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Universal Joint Maximum Minimum Speed

Power Transmission and Technology

The Universal Joint. - This form of coupling, originally known as a Cardan or Hooke's coupling, is used for connecting two shafts the axes of which are not in line with each other, but which merely intersect at a point. There are many different designs of universal joints or couplings, which are based on the principle embodied in the original design. One well known type is shown by the accompanying diagram.

As a rule, a universal joint does not work well if the angle α (see illustration) is more than 45 degrees, and the angle should preferably be limited to about 20 degrees or 25 degrees, excepting when the speed of rotation is slow and little power is transmitted.

Universal Joint

Variation in Angular Velocity of Driven Shaft: Owing to the angularity between two shafts connected by a universal joint, there is a variation in the angular velocity of one shaft during a single revolution, and because of this, the use of universal couplings is sometimes prohibited. Thus, the angular velocity of the driven shaft will not be the same at all points of the revolution as the angular velocity of the driving shaft. In other words, if the driving shaft moves with a uniform motion, then the driven shaft will have a variable motion and, therefore, the universal joint should not be used when absolute uniformity of motion is essential for the driven shaft.

Determining Maximum and Minimum Velocities:

If shaft A (see diagram) runs at a constant speed, shaft B revolves at maximum speed when shaft A occupies the position shown in the illustration, and the minimum speed of shaft B occurs when the fork of the driving shaft A has turned 90 degrees from the position illustrated.

The maximum speed of the driven shaft may be obtained by multiplying the speed of the driving shaft by the secant of angle α. The minimum speed of the driven shaft equals the speed of the driver multiplied by cosine α. Thus, if the driver rotates at a constant speed of 100 revolutions per minute and the shaft angle is 25 degrees, the maximum speed of the driven shaft is at a rate equal to 1. × 100 = 110.34 rpm. The minimum speed rate equals 0. × 100 = 90.63; hence, the extreme variation equals 110.34 &#; 90.63 = 19.71 rpm.

maximum speed of the driven shaft

Smax = S1 · ( 1 / cosα )

Minimum speed of the driven shaft

Smax = S1 · cosα

Related:

Truck and Car Universal Joint Design and Engineering Equation

References:

Machinery's 30th edition

How does a universal joint work?

The invention of universal joints dates back many centuries. Even though the universal joint&#;s mechanism seems simple, the physics behind this mechanism are rather complicated and interesting. In most of the literature, readers who are trying to understand the physics behind universal joints are bombarded with complex mathematical relationships. In this article we will understand the working of universal joints in a simple yet logical manner.

Why universal joints are used?

Universal joints also known as Hooke&#;s joints are commonly used to transfer mechanical power between 2 shafts when their axes are at an angle to each other. The way power is transmitted in a rear wheel drive, vehicle might have got your attention. They use universal joints. As you can see in the Fig 1, two universal joints are required to transmit power from the engine to differential.

Fig 1 : Use of universal joint

The basic parts

The universal joint has 3 basic parts, two yokes and a cross(refer Fig 2). The yokes are connected through a cross as shown in below image. With this arrangement, the output shaft can be turned to a wide range of angles. Now, let&#;s consider different power transmitting scenarios.

Fig 2 : The basic parts of universal joint

The shafts connected straight

In this case, the input and output shaft are connected in a straight line(refer Fig 3). Motion is really simple. The input shaft will turn the cross, and the cross will turn the output shaft. It is clear that both the input and output shafts will turn at the same speed.

If you are looking for more details, kindly visit Differences between single, double and telescopic joints.

Fig 3 : Universal joint under a straight motion

The shafts are at an angle

Now, let&#;s see what happens if the axes are at an angle. Assume that the input shaft is moving at a constant speed.

The spin of the cross

When the shafts are at an angle the motion is quite different. To understand why, just note the behavior of the red and green ends of the cross. You can see that the green ends, which are connected to the input shaft, turn along a vertical plane, while the red ends, which are connected to the output shaft, have to move along a different plane(refer Fig 4). To make the red ends move along the inclined plane, the cross has to spin along the axis connecting the green ends. If you observe the mark on the cross, you can see this phenomenon in Fig 5. To make the cross spin concept clearer, just imagine what happens when the spin of the green axis is halted. Such a hypothetical motion is depicted in the Fig 5.

Fig 4 : The shaft connecting the green ends should rotate

Fig 5 : hypothetical movement to illustrate the need of cross spin

It is clear that, such a situation is impossible. This means without this spin, the motion of the inclined hook joint is impossible.

The effect of cross spin

The spin of the cross makes a huge difference in the speed of the output shaft. The cross has 2 kinds of motion : rotation and spin. It is clear that, when the cross is spinning as well as rotating, the velocity of the output shaft will have an added effect. You can see here that, for the first 90 degrees of the input shaft rotation, the green axis spins to its maximum angle(refer Fig 6). The forward spin aids and changes the output shaft rotation as shown in the graph. The output angle will get an added effect during this period (refer Fig 7).

Fig 6 : Forward spin of the shaft during the first 90 degrees

Fig 7 : Angular displacement of the output shaft during the first 90 degrees

But for the next 90 degrees, it should spin back to the initial zero position. The reverse spin will have an opposite effect on the output shaft rotation. So the motion of the output shaft will look as shown in the Fig 8. Just by taking a simple time differential of this displacement graph we can find out speed of the output shaft. This is shown in the following graph of Fig 9.

Fig 8 : Angular displacement of the output shaft during 180 degrees turn

Fig 9 : Variation of output shaft speed with angle

It is clear that, the output shaft has a fluctuating speed. More the angle between the shafts more will be the speed fluctuation.

Double universal joint

This means, the universal joint is not a constant velocity joint. This jerky rotation makes the universal joint useless in its original form. But you can make it a constant velocity joint by incorporating one more joint, as shown. If a constant velocity input gives fluctuating output, a fluctuating input will give a constant velocity output. Thus, the double universal joint acts as a constant velocity joint. You can see a similar arrangement in rear wheel driven automobiles (refer Fig 10). You can see that the drive shaft is fitted between two universal joints. So the speed output at the second universal joint will be same as the input.

Fig 10 : Use of double university joint in eliminating jerky motion

Constant velocity joints

The double universal joint described in the constant velocity joint. However more efficient constant velocity joint designs, they do not require an intermediate shaft have evolved over time. Some of the popular constant velocity joints are listed below.

• Tracta joints

• Rzeppa joints

• Weiss joints

• Tripod joints

• Coupling

That's all in this article. I hope you have learned how universal joints works.

Thanks for reading!

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