator should use care that the dial indicator  62  does not register any relative movement during these retightening procedures. He should then remove the two magnetic bases  64  and retighten any bolts  24  that were inaccessible due to the positioning of the stands  64 . The operator then opens the valve  58  on the bottle jack  54  and manually pushes the piston  57  back into the bottle  54 . He removes the bottle jack  54  and holder  55  and center post  51  from its positioning support base  40  and reattaches the tire and rim assembly  10  to the tractor in the same orientation that it was removed from. To do this the operator simply lines up the marks  6  he made and the center disk  22  and the axle  11 . Before tightening the bolts  24 , he lets the weight of the assembly  10  rest on the axle hub  11 . This will position the disk and hub in the same contacting configuration it had prior to correcting the runout. 
     As a precautionary measure, the operator may then wish to place the runout measuring device  30  in contact with the tire  14  to reverify the runout condition after this correction. To do this he simply repeats the steps that were discussed in the procedure for measuring the runout. 
     After the correction, the first harmonic runout should be greatly minimized. It should be noted that not all tires and rim assemblies  10  have perfect first harmonic radial runout conditions and that there may be secondary runout conditions. Nonetheless, the adjustment discussed above will minimize the first harmonic input, thus greatly reducing the amount of vibration that the operator of the vehicle was experiencing. 
     As was noted in the above description, at no time did the operator have to deflate the tire  14  and unseat the tire beads to move the tire relative to the outer rim assembly. Eliminating this procedure saves a tremendous amount of time in correcting the radial runout condition. 
     As shown in FIG. 8, the resultant first harmonic runout on reverification should look as shown in the figure. The rim disk displacement has been compensated for the first harmonic of the tire  14  and rim  20  combination resulting in a much lower amount of radial runout. FIG. 8 is representative of an ideal corrective measure. 
     As shown in FIGS. 9A,  9 B and  9 C, the vertical displacement is illustrated of an exemplary tire and rim assembly. The data for the control tire is shown as the first bar from left to right and its vertical displacement is given at varying pressures ranging from 1.66 bars to 0.55 bars. The second bar (without cross-hatching in the middle) shows the radial first harmonic being calculated in an alternative less preferred method and then being corrected according to the invention. The runout was measured at each lug  72  and then compiled in a computer algorithm to locate and calculate the radial first harmonic displacement. The displacement was corrected using the data and the inventive corrective method of shifting the disk relative to the rim and tire. The third bar farthest right graphically represents a correction whereby the tire and rim assembly was corrected for the measured radial runout using the simplified inventive procedure. As shown in FIGS. 9A,  9 B and  9 C at all inflation pressures the two corrective procedures are approximately the same. As shown in FIG. 9C, the vertical displacement is very severe at the 42 km/h (26 mph) speed. 
     From FIGS. 9A,  9 B and  9 C it can be observed that the vertical displacement generally increases with increases in speed and/or decreases in pressure. The vertical displacement will reach a maximum value, as shown in FIG. 9C (0.83 bars) before it drops off sharply. At this point the tractor system is vibrating near its critical frequency. 
     It is believed that as vehicle speeds increase on agricultural type vehicles that it will be necessary that the radial runout first harmonic is minimized. The procedure discussed above provides a relatively simple technique in compensating for the radial runout and has demonstrated to be approximately equal to the much more complicated matched mounting procedures known in the prior art.