WEEKS 2 Dynamics of Machinery References Theory of Machines and Mechanisms, J.J. Uicker, G.R.Pennock ve J.E. Shigley, 2003 Makine Dinamiği, Prof. Dr. Eres SÖYLEMEZ, 2013 Uygulamalı Makine Dinamiği, Jeremy Hirschhorn, Çeviri: Prof.Dr. Mustafa SABUNCU, 2014 Prof.Dr.Hasan ÖZTÜRK Dr.H.ÖZTÜRK-2010

Example:This slider-crank mechanism is in static equilibrium in the shown configuration. A known force F acts on the slider block in the direction shown. An unknown torque acts on the crank. Our objective is to determine the magnitude and the direction of this torque in order to keep the system in static equilibrium. 3 2 4 Prof.Dr.Hasan ÖZTÜRK

Simplified FBD method: Numerical values for the link lengths are L2 = 2 m and L3 = 4 m. From the figures we extract the following measurements: a = 1.8 m , b = 1 m , c = 2 m , d = 3.6 m. Assume the applied force is given to be F = 10 N in the negative direction. Simplified FBD method: The connecting rod of this mechanism is a two-force member. The reaction forces at A and B must be equal but in opposite directions. These reaction forces are named F2 3 and F 43 , and given arbitrary directions Prof.Dr.Hasan ÖZTÜRK

Graphical: Prof.Dr.Hasan ÖZTÜRK

Coulomb Friction: Coulomb friction can be included between two contacting surfaces in a static force analysis. Given the static coefficient of friction, μ (s) , the friction force can be described as the product of the coefficient of friction and the reaction force normal to the contacting surfaces. The friction force must act in the opposite direction of the tendency of any motion. Prof.Dr.Hasan ÖZTÜRK

Kinematics of meshing gears. GEAR KINEMATICS The kinematic function of gears is to transfer rotational motion from one shaft to another. Since these shafts may be parallel, perpendicular, or at any other angle with respect to each other, gears designed for any of these cases take different forms and have different names: spur, helical, bevel, worm, etc. pitch diameter number of teeth module tangential acceleration Kinematics of meshing gears. Prof.Dr.Hasan ÖZTÜRK

Spur Gear Force Analysis (Static): The reaction forces between the teeth occur along the pressure line AB, tipped by the pressure angle, tipped by the pressure angle  from the common tangent to the pitch circles. In applications involving gears, the power transmitted and the shaft speeds are often specified. remembering that power is the product of force times velocity or torque times angular velocity, we can find the relation between power and the transmitted force. Using the symbol P to denote power, we obtain

Spur Gear Force Analysis (Dynamic): The reaction forces between the teeth occur along the pressure line AB, tipped by the pressure angle, tipped by the pressure angle  from the common tangent to the pitch circles. Prof.Dr.Hasan ÖZTÜRK

Helical Gears Fa: axial, Fr: radial Ft: tangential t: transverse pressure angle : helix angle Prof.Dr.Hasan ÖZTÜRK

Straight Bevel Gears Prof.Dr.Hasan ÖZTÜRK

Dynamic Force Analysis

Sometimes it is convenient to arrange these mass moments of inertia and mass products of inertia into a symmetric square array or matrix format called the inertia tensor of the body:

Dynamic Force Analysis D'Alembertls principle: The vector sum of all external forces and inertia forces acting upon a system of rigid bodies is zero. The vector sum of all external moments and inertia torques acting upon a system of rigid bodies is also separately zero. inertia force Fi has the same line of action of aG but is in opposite direction inertia torque Ti  is in opposite sense of the angular acceleration a Prof.Dr.Hasan ÖZTÜRK

Slider –Crank Mechanism external force and torque, F4 and T2 All frictions are neglected except for the friction at joint 14 Prof.Dr.Hasan ÖZTÜRK

EXAMPLE We use the four-bar linkage of the below Figure. The required data, based on a complete kinematic analysis, are illustrated in the Figure and in the legend. At the crank angle shown and assuming that gravity and friction effects are negligible, determine all the constraint forces and the driving torque required to produce the acceleration conditions specifıed. Prof.Dr.Hasan ÖZTÜRK

We start with the following kinematic information. Next we calculate the inertia forces and inertia torques. Because the solution is analytical, we do not need to calculate offset distances nor do we replace the inertia torques by couples. The six equations are

Considering the free-body diagram of link 4 alone, we formulate the summation of moments about point 04: Also, considering the free-body diagram of link 3 alone, we formulate the summation of moments about point A: Prof.Dr.Hasan ÖZTÜRK

Prof.Dr.Hasan ÖZTÜRK

Prof.Dr.Hasan ÖZTÜRK

Prof.Dr.Hasan ÖZTÜRK

PLANAR ROTATION ABOUT A FIXED CENTER Application of the parallel-axis theorem for mass moments of inertia For fixed-axis rotation, it is generally useful to apply a moment equation directly about the rotation axis O. Prof.Dr.Hasan ÖZTÜRK

Center of percussion P P P P Prof.Dr.Hasan ÖZTÜRK

Prof.Dr.Hasan ÖZTÜRK

Prof.Dr.Hasan ÖZTÜRK