Simulations
Simulation of air bearings
Simulation of drive systems

Simulations

At AeroLas, simulations are an indispensable tool for the development of products, regardless of their level of complexity. When beginning a new task with predefined project goals, they help to quickly evaluate different potential solutions. Subsequently, the chosen design can be implemented in a quick, cost-effective manner. At AeroLas, we use from the outset a variety of different simulation methods during the design phase, to find the best and favourable solution for our customers.

For the calculation of air bearings, AeroLas has been developing a unique simulation software for more than twenty years, which is especially tailored to the properties of air bearings with micro nozzles. The simulation tool is continuously further developed and expanded. The results from the calculations have been verified in countless measurements.


For the development of complex air bearing systems, such as multi-axis drives, air bearings with integrated functionalities, ultra-precise or high-speed spindles, the calculation of air bearings is combined with an FEM simulation of the entire system, or combination of critical parts. For example, the static and dynamic deformations of components are calculated, the frequencies of natural vibrations (modal analysis) or the thermal deformations are determined. The results from these simulations are then used to optimise the static and dynamic properties of the air bearing to match a load scenario in the application.

AeroLas’s expertise in the design of complex air bearing systems allows us to analyse different approaches to the tasks presented to us by our customers. The optimal solution can already be found during the feasibility study without the need to produce a prototype thanks to the integrated insights from the air bearing calculations and FEM simulations.


Solutions with unique selling points often result from the use of the special simulation software, which is only available from AeroLas. They provide our customers with a competitive advantage.

above: Pressure curve in the bearing gap of a flat bearing; below: Structural analysis of a dynamically moving component (FEM)

Simulation of air bearings

Air bearings have excellent properties in many applications. However, they are seldom used to their full potential due to incorrect or inadequate mathematical calculations. All too often, air bearings are even rated as unsuitable, even though a superior system could have been achieved if the physical properties had been calculated correctly.


AeroLas uses its own bespoke simulation software tailored to the calculation of air-guided systems. Its development was based on exact theoretical models. This enables calculation tasks to be solved that are far beyond the possibilities of all previous design formulas and numerical calculations.

Figure 2: Pressure curve in the bearing gap of a high-frequency spindle

The calculation possibilities offered by AeroLas significantly increase the safety and speed of developments for the customer. Regardless of whether only individual air bearings, or bearings for complete drive systems are simulated, the calculations always provide an optimal representation of the actual conditions. This way, we can quickly resolve problems faced by customers with their previous, conventional air bearings.

Here are some different calculations offered by AeroLas:

  • Theoretical modelling
    The calculation of air bearing properties is based on the simulation of flow developments in the bearing gap and in the micro nozzles. The pressure curve in the bearing gap and all static parameters result from this. At AeroLas, no arbitrary parameters are included in the calculations, as is often the case with air bearings. Results are based on the exact definition of physical effects and give a clear image of future real conditions
  • Tilting stiffness 
    For many applications, the tilting stiffness of a bearing component or complete drive is of uttermost importance. The simulation also provides parameters for this. Here, AeroLas’s air bearing technology has advantages over conventional air bearings – It helps develop a load-bearing air cushion exactly where required.
  • Speed 
    Flat air bearings that are moved tilt due to aerodynamic effects in the gap. Depending on the tilting stiffness of the air bearing, its load-bearing capacity decreases as the speed increases towards a limit at which it fails. For air bearings with the underlying AeroLas technology, this speed limit is a few dozen m/s, depending on the design. For air bearings with chambers and a variety of channel structures, however, speeds of a few m/s can be dangerous.
  • Deformation
    The stiffness of an air bearing body is often overestimated compared to the stiffness of the air cushion. We simulate the resulting deformations of the bearing surface for a seemingly rigid air bearing body.
  • Based on such theoretical calculations, both the material for the air bearing body, and the positioning and number of micro nozzles are calculated to specifically adapt to the deformation. The deformation of the bearing surface due to the surface load of the air cushion is calculated using structural analysis (FEM). The result is then used as a parameter to calculate the air bearing properties. Using an iterative process, the actual deformation and pressure profile can be calculated for each point on a characteristic curve.
  • Spindles and cylindrical air bearings
    The simulation software from AeroLas also enables the calculation of rotationally symmetric components. Load-bearing capacity, stiffness, tilting stiffness and air consumption for an air-guided spindle can be calculated accurately at standstill and at speed (including dynamic effects). In this way, it is possible to predict the maximum speed and natural frequencies, an indispensable prerequisite for the design of reliable, high-performance spindles. Cylindrical air bearings can be optimised with this calculation method, for example with regards to their stiffness, air consumption and the impact of manufacturing tolerances during the production.
  • Spherical air bearings
    A separate software version is available for the calculation of spherical air bearings. 
  • Calculation accuracy
    The calculation models have been validated in multiple measurements, as well as by customers. Typically, the results fall within a 5% range of the actual load-bearing capacity and 10% range for the actual stiffness. Deviations are not a result of calculation error but result from properties of the actual bearing surface (shape deviations, etc.).

Simulation of  drive systems

At AeroLas, all air-guided drive systems are optimised for their respective application. This way, AeroLas can draw from a wealth of experience and successfully implemented systems, including:

  • Linear drives for the production technology with accelerations up to 80 g (800 m/s²)
  • Highly dynamic x-y-theta drives for semiconductor production with bi-directional repeatability
  • Rotary tables for measurement technology with guide deviations smaller than 10 nm
  • High-frequency spindles for banknote productions with dynamic deviations at the point of the cutter smaller than 1,5 µm at 180.000 U/min

In addition to the in-house air bearing simulation tool, a powerful FEM simulation package is available for the simulation of drive systems. They help calculate, for example, natural frequencies of the system, static and dynamic deformations of the bearing surface and thermal influences.

Example of highly dynamic, high-precision x-y-theta drive

For the design of the drive, it is essential that the moving masses of the x and y units are as small as possible, for required accelerations to be achieved with an ironless linear motor. At the same time, natural frequencies of the system must be as high as possible so that the axes can be precisely controlled. The air bearing must also have a high load-bearing capacity and tilting stiffness so acceleration forces and moments can be absorbed. The air bearing and system components are iteratively optimised to meet all these requirements.


The motor is first selected together with a roughly defined air bearing for the basic design idea. The calculated stiffnesses are used to determine the natural frequencies and deformations at specified accelerations. The geometry is then optimised in terms of its mass and stiffness. The findings resulting from the simulation and the optimised geometry are then used to adapt the air bearing to external loads with the help of the simulation software. Once the air bearing parameters are in place, a thorough FEM calculation of the entire system is carried out. If necessary, the air bearing and geometry are re-adjusted. A few iterative steps result in a drive design with optimised geometry and air bearings. Our customers are continuously amazed how little time it takes for us to develop a new, reliable product that meets their specifications.

Figure 3: Calculation of an optimised design for an air-guided drive system

Figure 4: Highly dynamic x-y-theta drive. 1st and 2nd eigenmode (left) and deformation of the air bearing under acceleration (right)

Example of high-frequency spindle

In addition to the calculations mentioned above, other influences on the bearing are determined analytically with the help of physical models, for example the change of the bearing gap with variations in frequency for an air-guided high-frequency spindle. In this sample application, the centrifugal force and air friction in the bearing gap result in a rise in temperature at the drive shaft and bearing bush. This leads to increases in the bearing gap, a property that is taken into consideration for operational safety when designing the air bearing.

Figure 5: Reduction of the gap due to centrifugal force and thermal expansion