Spatial Frequency Analysis of a Gear-Box as an Continuation for Modeling of a Harmonic Drive ® Gear-Box 36 Spatial Frequency Analysis of a Gear-Box as an Continuation for Modeling of a Harmonic Drive ® Gear-Box P. Häuptle Faculty of Electrical Eng. & Information Tech. Slovak University of Technology Bratislava, Slovakia e-mail: haeuptle@hs-heilbronn.de G. Gruhler Faculty of mechanics & electronics Heilbronn University Heilbronn, Germany e-mail: gruhler@hs-heilbronn.de P. Hubinský Faculty of Electrical Eng. & Information Tech. Slovak University of Technology Bratislava, Slovakia e-mail: peter.hubinsky@stuba.sk Abstract 1 The Spatial frequency analysis can be seen as an advanced modeling technique of a gear-box. This would allow a better prediction/estimation of gear- box dynamics in sense of a gear-box meshing within CAD/CAE environments. Within a gear-box or at least in a combination together with an electrical motor (a so called mechatronic drive), "semi- steady-state"-effects like the "kinematic error" can arise and lead to an unwanted oscillation. To draw back such effects to the mechanical origin, the method of spatial frequency analyses will be introduced here. Along an especially built up experimental setup, real measurements investigating an i.e. harmonic drive ® gear-box have been made. The results as well as the technique itself will be introduced in the following. 1. Introduction Fourier’s work about describing heat expansion was one of the biggest enrichments for engineering. Especially in telecommunication the technique of Fourier is widely used and allows time signals to be transformed to their frequency interpretation [1, et al.]. Also the inverse from frequency back to time domain is possible which allowed an huge amount of filter techniques in signal processing like [2, et al.]. With the frequency interpretation of signals many additional information of a system [3, et al.] or a specific hardware like a motor [4, et al.] as well as a gear-box [5, et al.] can be extracted. The idea in this contribution is based on the question why not using something else like “position to spatial frequency”- Proceedings of the 13 th international workshop on computer science and information technologies CSIT’2011, Garmisch-Partenkirchen Germany, 2011 domain instead of “time to frequency”-domain. The spatial frequency investigation is often used in biology or human medicine research like [6, et al.]. When for instance a gear-box should be modeled in a CAD/CAE system, then analyses like: Finite-Element-, Stress- or Modal-analyses are well known. Especially the Modal- analyses where dynamic properties like a resonance oscillation frequency can be computed, the Fourier techniques (among others) were used for numerical calculations. Hence, a Spatial-Frequency-Analyses based also on Fourier’s work like the Modal-analyses, might also offer additional information to a CAD/CAE user. A deeper understanding of gear-meshing, kinematic error or even friction issues investigated so far due to [7, 8, 9, et al.] might be available in a future CAE-analyses. Therefore measurements of an experimental setup need to be made first, to test the “Spatial-Fourier-Analysis”. The theory as well as the results (measured at our experimental setup and analyzed) will be introduced and discussed in the following. 2. Theory The Fourier transform for a continuous time signal i.e. h (t) is defined like shown in Equ. 1 [1, et al.]: [ ] ) ( ) ( ) ( f t f h F h = (1) Then the inverse Fourier transform can be stated out to Equ. 2 [1, et al.]: [ ] ) ( ) ( ) ( t f t h F h = (2) As already mentioned, the idea in this contribution is, why not using the position (“spatial”) instead of time like the following Table: