DME-III_Design of Machine Elements

DME-III_Design of Machine Elements_Cottter Joint

- March 31, 2020

DESIGN PROCEDURE OF COTTER JOINT

Cotter Joint Introduction

Before going into detailed steps to design and find dimensions of cotter joint, it is necessary to understand clearly the various components, their functions and assembly of cotter joint. Here is the exploded view of cotter joint.

Exploded View of Cotter joint assembly

Spigot is the male part of the joint , it has a rectangular slot for passing the cotter through it. Spigot has a collar which rests against the socket end.

Socket is the female part of the joint, it also has a rectangular slot for passing the cotter through it. It has a circular hole in which spigot fits.

Cotter is a wedge shaped piece of metal which actually connects two parts which are non rotating. Cotter is fitted in the slot and remains in its position by wedge action.
Taper is provided to, i) With taper it is easy to remove the cotter and dismantle the joint ii) It ensures tightness of the joint in operation and prevents loosening of the parts.

Cotter is driven in or out using the hammer. Value of taper on cotter is 1 in 48 to 1 in 24 .

DESIGN PROCEDURE OF COTTER JOINT

Notations used in design are as follows,

P= Load on the joint or pull acting on rods, d= Diameter of the rod, d1= outer diameter of socket,d2= Diameter of spigot or inside diameter of socket, d3= Outside diameter of spigot collar,d4= Diameter of socket collar, t1= Thickness of spigot collar, a = Distance from the end of the slot to end of spigot, c= thickness of socket collar, b,t,l= width , thickness and length of cotter.

Step 1 : Design of rod( ‘d’)

Tensile failure of rod

Load = Stress * Area

P=(Area Resisting Tension)*(Allowable Stress)

...From this equation diameter d of the rod is determined.

Step 2 : Design of Spigot { ‘d₂’,’d3’,t1’,’a’}

Tensile failure of Spigot

The spigot end may fail under tension into two parts as shown in figure below, Since the plane of failure is perpendicular to the direction of force it is tensile failure,

the area resisting the failure is shown by red in the diagram, since it is circular minus a rectangle the equation will be,

………….From this equation the diameter of spigot end d₂ can be found.

Emperical Relations

{Other three dimensions of Spigot are decided on the basis of emperical relations and then checked whether the stress induced is withing safe limits or not}

Crushing failure of Spigot ( Check crushing stress induced)

……...Find $\sigma_c$ Using this equation and check if it is within safe limits or not .

Shear failure of Spigot ( Check Shear stress induced)

……...Find $\tau$ Using this equation and check if it is within safe limits or not .

Diagram showing the Shear failure of Spigot end

Step 3 : Design of Socket { ‘d1’,’d4’,’c’}

Following dimensions of socket are to be found and stresses induces must be checked for safe limit.

Tensile failure of Socket

The socket may also fail under tension into two parts as shown in figure below, since the plane of failure is perpendicualr to direction of force it is the tensile failure.

Area resisting is a hollow square minus a rectangular strip having length (d1-d2) and thickness t, so the strength equation becomes,

………...From this equation diameter d₁ can be determined, again there is quadradic equation formation. Refer to numerical problems section to view the detailed solution.

Emperical Relations

{Other three dimensions of Socket are decided on the basis of emperical relations and then checked whether the stress induced is withing safe limits or not}