### Profile

Working group 1.21 is responsible for the realization and transfer of the physical quantity "force". The force scale is realized by means of force standard machines (FSM) working on different principles. In deadweight force standard machines the force is generated by the weight force of mass stacks in the gravity field of the earth (up to 2 MN). Higher forces (up to 16.5 MN) are realized by hydraulic amplification of deadweight forces.

Transfer of the force scale is ensured by the testing and calibration of force measuring devices in the Working group's force standard machines using different measuring methods. In addition to the work carried out to realize and transfer the force scale, basic research is pursued in the field of force measurement. This includes, for example, the development and investigation of new measuring facilities and devices for the measurement of static and dynamic forces or international comparisons.

### Research/Development

## Realization of the force scale for compression and tension forces up to 16.5 MN

The force is a derived vectorial physical quantity with the unit Newton (N). One Newton is defined as the force required to impart to a body of 1 kg mass an acceleration of 1 m/s². Force standard machines are the highest national standards for the physical quantity force. The standards realize the unit of force - the Newton - statically in discrete values in the range from 0.5 N to 16.5 MN and periodically with different frequencies in the range from 10 N to 2 kN.

## Investigations of force standard machines, force calibration machines, and force transducers

Force standard machines and calibration machines are investigated theoretically and experimentally to determine and reduce the measurement uncertainty. Precision force transducers are used as transfer standards for these investigations. The tranducer characteristics such as reproducibilty, creep, hysteresis and linearity are analysed.

## Investigation and reduction of disturbing influneces on the dissemination of the force unit

The new 200 kN Force Standard Machines has some new design features which make it possible to investigate such specialties like continuous force calibrations in a dead-weight machine, the consideration of climatic influences and the transition from compression to tension forces and back. Extensive research is carried out for this purpose.

## Stress calculations by finite element methods

For the theoretical analysis of the action of forces in force standard machines, in force transducers or complex force measuring devices, numerical calculation methods are used, e.g. the method of finite elements.

## International comparison measurements

International intercomparison measurements are carried out with force transfer standards to ensure uniformity of the force scale all over the world. 1.21 is a pilot laboratory of the CIPM and EUROMET Key Comparisons for the quantity "force".

### Services

## Calibration of force transducers and comparison measurements

The transfer of the force scale to laboratories in research and industry is ensured by the calibration of force measuring devices and by comparisons with force calibration machines.

## Assessment of calibration laboratories for force and testing machines by order of the German Accreditation Body

The assessment of calibration laboratories is carried out by order of the German Accreditation Body (DAkkS).

### Information

## 200 N Force Standard Machine

Short name | 200-N-K-NME |

Principle | deadweight |

Rel. exp. (k=2) uncertainty | 2·10^{-5} |

Force steps | 0.5 N, 1 N, ..., 5 N 1 N, 2 N, ..., 10 N 2 N, 4 N, ..., 20 N 5 N, 10 N, ..., 50 N 5 N, 10 N, ..., 100 N 10 N, 20 N, ..., 200 N |

## 2 kN Force Standard Machine

Short name | 2-kN-K-NME |

Principle | deadweight |

Rel. exp. (k=2) uncertainty | 2·10^{-5} |

Force steps | 50 N, 100 N, 150 N, 200 N, 250 N 300 N, 350 N, 400 N, 500 N, 500 N, 600 N, ..., 1000 N, 1200 N, 1400 N, ..., 2000 N |

## 20 kN Force Standard Machine

Short name | 20-kN-K-NME |

Principle | deadweight |

Rel. exp. (k=2) uncertainty | 2·10^{-5} |

Force steps | 0.25 kN, 0.5 kN, ..., 2 kN, 2.5 kN, ..., 5 kN, 6 kN, ..., 10 kN, 12 kN, ..., 20 kN |

## 100 kN Force Standard Machine

Short name | 100-kN-K-NME |

Principle | deadweight |

Rel. exp. (k=2) uncertainty | 2·10^{-5} |

Force steps | 2 kN, 4 kN, 5 kN, 6 kN, 8 kN, 10 kN, 12 kN, 14 kN, 15kN, 16 kN, 18 kN, 20 kN, 25 kN, ..., 50kN, 60 kN, ..., 100kN |

## 200 kN Force Standard Machine

Short name | 200-kN-K-NME |

Principle | deadweight |

Rel. exp. (k=2) uncertainty | 2·10^{-5} |

Force steps | 5 kN, 5.05 kN, 5.1 kN, ..., 200 kN |

## 1 MN Force Standard Machine

Short name | 1-MN-K-NME |

Principle | deadweight |

Rel. exp. (k=2) uncertainty | 2·10^{-5} |

Force steps | 20 kN, 40 kN, 50 kN, ..., 1000 kN |

## 2 MN Force Standard Machine

Short name | 2-MN-K-NME |

Principle | deadweight |

Rel. exp. (k=2) uncertainty | 2·10^{-5} |

Force steps | 50 kN, 60 kN, 70 kN, ..., 2000 kN |

## 5 MN Force Standard Machine

Short name | 5-MN-K-NME |

Principle | hydraulic amplification |

Rel. exp. (k=2) uncertainty | 1·10^{-4} |

Force steps | 50 kN, 100 kN, 150 kN, ..., 5000 kN |

## 16.5 MN Force Standard Machine

Short name | 16,5-MN-K-NME |

Principle | hydraulic amplification |

Rel. exp. (k=2) uncertainty | 1·10^{-4} |

Force steps | 0.1 MN, 0.2 MN, ..., 16.5 MN |