CAM

 

CAM

Cams come under higher pair mechanisms. As we already know that in higher pair the contact between the two elements is either point or line contact, instead of area in the case of lower pairs.

clip_image001

In CAMs, the driving member is called the cam and the driven member is referred to as the follower. CAM is used to impart desired motion to the follower by direct contact. Generally the CAM is a rotating or reciprocating element, where as the follower may de rotating, reciprocating or oscillating element. Using CAMs we can generate complex, coordinate movements that are very difficult with other mechanisms. And also CAM mechanisms are relatively compact and easy it design. Cams are widely used in automatic machines, internal combustion engines, machine tools, printing control mechanisms and so on. Along with cam and follower one frame also will be there with will supports the cam and guides the follower.

A follower can be classified in three ways

  1. According to the motion of the follower.
  2. According to the nature of contact.
  3. According to the path of motion of the follower

According to the motion of the follower

1. Reciprocating or Translating follower

: When the follower reciprocates in guides as the can rotates uniformly, it is known as reciprocating or translating follower.

2. Oscillating or Rotating follower

: When the uniform rotary motion of the cam is converted into predetermined oscillatory motion of the follower, it is called oscillating or rotating follower

According to the nature of contact:

1. The Knife-Edge follower

: When contacting end of the follower has a sharp knife edge, it is called a knife edge follower. This cam follower mechanism is rarely used because of excessive wear due to small area of contact. In this follower a considerable thrust exists between the follower and guide.

2. The Flat-Face follower

: When contacting end of the follower is perfectly flat faced, it is called a flat faced follower. The thrust at the bearing exerted is less as compared to other followers. The only side thrust is due to friction between the contact surfaces of the follower and the cam. The thrust can be further reduced by properly offsetting the follower from the axis of rotation of cam so that when the cam rotates, the follower also rotates about its axis. These are commonly used in automobiles.

3. The Roller follower

: When contacting end of the follower is a roller, it is called a roller follower. Wear rate is greatly reduced because of rolling motion between contacting surfaces. In roller followers also there is side thrust present between follower and the guide. Roller followers are commonly used where more space is available such as large stationary gas or oil engines and aircraft engines.

4. The Spherical-Faced follower

: When contacting end of the follower is of spherical shape, it is called a spherical faced follower. In flat faced follower�s high surface stress are produced. To minimize these stresses the follower is machined to spherical shape.

According to the path of motion of the follower:

1. Radial follower

: When the motion of the follower is along an axis passing through the centre of the cam, it is known as radial follower.

2. Off-set follower

: When the motion of the follower is along an axis away from the axis of the cam centre, it is called off-set follower.

A Cam can be classified in two ways:

1. Radial or Disc cam

: In radial cams, the follower reciprocates or oscillates in a direction perpendicular to the cam axis.

2. Cylindrical cam

: In cylindrical cams, the follower reciprocates or oscillates in a direction parallel to the cam axis. The follower rides in a groove at its cylindrical surface.

CAM NOMENCLATURE

The various terms we will very frequently use to describe the geometry of a radial cam are defined as fallows.

1. Base Circle

: It is the smallest circle, keeping the center at the camcenter, drawn tangential to cam profile. The base circle decides the overall size of the cam and thus is fundamental feature.

2. Trace Point

: It is a point on the follower, and it is used to generate the pitch curve. Its motion describing the movement of the follower. For a knife-edge follower, the trace point is at knife-edge. For a roller follower the trace point is at the roller center, and for a flat-face follower, it is a t the point of contact between the follower and the cam surface when the contact is along the base circle of the cam. It should be note that the trace point is not necessarily the point of contact for all other positions of the cam

clip_image003

The various terms we will very frequently use to describe the geometry of a radial cam are defined as fallows.

3. Pitch Curve

: It is the curve drawn by the trace point assuming that the cam is fixed, and the trace point of the follower rotates around the cam, i.e. if we hold the cam fixed and rotate the follower in a direction opposite to that of the cam, then the curve generated by the locus of the trace point is called pitch curve.
For a knife-edge follower, the pitch curve and the cam profile are same where as for a roller follower they are separated by the radius of the roller.

4. Pressure Angle

: It is the measure of steepness of the cam profile. The angle between the direction of the follower movement and the normal to the pitch curve at any point is called pressure angle. Pressure angle varies from maximum to minimum during complete rotation. Higher the pressure angle higher is side thrust and higher the chances of jamming the translating follower in its guide ways. The pressure angle should be as small as possible within the limits of design. The pressure angle should be less than 450 for low speed cam mechanisms with oscillating followers, whereas it should not exceed 300 in case of cams with translating followers. The pressure angle can be reduced by increasing the cam size or by adjusting the offset.

5. Pitch Point

: The point corresponds to the point of maximum pressure angle is called pitch point, and a circle drawn with its centre at the cam centre, to pass through the pitch point, is known as the pitch circle.

6. Prime Circle

: The prime circle is the smallest circle that can be drawn so as to be tangential to the pitch curve, with its centre at the cam centre. For a roller follower, the radius of the prime circle will be equal to the radius of the base circle plus that of the roller where as for knife-edge follower the prime circle will coincides with the base circle.

DESCRIPTION OF THE FOLLOWER MOTION

The cam is assumed to rotate at a constant speed and the follower rotates over it. A complete revolution of cam is described by displacement diagram, in which follower displacement i.e. the movement of the trace point, is along y axis and is plotted against the cam rotation �


. The maximum follower displacement is referred to as the lift L of the follower. The inflexion points on the displacement diagram i.e., the points corresponding to the maximum and minimum velocities of the follower correspond to the pitch points. In general the displacement diagram consists of four parts namely.

1. Rise

: The movement of the follower away from the centre of the cam. The follower rises upwards in this motion.

2. Dwell

: In this phase there is no movement of the follower. In this dwell, the distance between the centre of the cam and the contact point is maximum.

3. Return

: The movement of the follower towards the cam centre.

4. Dwell

: The movement of the follower is not present in this phase. In this dwell, the distance between the centre of the cam and the contact point is minimum.

Construction of Displacement Diagrams

Though the follower can be made to have any type of desired motion, we are going to discus the construction of the displacement diagrams for the basic follower movements as mentioned below.

  1. Uniform motion and its modifications.
  2. Simple harmonic motion.
  3. Uniform acceleration motion i.e. parabolic motion.
  4. Cycloidal motion.

In uniform motion the velocity of the followers is constant. As the displacement is from y = 0 to y = L then the cam rotates from θ = 0 to θ = θri, and thus the straight line joining the two points (θ = 0, y = 0) and (θ = θri, y = L) represents the displacement diagram for uniform motion.

Uniform motion and its modifications

clip_image005clip_image007

As there is an instantaneous change from zero velocity at the beginning of the rise and a change to zero velocity at the end of the rise, the accelerations at this instance attain a very high value. To avoid this, the straight line of the displacement diagram is connected tangentially to the dwell at both ends of the rise by means of smooth curves of any convenient radius and the bulk of the displacements take place at uniform velocity, whish is represented as straight line as shown in the diagram. So, most part of the time the velocity of the follower is uniform.

  1. Simple harmonic motion.

The displacement diagram for simple harmonic motion can be obtained as shown in figure.5. The line representing angle �


ri is divided into a convenient number of equal lengths. A semicircle of diameter L is drawn as shown and divided into same number of circular arcs of equal length. Horizontal lines are drawn from the points so obtained on the semicircle, to meet the corresponding vertical lines through the points on the length �


ri. For SHM we always have finite velocity, acceleration, jerk, and higher order derivatives of displacements.

clip_image009

Uniform Acceleration motion

In such cam and followers, there is acceleration in the first half of the follower motion whereas it is deceleration during the later half. With dwell at the beginning and at the end of the rise, when lift of the follower has to take place in a given time, it is easy to show that the maximum acceleration will be the least if the first half of the rise takes place at a constant acceleration and the remaining displacement is at a constant deceleration of same magnitude. For this reason the parabolic motion is very suitable for high speed cams as it minimizes inertia force.
While locating the vertical divisions in the displacement diagram, the fact used is that at constant acceleration the displacement is proportional to the square of the time i.e. it is proportional to the square of the cam rotation as the cam rotates at constant speed. The displacement diagram for such cam and followers is shown in figure 6.(a). This is also applicable for deceleration.

clip_image011

Modified Uniform Acceleration motion

For cam operating valves of internal combustion engines, the modified uniform acceleration motion is used for the follower. It is desired that the valves should open and close quickly, at the same time maintain the aforementioned advantage of parabolic motion. In modified parabolic motion, the acceleration f1 during the first part of the rise is more than the deceleration f2 during the rest of the rise as shown in fig.6(b).

clip_image013

Let
clip_image014
Then it is easy to prove that,
clip_image015
Where,
clip_image016= angle of cam rotation when the acceleration is f1,
     K θa = angle of cam rotation when the deceleration f2.
The lift L is given by,
clip_image017
Where
     L1 = rise with acceleration clip_image018, and
     K L1= rise with deceleration f2.

.

Cycloidal Motion

Cycloidal motion is obtained by rolling a circle of radius L/(2п) on the ordinate of the displacement diagram. A point P rolling on the ordinate describes a cycloid. A circle of radius L/(2п) is drawn with centre at the end A of the displacement diagram. This circle is divided into equal number of divisions as the abscissa of the diagram representing the cam rotation θri. The projections of the on the circumference are taken on the vertical diameter, represented by 1’, 2’,…6’. The displacement diagram is obtained from the intersection of the vertical lines through the points on the abscissa and the corresponding lines parallel to OA. The following figure will show the displacement diagram for Cycloidal motion with construction details.

clip_image020

Advertisements

One thought on “CAM

  1. I like you article about cam follower mechanism. You have written about all type of cam follower mechanism. I have made cam follower prototype for clean energy cheaper than coal. You can find my prototype video at youtube.com

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s