Motion System Design

Making a U turn

Some mechanical drives require torque be transmitted through an angle. If the angle of misalignment is small — under 3° or so — several coupling types can join the drive and driven shaft. For situations of greater misalignment or where the misalignment varies, universal joints are often the most suitable choice.

First, let's review some definitions. Universal joints are appropriate for applications involving angular misalignment — where the shaft centerlines intersect at an angle. They can also be used where there is axial displacement between the shafts — a lateral displacement. In these situations, the U-joint must accommodate resulting movement in one of the shafts. As the drive shaft turns, rotational vectors are redirected by the U joint to turn the driven shaft. The greater the misalignment, the smaller the resulting vector. (Then wear surfaces must bear the other unusable load.)

There is another kind of misalignment. Sometimes shafts have parallel misalignment — where driving and driven shafts lie in the same plane, but are displaced from each other. These can be connected by a double U joint or by two single U joints. When double joints are used, the pins of each must lie in the same plane. This way, one joint corrects for the rotational error of the other, and near-constant velocity is achieved.

U-joint physics

Conventional U joints are not constant-velocity devices; load and velocity accelerate and decelerate sinusoidally with each cycle. The greater the misalignment, the greater this velocity fluctuation with each rotation. For instance, with 10° of misalignment velocity varies about 3% or so. With 20° of misalignment, a 13% speed variation is average. Also, because torsional vibration is created by accelerating and decelerating the cyclical load, high angles of misalignment must be turned at low speeds only. It's not uncommon for U joints to operate for years at a misalignment of 15° — five times greater than typical flexible-coupling capabilities. At lower speeds, some even handle misalignment to 35° or higher. Occasionally, double U joints even make torque go around a corner, to 70° of total misalignment.

Estimating size

The first step in estimating a U joint's size is to determine the maximum angle of misalignment the joint will experience. One drawback of block-and-pin U joints is that this design is not suited to high-speed applications, so a speed-angle limit (speed multiplied by misalignment angle) of 15,000 applies. This means two shafts with a misalignment of 10° must not exceed a rotating speed of 1,500 rpm; with a 25° angle, speed must not exceed 600 rpm. However, their extreme utility is essential in everything from mobile-equipment steering columns to commercial washing machines.

The misalignment angle should be multiplied by speed for a use factor to estimate how much fatiguing the joint will undergo. Using this factor, another use factor should be calculated according to:

0 to 3,000 10
3,001 to 9,000 20
9,001 to 15,000 40

The next step after determining the use factor is to calculate the input load. The input load should be calculated according to

Input load = 63,000 3 hp / rpm

Lastly, multiply the use factor times the input load and use that value to select a u-joint from the table with a static torque rating equal to or greater than the value derived.

To illustrate, let's assume a 15° operating angle and speed of 300 rpm. This works out to a use factor of 20 because 15 × 300 = 4,500 speed/angle factor. Given 5 hp and the 300 rpm, the input load works out to 1,050 lb-in. This multiplied by the use factor of 20 yields the static torque carrying capacity of 21,000 lb-in. Then, according to the selection table (found on page 38) the appropriate U joint for this application has an outer diameter of 2 in.

Some options

Block-and-pin joints have excellent torque capacity and tolerance for overloads and vibration. Some designs have both a small and large bearing pin; in these units, the small pin goes through (or intersects) the middle of the large pin. The small bearing pin is sometimes carburized and case hardened for both ductility and wear. Under excessive loads, it shears and breaks with no damage to more costly component parts. Newer disassembling designs enable users to take standard off-the-shelf universal joints and machine them to their individual requirements. This disassembly feature also facilitates replacement of worn component parts, literally in a couple of minutes.

Wear is reduced by the use of dissimilar materials. For example, the yokes on an alloy steel universal joint might be made of 4140 grade steel with induction-hardened ears, while the bearing pins are 8620 alloy. For corrosion-prone environments (as in food processing and marine applications) joints of 303, 304, and 316-grade stainless steel are appropriate. Naval bronze, nickel-aluminum bronze, and nickel copper (400 and 500 series monel) alloys materials are also suitable. In addition, protective covers in PVC, neoprene, and silicone rubber boots can seal in lubrication, reducing wear for applications that are required to run for extended periods of time. They also seal out debris in harsh environments, thereby increasing joint life by protecting the joint's bearing area of from harmful contamination.

Here we've focused on pin-and-block U joints. However, another style exists: the cross-type fitted with needle bearings. Pin-and-block types are more versatile because they occupy less physical space — often not much larger in diameter than the shafts they connect. They also carry greater load, and are no more complicated to attach than a gear or sheave, using set screws, keyways, or locking pins. For this reason, they are used in equipment where space is restricted, such as canning and bottling machines or pin spotters in bowling alleys. Unlike cross types, they have little tendency to freeze with rust when lubricant runs out of needle bearings, and for this reason are commonly specified for applications where maintenance is minimal. In a few cases, these joints are used where lubrication cannot be used due to high ambient temperatures; flue dampers and glass-manufacturing equipment are a couple examples.

U-joint applications

The torque capacity of pin-and-block U joints ranges from 140 lb-in. for small articulating drives to almost 131,000 lb-in. for those used on steel roll levelers, for example. They are appropriate for applications requiring enduser modifications, minimal maintenance, compact design, and ease of installation and part replacement. U joints are also appropriate in hot, abrasive, and corrosive conditions in marine, washdown, and petrochemical environments where moderate speed (inversely related to angle of misalignment) and occasional overloads are probable. These situations are often found in marine and sea-water applications, power-generating applications, certain food-processing machinery, and paper-making equipment.

Selection table
140 425 900 1,610 1,800 3,050 3,500 5,500 9,000 14,000 22,000 32,000 55,000 131,000

1,200 2,000 3,200 4,600 5,600 6,000 8,800 14,000 18,000 25,000 35,000

3/8 1/2 5/8 3/4 7/8 1 1-1/8 1-1/4 1-1/2 1-3/4 2 2-1/2 3 4

3/16 1/4 5/16 3/8 7/16 1/2 9/16 5/8 3/4 7/8 1 1-1/4 1-1/2 2

1-3/4 2 2-1/4 2-11/16 3 3-3/8 3-1/2 3-3/4 4-1/4 5 5-7/16 7 9 10-5/8

11/16 3/4 13/16 31/32 1-1/32 1-3/16 1-7/32 1-1/4 1-11/32 1-9/16 1-5/8 2-3/32 2-27/32 3-1/8

3/8 1/2 5/8 3/4 15/16 1 1 1-1/4 1-9/16 1-7/8 2-3/16 2-13/16 3-5/16 4-3/8

Highlighted is the most appropriate joint for a 15° operating angle running at 300 rpm.
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