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PostPosted: Mon Sep 01, 2014 3:54 pm 
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Joined: Thu Aug 11, 2005 10:45 am
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Location: Ames, IA
Let's start by looking at the definitions for static and dynamic balance as they pertain to tires, then we'll look at what beads can and cannot do, cover a little science, and finish with how beads work. Below are links to 5 sites that offer varying levels of detail to explain static and dynamic tire balance.

Define Static and Dynamic Balance
Bridgestone Truck Tires – Why are there TWO kinds of Balance?
http://www.bridgestonetrucktires.com/us ... doctor.asp
This link contains good information but with red print on a blue background, it is difficult to read. If you click your curser on the site's text and "Select-All" in your browser (with Control-A or Ctrl-A), it is much easier to read while the text is selected. Also, while not documented in the legend, the little blue squares with a white "W" on the tire graphics indicate where the weights are placed—this is helpful in understanding the corresponding text. (Deselect the text to see the weight markers.)

AGCO Corp – Wheel Balance, Shimmy and Vibration
http://www.agcoauto.com/content/news/p2_articleid/110

Road Force Touch – What choices do I have in balancing a wheel?
http://www.gsp9700.com/technical/4202T/6GLOS003.htm

Wikipedia – Tire balance
http://en.wikipedia.org/wiki/Tire_balance

Balance Technology Inc.
http://balancetechnology.com/resources.html
Balance Technology Inc. has great information on the physics involved in all types of balancing available in 2 downloadable PDF documents: Basics of Balancing 101 and 202. The sections in each document for "Static Unbalance" pertain directly to bead balancing.

Bent Wheels and Out of Round Tires
Beads won't help bent wheels and out of round tires. While bent wheels and out of round tires can be corrected for balance—both dynamic and static—they will not roll smooth. A square tire could be balanced but it won't roll smooth. Circles roll smooth. Wheels can be checked for roundness runout with a dial indicator. With the tire removed from the wheel, spin the wheel on a front axle hub and take measurements. I like to see measurements less than .035" for both roundness and wobble on a 16" steel wheel. Out of round tires can be more difficult to measure. Drive a few miles with the tire in question mounted on the front to get it warm. Jack up the front axle and slowly spin the tire. Use a jack stand as an axle-high reference point and use a ruler to find the high and low points of the tread. The tire runout should be less than 3/32" (or about .090). Unfortunately, some tires that are out of round may not show the severity of the defect until reaching highway speeds.

As an alternative to measuring rim and tire runout, a shop with a Hunter Road Force Balancer has the equipment to detect runout/roundness problems. As a troubleshooting tool for out of round tires, the Road Force balancer is a great machine. The idea is to match the tire runout with the wheel runout for the lowest runout match possible on the tire/wheel assembly—before adding rim weights. The challenge is to get the operator to take the time to measure the runout (force in pounds) and break down and remount the tire as many times as necessary to get the best match possible before adding wheel weights. In practice, it really depends on the operator's skill and level of effort applied to solve the problem—the same applies to all operators and balancing equipment.

Hops & Wobbles
Beads will cure hops but not wobbles. For an oversimplified description of what static and dynamic balancing do for a tire/wheel assembly, it all comes down to Hops & Wobbles:

Hops — caused by a heavy spot on a single plane (static imbalance).
Wobbles — caused by the two sides of a tire having differing heavy spots (dynamic imbalance).

Hops are corrected when weight is applied 180 degrees across the plane from the heavy spot. This is static balance and can be measured with a simple bubble balancer. Hops can be corrected with beads.

Wobbles are corrected when weight is applied along 2 planes: the inside rim of the wheel; and the outside rim of the wheel. The most common way to measure for wobbles, or dynamic balance, is with a computer balancer where axis forces are calculated for the inside and outside planes of the wheel. Rim weights are mounted in fixed locations along these two planes. Once corrected with fixed weights, the relative side-to-side balance does not change—at least until tire wear causes a new imbalance.

When beads are used inside a tire, they travel in the circumference center plane of the tire. Because of this, beads are only helpful in achieving a static balance. If beads are used in a tire with bad dynamic balance, the wobble will persist as beads have no ability to correct for a side-to-side imbalance—they just ride along in the center plane, keep the tire in static balance, and have no positive or negative effect on the side-to-side wobble.

After the dynamic balance has been corrected with computer balancing and rim mounted wheel weights (if needed), beads added to the wheel assembly will keep the tire in static balance for the life of the tire. This represents the long-term static balance and the beads prevent the need for additional computer balancing with rim mounted wheel weights. (In practice, I usually start with good tires, skip the computer balancer, put beads in the tires, and go for a test drive. If a tire is manufactured with a slight dynamic imbalance, it is often minor enough so as not to cause a wobble.)

Static Imbalance—Rotational Mass Axis vs. Wheel Axle
Because an object of any shape will rotate around its center of mass, an out of balance tire rolling down the road will have its heavy spot move in a circle the closest to the rotational mass axis while the lightest portion of the tire will circle the farthest away from the rotational mass axis. This, of course, is limited by the vehicle's spring travel and shock absorber dampening the movement.

The problem is that the tire/wheel assembly already has an axis—the axle to which it is mounted at the dimensional center of the tire/wheel assembly. With each axis, the rotational mass axis and the physical axle hub, claiming rotational rights, the tire/wheel assembly will attempt to satisfy both and roll in more of an oval path instead of a circle—it hops instead of rolls. For the tire/wheel assembly to be in balance and roll smooth, the rotational mass axis (which is force derived) must be moved to match the point of the fixed axle axis. This is accomplished with weights to counter-balance the heavy spot on a tire.

Photo 1 — Rotational Mass Axis away from Axle
If a hammer were round like a tire, it would be severely out of balance. For this hammer/tire example, ignore the fact that a hammer is not round. Drawn circles will represent the hammer/tire to make it round.

The gray tape represents the dimensional center and lug nut mounting point for the hammer/tire. The gray arrow points to the vehicle axle/hub to which the hammer/tire is mounted. The gray circle indicates the outline of the hammer/tire rotating on the vehicle's axle.

The blue tape is the mass balance point of the hammer/tire and the blue arrow points to the rotational mass axis. The blue circle indicates the outline of the hammer/tire rotating on the mass axis.

The hammer/tire is shown balanced on the chair at the blue tape. This is the point and axis upon which the hammer/tire will rotate according to its mass. This point is not fixed and can be altered with the addition of balance weights. The gray tape representing the axle/hub is a fix point and cannot change because the hammer/tire is bolted to the vehicle with lug nuts. The objective is to align the blue and gray arrows to balance the hammer/tire. As shown, the distance between the blue and gray arrows indicates that the hammer/tire is out of balance (by a large amount) because the rotational mass axis and the vehicle axle are not at the same point.

Photo 2 — Rotational Mass Axis Matching Axle
When we add weight to balance the hammer/tire, the mass balance point and rotational mass axis (the blue marks) are moved to the center of the hammer/tire. With the blue and gray marks aligned on a point, the hammer/tire is now in balance. The rotational paths are the same, the rotational mass axis and the vehicle axle are the same, and the hammer/tire will now roll smoothly down the road. (Ok, so it's not quite round enough for a smooth ride, but you get the idea.)

How Beads Work
Balancing the tire is a byproduct of the beads trying to escape. (For simplicity, we will recognize centrifugal force.)

Beads will correct for static balance where weight is applied 180 degrees across the plane from the heavy spot on the tire/wheel assembly. Unlike fixed rim mounted weights, beads are loose inside the tire and are free to go wherever the forces take them. As the tire rotates, the beads move around freely until around 20 mph when centrifugal force keeps them at the outer circumference of the tire.

While the beads are held captive inside the tire, they are still trying to escape—outward—away from the axis. Because of this, the beads will travel along the circumference of the tire until they find the longest radius away from the rotational axis—a point 180 degrees across from the heavy spot on the tire.

In the hammer/tire example in Photo 1, the longest radius distance from the rotational mass axis (blue arrow) is to the lightest spot—the end of the hammer handle. In the same photo, the shortest distance from the rotational mass axis (blue arrow) is to the heaviest spot—the head of the hammer. Instead of using another hammer for balance weight, we could use beads. When the hammer/tire rolls up to speed with beads for balance weights, the beads would accumulate at the longest radius (end of hammer handle) and balance the heavy spot (the hammer head.)

Remember that the rotational mass axis is not fixed and will move with a weight shift—as shown in Photo 2 where the blue arrow is in center rather than near the hammer head. If too many beads accumulate at the end of the hammer handle (the longest radius), then the handle will become the heavy spot and the radius will thus be shortened as the rotational mass axis moves toward it. The result of a heavy handle with the beads is that the hammer head will have the longest radius and beads will travel to it. The beads are still just trying to escape by finding the longest radius.

As some of the beads start to travel toward the hammer head, the rotational mass axis will change again and alter the radius lengths. This continues until the rotational mass axis settles to a point whereby all of the radiuses are equal and the beads have nowhere else to go to try to escape the tire. With the beads settled in and the radiuses being equal, the rotational mass axis is aligned with the fixed axle/hub (the dimensional center of the wheel), and . . . this also means that the tire is balanced.

Through the movement of the beads, normalization occurs and the beads settle in with just enough beads to equal the heavy spot located 180 degrees across from the heavy spot in the tire. The remaining beads that are not needed to counter the weight of the heavy spot then neutralize around the circumference of the tire cancelling out each other. The result is a tire assembly that is in static balance.

Once up to speed (around 20 mph when centrifugal force captures the beads), the balancing activities are completed in less than a couple seconds. This will occur whenever the tire gets up to speed—a perfect balance every time.

Chuck Meadows
'99 24RB PSD

Note: The above information was posted for the author by the Website Administrator (bfadmin-2). He can be contacted at the following email address if you have any questions: charles.m.meadows@gmail.com


Attachments:
photo 1 -- rotational mass axis away from axle.jpg
photo 1 -- rotational mass axis away from axle.jpg [ 279.61 KiB | Viewed 3124 times ]
photo 2 -- rotational mass axis matching axle.jpg
photo 2 -- rotational mass axis matching axle.jpg [ 250.5 KiB | Viewed 3124 times ]

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