Kjell Ahlin

HIGH FREQUENCY MEASUREMENTS OF CUTTING FORCES IN MILLING BY INVERSE FILTERING

Accurate estimates of cutting forces are important in the evaluation of different cutting tool geometries and concepts. However, dynamic influences from the measurement system affect the result, which can make the obtained cutting force data erroneous and misleading. This article presents a method to obtain an inverse filter which compensates for the dynamic influences of the measurement system. Using this approach, unwanted dynamic effects of the measurement system can be counteracted, making it possible to retain information related to the cutting forces contained in the high frequency region. The advantage of the proposed method is illustrated by comparing simulated, inverse- and low-pass filtered forces to unfiltered forces under different cutting conditions. The results show that inverse filtering increases the usable frequency range of the force dynamometer and thereby provide more reliable results compared to both low-pass and unfiltered forces.

Dynamic characteristics of a combined bellows and liner flexible joint

Abstract A bellows combined with an inside liner and an outside braid is commonly used as a flexible joint in automobile exhaust systems to reduce transmission of engine movements to the exhaust system. It greatly influences the dynamics of the complete system. Understanding of its dynamic characteristics and a modelling method that facilitates systems simulation are therefore desired. This has been obtained in earlier works for the bellows itself. In this work an approach to the modelling of the combined bellows and liner joint is suggested and experimentally verified. Simulations and measurements show that the liner adds significant non-linearity and makes the characteristics of the joint complex. Results are presented for the axial and the bending load cases. In torsion, influence of the liner is negligible. Peak responses are significantly reduced when the excitation level approximately corresponds to the friction limit of the liner. The complexity of the combined bellows and liner joint is important to know of and consider in exhaust system design and proves the necessity of including a model of the liner in the theoretical joint model when this type of liner is present in the real joint to be simulated.

Bias errors due to leakage effects when estimating frequency response functions

Frequency response functions are often utilized to characterize a systems dynamic response. For a wide range of engineering applications, it is desirable to determine frequency response functions for a system under stochastic excitation. In practice, the measurement data is contaminated by noise and some form of averaging is needed in order to obtain a consistent estimator. With Welchs method, the discrete Fourier transform is used and the data is segmented into smaller blocks so that averaging can be performed when estimating the spectrum. However, this segmentation introduces leakage effects. As a result, the estimated frequency response function suffers from both systematic (bias) and random errors due to leakage. In this paper the bias error in the H1 and H2-estimate is studied and a new method is proposed to derive an approximate expression for the relative bias error at the resonance frequency with different window functions. The method is based on using a sum of real exponentials to describe the windows deterministic autocorrelation function. Simple expressions are derived for a rectangular window and a Hanning window. The theoretical expressions are verified with numerical simulations and a very good agreement is found between the results from the proposed bias expressions and the empirical results.

Influence of a bellows-type flexible joint on exhaust system dynamics

Abstract Most modern cars have a bellows-type flexible joint between the manifold and the catalytic converter to allow for thermal expansion and to decouple large engine movements and vibrations from the rest of the exhaust system. To obtain better understanding of the influence of this joint, the dynamic response of a typical exhaust system is studied when excited via different joint configurations. Measurements show the great order of reduction in vibration transmission to the exhaust system that a bellows joint, with and without an inside liner, gives in comparison with a stiff joint. For the combined bellows and liner joint, vibration transmission is, however, higher than for the bellows alone. Together with some other aspects this makes the choice of including a liner in the exhaust system application complex. For a system in general the possibility of tuning the friction limit of the liner, to minimize overall vibrations through friction-based damping, depends on how close to ideal the excitation source is and its location. Anyhow, the combined bellows and liner joint makes the exhaust system behaviour significantly non-linear, whereas the system behaviour proves to be essentially linear when the bellows has no liner, which imply that the liner needs to be included in theoretical models when present in the real system.

Using MATLAB for Advanced Noise and Vibration Analysis

Commercial tools for measurement and analysis of noise and vibration signals have traditionally been very expensive. In the last decade, however, multi-channel measurement systems have become relat ...