Presentation on theme: "Lecture #25 SPUR GEAR Tooth Loads and Mass Moment of Inertia Course Name : DESIGN OF MACHINE ELEMENTS Course Number: MET 214."— Presentation transcript:
Lecture #25 SPUR GEAR Tooth Loads and Mass Moment of Inertia Course Name : DESIGN OF MACHINE ELEMENTS Course Number: MET 214
In order to develop an understanding of the factors affecting tooth size and the forces that can be transmitted by a tooth consider the diagram provided below.
The forces to be transmitted between a pair of gear teeth are transferred between the teeth at the point of contact. As the gears rotate, the point of contact existing between a pair of teeth changes its location on each tooth. Due to the shape chosen for the teeth, the direction of the forces to be transmitted between the teeth lies along the line of action, or as referred to in the diagram on the previous slide, the axis of transmission. As to be noted from the diagram provided above, the point of contact on the driven gear starts out near the top of the tooth and proceeds toward the root. In addition, it must be noted that the forces to be transmitted between the teeth are distributed along the width of the teeth. In addition, the teeth of meshing gears make contact only for a small portion of a revolution. These features of meshing gears are summarized in the figure provided in the figure on the next slide.
In order to analyze the loads that can be transmitted between a pair of teeth, a worst case analysis may be performed. In the case of the forces acting on a gear tooth, the most extreme situation involved with transmitting a force between teeth occurs when the force to be transmitted between the teeth is applied at the tip of one of the teeth as indicated below. The force to be transmitted acts along the line of action and may be resolved into tangential and radial components as shown in the figure on the next slide. Each force component leads to different types of stresses in the tooth. It should be noted that the figure on the next slide was copied from a different source and therefore the orientation of the load is different that what has been shown in the previous slides. Such a change in perspective should not be the source of any confusion.
Due to the fact that the teeth in contact are in contact only over a very small area of the tooth at any particular point of contact, the loads to be transmitted between teeth are distributed over a very small area which can lead to very high stress levels in a tooth as illustrated below. As indicated in the diagram provided on a previous slide, the repetitive nature of how the teeth of a pair of gears engage one another, the high stress levels associated with the small area of contact can lead to pitting of the gear face as indicated below. In addition, as was noted in the previous lecture, the teeth of a pair of mating gears slide relative to one another which also contributes to the wear of the gear teeth. A geometry necessary for analyzing the level of stress due to the small area of contact existing between a pair of teeth is shown on the next slide.
The modification to the Lewis equation necessary to utilize the equation in practice involves many factors that are discussed in detail in books addressing the design of gears. The reader interested in the material may consult any number of texts books concerned with machine design including the book by Mott. The system shown below is referred to as a rack and pinion and can be used to convert rotational motion to linear motion and vise versa. The rack is in essence a spur gear with an infinite pitch radius so as to evolve to a shape that has zero curvature along the pitch line of the rack as shown in the figure.
In order to relate the system level requirement pertaining to the acceleration of the rack to the force to be transmitted between gear teeth, consider the system shown below. The system contains a motor driving a pinion which in turn drives a rack which is attached to a ball slide. The ball slides offers very low resistance to linear motion. In order to relate the acceleration of the ball slide, which is the same as the acceleration of the rack since the rack is attached to the ball slide, use Newtons law of motion to describe the acceleration of the slide.