300764: Mechanical Design - 3-D Stress State and Elastic Failure - Engineering Assignment Help

Assignment Task:

Question 1: 3-D Stress State and Elastic Failure Criteria 

For the following triaxial state of stress at a point in a machine part which is subjected to combined static loadings (P is the last three digits of your student identification number),

As a mechanical/mechatronic engineer, you are required to 

a) plot these normal and shear stresses in a cubic infinitesimal element using an appropriate sign convention;

b) determine maximum principal stresses, maximum shear stresses and absolute maximum shear stress;

c) plot these principal stresses in a cubic stress element and 3-D Mohr’s circles for this principal stress state;

d) if a ductile material with a yield strength of 350 + P/100 MPa with choosing an appropriate design factor 3, determine whether or not it is safe using the following three failure criteria - Yield Strength theory; Tresca theory; and von Mises theory; and

e) conduct a discussion on which failure criterion is the most conservative one among these three elastic strength theories for ductile materials. 

You may use the following equations:

Question 2: Belt Drives Analysis 

Two pulleys of a 450-mm diameter and a 250-mm diameter, respectively, are on parallel shafts with a distance of 2.0 + P/1000 m apart and wrapped by two methods – ‘open belt’ and ‘cross belt’, respectively. 

For both two wrapping cases, you are required to sketch two belt drives in a graphic paper using proper scales and conduct design analyses to determine: 

a) the total length of the belt required and the angles of wrap at two pulleys for each case; b) the power can be transmitted by the two belts when the small pulley rotates at 1500 rpm, if the maximum permissible tension in the belt is 2.0 + P/1000 kN, and the coefficient of friction between the belt and the pulley is 0.2. c) the speed of the large pulley when the maximum powers could be transmitted; and d) the differences between two wrapping ways of the belt drive. 

You may use the following equations: 

Open belt: 

Question 3: Kinematics of Gears  

A gear train system is shown in Fig. 1 and the input motor drives the gear 9 axle. The arm connected to gear 6 and gear 1 is fixed to the output axle. Gears 2 and 3, 4 and 5, 6 and 6, 7 and 8 are fixed together as compound gears, respectively. Gears 2 and 3, and 9 are fixed in space but allowed to rotate. If the tooth numbers are N1 = 15, N2 = 40, N3 = 20, N5 = 48, N6 = 12, N8 = 35, N9 = 11. 

You are required to determine: 

a) the gear sets existing in the system and the epicyclical gear trains (EGTs); b) the power flow in this gear system from input to output; c) the overall gear ratio and speed ratio of the 9-gear system; d) the velocity of the output shaft if the input speed is 100.0 + P/1000 rpm CW; and e) the output torque assuming the system has an efficiency of 100% - P/1000%, if the 

applied input torque is 50. 0 + P/1000 N?m. 

Figure 1: A 9-gear system. 

You may use the following equations:

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