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As for pretty much everything in life also for spindle design it is all about the best compromise between resulting spindle properties. Maximizing stiffnes, for expample, would lead to high hear losses in the bearing gap at shaft rotation at the same time.

Looking at an entire spindle system, you end up with dozens of design parameters like shaft diameter or bearing gaps e.g. as well as dozens of target properties like load capacity, stiffness or damping. Along with nonlinear functions betwen parameters and properties this leads to equations systems you can’t solve analytically anymore.

However, by defining value ranges for all n-parameters you can generate a population of n random parameter sets with possible, but not optimal m solutions in the objective space. By using population based genetic algorithms like heredity and/or muation individuals can transfer their properties to a child which can then be compared with their parents. The worst individual can then be removed from the population.

The entire population or genrations then evolve towards local and global maxima. After the population has converged every single point in the population represents an optimized solution. The decision maker or designer now can chose a certain fixed property and knows that the point he picked represents the best values for all other parameters. In the paper the elite group, degeneration and parallel computing of population groups is discussed.

Based on a two dimensional optimization of an aerostatic axial bearing these principles are applied and then transferred to a three dimensional problem and explained how to transfer them to a n-dimensional design problem.


  • Genetic coding applied to aerostatic axial bearings
    • Heredity and mutation, 2D
    • Preserving areas with a low population density, 2D
    • Preserving local maxima, 2D
    • Ensure and improve convergence
  • Applying gentic coding to optimize entire spindle systems
  • Summary and outlook


Author: Dr. Ralf Dupont
Issue: Conference, November 18th 2021

„Genetic Coding and Population based Multi Objectove Optimization applied to Spindle Design“,

EUSPEN virtual conference, Nov-18 2021,