Hello everyone, I am Sachin Rattor from Walsh Chant, Institute of Technology, Solapur. Today we are dealing with Contact Reshops Square Gear. The learning outcome of this session is, students will be able to understand the concept of contact ratio of gear. The contact ratio of gear is one of the important design aspects of square gear. 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 meshing 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 random 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 definition 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. Suppose this is a d-dendom circle, add-endom circle and pitch circle of one gear. This is a gear number one, we will give you name as a center as O1. Similarly this is a gear number two having d-dendom circle, pitch circle and add-endom circle. So this gear number one and two at meeting at this point is called as a pitch point. And suppose this is a two of the gear number one and this is a two 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 these engagements 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 the 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 a law of gearing already we have seen in previous lecture. So this is nothing but the pitch point and this is a, we can give a name as a m-n. 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 and this should be the perpendicular. The engagement point will be this, we will give name as a k, pitch point p and this engagement 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 segments that is kp and pl, kp is called as a length of path of approach and pl is called as the 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 the pressure angle indicated by the letter phi. So if I join the length o1 to l as well as o2 to k. So now we have to find out the length of path of contact that is nothing but the ks. So we are getting the by the geometrical consideration, we are getting the length of path of contact 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 r-dnum circle. capital R indicates the radius of pitch circle phi is nothing but the pressure angle. Similarly, small ra radius of r-dnum 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 you 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 r-traced along the pitch circle from engagement to the disengagement. That means if the engagement is occurred at this point, we can give them along the pitch circle we are getting the g point. There is a p point, pitch point. So r-traced along the pitch circle is gp, we are getting the disengagement at this point. So gp h 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 this equation, we are getting the contact ratio. So I have taken these references. Thank you.