Geometric Displacement Volume

The geometric displacement volume describes the volume of hydraulic fluid that a positive-displacement pump or hydraulic motor theoretically delivers or receives per revolution, based on the design dimensions of the displacement chambers. It is a purely geometrically defined parameter, expressed in cm³/rev, that directly characterizes the size of a hydraulic machine.

Fundamentals of Geometric Displacement

The geometric displacement volume is one of the key design parameters in hydraulics. It determines how much fluid a pump displaces per revolution of its drive shaft or how much a motor displaces per revolution. Since the value is derived exclusively from the structural dimensions of the displacement chambers, it is independent of operating conditions such as pressure, temperature, or speed. Manufacturers specify the geometric displacement volume in their data sheets because it represents a standardized, measurable quantity that allows for a direct comparison of different sizes.

Geometric Displacement Volume versus Effective Displacement Volume

In practice, the geometric displacement volume is not equivalent to the effective displacement volume. The effective displacement volume describes the actual measured volume delivered per revolution under defined operating conditions. Internal leakage, fluid compressibility, and filling losses cause the effective displacement volume to deviate from the theoretical value. The effective displacement volume is generally slightly lower than the geometric displacement volume, as leakage losses must be compensated for by a higher flow rate. The relationship between the two values is established by the volumetric efficiency.

The Role of Volumetric Efficiency

Volumetric efficiency describes the ratio between the actual flow rate and the theoretically possible flow rate, which is determined by the geometric displacement volume and the rotational speed. It indicates how much of the theoretical flow rate the hydraulic machine actually delivers. Modern axial piston pumps achieve volumetric efficiencies of over 95 percent, while gear pumps range from 85 to 95 percent depending on design and operating pressure. A high volumetric efficiency means that the pump operates close to its geometric displacement volume and only minimal internal losses occur.

Geometric displacement volume for different designs

Each type of positive displacement machine generates its geometric displacement volume in a specific way. The design differences are reflected in the typical value ranges and areas of application.

Gear pumps

In gear pumps, the geometric displacement volume results from the gear geometry, specifically the tooth width, tooth diameter, and number of teeth. With each revolution of the gears, fluid is transported from the suction side to the discharge side. Gear pumps are positive displacement pumps; their geometric displacement volume is therefore fixed and cannot be changed during operation. Typical values range from about 1 cm³/rev for small series up to 60 cm³/rev and above for larger models. Due to their simplicity and robustness, gear pumps are used in numerous industrial and mobile applications.

Axial piston pumps

Axial piston pumps generate their geometric displacement volume through the axial movement of multiple pistons in cylinder bores. The number of pistons, the piston diameter, and the stroke determine the size of the displacement volume. In variable-displacement pumps with a swivel disc or swash plate, the stroke—and thus the geometric displacement volume—can be continuously adjusted, enabling a variable flow rate at a constant speed. Typical displacement volumes range from 10 to 500 cm³/rev. Axial piston pumps are used in applications that require high pressures and precise control, such as in injection molding machines or presses.

Radial piston pumps

Radial piston pumps arrange their pistons in a star pattern around an eccentric shaft. The geometric displacement volume results from the number of pistons, the piston diameter, and the eccentric stroke. Radial piston pumps are characterized by very high operating pressures, which can exceed 400 bar. Their displacement volumes range from approximately 20 to 1000 cm³/rev. They are primarily used in stationary high-pressure systems, such as in machine tools and test benches.

Vane Pumps

Vane pumps use rotating vanes that turn inside an eccentric housing, alternately creating enlarged and reduced chambers. The geometric displacement volume depends on the rotor width, the eccentricity, and the number of vanes. Vane pumps operate relatively quietly and deliver a steady flow rate. Their displacement volumes range from 1 to approximately 50 cm³/rev. They are suitable for applications with moderate operating pressures, such as in lubrication or cooling circuits.

Fixed-displacement pumps and variable-displacement pumps

The geometric displacement volume differs fundamentally between fixed-displacement pumps and variable-displacement pumps. Fixed-displacement pumps have a fixed, unchanging displacement volume. The delivered flow rate can only be regulated via the speed of the drive motor. Variable-displacement pumps, on the other hand, allow the displacement volume to be adjusted during operation. In axial-piston variable-displacement pumps, this is achieved by changing the swivel angle of the swash plate; in radial-piston variable-displacement pumps, by adjusting the eccentricity. The adjustment can be controlled hydraulically, electrohydraulically, or electronically. Variable-displacement pumps offer the advantage of adjusting the flow rate to meet demand, thereby saving energy, since fluid not being delivered does not need to be bypassed via pressure relief valves.

Significance for Hydraulic Motors

For hydraulic motors, the geometric displacement volume is considered the displacement volume. It describes the volume of fluid that the motor takes in per revolution to perform mechanical work. A larger displacement volume generates higher torque at the same pressure, while a smaller displacement volume allows for higher speed at the same flow rate. Variable displacement motors adapt their displacement volume to the load condition, thereby combining high torques during start-up with higher speeds in the partial-load range. This flexibility makes them indispensable in applications such as winches, travel winch drives, and mixers.

Impact on Design and System Efficiency

The geometric displacement volume is a key parameter in the design of hydraulic systems. It directly influences the theoretical flow rate, which is the product of displacement volume and speed. At the same time, it determines the torque that a hydraulic machine can deliver or absorb at a given pressure. Design engineers therefore select the displacement volume so that the required power is achieved at an economical speed and within an acceptable operating pressure range.

Energy Efficiency and Loss Mechanisms

The deviation between the geometric displacement volume and the actual flow rate arises from various loss mechanisms. Internal leakage between the pressure and suction sides, referred to as gap losses, reduces the effective flow rate. Compressibility effects of the hydraulic fluid play a role, particularly at high operating pressures. Additionally, incomplete filling of the displacement chambers at high speeds can lead to filling losses. Careful design of the clearance dimensions, selection of suitable seals, and adherence to the operating conditions specified by the manufacturer minimize these losses and maintain high volumetric efficiency.

Standardization and Designation

The standardization of the geometric displacement volume is governed by various ISO standards. ISO 3662 specifies the test methods for hydraulic pumps and defines the conditions under which the displacement volume is measured. ISO 4391 establishes definitions and graphical symbols for hydrostatic pumps and motors, including the notation for the geometric displacement volume. In manufacturers’ data sheets and catalogs, the geometric displacement volume is usually denoted by the symbol Vg and specified in cm³/rev. This standardized designation facilitates the comparison of machines from different manufacturers and of different designs.

Practical Considerations for Selection

When selecting a hydraulic pump or motor, the decision regarding a specific geometric displacement volume depends on several factors. The required flow rate, the available installation space, the permissible speed, and the maximum operating pressure determine the size. In practice, designers often work with series that offer the same housing format with different displacement volumes. This allows the displacement volume to be adapted to the specific application within a series without changing the mounting dimensions or installation configuration. HK Hydraulik offers a wide range of pumps and motors with different displacement volumes, suitable for a variety of industrial requirements.

Summary

The geometric displacement is a fundamental parameter in hydraulics that characterizes the size and performance of a positive-displacement machine. As a purely design-determined parameter, it forms the basis for calculating flow rate, torque, and power. The difference from the effective displacement is described by the volumetric efficiency, which quantifies the internal losses of a hydraulic machine. Selecting the correct geometric displacement is crucial for the energy efficiency and functionality of the entire hydraulic system.