Osman Kopmaz

On the Curvature of an Euler–Bernoulli Beam

This paper deals with different approaches to describing the relationship between the bending moment and curvature of a Euler—Bernoulli beam undergoing a large deformation, from a tutorial point of view. First, the concepts of the mathematical and physical curvature are presented in detail. Then, in the case of a cantilevered beam subjected to a single moment at its free end, the difference between the linear theory and the nonlinear theory based on both the mathematical curvature and the physical curvature is shown. It is emphasized that a careless use of the nonlinear mathematical curvature and moment relationship given in most standard textbooks may lead to erroneous results. Furthermore, a numerical example is given for the reader to make a quantitative assessment.

Dynamic analysis of a mechanical press equipped with a half–toroidal continuously variable transmission

This paper proposes a novel mechanical press concept that consists of a half–toroidal continuously variable transmission (CVT) to obtain more speed flexibility than the classical one. In this way, one can achieve a quite wider range of speed variation, e.g., from 0.5 to 2, which cannot be provided efficiently by using other methods such as electrical inverter technique. Moreover, using this new design concept enables us to increase the crankshaft speed beyond the one achieved from the nominal speed of the motor. This feature is not feasible in classical mechanical presses. Thus, the different manufacturing processes such as cutting, bending, punching, to some extent deep drawing can be operated by the same press without any change in the system components. For analysing the dynamics of this new system, a theoretical model is established by combining the equations of motion of classical mechanical press and CVT. The speed fluctuations of crank shaft are investigated under the different CVT ratios. The results of simulations indicate that adding a CVT to a mechanical press is feasible in all conditions provided that an additional flywheel is added to the system.

Experimental validation of the Carbone–Mangialardi–Mantriota model of continuously variable transmissions:

We present detailed experiments to validate the Carbone–Mangialardi–Mantriota model of continuously variable transmissions. Experimental tests were carried out in different working conditions for increasing values of the torque load. Steady-state conditions as well as shift manoeuvres were considered. A detailed comparison with the theoretical predictions of the Carbone–Mangialardi–Mantriota model shows good agreement with the experimental results. This is even more remarkable when it is considered that the Carbone–Mangialardi–Mantriota model is fully self-consistent and completely predictive. It does not need any parameter to be specifically tuned or measured. The results from the present research allows the Carbone–Mangialardi–Mantriota model to be definitely proposed as a very accurate and completely predictive model of the continuously variable transmission variator, and as a very promising tool to develop advanced real-time control of continuously variable transmissions for engineering applications.

Toroidal Continuously Variable Transmission Systems: Terminology and Present Studies

Havacilik, robotik, makine ve otomotiv sanayi gibi bircok farkli alanlarda sabit cevrim oranli hiz donusturuculere alternatif surekli degisken aktarma (SDA) sistemlerinin kullanimi giderek yayginlasmaktadir. Ozellikle otomotiv sanayinde motorun surekli optimum devirde calismasina imkan vererek onemli yakit tasarrufu ve bunun sonucu daha dusuk emisyon degerleri, yuksek ivmelenmeye ve sessiz calismaya imkan saglamalari gibi nedenlerden dolayi son zamanlarda kullanimlari artmaktadir. SDA sistemlerinin kayisli, zincirli, bilyeli, toroidal vb. gibi bircok degisik cesitleri mevcuttur. Bu calismada elastohidrodinamik ilkelere gore calisan toroidal SDA sistemleri ele alinmis olup bunlar hakkinda son yirmi yilda onem arz eden temel calismalar gozden gecirilmistir. Incelenen literaturun daha iyi anlasilmasina katkida bulunmasi icin konuya iliskin terminolojiyle birlikte sistemlerin dinamigi ve kontrolune de yer verilmistir. Mevcut arastirma calismalarinda bazi onemli konularin eksikligine dikkat cekilmis ve gelecekteki muhtemel calismalara isaret edilmistir. Yazarlarin tespit edebildigi kadariyla bu calisma, toroidal SDA sistemleri uzerine Turkce literaturde ilk inceleme calismasini olusturmaktadir

A new approach to the kinematic analysis of universal joints

Abstract This work is the continuation of a study which is concerned with the kinematics of an universal joint and its use in shaft connections. In the present work, case studies are carried out by numerical implementation of the kinematic formulas illustrated in a previous paper in which two different systems for transmission of rotational motions are kinematically analysed. The first of these systems consists of two shafts (an input and an output shaft) connected via an universal joint, while the other comprises three shafts (an input, an intermediate, and an output shaft) and two universal joints connecting them. Furthermore, it is investigated how the angles between shaft axes, the arm lengths of the cross pieces, the angles between cross arms, and the angle between yoke planes of the intermediate shaft affect the characteristics of output motion. For both systems, the relationships between rotation angles of shafts are derivated by applying the rigidity condition on the cross arms. The case studies show that the arm lengths of cross pieces have no effect on the angular relations, independently of the angles between arms. However, in a coplanar system of the second type, either parallel or crossed assembled, it is concluded that an input rotation cannot be transmitted onto the output shaft without losing its kinematic features as far as the angles between the cross arms in each joint deviate from 90°, and also the angle between the yoke planes from 0°, respectively. The interference of the working planes of the joint is not included in the study.

Transient phenomena during engagement phase of a clutch

This paper deals with the transient behaviour of two main parts of a clutch, i.e., friction plate and hub, in a passenger car, during engagement phase. The present work aims to develop a simple discrete model that might enlighten the vibrations of interior part of a clutch. The second part of the work is devoted to examining the effect of torsional stiffnesses, external loading torque, friction gradient and viscous damping on the transient behaviour of clutch parts along with other components. Case studies are carried out based on two different scenarios for clutch and gas pedals actions.

A new approach to the kinematical analysis of universal joints

In this paper, universal joint is treated from the viewpoint of the theory of mechanisms, and firstly, its degree of freedom as a spherical mechanism is calculated and discussed. Then, two different systems which are used to transmit rotational motions, are kinematically analysed. The first of these systems consists of two shafts connected via a universal joint, while the other comprises of three shafts and two universal joints connecting them. For both systems, the relationships between rotation angles of shafts are derivated by applying the rigidity condition on the cross arms.