Displacement Volume

Displacement volume, also known as displacement capacity or stroke volume, is a crucial parameter in hydraulics. It describes the volume of fluid that is displaced or flows through a hydraulic component such as a pump, motor, or cylinder per unit of time or per unit of movement. This volume is fundamental for determining the performance and operating behavior of hydraulic systems.

Basics of displacement volume in hydraulics

Displacement volume is a measure of the amount of fluid that a displacement unit moves per working cycle. For pumps and motors, this typically refers to the volume per revolution of the drive shaft. For cylinders, it is the volume displaced per stroke of the piston. Knowing the displacement volume is essential for calculating the flow rate of a pump, the speed of a motor, or the speed of a cylinder.

Definition and units

The displacement volume is usually specified in cubic centimeters per revolution (cm³/rev) or cubic meters per second (m³/s). These units illustrate the relationship to the movement of the component.

Geometric displacement volume

The geometric displacement volume is a theoretical value that is derived exclusively from the design dimensions of a component. In a hydraulic cylinder, it is calculated from the piston area multiplied by the stroke length. For pumps and motors, it is derived from the dimensions of the displacement elements, such as gears, vanes, or pistons. This value does not take into account internal leaks or compressibility effects of the fluid.

Theoretical and effective displacement volume

The theoretical displacement volume is often slightly larger than the geometric displacement volume, as it assumes ideal conditions without losses. The effective displacement volume, on the other hand, is the value actually measured. It takes into account internal leaks and the compressibility of the hydraulic fluid. For pumps, the effective displacement volume is the quotient of the actual flow rate and the speed.

Significance of displacement volume for hydraulic components

The displacement volume has a significant influence on the performance parameters of hydraulic pumps, motors, and cylinders.

Hydraulic pumps

In hydraulic pumps, the displacement volume in conjunction with the speed determines the theoretical flow rate. A pump with a larger displacement volume delivers a greater amount of fluid at the same speed. This is crucial for the speed at which an actuator can be moved.

Hydraulic motors

For hydraulic motors, the displacement volume is an indicator of the torque that the motor can generate at a given pressure. A motor with a larger displacement volume generates higher torque at the same pressure, but also requires a higher volume flow to reach a certain speed.

Hydraulic cylinders

For hydraulic cylinders, the displacement volume is directly proportional to the piston area and the stroke. It determines how much fluid is needed to move the piston over a certain distance. This is relevant for calculating the cylinder speed and fluid consumption.

Calculation of displacement volume

The calculation of the displacement volume depends on the type of hydraulic component.

For hydraulic cylinders

The basic formula for the displacement volume of a single-acting hydraulic cylinder is:

V = A * H

Where:

V = the displacement volume
A = the piston area
H = the stroke length

For double-acting cylinders, the volume for the piston rod side must be calculated separately, as the effective area is reduced by the piston rod.

For hydraulic pumps and motors

For displacement pumps and motors, the displacement volume is the volume displaced per revolution of the drive shaft. For variable displacement pumps and motors, the displacement volume can be adjusted. This is often expressed by an adjustment angle or a volume setting (α):

V_i = α * V_{i,max}

Where:

V_i = The current displacement volume
α = The displacement factor (between 0 and 1)
V_{{i, max}} = The maximum displacement volume

Influencing factors and practical applications

The displacement volume is not just a theoretical quantity, but has a direct impact on the design and operation of hydraulic systems.

Compressibility of the fluid

Hydraulic fluids are virtually incompressible, but under high pressure, a slight reduction in volume can occur. This additional volume, which is pressed into the pressurized fluid, must be provided by the pressure source each time the drive is switched on. In systems with many drives and large volumes, this compression volume flow cannot be neglected.

Leakages

Internal leaks in pumps, motors, and cylinders result in the effective displacement volume being less than the geometric volume. These leaks are an important factor in the efficiency of hydraulic components.

System design

When designing hydraulic systems, the displacement volume is crucial for selecting the right components. It influences the achievable speeds, forces, and torques as well as the energy consumption of the system. Precise matching of the displacement volume of the pump to the requirements of the actuators is essential for efficient operation.

What is the displacement volume and why is it important in hydraulics?

The displacement volume, also called displacement or stroke volume, indicates how much fluid a hydraulic component (pump, motor, cylinder) displaces per unit of movement (revolution, stroke). It is crucial for performance, as it directly influences the flow rate, torque and speed of hydraulic systems.
How does the geometric displacement volume differ from the effective displacement volume?

The geometric displacement volume is a theoretical value that results only from the design dimensions of the component. The effective displacement volume is the actual measured value and takes into account losses such as internal leakage and the compressibility of the fluid. For pumps, it is the quotient of the actual flow rate and speed.
What influence does the displacement volume have on hydraulic pumps, motors and cylinders?

For pumps, the displacement volume together with the speed determines the flow rate and thus the speed of actuators. For motors, it is an indicator of the torque at a given pressure. For cylinders, it directly influences the fluid volume required for a stroke and therefore the speed and consumption.
How is the displacement volume for hydraulic cylinders calculated?

For single-acting hydraulic cylinders, the displacement volume (V) is calculated using the formula V = A * H, where A is the piston area and H is the stroke length. For double-acting cylinders, the volume for the rod side must be calculated separately.
How is the displacement volume specified for variable displacement hydraulic pumps and motors?

For variable displacement components, the actual displacement volume (V_i) is often specified by a displacement factor (α, between 0 and 1) multiplied by the maximum displacement volume (V_{i,max}): V_i = α * V_{i,max}.
What practical factors influence the effective displacement volume in a hydraulic system?

Important influencing factors are the compressibility of the hydraulic fluid, which can lead to a reduction in volume under high pressure, and internal leakages in the components. These factors reduce the effective displacement volume compared to the geometric volume and influence the efficiency of the system.
Why is it so important to match the displacement volume when designing the system?

Precisely matching the displacement volume of the pump to the requirements of the actuators is crucial for efficient operation. It directly influences the achievable speeds, forces and torques as well as the energy consumption of the entire hydraulic system.