# Modeling a Milling Dynamometer as a 3 DOF Dynamic System by Stiffness Identification
## 1 Introduction
Regardless of the type of dynamometer used, it must meet a number of conditions, such as the following [14]:  
* Sensitivity, expressed by the accuracy of the measured data;
* Stiffness, which means that the dynamometer has to be able to withstand the forces without causing much deflection, which may affect the machining condition;
* Cross sensitivity, such that one force does not affect the measurement of the other forces;
* Quick response time;
* High-frequency response such that the readings are not affected by vibrations within a reasonably high range of frequency;
* Stability against humidity and temperature;
* Increased maneuverability. The dynamometers are mounted on the machine table and are aligned with the feed direction. In applications, the workpiece must be limited in its dimensions and mass, because a large mass strongly influences the dynamic response of the dynamometer. Using force transducers, an important goal is achieved: measuring, at the same time, the force signal magnitude of the force and frequency content. Regardless of the method used, in addition to the maximum value of cutting force that can be measured, another characteristic to watch for is the frequency range in which these forces occur. This is closely related to the analyses that can be performed on the milling process in both domains: the time domain and frequency domain. Therefore, dynamometers must ensure that measurements can be made both in the time range and in the frequency range over as wide of a range as possible for the amplitude of forces, encompassing the frequencies of vibrations resulting from the milling process. In the present paper, a dynamometer design based on octagonal-ring elastic elements and force transducers produced by the company Bruel & Kjaer (Virum, Denmark) is presented. The basic structure of the dynamometer is the classic one, but the strain gauges used for the deflection measurements are replaced with calibrated force transducers. Thus, the values of the dynamic forces in the three directions and their associated frequencies can be determined. At the same time, static and dynamic calibrations and a study of the dynamic behavior are conducted. The use of such systems is important in current practice for the study of various aspects involved in technological processes. An important advantage is the fact that the use of calibrated force transducers produced by different companies offers the possibility to connect them to any data acquisition platform while considering their sensitivity characteristics. At the same time, using the direct frequency analysis, offered by soft applications tied with acquisition platforms, permits the damping ratio and transmissibility rate to be found. The aim of this study is to create a model to study the dynamic behavior of the considered dynamometer with force transducers. The stiffness of the rings is found using three different methods: analytic, experimental, and using the FEM. Based on these characteristics and considering the damping coefficient found in a previous paper [9], it is described as a three-degrees-of-freedom model.