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# Power Transmission – Belt drives, gear trains, balancing, mechanisms and flywheels — 2 Essay Example

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Mathematics
• Document type:
Assignment
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2
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1387

In this research paper there is presentation of solutions to tasks under the area of mechanical principles. In task 1 there is a look at the was power is transmitted by v-belt and flat. Problems involving power transmission through gears was what was addressed in task 2 this included epicyclical gear mechanism while problems to do with clutches was addressed in task 3. Balancing of masses is very important in machines where rotation at high speed is involved and this important issue was addressed in task 4. Flywheel problems was addressed in task 5; task 6 involved analysis of mechanism. The last task in this paper gave a solution to a coupling problem.

From task 1B, if the cross sectional area is changed to 400 mm2 and the other details remain the same, determine the maximum power, which can be transmitted, and the diameter of the motor pulley.

For maximum power with regard to a heavy flat belt we have the following relationship

Determination of mass of belt resulting to centrifugal force considering 1m length of belt.

Volume of 1mlength of belt when we consider the cross section

Maximum stress = T1

T1 = 800kN

Using

With knowledge

Power transmission is given by

TC = 266.67

Calculating diameter of the motor pulley:

N = 1400rpm

is the maximum velocity associated with angular velocity

From task 3A, the outside diameter of the plates is increased to 200mm. Determine the torque, end thrust and number of plates required.

With ‘N’ = 2000rpm

From the relationship

W = end thrust (N)

P = pressure = 150kN/m2

T = torque =358.1Nm

W = end thrust 3534.3N

= is outer radius = 0.1m

= is inner radius = 0.05m

n = number of driven plates

Rounding up we n=6 pairs

Compare the answers you have obtained from tasks 3A and 3D. You must critically evaluate the answers you have obtained.

From task 3B, assuming the axial force and coefficient of friction remain the same, explain how the other values could be modified to increase the torque transmitted. Two methods should be included and fully explained.

One of the way of increasing the torque is through reducing the cone angle. We know that torque is given by the following relationship

. This clearly shows that reducing the cone angle will result to the value of reducing being small and this when divided by the will result to a bigger value of torque T.

The other was of increasing the toque T is by increasing the width of the clutch b. Increasing the breath increases the area of contact which is governed by the relation. The ratio r/b from 2.25 to 4. In order to have high torque to be transmitted the b=width b should result to the smallest possible ratio of r/b. This will result to increased torque T.

Explain where slider crank mechanisms are used in engineering applications.

Crack mechanisms are very important as they are used in most combustion engine in changing reciprocating movement to rotary movement. Crank mechanisms are also found in heavy machines such as agricultural loaders and road construction machines

From task 7A, how could the kinetic energy of the shaft be increased?

Kinetic energy can be increased increasing its mass since kinetic energy depends on the mass of the shaft. The other way is to have radius of gyration of the shaft increased since the kinetic energy of the shaft is dependant of the square of radius of gyration. The radius of gyration is the point where the mass of the shaft is assumed to be concentrated. This is because the kinetic energy of the shaft is given by the relationship where m is the mass of the shaft and k is the radius of gyration of the shaft.

Now considering the shaft that draws power from the gear box , it will be found for there to be high kinetic energy in the shaft there should be low loss energy in the gear box. This is to be achieved by reducing the wait of the rotating gears in the gear box. This is because it will require high energy to be consumed to rotate the gears if they are much heavy compared to if the gears are much lighter. One of the ways of reducing the weight of the rotating gears is by reducing the amount of materials used in making gears and through using lower density materials.

Discussion

With regards to power transmission of power by belts (flat belts v-belts) in finding the solution it is assumed that we have maximum tension in the belts. From the framing of the questions it was clear that the belts used in transmission were heavy and this called for using equations that puts into consideration the centrifugal force. The centrifugal force can go to a maximum of a third of the maximum sustainable by the belt in use. In the solutions that addressed in this paper , it was clear that v-belts are able to transmit higher power than flat belts for the same cross consideration. Also with regards to belts the solutions it is noted that high density belt put a limit to the maximum speed that the mechanism can attain. This is seen it the equation where the increase in unit mass lowers the velocity. In choosing the belt for transmission one need to go for a belt that will withstand high stress , be light (lower density ) and there is need to have high coefficient of friction between the pulley and the belt the point of contact.

Task 2 was about transmission of power with gears. One important point with regard to gear transmission is that there can only be transmission of power in gears when the gears enmesh have the same profile. In solving a problem involving epicyclical gears , there is need to look for the solution by having a table and then fill the table by subjecting the system into some appropriate movement and then coming up with the solution. Taking note of the direction of movement and assigning negative and positive; usually negative sign is assigned to anticlockwise movement.

Task three involved in-depth analysis of clutches. In clutches the aim is to have maximum power being transmitted. Power transmission is dependant on the torque involved. In order to have high torque the area of contact should be increased, having high thrust and through having sufficient coefficient of friction. By increasing the number of pairs of plates involved in power transmission we have increased are of contact and thus the power transmission. Increasing the diameter of the pair of plates in contact is a way of increasing the area of contact for a pair of surfaces in contact.

Balancing of masses is very in mechanics especially where there is rotation in machines at high speed. Unbalanced masses may lead to unnecessary vibrations that could result to noise and even damage in machines. In order to visualize and to get the solution the system is usually represented diagrammatically. The solution is obtained by appreciating that the quantities that are being dealt with are vector quantities that need to be drawn to scale so as reflect the magnitude. Also the direction is put into consideration. Both the couples and forces are quantities that are used in obtaining the solution by having two diagram for each of these quantities. In drawing the force and the couple diagrams accuracy is of utmost important.

A flywheel was used in the pressing operation in which case it was important to obtain the required force that can be able to perform the task. Just as in task 5, in task 6 which involved crank mechanisms it was important to present the problem diagrammatically. Task 7 was the last task where there was solution that dealt with a gearbox where it called for knowledge of moment of inertia and also kinetic energy in order for the solution to be obtained.

Conclusion

By applying appropriate laws solutions of some practical problems can be found. In obtaining the solutions it is important to be aware of the units of the quantities that are being dealt with. Drawing skills come in handy when solving some of the problems