 Hello everyone, I am Sachin Rathod from Walsh Chant Institute of Technology, today we are dealing with contact ratio of supergear. The learning outcome of this session is student will able to understand the concept of contact ratio of gear. The contact ratio of gear is one of the important design aspect of supergear. This is a number which indicates the average number of pairs of teeth in contact. So, you can think about this, the contact ratio required for designing gear. So, whether we require the contact to find out the contact ratio while designing the gear, you can think about this. So, we will see this. Gears are generally designed to have a contact ratio larger than 1.2 because any inaccuracies in mounting of the gears might reduce the contact ratio and increasing the possibility of impact between the mashing teeth and consequently the noise level. It is obviously necessary that the tooth profile be proportionate so that the second pair of the mating teeth comes into contact before the first pair of out of contact that is to check the contact ratio. The contact ratio is equal to length of arc of contact divided by the circular pitch. So, we have to know what is mean by length of path of contact, arc of contact for getting the concept of contact ratio. The length of path of contact is nothing but the length of common normal cut by addendum circle of the gear and pinion and the length of arc of contact is nothing but the path traced by a point on a pitch circle from beginning to the end of the engagement of two mating teeth. And from these two definitions, we can get the contact ratio is nothing but the ratio of length of arc of contact to the circular pitch. So, we will see the concept of contact ratio. This is a didendum circle, addendum circle and pitch circle of one gear. This is a gear number one. We will give name as a centrize O1. Similarly, this is a gear number two having didendum circle, pitch circle and addendum circle. So, this gear number one and two are meeting at this point. It's called as a pitch point. And suppose this is a tooth of the gear number one and this is a tooth of the gear number two. And meeting, engaging point occurs at this point. Similarly, this teeth of the gear number two and gear number one. The engagement of the gear tooth occurs at this point and disengagement occurs at this point. So, the contact ratio is nothing but the average pair of the teeth are remains in contact from this point to this point. So, you have to find out this contact ratio. If you draw the common tangent to the base circle, that must should pass through the pitch point. This is the law of gearing already we have seen in previous lecture. So, this is nothing but your pitch point and this is a, you can give a name as a mn. This is a, if you join the axis of the two gear. This is the axis of the two gear. It should be the perpendicular. The engagement point will be this. We will give name as a k pitch point p and disengagement occurs at l point. So, kpl is nothing but the length of path of contact. Which is nothing but the length cut along the common normal from addendum circle of gear and pinion. So, that kpl is nothing but the length of path of contact. The engagement of this tooth occurs from k to l disengagement point. Kp is, it is having the two segment that is a kp and pl. Kp is called as a length of path of approach and pl is called as a length of path of recess. So, we have to find out the length of path of contact and length of path of recess. For that purpose, we have to do the one construction. If you join this, this is nothing but to the pressure angle indicated by the letter phi. So, if I join the length o1 to l as well as o2 to k, now we have to find out the length of path of contact. That is nothing but the kl. So, we are getting the, by the geometrical consideration, we are getting the length of path of contact. And that kl is equal to square root of rA square minus r square cos square phi plus square root of rA square minus r square cos square phi minus r plus r sin phi. rA is nothing but radius of addendum circle, capital R indicates the radius of pitch circle, phi is nothing but the pressure angle. Similarly, small rA, radius of addendum circle of the pinion, radius of pitch circle, small r and phi is the pressure angle. So, from this equation, we can easily find out the length of path of contact. If we are getting the length of path of contact, we can find out length of arc of contact is equal to length of path of contact divided by cos phi. This length of arc of contact is nothing but the arc traced along the pitch circle from engagement to the disengagement. If the engagement occurs at this point, we can give a name along the pitch circle, we are getting the g point. Here is a p point, pitch point. So, arc traced along the pitch circle is gp, we are getting the disengagement at this point. So, gph gives the length of arc of contact, we are getting by this equation and the contact ratio is calculated by length of arc of contact divided by circular pitch. So, by using this equation, we are getting the contact ratio. I have taken these references. Thank you.