Profil düzeltme faktörünün sikloidal dişlerde meydana gelen kuvvetler üzerindeki etkisinin sonlu elemanlar yöntemi analizleri ile incelenmesi
Investigation of the effect of profile correction factor on forces occuring in the cycloid teeth by finite element method analyses
Yazar: SÜLEYMAN LEVENT UZUN
Danışman: DR. ÖĞR. ÜYESİ İBRAHİM MEHMET PALABIYIK
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Konstrüksiyon Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Sikloid redüktörler yüksek momentlerin ve hassas pozisyonlama ile birlikte küçük boyutlar gerektiren tüm alanlarda en iyi seçenek olarak karşımıza çıkmaktadır. Diş formunun adını aldığı sikloidal eğri formunda olması evolvent dişlerdeki diş kırılması tehlikesini ortadan kaldırmaktadır. Sikloid dişliler tahrik aldığı anda sahip olduğu dişlerin teorik olarak yarısı kuvvet aktarımında görev yaparken diğer yarısı fener dişlisine herhangi bir kuvvet aktarımına karışmaksızın temas halinde kalmaktadır. Bu durum sikloid redüktörlerin yüksek moment aktarımlarına imkan tanımaktadır.  
ADY uydu takibi yapacak olan büyük reflektör çaplarına sahip uydu yer takip sistemlerinin birincil problemi sistemin faydalı yükün ve rüzgar yükünün hareket eksenlerinde meydana geterdiği momentlerin karşılanabilmesidir. Bu tez kapsamında belirli bir dişli çapında ve aktarma oranında, en yüksek kuvvet aktarımını sağlayacak bir sikloid dişlinin nasıl elde edilebileceği hakkında bir öneri ve bu önerinin doğrulama yöntemlerine yer verilmiştir.
Yapılan bu çalışmada belirlenmiş bir çaptaki sikloid dişlinin kuvvet aktarım kabiliyetinin nasıl arttırılabileceği ile ilgili sikloid dişlilerdeki kuvvet aktarım teorisinden hareketle bir yaklaşım sunulacaktır. Bu yaklaşımlar Ansys sonlu elemanlar analizi programı ve MSC Adams çoklu gövde dinamik simülasyonlar ile çalışılarak doğrulama yoluna gidilmiştir.
Tezde öncelikle sikloid eğri tarihinden, çeşitlerinden ve bu eğrilerin nasıl elde edileceğinden bahsedilmiştir. Ardından sikloid redüktörlerin çalışma prensibi, kullanım alanları ve kabiliyetlerine değinilmiştir.
Tasarım aşamasına geçildiğinde sistemde kuvvet aktarımında görev alan tüm elemanların tasarım esasları sikloid dişli tasarımı üzerinden ele alınmıştur. Burada CAD uygulaması için SolidWorks programından yararlanılmıştır. Ardından dişliye gelen tüm kuvvetler teorik olarak elde edilmiştir. Bu noktadan sonra dişlere gelen kuvvetin azaltılarak sistemin daha fazla yük taşıyabilmesine imkan tanıyan profil düzeltme faktörünün değişimi yaklaşımı sunulmuştur. Bu yaklaşımın sikloid dişli dişlerindeki etkisinin görülmesi adına farklı katsayılarda elde edilmiş dişlilerde teorik hesaplar yapılmıştır. Ardından bu farklı dişli formuna sahip dişlilerin analizi için Ansys ve MSC Adams'a ayrı ayrı olacak şekilde simülasyon modelleri oluşturularak analizler gerçekleştirilmiştir. Teorinin bu iki analiz programından elde edilen sonuçlarla bağdaşması yorumlanmış ve elde edilen neticede PDK (profil düzeltme faktörü) değişiminin dişlinin mukavemetine doğal olarak sikloid redüktör sisteminin yük taşıma kapasitesine olan katkısı değerlendirilmiştir.

Abstract:
The word cycloid represents the family of curves. It aroused interest among mathematicians in the 16th and 17th centuries. Studies of properties of plane curves helped to awaken this interest.
Galileo Galilei named the curve in 1599 as its current name. Cycloid is defined as the curve drawn by a selected point on the circle when the circle rolling with a non-slip rolling motion on a straight line. 
Cycloidal gearboxes were discovered in 1929 by Lorenz Braren, an engineer at Deckel in Munich. Later, the invention was developed and Lorenz Braren founded Cyclo Getribebau. On behalf of this new reducer; κύκλος / Kyklos, which means circle in Greek, is called a cycloid. Today, Cyclo® or cycloid refers to an eccentric gearbox with a cycloid disc.
Cycloidal gearboxes have many features such as being able to withstand high torques, low clearance rates, small size and high transfer rates due to their working principle. These properties make the cycloid gearboxes the best choice in areas where a small dimension of high torque transfer and low positioning error are required. These applications include satellite tracking systems, surgical applications, robotic applications, CNC magazines, etc. The system consists of five main parts. These; input shaft, eccentric bearing, cycloid gear, spindle gear and output shaft. The movement starts with drive from the input shaft. When the shaft starts to rotate, the eccentric bearing starts to rotate. Due to the eccentricity, the cycloid gear moves within the ring gear. During movement, all the teeth of the cycloid gear are in contact with the peripheral gear teeth. Half of these contact pairs are involved in the transmission of force. The other half only makes contact. Continuous contact ensures vibration-free operation of the system. The output shaft has a number of pins. These pins make tangential contact with the holes on the surface of the cycloid gear. When the cycloid gear rotates, it moves these pins and the output shaft is rotated. At this point, the transmission ratio from the input shaft to the output shaft is transferred in multiples.
When the working principle of cycloid reducer is examined, the force transfer of the cycloid gear with half of the total number of teeth provides the system to withstand more torque than the gearboxes with conventional gears. In addition, this allows it to be smaller in size than conventional gear units. In the case of cycloid gearboxes, the transfer rate is the number of teeth of the cycloid gear. This means that the system can achieve high transmission rates. There is no gap as the cycloid and the peripheral gear are in constant contact. Thanks to this feature, cycloid reducers have precise positioning. Finally, the cycloid gear in the structure of the system is unbreakable as in evolvent teeth. There are two reasons for this. The first is that the teeth have a cycloid curve form. The other is the transfer of force by half of the total number of teeth that the gear has when moving in the system. These features are the most significant difference between cycloid gearboxes and conventional gearboxes.
Commercially available cycloidal gear units have certain nominal output torques. If higher output torque is desired, larger size and weight cycloid gearboxes are produced. As nominal output torque increases, so does size and weight. In this thesis, an approach will be presented about how to obtain the highest rated output torque without increasing the size of the cycloid reducer. Accordingly, the effect of the change of profile correction factor in the cycloid tooth profile equation on the forces coming to the cycloid gear was investigated. The profile correction factor changes only the tooth profile without changing the size of the cycloid gear. However, it has been observed that the contact angles of the cycloid gear tooth and the ring gear tooth are changed. This means that as the cycloid tooth tooth profile changes, so does the force to the teeth. Working on profile correction factor is the most appropriate way for the purpose of this thesis.
In this thesis, theoretical information about cycloid reducer design is presented as a result of literature research. This theoretical information is given by considering the aim of the thesis. Design constraints were determined before moving on to design. Then, the types of cycloid gear profile and how this profile curve is obtained are mentioned. Later, the parametric equation of the curve is presented. Variables in this profile curve equation are explained. The design of the cycloidal gear directly affects all other main components in the cycloid reducer. Therefore, it is explained how to dimension other components via the cycloid gear. The aim here is to ensure that the variables are expressed correctly and to understand their effects correctly.
When the gear unit is moved from the input shaft, three types of force transmission occur in the system. The first of these is the force transfer between the cycloid gear and the spur gear. The other is the force transfer between the cycloid gear and the output shaft. The last one is the force transfer between the cycloid gear and the input shaft. How these three force transmissions occur and theoretical calculations are explained. The relationship between torques and force transfers in the system is explained.
According to theoretical calculations, the effect of profile correction factor on force distribution in cycloid teeth was investigated. For this study, firstly, 4 different profile correction factor values were determined as 0.2, 0.4, 0.6 and 0.8. This means cycloid gears with four different tooth profiles. For each gear, the forces occurring in the teeth were found. It is mentioned how to calculate all the variables required to find these forces. Calculated values are presented. As a result of the theoretical studies, it is seen that as the profile correction factor approaches zero, the total forces occurring in the teeth decrease.
It is also desirable to realize this situation with finite element method analysis. First, the effect of the profile correction factor will be investigated by ANSYS finite element analysis. For this purpose, a design suitable for the analysis was made in the SolidWorks environment. In determining this design, the articles found during the literature research were used as reference. After determining the design suitable for the analysis, simulation setup is created within ANSYS program. This step is to ensure that the model responds correctly while running the simulation. Afterwards, an appropriate mesh study was carried out in order to provide accurate calculation of the forces formed between the cycloid gear and the ring gear pin by ANSYS. The meshes are concentrated in contact areas. These steps were applied to four different cycloid gears and simulated. When the results obtained using ANSYS finite element analysis were examined, it was seen that similar results were obtained with the theoretical data. Theoretical results and the results obtained from ANSYS were compared using graphs.
Another finite element analysis program to examine the effect of profile correction factor is Msc Adams. As in ANSYS, a simulation model was first created. Material assignment of all components within the model was then performed. The assigned material is not important at all. Because the material under load status is not concerned. It is desirable to have forces occurring in the contact zones. After the material identification is completed, all connection types are determined. The contact function is then established between the contacting parts. The reason for all these steps is to ensure that the model reacts correctly when the simulation is run. Then, how the input torque is applied in simulation torque is determined and simulation is performed. Results were obtained for all cycloid gears. The results are presented graphically. When the results obtained using MSC Adams were examined, it was seen that similar results were obtained with theoretical data. Theoretical results and the results obtained from ANSYS were compared using graphs.
The effect of the profile correction factor on the forces coming to the cycloid gear teeth was investigated using ANSYS and Msc Adams. The results were confirmed by theoretical data.In this study, the effect of the change of the tooth form in the cycloid gears, which give the name of the cycloid reducers, to the forces to which the teeth are exposed is obtained by using the finite element program ANSYS and MSC Adams, a multi-body dynamic simulation program. ANSYS and MSC Adams were used in these effects and in-program images and explanations were supported.
As the profile correction factor, which is one of the parameters in the curve equation used to obtain the cycloid gear, goes from 1 to 0, it is theoretically seen that the forces in the teeth exposed to force decrease even if the applied torque value remains the same and this situation of the finite element analysis and multibody dynamic simulation programs can be inferred. Within the scope of the thesis, it is seen that the theory and finite element method analyzes confirm each other. This thesis made experimental study possible.