# Theoretical Calculations

## Theoretical calculations of vibrating tables / shakers for reliability and fatigue testing as well as transportation simulation

The various VIBROTEST shakers were continuously optimized and are known as very reliable and long lasting systems.

The active mechanical component of the system is the elastically suspended table surface with an electromechanical drive. Two phase coupled rotating unbalances are generating the vertical sinusoidal motion of the table surface. Displacement and acceleration are depending on the total unbalancing moment, the frequency and the load, according to the following equations.

Definitions: | |||

max. total unbalancing moment | = | U0 | [kg*m] |

total unbalancing moment | = | U | [kg*m] |

set-up angle | = | b | [deg] (0...160°) |

frequency | = | f | [Hz] |

dynamical mass | = | M | [kg] |

load | = | m | [kg] |

displacement | = | s | [m] |

acceleration | = | a | [m/s2] |

Equations: | |||

U | = | U0 * cos(b/2) | (to adjust while standstill, except for Series 4W) |

s | = | 2 * U / (M + m) | (independent from f) |

a | = | 39.5 * U * f2 / (M + m) | (proportional to f2) |

These equations are only valid for frequencies outside the resonance of the vibration system or the load. Concerning the technical data the load is assumed as an inelastic, rigid mass. The centre-of-mass of the load generally has to be above the middle of the table surface.

The unbalances are easy to adjust while standstill. The setting value can be determined by the VIBROCONTROL PC software. Also the limits of the system concerning force, frequency range and displacement are considered by the software automatically.

Because of the elastic suspension and the danger of resonance the clamping surface requires a free horizontal moving space of 5 mm, a free declination space of approx. 3° and the absence of appreciable external forces except the gravitation force. This has to be considered for example in case of climatic-chamber inlets.

Example calculations: | |||

Shaker: VS 10002 | |||

total unbalancing moment | U | = | 0.012 - 0.12 kg*m |

max. total unbal. moment | U0 | = | 0.12 kg*m |

dynamical mass | M | = | 95 kg |

| |||

s | = | 2 * 0.12 kg*m / (95 + 100) kg | |

= | 0.0012 m | ||

= | 1.2 mm | ||

| |||

a | = | 39.5 * 0.12 kg*m*55² 1/s² / (95 + 100) kg | |

= | 73 m/s2 | ||

= | 7.4 g | ||

| |||

U | = | 0.12 kg*m * cos(160/2) | |

= | 0.021 kg*m | ||

= | 2 * 0.021 kg*m / (95 + 100) kg | ||

= | 0.00021 m | ||

= | 0.2 mm |

#### Contact Person

In terms of questions in the area of testing tables please contact:

**Peter Ortmann**

08171 - 6295-24

E-Mail