Q1. Assuming that the crane is loading as shown in Figure 2. Develop an Excel spreadsheet to calculate the reactions at the supports

Figure 1 Overhead Cranes

LO1 Solve problems within static mechanical systems.

 Q1. Assuming that the crane is loading as shown in Figure 2. Develop an Excel spreadsheet to calculate the reactions at the supports: R_A and R_B;  shear forces (SF); and bending moments (BM) for a simply supported beam with applied point-loads, as defined below. The spreadsheet should also produce SF and BM diagrams for the beam.

Inputs to the spreadsheet are:

• Length of beam

• Load values (kN): W₁, W₂, …., W_n
• Distances of each load from the left hand end of the beam (m): d₁, d₂, …., d_n

A fully referenced report is to be prepared under the section headings:

1. Introduction
2. Analysis – What would the difference be for different fixing of the bean and different types of beam, What type of columns would be needed to support the crane and what affects on the columns could cause the crane to fail
3. Spreadsheet Realisation                                                                                                                      
4. Results
5. Discussion / Conclusions                                                                                                                      
6. References

(word count for this section max 800) 10%

The theory of torsion in solid and hollow circular shafts

Torsion Example

Note:  In the following questions, the words ABC AB, or BC are numbers from your student number. For example: If your student number is 2389259, which corresponds to OABCDEF

L01 . Q2 On the crane, a motor for the hoist is driven by a shaft. The solid circular shaft is used to transmit a torque of ‘ABC’ kNm. The shaft material has a modulus of rigidity of 70GPa

(a) What is the diameter of the shaft, if the shear stress is not to exceed 90 MPa?

(b) What is the angle of twist in a 2 m length of shaft? (5%)

L01 . Q3 What would be the external diameter of a hollow shaft needed to transmit a torque of ‘AB’ kNm if the shear stress is not to exceed 70 MPa and the shaft has an external diameter 1.3 times the internal diameter?  What is the maximum power that can be transmitted by the shaft rotating at 18 rev/s?                                                                  

Calculate and analysis the differences with respect to power output, costs and weight. (5%)

LO2  Investigate the effect of constraints on the performance of a dynamic mechanical system.

Energy and work:

The principle of conservation of energy and work-energy transfer in systems

LO2 Q1 -  A multi-plate clutch has “A” surfaces in contact, a speed of “B” rev/min, diameters of “C” mm and “D”mm. The coefficient of friction is “E” and the axial force is “F”N. Calculate the power that can be transmitted without slipping using both the uniform wear and the uniform pressure theories.

A simple gear train in an aircraft transmission drives a hydraulic pump and has 3 gears. Gear A has “A” teeth and is the input. Gear C has “B” teeth and is the output. Gear A rotates at “C” rev/min clockwise. If the input torque is “D” Nm and the whole system is “E”% efficient, what is the gear ratio, the output speed and torque (5%)

Linear and angular velocity and acceleration

LO2 Q2 -  A fly wheel with a mass of “AC” kg is accelerated by an electric motor from rest to an angular velocity of 120rads/s in 14 seconds, if the value of k is 0.3m and there is a frictional torque of 0.07Nm calculate the torque applied, total work and the power from the motor. (5%)

LO2 Q3 -  A car of mass ‘BCD’ kg is travelling on a round circuit with a diameter of 350m. If its velocity is 38m/s calculate its centripetal force opposed by the tyres and the centripetal acceleration.  (5%)

LO2 Q4 -  A quad bike rolls down a hill with an incline of 20° to the horizontal, when the velocity is 10m/s the brakes are applied with a total braking torque of 1100Nm.  

If the rolling resistance is equivalent to 50Nm and the mass of the vehicle body is ‘ADE’ kg and each of the four wheels, which are 0.6m in diameter are 50kg calculate the following.

• Holding torque for the vehicle on the incline.
• The distance travelled after the brakes are applied.
• The power dissipated by the brakes.

(5%)

Assume the acceleration is constant.

Velocity and acceleration diagrams of planar mechanisms

LO2 Q5-  The system shown in figure 3 is out of balance. Determine the masses and the angles that must be used to balance the system in plane A and plane D at a radius of 85 mm. The radius of Ball B is ‘CDE’ mm and the radius of Ball C is 95 mm. The masses of ball B is 5.5kg and Ball C is 1.5 kg  (5%)

LO2 Q6 -  Figure 4 shows a “four bar linkage” mechanism. The members P and H are fixed points on the same plane. The member KH rotates at “ABC” revs/min. Determine the magnitude and direction of the acceleration of point Q. assume Angular velocity is 60 radians/sec  (5%)

The lengths of the links are as follows.

KH = 25 mm QK = 100 mm QO = 50 mm PH = 90 mm

Part 2: simple mechanical power transmission systems and natural and damped vibrations within translational and rotational mass-spring systems 

Note:  In the following questions, the words ABC AB, or BC are numbers from your student number. For example: If your student number is 2389259, which corresponds to OABCDEF 

LO3 Investigate elements of simple mechanical power transmission systems 

Simple systems: Gears 

The diagram below shows a geared system with two gears A and B. If Gear A is the drive gear and has an applied torque of  ‘AB’ Nm calculate the number of teeth required to achieve an angular accelerating of 8.4 rads/s². (5%)

Simple systems  :Compound gears 

A simple gear train has 3 gears. Gear A is the input and has 50 teeth, Gear C is the output and has 150 teeth. Gear A rotates at 1500 rpm ACW. What is the gear ratio and output speed. Also calculate the output power and torque if input torque is ‘FB’ Nm working at 75% efficiency (5%) 

Simple systems  :Lead screws and screw jacks 

An acro-prop support is being used to raise a load on a building site; the vertical force required from the acro-prop is 4,500N. 

The screw has a pitch of 7mm and a diameter of 70mm  

The bar used to raise the load is ‘ACD’ mm long and the coefficient of friction is 0.2  

From this information calculate the efficiency of the system and the effort required to raise the load. (5%)

Couplings and energy storage: Universal coupling and constant velocity 

Find βW for the torque diagram shown; find the moment of inertia and the mass of a suitable flywheel. Take radius of gyration as 0.5m

A1 = ‘AB’ 

A2 = ‘BC’ 

A3 = ‘CD’ 

A4 = ‘DE’ 

Mins speed = ‘ABC’ rev/min 

Max speed = ‘ABD’ rev / min

5. A flywheel is coupled with another. The first one has a moment of inertia of “AB” kg m² and an angular displacement of “BC” rad/sec. The second “CD” kg m²  and “DE” rad/sec respectively. Calculate the speed when they are engaged and calculate the energy lost. (5%)

Couplings and energy storage: Importance of energy storage elements and their applications 

6. Find the largest and smallest velocity ratios of two shafts joined with a universal coupling when the axis are a ‘AB’° 

Giving suitable examples of engineering applications analyse the limitations of Hooke’s joint when used to transfer angular velocity in a mechanism. Some reference to the joints operation and transfer speeds should be included with suitable diagrams where necessary.  

Describe how the limitations of the Hooke’s couple are over come in engineering systems.(5%)

LO4 Analyse natural and damped vibrations within translational and rotational mass-spring systems  

Simple harmonic motion :  Natural frequency of vibration in mass-spring systems.

A machine has mass of `A` kg and supported by a spring of stiffness B kN/m.  If the damping ratio is known to be 0.4. Determine: 

1. The natural frequency. 

2. The damped frequency.               

3. The natural frequency when the same spring is added parallel to the original spring.       

4. The natural frequency when the same spring is added in series to the original spring. (5%) 

2.       A machine of ‘A’ Kg mass is supported by springs of total stiffness of ‘B’ kN/m. It has an unbalanced mass, which results in a disturbing force of 310 N at a speed of 3600 rpm. Given a damping ratio of 0.15, calculate:(5%) 

1. The amplitude of the motion of the mass. 

2. The transmissibility.

Damped systems:  mass-spring-damper systems 

3.       A machine of ‘A’ Kg is mounted on springs of total stiffness ‘A’ kN/m. Its operation at a speed of 500 rpm results in a harmonic disturbing force of ‘CDE’ N amplitude. The damping ratio is 0.3. (5%) 

Calculate: 

• The natural frequency of the system. 

• The damped frequency of the system 

• The static deflection of the system.  

The amplitude of the motion of the machine. 

4.       A machine of 90 Kg mass is supported by springs of total stiffness of ABC kN/m. It has an unbalanced mass, which results in a disturbing force of 310 N at a speed of 3600 rpm. Given a damping ratio of 0.15, calculate:(5%) 

1. The amplitude of the motion of the mass. 

2. The transmissibility. 

3. The force transmitted to the foundations

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LEARNING OUTCOMES:

1. Solve problems within static mechanical systems.

2. Investigate the effect of constraints on the performance of a dynamic mechanical system.

3. Investigate elements of simple mechanical power transmission systems.

4. Analyse natural and damped vibrations within translational and rotational mass-spring systems.

ACADEMIC SKILLS OUTCOMES:

●        The Academic Skills Outcomes to be developed by completing this assignment  can be found here.

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