Error Mechanism and Control Approaches for Measuring Complex Modulus of Materials

Author:Qu Zhong Peng

Supervisor:sheng mei ping


Degree Year:2018





The complex modulus of materials,as one of the necessary parameters for vibration and noise reduction designing,has been widely measured and utilized in various industrial fields.Currently,measurement methods are based on different physical models and are applicable to different objects and frequency bands.The measurement accuracy of different methods is quite different.In this dissertation,we aim to improve the accuracy of four commonly used measurement methods,that is,the non-resonance method,classical resonance method,improved resonance method and flexural resonance method.The influences of model errors,inverse errors and other three kinds of special errors are investigated systematically,and accordingly techniques to improve the measurement accuracy are proposed.By using the uniform parameters,a simple method is presented for estimating and correcting the model errors.For the non-resonance and classical resonance method,model errors are determined by the product of the wave number and the specimen length.For the improved resonance and flexural resonance method,model errors are determined by the product of the wave number and the gyration radius and the thickness of the specimen section,respectively.The larger these products are,the larger the model errors are.In order to estimate the model errors quickly,we calculate reference tables between the model errors and the above products.Moreover,for the non-resonance method and classical resonance method,the model error curves are fitted with cubic polynomial,from which the test results can be corrected.The corrected method is accurate enough and simpler than the traditional iterative method.Then the influence of the inverse errors on the measurement is further investigated.The advantages and disadvantages of non-resonance method,classical resonance method and improved resonance method are emphatically analyzed and compared,while the detailed control method of the inverse errors of the flexural resonance method is proposed.The advantage of the non-resonance method is that the inverse errors do not change with the frequency,so the measurement results in the applicable frequency band are more stable theoretically.The advantage of the classical and improved resonance method is that the measurement accuracy near the resonance frequency is high,which is not affected by the material damping.In order to control inverse errors of the flexural resonance method,the frequency resolution and the computation bandwidth should be increased for uniform beam specimens.In the case of free-layer and symmetric free-layer damped beam specimens,the modulus ratio and thickness ratio between the damping layer and the base layer should be increased.For sandwich beam specimens,modes with the moderate stiffness ratio should be selected for calculating,and the length of the specimen and the modulus ratio should be increased,while the thickness of the base and damping layer should be reduced(in the case of thickness ratio less than 1).Furthermore,for all the three kinds of composite beams,measuring errors of the frequency and the mass should be strictly controlled.Finally,the generation mechanism of three kinds of special errors is revealed and techniques to improve the measurement accuracy are put forward.The influence of the fixture vibration is studied for the non-resonance method.The smaller the fixture’s stiffness,and the greater the difference between the fixture damping and the material damping,the lower the test accuracy.When the fixture is not fully restrained,the lighter the weight of the fixture and the greater the stiffness of the specimen,the lower the low-frequency limit.The fixture resonance will decrease the measurement accuracy,but the measurement accuracy is high near the non-resonant frequencies.For the flexural resonance method,as the classical formulas ignore the base damping,modified formulas taking into account the base damping are put forward.It is found that the classical formulas’ error is great when the stiffness ratio and the loss factor ratio is small.For sandwich beam specimens,when the stiffness ratio is close to its maximum,classical formulas are also prone to have large errors.In all these cases,the accuracy of the modified formulas are higher.The effect of the "splitting" phenomenon is researched for the flexural resonance method,and the identification method of the "splitting" curves is proposed.It is found that the "splitting" phenomenon is caused by flexural vibration modes and torsional vibration modes disturbance in the orthogonal direction.By comparing the resonant frequency in the different directions of the specimen,the main resonance peak and the interference peak can be effectively resolved.Thus the "splitting" curves can be identified.Moreover,it is discovered that the "splitting" phenomenon can readily be removed by adjusting the position of the exciter.In order to show the feasibility of the techniques proposed in this dissertation,relevant experiments are taken and the results are discussed at the end of each chapter.It shows that errors of the complex moudulus can be lowered by 10%~80% in different experiments.This proves that,by using the the techniques proposed in this dissertation,the model errors and inverse errors,and the other three kinds of special errors can all be efficiently controlled.Thus the accuracy of the complex modulus can be effectively improved.