What is the mechanism of the Cardan shaft?

Introduction

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Hey there! Today, lets get to know about Industrial Cardan Shafts. What is it, you may ask? Well, it is a type of mechanical power transmission system that transmits torque and rotational power from the engine to different parts of industrial machinery. Sounds technical, doesnt it? But dont worry, well break it down for you.

First things first, lets talk about the applications of Industrial Cardan Shafts. They are widely used in various industries such as steel manufacturing, paper mills, cement plants, and even in large ships. They play a crucial role in transmitting power to the equipment while also accommodating misalignments between the driving and driven components.

Now, lets talk about the design and construction of Industrial Cardan Shafts. They are made up of u-joints, shafts, and slip yokes, all of which are designed to withstand high levels of torque and rotation. The construction of these shafts is vital to their performance, allowing them to withstand the harsh industrial environment and operate efficiently.

In summary, the Industrial Cardan Shaft is an essential component in various industrial sectors. Its design and construction are critical to its performance in transmitting torque and rotational power from the engine to necessary equipment.

Working Principle

You might not know what a cardan shaft is, but chances are youve seen its effects. You know that spastic movement of the exhaust pipe of a large truck or a ships propeller. Thats due to the mechanism of torque and speed transmission of an industrial cardan shaft. How does it work, you ask?

Well, the answer lies in the humble u-joint. These u-shaped joints connect two rods in an offset manner, allowing for a greater degree of torque transfer and a greater angle of movement. In industrial cardan shafts, this mechanism is accomplished by two different u-joints positioned at opposite ends, allowing the shaft to transmit torque and speed at different angles. But there is a catch- misalignment can cause cracking and failure in the shaft.

Thus, the mechanism of industrial cardan shafts is simple yet effective. A shaft that can transmit power at different angles. Industrial cardan shafts now come in all shapes and sizes, from single to double u-joint shafts, telescopic shafts and slip yoke shafts.

But wait, theres more! The material and design of the shaft also play a crucial role in selection criteria. Speed limitations, torque and power ratings, and environmental factors also need to be taken into account. In the installation and maintenance phase, proper alignment procedures, lubrication requirements, and preventive maintenance practices ensure a long service life.

So, now you know how a simple u-joint has revolutionized the movement of heavy machinery. Imagine, all this from just a humble u-joint.

Types of Industrial Cardan Shafts

Lets talk about the different types of Industrial Cardan Shafts!

First up, we have the Single u-joint shafts simple and easy to use, but not great for high torques.

Next, we have the Double u-joint shafts perfect for transmitting torque and rotational force in high-speed applications.

Moving on to Telescopic shafts great for applications that require variable distance between shafts, but can be a bit more complex to install.

Lastly, we have Slip yoke shafts great for machines with limited space, but not ideal for long-distance transmission.

So, depending on the torque, speed and operational environment factors, each type of shaft has its own advantages and disadvantages.

But lets be honest, we all have that one favorite type of Industrial Cardan Shaft, dont we?

Selection Criteria

So, youve decided to take a deep dive into the fundamentals of industrial cardan shafts. Good for you! Now, lets move on to the tricky part- selecting the right cardan shaft for your application.

One of the most important factors to consider while selecting an industrial cardan shaft is torque and power ratings. These ratings determine the amount of power the shaft can efficiently transmit without suffering damage. So, its crucial to ensure that the cardan shaft you choose has a high enough torque and power rating to handle your applications power requirements.

Another key factor to consider is speed limitations. Every cardan shaft has a maximum speed limit beyond which the shafts bearings cant handle the load, causing them to fail. So, before selecting your shaft, check what the maximum operational speeds are in your application and select a cardan shaft with a suitable speed rating.

Misalignment acceptance is another factor that deserves attention while selecting an industrial cardan shaft. Misalignment can cause excessive vibration, leading to early wear and tear. Thats why its important to choose a cardan shaft with a high misalignment acceptance rating.

Finally, your operational environment factors can affect the performance of your cardan shaft. Factors like temperature, corrosive fluids, and shock loads can severely impact your cardan shafts life and performance. Thats why its essential to select a cardan shaft that is suitable for your operational environment, ensuring a long, healthy life for your shaft.

Installation and Maintenance

So now that we know what Industrial Cardan Shafts are, lets talk about how to install and maintain them to ensure their longevity.

Proper alignment procedures are crucial in the installation of Industrial Cardan Shafts. Any sort of misalignment can cause excessive vibration and lead to premature wear and tear. Therefore, its essential to align the shafts perfectly to ensure optimal performance.

Moving on to lubrication requirements, Industrial Cardan Shafts need to be lubricated frequently to avoid overheating and breakdowns. Over lubrication can harm as much as under-lubrication, so its essential to follow the manufacturers instructions on lubrication.

Inspection techniques for wear and damage are also critical in maintaining Industrial Cardan Shafts. Regular inspections help to prevent failure and ensure the highest levels of productivity. If you notice any issues, its essential to address and repair them quickly to prevent further damage.

Lastly, preventive maintenance practices should be performed regularly. The frequency of these preventive maintenance practices should match the intensity of usage. These practices include removing dirt accumulation, scheduled maintenance, and repairs.

A proactive approach towards Industrial Cardan Shaft maintenance is critical to ensuring optimal performance, help extend its service life, and maintaining safety on the worksite.

Advancements in Industrial Cardan Shafts

Lets talk about the future of industrial cardan shafts! With the rapid advancements in technology, traditional cardan shafts are getting smarter and better. Incorporation of smart technology in cardan shafts has made them capable of monitoring temperature, vibration, and alignment in real-time. This real-time data can be used to prevent potential failures and downtime.

Additionally, the materials and manufacturing processes continue to improve. Advanced materials such as composite materials and carbon fiber are being used to make cardan shafts lighter and more durable. Manufacturing processes like 3D printing and precision machining are producing cardan shaft components with better tolerances and accuracy.

So, the future of industrial cardan shafts is looking promising. The integration of smart technology and enhanced materials and manufacturing processes are making them more efficient, durable, and reliable. Its exciting to see where this technology will take us in the future.

Conclusion

In summary, industrial cardan shafts are vital parts of various machinery across multiple industries such as automobile, aerospace, and construction, among others. They provide the required torque and speed while transferring power from the source to the driven machine parts. Choosing the right type of industrial cardan shafts depends mainly on operational conditions and key specifications such as torque, speed ratings, and environment, among others. Regular maintenance is a must to ensure safety, reduced downtime, and extended life. New technological advancements aim to improve the performance, reliability, and durability of industrial cardan shafts.

Mechanism with bendable rotation axis

"U-joint" redirects here. For the plumbing fixture, see U-bend

A universal joint

A universal joint (also called a universal coupling or U-joint) is a joint or coupling connecting rigid shafts whose axes are inclined to each other. It is commonly used in shafts that transmit rotary motion. It consists of a pair of hinges located close together, oriented at 90° to each other, connected by a cross shaft. The universal joint is not a constant-velocity joint.[1]

U-joints are also sometimes called by various eponymous names, as follows:

• Cardan joint, after Gerolamo Cardano, a polymath of the 16th century who contributed to knowledge of various clever mechanisms, including gimbals
• Hooke joint or Hooke's joint, after Robert Hooke, a polymath of the 17th century who contributed to knowledge of various clever mechanisms
• Spicer joint, after Clarence W. Spicer and the Spicer Manufacturing Company, who manufactured U joints
• Hardy Spicer joint, after the Hardy Spicer brand, a successor to the Spicer brand

History

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This video shows different parts and operation of the universal shaft. Spicer universal joints for motor cars, .

The main concept of the universal joint is based on the design of gimbals, which have been in use since antiquity. One anticipation of the universal joint was its use by the ancient Greeks on ballistae.[2] In Europe the universal joint is often called the Cardano joint (and a drive shaft that uses the joints, a Cardan shaft), after the 16th century Italian mathematician, Gerolamo Cardano, who was an early writer on gimbals, although his writings mentioned only gimbal mountings, not universal joints.[3]

The mechanism was later described in Technica curiosa sive mirabilia artis () by Gaspar Schott, who mistakenly claimed that it was a constant-velocity joint.[4][5][6] Shortly afterward, between and , Robert Hooke analysed the joint and found that its speed of rotation was nonuniform, but that property could be used to track the motion of the shadow on the face of a sundial.[4] In fact, the component of the equation of time which accounts for the tilt of the equatorial plane relative to the ecliptic is entirely analogous to the mathematical description of the universal joint. The first recorded use of the term 'universal joint' for this device was by Hooke in , in his book Helioscopes.[7][8][9] He published a description in ,[10] resulting in the use of the term Hooke's joint in the English-speaking world. In , Hooke proposed a solution to the nonuniform rotary speed of the universal joint: a pair of Hooke's joints 90° out of phase at either end of an intermediate shaft, an arrangement that is now known as a type of constant-velocity joint.[4][11] Christopher Polhem of Sweden later re-invented the universal joint, giving rise to the name Polhemsknut ("Polhem knot") in Swedish.

In , the English scientist Robert Willis analyzed the motion of the universal joint.[12] By , the French engineer and mathematician Jean-Victor Poncelet had analyzed the movement of the universal joint using spherical trigonometry.[13]

The term universal joint was used in the 18th century[10] and was in common use in the 19th century. Edmund Morewood's patent for a metal coating machine called for a universal joint, by that name, to accommodate small alignment errors between the engine and rolling mill shafts.[14] Ephriam Shay's locomotive patent of , for example, used double universal joints in the locomotive's drive shaft.[15] Charles Amidon used a much smaller universal joint in his bit-brace patented .[16] Beauchamp Tower's spherical, rotary, high speed steam engine used an adaptation of the universal joint c..[17]

The term 'Cardan joint' appears to be a latecomer to the English language. Many early uses in the 19th century appear in translations from French or are strongly influenced by French usage. Examples include an report on the Exposition Universelle of [18] and an article on the dynamometer translated from French in .[19]

In the 20th century, Clarence W. Spicer and the Spicer Manufacturing Company, as well as the Hardy Spicer successor brand, helped further popularize universal joints in the automotive, farm equipment, heavy equipment, and industrial machinery industries.

Equation of motion

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Diagram of variables for the universal joint. Axle 1 is perpendicular to the red plane and axle 2 is perpendicular to the blue plane at all times. These planes are at an angle β with respect to each other. The angular displacement (rotational position) of each axle is given by

γ 1 {\displaystyle \gamma _{1}}

γ 2 {\displaystyle \gamma _{2}}

Goto Jundi to know more.

x ^ 1 {\displaystyle {\hat {x}}_{1}}

x ^ 2 {\displaystyle {\hat {x}}_{2}}

x ^ 1 {\displaystyle {\hat {x}}_{1}}

x ^ 2 {\displaystyle {\hat {x}}_{2}}

A sample universal joint colour-coded to the diagrams about the equation of motion. The red and blue planes are visible.

ω 2 {\displaystyle \omega _{2}\,}

γ 1 {\displaystyle \gamma _{1}\,}

β {\displaystyle \beta \,}

Angular (rotational) output shaft speedversus rotation anglefor different bend anglesof the joint

γ 2 {\displaystyle \gamma _{2}\,}

γ 1 {\displaystyle \gamma _{1}\,}

β {\displaystyle \beta \,}

Output shaft rotation angle,versus input shaft rotation anglefor different bend anglesof the joint

The Cardan joint suffers from one major problem: even when the input drive shaft axle rotates at a constant speed, the output drive shaft axle rotates at a variable speed, thus causing vibration and wear. The variation in the speed of the driven shaft depends on the configuration of the joint, which is specified by three variables:

1. γ 1 {\displaystyle \gamma _{1}}

2. γ 2 {\displaystyle \gamma _{2}}

3. β {\displaystyle \beta }

These variables are illustrated in the diagram on the right. Also shown are a set of fixed coordinate axes with unit vectors x ^ {\displaystyle {\hat {\mathbf {x} }}} and y ^ {\displaystyle {\hat {\mathbf {y} }}} and the planes of rotation of each axle. These planes of rotation are perpendicular to the axes of rotation and do not move as the axles rotate. The two axles are joined by a gimbal which is not shown. However, axle 1 attaches to the gimbal at the red points on the red plane of rotation in the diagram, and axle 2 attaches at the blue points on the blue plane. Coordinate systems fixed with respect to the rotating axles are defined as having their x-axis unit vectors ( x ^ 1 {\displaystyle {\hat {\mathbf {x} }}_{1}} and x ^ 2 {\displaystyle {\hat {\mathbf {x} }}_{2}} ) pointing from the origin towards one of the connection points. As shown in the diagram, x ^ 1 {\displaystyle {\hat {\mathbf {x} }}_{1}} is at angle γ 1 {\displaystyle \gamma _{1}} with respect to its beginning position along the x axis and x ^ 2 {\displaystyle {\hat {\mathbf {x} }}_{2}} is at angle γ 2 {\displaystyle \gamma _{2}} with respect to its beginning position along the y axis.

x ^ 1 {\displaystyle {\hat {\mathbf {x} }}_{1}} is confined to the "red plane" in the diagram and is related to γ 1 {\displaystyle \gamma _{1}} by:

x ^ 1 = [ cos γ 1 , sin γ 1 , 0 ] {\displaystyle {\hat {\mathbf {x} }}_{1}=\left[\cos \gamma _{1}\,,\,\sin \gamma _{1}\,,\,0\right]}

x ^ 2 {\displaystyle {\hat {\mathbf {x} }}_{2}} is confined to the "blue plane" in the diagram and is the result of the unit vector on the x axis x ^ = [ 1 , 0 , 0 ] {\displaystyle {\hat {x}}=[1,0,0]} being rotated through Euler angles [ π / 2 , β , γ 2 {\displaystyle [\pi \!/2\,,\,\beta \,,\,\gamma _{2}} ]:

x ^ 2 = [ cos β sin γ 2 , cos γ 2 , sin β sin γ 2 ] {\displaystyle {\hat {\mathbf {x} }}_{2}=\left[-\cos \beta \sin \gamma _{2}\,,\,\cos \gamma _{2}\,,\,\sin \beta \sin \gamma _{2}\right]}

A constraint on the x ^ 1 {\displaystyle {\hat {\mathbf {x} }}_{1}} and x ^ 2 {\displaystyle {\hat {\mathbf {x} }}_{2}} vectors is that since they are fixed in the gimbal, they must remain at right angles to each other. This is so when their dot product equals zero:

x ^ 1 x ^ 2 = 0 {\displaystyle {\hat {\mathbf {x} }}_{1}\cdot {\hat {\mathbf {x} }}_{2}=0}

Thus the equation of motion relating the two angular positions is given by:

tan γ 1 = cos β tan γ 2 {\displaystyle \tan \gamma _{1}=\cos \beta \tan \gamma _{2}\,}

with a formal solution for γ 2 {\displaystyle \gamma _{2}} :

γ 2 = tan 1 [ tan γ 1 sec β ] {\displaystyle \gamma _{2}=\tan ^{-1}\left[\tan \gamma _{1}\sec \beta \right]\,}

The solution for γ 2 {\displaystyle \gamma _{2}} is not unique since the arctangent function is multivalued, however it is required that the solution for γ 2 {\displaystyle \gamma _{2}} be continuous over the angles of interest. For example, the following explicit solution using the atan2(y, x) function will be valid for π < γ 1 < π {\displaystyle -\pi <\gamma _{1}<\pi } :

γ 2 = atan2 ( sin γ 1 , cos β cos γ 1 ) {\displaystyle \gamma _{2}=\operatorname {atan2} \left(\sin \gamma _{1},\cos \beta \,\cos \gamma _{1}\right)}

The angles γ 1 {\displaystyle \gamma _{1}} and γ 2 {\displaystyle \gamma _{2}} in a rotating joint will be functions of time. Differentiating the equation of motion with respect to time and using the equation of motion itself to eliminate a variable yields the relationship between the angular velocities ω 1 = d γ 1 / d t {\displaystyle \omega _{1}=d\gamma _{1}/dt} and ω 2 = d γ 2 / d t {\displaystyle \omega _{2}=d\gamma _{2}/dt} :

ω 2 = ω 1 ( cos β 1 sin 2 β cos 2 γ 1 ) {\displaystyle \omega _{2}=\omega _{1}\left({\frac {\cos \beta }{1-\sin ^{2}\beta \,\cos ^{2}\gamma _{1}}}\right)}

As shown in the plots, the angular velocities are not linearly related, but rather are periodic with a period half that of the rotating shafts. The angular velocity equation can again be differentiated to get the relation between the angular accelerations a 1 {\displaystyle a_{1}} and a 2 {\displaystyle a_{2}} :

a 2 = a 1 cos β 1 sin 2 β cos 2 γ 1 ω 1 2 cos β sin 2 β sin 2 γ 1 ( 1 sin 2 β cos 2 γ 1 ) 2 {\displaystyle a_{2}={\frac {a_{1}\cos \beta }{1-\sin ^{2}\beta \,\cos ^{2}\gamma _{1}}}-{\frac {\omega _{1}^{2}\cos \beta \,\sin ^{2}\beta \,\sin 2\gamma _{1}}{\left(1-\sin ^{2}\beta \,\cos ^{2}\gamma _{1}\right)^{2}}}}

Double Cardan shaft

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Universal joints in a driveshaft

A configuration known as a double Cardan joint drive shaft partially overcomes the problem of jerky rotation. This configuration uses two U-joints joined by an intermediate shaft, with the second U-joint phased in relation to the first U-joint to cancel the changing angular velocity. In this configuration, the angular velocity of the driven shaft will match that of the driving shaft, provided that both the driving shaft and the driven shaft are at equal angles with respect to the intermediate shaft (but not necessarily in the same plane) and that the two universal joints are 90 degrees out of phase. This assembly is commonly employed in rear wheel drive vehicles, where it is known as a drive shaft or propeller (prop) shaft.

Even when the driving and driven shafts are at equal angles with respect to the intermediate shaft, if these angles are greater than zero, oscillating moments are applied to the three shafts as they rotate. These tend to bend them in a direction perpendicular to the common plane of the shafts. This applies forces to the support bearings and can cause "launch shudder" in rear wheel drive vehicles.[20] The intermediate shaft will also have a sinusoidal component to its angular velocity, which contributes to vibration and stresses.

Mathematically, this can be shown as follows: If γ 1 {\displaystyle \gamma _{1}\,} and γ 2 {\displaystyle \gamma _{2}\,} are the angles for the input and output of the universal joint connecting the drive and the intermediate shafts respectively, and γ 3 {\displaystyle \gamma _{3}\,} and γ 4 {\displaystyle \gamma _{4}\,} are the angles for the input and output of the universal joint connecting the intermediate and the output shafts respectively, and each pair are at angle β {\displaystyle \beta \,} with respect to each other, then:

tan γ 2 = cos β tan γ 1 tan γ 4 = cos β tan γ 3 {\displaystyle \tan \gamma _{2}=\cos \beta \,\tan \gamma _{1}\qquad \tan \gamma _{4}=\cos \beta \,\tan \gamma _{3}}

If the second universal joint is rotated 90 degrees with respect to the first, then γ 3 = γ 2 + π / 2 {\displaystyle \gamma _{3}=\gamma _{2}+\pi /2} . Using the fact that tan ( γ + π / 2 ) = 1 / tan γ {\displaystyle \tan(\gamma +\pi /2)=1/\tan \gamma } yields:

tan γ 4 = cos β tan γ 2 = 1 tan γ 1 = tan ( γ 1 + π 2 ) {\displaystyle \tan \gamma _{4}={\frac {\cos \beta }{\tan \gamma _{2}}}={\frac {1}{\tan \gamma _{1}}}=\tan \left(\gamma _{1}+{\frac {\pi }{2}}\right)\,}

and it is seen that the output drive is just 90 degrees out of phase with the input shaft, yielding a constant-velocity drive.

NOTE: The reference for measuring angles of input and output shafts of universal joint are mutually perpendicular axes. So, in absolute sense the forks of the intermediate shaft are parallel to each other. (Since, one fork is acting as input and the other fork is acting as output for shafts and above 90 degree phase difference is mentioned between the forks.)

Double Cardan joint

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A double Cardan joint consists of two universal joints mounted back to back with a centre yoke; the centre yoke replaces the intermediate shaft. Provided that the angle between the input shaft and centre yoke is equal to the angle between the centre yoke and the output shaft, the second Cardan joint will cancel the velocity errors introduced by the first Cardan joint and the aligned double Cardan joint will act as a CV joint.

Thompson coupling

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A Thompson coupling is a refined version of the double Cardan joint. It offers slightly increased efficiency with the penalty of great increase in complexity.

See also

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Notes

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References

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• Theory of Machines 3 from National University of Ireland

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