Cams MCQ Quiz - Objective Question with Answer for Cams - Download Free PDF

Explanation:

Cam Profile:

• The cam profile is the actual shape or contour of the cam that determines the motion of the follower. It is critical in cam-follower mechanisms to control the timing, displacement, velocity, and acceleration of the follower. These profiles are designed with precision to meet specific motion requirements in machines such as engines, automation systems, and other mechanical devices.
• In cam mechanisms, the primary elements that define the profile include the prime circle, base circle, and trace point, which are used to generate the cam's shape and ensure the desired motion of the follower.

Addendum:

• Addendum is a term commonly used in gear terminology and refers to the radial distance between the pitch circle and the top of the gear tooth. It plays a significant role in the design and functioning of gears but has no relevance to the cam profile or its design parameters.

Additional InformationPrime Circle:

• The prime circle is the smallest circle that can be drawn tangentially to the cam profile.

Trace Point:

• The trace point is a specific point on the follower that is used to define the follower’s motion.

Base Circle:

• The base circle is the smallest circle that can be drawn tangentially to the cam profile, excluding the follower's motion.

Concept:

For Simple Harmonic Motion (SHM), the displacement of a follower is given by:

\( s = \frac{h}{2} \left(1 - \cos\left(\frac{\pi \theta}{\beta}\right)\right) \)

Where,

• \( h = 40 \, \text{mm} \) (total rise),
• \( \beta = 90^\circ = \frac{\pi}{2} \, \text{rad} \) (angle for rise),
• \( \omega = 30 \, \text{rad/s} \) (cam angular velocity).

The velocity is the time derivative of displacement:

\( v = \frac{ds}{dt} = \frac{h}{2} \times \frac{\pi}{\beta} \times \omega \times \sin\left(\frac{\pi \theta}{\beta}\right) \)

The maximum velocity occurs when \( \sin\left(\frac{\pi \theta}{\beta}\right) = 1 \), thus:

\( v_{\text{max}} = \frac{h}{2} \times \frac{\pi}{\beta} \times \omega \)

Calculation:

Substitute the values:

\( v_{\text{max}} = \frac{40}{2} \times \frac{\pi}{\pi/2} \times 30 = 20 \times 2 \times 30 = 1200 \, \text{mm/s} \)

Convert to m/s:

\( v_{\text{max}} = \frac{1200}{1000} = \boxed{1.2 \, \text{m/s}} \)

Concept:

When a follower moves with simple harmonic motion, its maximum acceleration during the outstroke can be derived using the principles of simple harmonic motion (SHM). The relevant parameters given are:

• S: Stroke of the follower
• \(\theta_o\): Angular displacement of the cam during the outstroke of the follower
• \(\omega\): Angular velocity of the cam in rad/sec

Calculation:

From the SHM equation:

Displacement of the follower is given by:

\( x = A \cos(\omega t) \)

Where A is the amplitude of motion, which is half of the stroke:

\( A = \frac{S}{2} \)

Velocity is given by:

\( v = - A \omega \sin(\omega t) \)

Acceleration is given by:

\( a = - A \omega^2 \cos(\omega t) \)

Maximum acceleration occurs when \(\cos(\omega t) = 1\), giving:

\( a_{\text{max}} = A \omega^2 \)

Substituting \(A = \frac{S}{2}\) , we get:

\( a_{\text{max}} = \frac{S}{2} \omega^2 \)

Using the relation for angular displacement:

\( \omega = \frac{\pi}{\theta_o} \)

We substitute into the acceleration equation:

\( a_{\text{max}} = \frac{S}{2} \left( \frac{\pi}{\theta_o} \right)^2 \)

Simplifying:

\( a_{\text{max}} = \frac{\pi^2 \omega^2 S}{2 \theta_o^2} \)

Explanation

Pressure angle – It the angle between the normal to the pitch curve at a point and the direction of the follower motion. It varies in magnitude at all instant of follower motion. The pressure angle represents the steepness of the cam profile. A high value of maximum pressure angle is not desired it might jam the follower in bearings.

Pitch point – It is the point at the pitch curve at which the pressure angle is maximum.

Pressure angle in case of flat-footed or mushroom follower is 0°.

Important Points

• Base circle – It is the smallest circle tangent to the cam profile drawn from the centre of rotation of a radial cam.
• Tracepoint – It is the reference point on the follower to trace the cam profile such as the knife of the knife-edge follower and centre of the roller of roller follower.
• Pitch curve – Curve is drawn by the tracepoint assuming that cam is fixed, and the tracepoint of the follower rotates around the cam.
• Pitch circle – It is the circle passing through the pitch point and concentric with the base circle.
• Prime circle – The smallest circle drawn tangent to the pitch curve is known as the prime circle.

Concept:

• Base Circle: It is the smallest circle, drawn tangential to the cam profile. The base circle decides the overall size of the cam and thus is a fundamental feature.
• Pitch Curve: 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 a pitch curve. For a knife-edge follower, the pitch curve and the cam profile are the same whereas, for a roller follower, they are separated by the radius of the roller.
• Pitch Point: Pitch point corresponds to the point of maximum pressure angle, and a circle drawn with its center at the cam center, to pass through the pitch point, is known as the pitch circle.
• Prime Circle: It is the smallest circle that can be drawn from the center of the cam and tangent to the pitch curve.

Concept:

Stroke or throw: 

The greatest distance or angle through which the follower moves or rotates.

It is the maximum distance of followers from the base circle.

Explanation:

Radial follower:

The follower is known as a radial follower if the line of movement of the follower passes through the centre of rotation of the cam.

Offset follower:

If the line of movement of follower is offset from the centre of rotation of the cam, the follower is known as an offset follower.

Function of offset-follower:

• The force exerted by a cam on the follower is always normal to the surface of the cam at the point of contact. The vertical component (Fcos α) lifts the follower whereas the horizontal component (Fsin α) exerts lateral pressure on the bearing.
• An offset provided in the radial cam-translating-follower mechanism is to decrease the pressure angle during the ascent of the follower because the high value of pressure angle is not desirable as it increases side thrust and performance will not be smooth. Its main concern is to move the follower in the upward direction because it comes down due to its own weight. 

Concept:

A cam mechanism usually consists of two moving elements, the cam, and the follower, mounted on a fixed frame. A cam may be defined as a machine element having a curved groove, which, by its oscillation or rotation motion, gives a predetermined specified motion to another element called the follower.

Base circle: 

• ​The smallest circle from the cam centre through the cam profile curve.

Pressure angle –

• It is the angle between the normal to the pitch curve at a point and the direction of the follower motion. 
• It varies in magnitude at all instant of follower motion. 
• The pressure angle represents the steepness of the cam profile.
• when pressure angle becomes 0° all transmitted force goes into the motion of follower and the direction of the axis of the transmission.
• When pressure angle becomes 90° there will be no motion of the follower.
• Therefore we would like to maintain the pressure angle as low as possible.
• The figure below clearly depicts that the pressure angle is inversely proportional to the base circle diameter. As we increase the size of the cam the pressure angle decreases, therefore to maintain pressure angle as low as possible base circle should be as big as possible.​

Additional Information

Pitch circle: 

A circle from the cam centre through the pitch point.

The pitch circle radius is used to calculate a cam of the minimum size for a given pressure angle.

Pitch curve: 

The path generated by the tracepoint at the follower is rotated about a stationary cam.

Prime circle (reference circle):

The smallest circle from the cam centre through the pitch curve.

Concept:

Depending upon the shape and axis of motion, the following types of cam followers are used in practice:

1. Pointed or knife-edge followers
2. Roller followers
3. Flat face followers and
4. Spherical followers.

Knife edge follower:

• In a knife-edge follower, a sharp knife edge is in contact with the cam. This type of follower is very little in practical use due to the high rate of wear at the knife edge. However, cam of any shape cam works with it.

Roller follower:

• In a roller follower, a roller is held by a pin to the follower assembly. This type of follower is very extensively used in practice, due to the low rate of wear and perfect rolling contact with the cam.
• Roller followers are used in gas and oil engines. They are also used in aircraft engines due to their limited wear at high cam peripheral velocity.

Flat follower:

• In a flat follower, the perfectly flat face is in contact with the cam. In this follower, there will be sliding motion between the contacting surfaces but the wear can be considerably reduced by off-setting the axis of the follower. This type of follower produces high surface stresses.

Spherical follower:

• In a spherical follower, the spherical surface is in contact with the cam.
• In order to minimize the surface stress produced in the flat follower, a spherical shape having a surface of a large sphere radius is given to the flat end.
• The spherical followers are also used in automobile engines.

Explanation:

• Cam is a mechanical element which is used to deliver the reciprocating or oscillating motion to another machine element known as a follower.
• A simple harmonic motion of constant amplitude in which the acceleration is proportional and oppositely directed to the displacement of the body from a position of equilibrium.
• A simple harmonic motion curve is widely used since it is simple to design. The curve is the projection of a circle about the cam rotation axis as shown in the figure.

where H = maximum height of follower in SHM motion

Calculation:          

Given:

Displacement of follower in SHM = 20 mm, angle of rise  θ = 90^o = π /2, speed of cam rotation  N = 15 RPM,

Angular velocity of cam ω = \(\frac{{2\pi N}}{{60}}\)

Now time period of the cam in SHM,

T = angle of rise in radian / angular velocity 

\(T = \frac{{\frac{\pi }{2}}}{{\frac{{2\pi N}}{{60}}}}\;\;\)

\(T = \frac{{\pi \times 60}}{{2 \times 2\pi N}}\)

T = 1 sec

Key Points

The time period in SHM is simply angle turned upon angular velocity.

Concept:

Cylindrical Cam:

A cylindrical cam or barrel cam is a cam in which the follower rides on the surface of a cylinder. In the most common type, the follower rides in a groove cut into the surface of a cylinder. These cams are principally used to convert rotational motion to linear motion parallel to the rotational axis of the cylinder.

Concept:

Base Circle: It is the smallest circle, drawn tangential to cam profile. The base circle decides the overall size of the cam and thus is a fundamental feature.

Pitch Curve: 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 tracepoint is called a pitch curve. For a knife-edge follower, the pitch curve and the cam profile are the same whereas, for a roller follower, they are separated by the radius of the roller.

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

Valves are used to open and close the inlet and exhaust passage of the cylinder. These are operated by the motion of camshaft.

Valve operating mechanism:

When the camshaft rotates, the cam lobe lifts the tappet upward. When the tappet moves up, it pushes the push-rod and one end of the rocker arm upwards. The other end of the rocker arm’s tip moves downward and the valve opens against the spring’s tension.

Thus the motion of the cam is transferred to the valve through the rocker arm.

Explanation:

Simple Harmonic Motion: Since the follower moves with a simple harmonic motion, therefore velocity diagram consists of a sine curve and the acceleration diagram is a cosine curve.

• velocity of the follower is zero at the beginning and at the end of its stroke and increases gradually to a maximum at mid-stroke.
• acceleration of the follower is maximum at the beginning and at the ends of the stroke and diminishes to zero at mid-stroke

Concept:

Depending upon the shape and axis of motion, the following types of cam followers are used in practice:

1. Pointed or knife-edge followers
2. Roller followers
3. Flat face followers and
4. Spherical followers.

Knife edge follower:

• In a knife-edge follower, a sharp knife edge is in contact with the cam.
• This type of follower is very little in practical use due to the high rate of wear at the knife edge.
• However, cam of any shape cam works with it.

Roller follower:

• In a roller follower, a roller is held by a pin to the follower assembly.
• This type of follower is very extensively used in practice, due to the low rate of wear and perfect rolling contact with the cam.
• Roller followers are used in gas and oil engines.
• They are also used in aircraft engines due to their limited wear at high cam peripheral velocity.

Flat follower:

• In a flat follower, the perfectly flat face is in contact with the cam.
• In this follower, there will be a sliding motion between the contacting surfaces but the wear can be considerably reduced by off-setting the axis of the follower.
• This type of follower produces high surface stresses.

Spherical follower:

• In a spherical follower, the spherical surface is in contact with the cam.
• In order to minimize the surface stress produced in the flat follower, a spherical shape having a surface of a large sphere radius is given to the flat end.
• The spherical followers are also used in automobile engines.