Short Answer:
A compound cylinder is a type of thick-walled cylinder made by shrinking one cylinder over another to form a single unit capable of withstanding high internal pressures. It is also called a built-up cylinder. The main purpose of a compound cylinder is to reduce the maximum hoop stress developed in the inner cylinder when subjected to internal pressure.
By using two or more concentric cylinders, the load is shared between them, resulting in a more uniform stress distribution. Compound cylinders are commonly used in gun barrels, high-pressure pipes, and hydraulic systems, where very high internal pressures are encountered.
Detailed Explanation:
Compound Cylinder
A compound cylinder (also known as a built-up cylinder) is a thick-walled pressure vessel formed by combining two or more cylinders—one placed inside another—so that they act together to resist internal pressure.
This design is used when a single thick cylinder would experience excessive stresses, or when it becomes uneconomical to make a very thick single piece. The compound cylinder improves the strength, durability, and safety of high-pressure vessels by reducing the maximum hoop stress that occurs at the inner surface.
The basic principle of a compound cylinder is to pre-stress the inner cylinder by applying compressive stress before the internal pressure acts. When pressure is applied, both cylinders share the stresses more evenly, preventing the inner cylinder from being overstressed.
Construction of Compound Cylinder
A compound cylinder is constructed by shrinking an outer cylinder onto an inner cylinder. The process involves the following steps:
- The inner cylinder is manufactured slightly smaller in outer diameter compared to the inner diameter of the outer cylinder.
- The outer cylinder is heated so that it expands, and then it is fitted over the inner cylinder.
- As the outer cylinder cools, it contracts and grips the inner cylinder tightly.
This creates an interference fit, generating compressive stress in the inner cylinder and tensile stress in the outer cylinder even before any internal pressure is applied. This pre-stressing helps distribute the load more evenly when the cylinder is later subjected to internal pressure.
Stresses in a Compound Cylinder
In a compound cylinder, three types of stresses are developed:
- Initial stresses (shrinkage stresses):
These are developed due to the shrinkage (interference fit) between the two cylinders before applying any internal pressure.- The inner cylinder experiences compressive hoop stress.
- The outer cylinder experiences tensile hoop stress.
- Stresses due to internal pressure:
When the internal pressure is applied, it causes the usual stresses:- Hoop stress (circumferential stress)
- Radial stress
- Final stresses:
The final stresses are the algebraic sum of the initial (shrinkage) stresses and the stresses due to internal pressure.
Analysis of Compound Cylinder
Let:
- = internal radius of the inner cylinder
- = common radius (contact surface between cylinders)
- = external radius of the outer cylinder
- = internal pressure (inside the inner cylinder)
- = pressure at the common surface (between cylinders)
- = external pressure (usually 0 for open cylinders)
Before Applying Internal Pressure
Before internal pressure is applied, the outer cylinder is shrunk onto the inner cylinder. This creates a radial pressure at the junction surface equal to .
- On the inner cylinder, this pressure acts externally.
- On the outer cylinder, it acts internally.
The stress distribution in each cylinder before applying internal pressure can be found using Lame’s equations:
where and are constants determined from the boundary conditions for each cylinder.
After Applying Internal Pressure
When internal pressure is applied, additional stresses are produced. The resulting radial pressure at the junction changes from the initial value. The final stresses in the two cylinders are obtained by superimposing:
- The shrinkage (initial) stresses, and
- The stresses due to internal pressure.
The design is optimized so that both cylinders have equal maximum hoop stress, which ensures that the material is used efficiently and safely.
Advantages of Compound Cylinder
- Reduced Maximum Stress:
The pre-stressing effect ensures that the maximum hoop stress in the inner cylinder is significantly lower compared to a single thick cylinder. - Uniform Stress Distribution:
The stresses across both cylinders are more evenly distributed. - Higher Pressure Capacity:
It can safely withstand higher internal pressures than a single thick-walled cylinder of the same size. - Material Saving:
Reduces material cost and weight compared to manufacturing a single massive thick cylinder. - Safety and Durability:
The pre-compression of the inner layer prevents crack formation and increases fatigue life.
Applications of Compound Cylinder
- Gun Barrels:
Used in cannons and firearms to resist the high pressure developed during firing. - Hydraulic Presses:
Cylinders that handle very high hydraulic pressures. - Boiler Drums:
To safely contain high steam pressures. - High-Pressure Gas Containers:
Used in industries to store gases like oxygen, nitrogen, and hydrogen. - Steam Turbines and Reactor Vessels:
Used where reliability under extreme pressure is essential.
Example of Stress Distribution
In a compound cylinder:
- The inner cylinder initially has compressive hoop stress (due to shrink fit).
- The outer cylinder has tensile hoop stress.
When internal pressure is applied, the inner cylinder’s compressive stress reduces, and the outer cylinder’s tensile stress increases.
By proper design, the stresses in both cylinders reach their safe limits simultaneously, achieving an efficient and balanced structure.
Conclusion
A compound cylinder is a built-up pressure vessel made by shrinking one thick cylinder over another to form a single, stronger unit. The purpose of this arrangement is to reduce the maximum hoop stress in the inner cylinder and distribute stresses more evenly across both cylinders. Using Lame’s equations, the stress variations are analyzed, ensuring both cylinders carry the load efficiently. This design provides greater strength, reliability, and economy, making compound cylinders ideal for high-pressure engineering applications like gun barrels, hydraulic presses, and gas storage vessels.