Çok elemanlı yapılarda malzeme sönümü ve temas özelliklerinin ölçülmesi
Measurement of material damping and contact properties of multibody structures
Yazar: MURAT CAN TÜZEL
Danışman: PROF. DR. KENAN YÜCE ŞANLITÜRK
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Mekatronik Mühendisliği Ana Bilim Dalı / Mekatronik Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2015
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Harmonik balans analizi = Harmonic balance analysis ; Histerezis eğrileri = Hysteresis curves ; Rijitlik = Stiffness ; Sönümleme katsayısı = Damping coefficient ; Sürtünme katsayısı = Friction coefficient ; Temas = Contact

Özet:
Özellikle makine endüstrisinde yapılan Ar-Ge çalışmalarında, yapıların veya makinelerin özellikle rezonans durumlarında sahip olacakları titreşim ve gürültü seviyelerinin prototip üretilmeden önce bilinmesi istenir. Ancak, çok elemanlı yapılarda oluşan temas yüzeylerinin davranışının tam olarak bilinmemesi ve bu sebeple modellenememesi, hassas analiz sonuçlarının elde edilememesine neden olmaktadır. Çok elemanlı yapılarda yapısal sönümün ana kaynağı, temas yüzeylerinde meydana gelen kuru sürtünme sönümüdür. Özellikle otomotiv alanında yapılan sayısal analiz çalışmalarında temas yüzeyleri modellenmemekte ve kuru sürtünme sönümünü temsil etmesi için empirik sönüm değerleri kullanılmaktadır. Kuru sürtünme sönümünün yanısıra yapıların sahip olduğu malzeme sönümü için de önceden belirlenmiş empirik sönüm değerleri kullanılmaktadır. Yapıların gerçekte sahip olduğu malzeme ve kuru sürtünme sönümü yerine empirik sönüm değerlerinin kullanıldığı analizler, titreşim genliği açısından hassas sonuçlar vermemektedirler. Temas yüzeylerinde meydana gelen direngenliğin doğru bir şekilde ölçülmesi ve modellenmesi ise analiz sonucunda doğal frekans değerlerinin daha hassas tahmin edilmesini sağlamaktadır.
Bu çalışmada, malzeme sönümü ve çok elemanlı yapılarda karşılaşılan temas yüzeylerindeki temas parametreleri olan direngenlik ve sürtünme sönümünün deneysel olarak hassas bir şekilde ölçülmesine çalışılmıştır. Basit çubuklar üzerinde çeşitli modal test çalışmaları yapılarak malzeme sönümünün en hassas şekilde ölçülmesi için uygun yöntem belirlenmiş ve daha sonraki çalışmalarda bu yöntemin karmaşık motor parçaları üzerinde de başarıyla uygulanabildiği belirlenmiştir. Özellikle otomotiv sektöründe karşılaşılan cıvatalı bağlantılardaki temas yüzeylerinin gerçekçi bir şekilde temsil edilebildiği bir test düzeneğinin geliştirilebilmesi amacıyla literatürde yapılan benzer çalışmalar incelenmiştir. Literatürdeki benzer çalışmalar içerisinde, bu çalışmanın amacına en uygun test düzeneği temel alınarak geliştirilen ölçüm sistemi kullanılarak, temas direngenliği ve kuru sürtünme sönümünün ölçülmesine çalışılmıştır. Bu çalışmada, literatürde önerildiği gibi, nonlineer bir davranış gösteren sürtünme kuvveti genliğe bağlı eşdeğer bir direngenlik olarak kabul edilmiş, 1. Derece Harmonik Denge Metodu uygulanarak lineer hale getirilmiş ve temas parametreleri hesaplanmıştır. Temas direngenliğinin hassas bir şekilde ölçülebilmesine rağmen, bu çalışmada sunulan yöntemle, sürtünme sönümü için pratikde kullanılabilecek güvenilir sonuçların elde edilemediği anlaşılmıştır. Yapılan çalışmalar sırasındaki gözlemler ve elde edilen sonuçlardan yararlanılarak, ölçüm sisteminin avantaj ve dezavantajları belirlenmiş ve gelecekte yapılacak benzer çalışmalar için öneriler sunulmuştur.

Abstract:
One of the most significant problems in the machinery industry, especially turbomachinery and automotive, is to decrease the high resonant vibration levels and sometimes the noise caused by these vibrations. Knowledge of resonant noise and vibration levels of prototype parts prior to production is desirable in development studies of machinery industry. To some extent, computation of vibrational properties is possible via finite element models. Nearly all the components in automotive industry are in contact with each other and in general, these components have dry friction surfaces. Main source of the structural damping is the frictional damping -with a percent up to 90%- between the contact surfaces of the assembly. The other parameter acting on dynamics at the contact surface is the contact stiffness. Accurate measurement and liable modelling of contact stiffness enables accurate finite element analysis results in terms of natural frequencies. Today, especially in automotive field, the dry friction surface is generally not modelled in finite element analyses. Because of this, a significant level of structural damping and any of the contact stiffness is not included in the model. Most common practice on these FE analyses is to use simply an empirical generic value for dry friction damping. As a result of this, no exact correlation between the finite element analyses and the experimental studies on prototypes in terms of vibration levels and natural frequencies can be ensured. 
Nonlinear nature of the contact dynamics and the lack of reliable experimental data are the main reasons of inexplicable behaviour of dry friction surfaces. Although there are many experimental studies on this topic in the literature, most of them do not include contact surfaces of bolted joints seen frequently in automotive industry. These studies provide only limited information for contact surfaces at the bolted joints used in automotive field and experimental studies suited for this kind of applications are required. 
Main goal of this study is to experimentally obtain contact parameters of the dry friction surfaces of bolted joints seen in automotive studies. As seen from the literature, such experimental studies are rather rigorous. The most important point of this study is, ensuring the test rig to serve for ease of application in the industry.
Another goal of this study is to obtain accurate material damping experimentally. General approach in the automotive industry is to use a generic empirical value in modelled components for this property. The study also includes the comparison of empirical values taken from industry and experimental values obtained via modal testing. 
This thesis investigates the material damping properties starting from simple geometric parts and continues to the generation of the properties on complex engine components. First, the approach to be used in the study is chosen by modal testing applications on simple quadratic beams and parameters affecting the experiments are determined. These parameters are found to be air in the environment, hanging position of the structure, hanging locations on the structure and measurement equipments. General results obtained from this application showed that the measurement equipment should be non-contact type as much as possible. 
After selection of the approach and equipment, the tests are performed on automotive parts with complex geometry in order to understand the applicability of the selected procedure. Results from this testing have verified the chosen procedure in the previous section is suitable for complex automotive components. Frequency response functions (FRF) and material damping values extracted from these FRF's are obtained from these tests. Following the experiments, finite elements analyses are performed using the experimental material damping values in the material definitions. In parallel, generic empiric values taken from industrial applications are also used in finite element analyses. These finite element analysis results are then compared to the real experimental FRF's. It is seen that the usage of experimental values have provided much accurate results with a percent of up to 99%. These results promote experimental values' usage in such applications. 
Another conclusion from this result is that, in the future works, the error caused in bolted joint modelling applications would be coming only from the dry friction surface related parameters since the material damping has been accurately measured and fed into the analysis. This feedback may aid in the improvement of dry friction modelling studies in the future.
To create a realistic and liable test rig for coupling pieces used in automotive industry, an extensive literature survey is conducted for similar applications. Amongst those studies, most suitable one is chosen to be a starting point to this study and a test rig is created for contact stiffness and dry friction damping measurement. As mentioned above, this test rig is carefully designed for ease of application. The only requirements of this measurement rig are 3 uni-axial accelerometers to obtain relative displacement between coupled parts and transmitted force, a modal shaker for harmonic excitation and force transducers under the bolt to regulate the pressure on the contact surface. Relative displacement is important for hysteresis loop creation which will enable the determination of the contact parameters. In the light of the tests performed with this rig, it is concluded that the main 3 parameters important for sufficient relative displacement are; normal force on the bolt, tangential excitation force amplitude and tangential excitation force frequency.
As proposed in the literature, friction force, exhibiting a nonlinear character, is modelled as an amplitude dependent equivalent stiffness and then linearized with the aid of "First Order Harmonic Balance Method". The contact parameters are then calculated under this approach. Different tests are ran for varying relative displacements obtained by varying tangential excitation forces and normal forces. Contact parameters changes with respect to relative displacements are monitored throughout these tests. As expected, contact stiffness has shown a decreasing trend as the relative displacement increased. Although the contact stiffness is found to be highly accurately measured and obtained in line with the expectations based on the literature, the same reliability and accuracy has not been able to be shown for friction damping with the methods used in this study. 
With observations and results obtained from the study, advantages and disadvantages of such test rigs and conclusions for future studies are identified. Main advantages can be given as ease of application of the rig, represent the bolted joints realistically and usage of interchangeable coupled parts establishing the contact surfaces. Main disadvantage is the limited minimum normal force which requires high tangential excitation force amplitudes and frequencies. Because of this, dynamic behaviour of the test rig under dynamic conditions is affected. This has resulted in incorrect contact surface parameter values extraction which has also eliminated the chance of macro slip behaviours of the contact surfaces.
For future studies, using controlled dead weights to create contact surface pressure can help to derive more reliable results. The experimental contact parameters and material damping values obtained in this study can also be used in future finite elements modelling of dry friction surfaces in industrial applications.