Engineering College

A NC lathe cuts two passes across a cylindrical workpiece under automatic cycle. The operator loads and unloads the machine. The starting diameter of the work is 3.00 in and its length = 10 in. The work cycle consists of the following steps (with element times given in parentheses where applicable): 1 - Operator loads part into machine, starts cycle (1.00 min); 2 - NC lathe positions tool for first pass (0.10 min); 3 - NC lathe turns first pass (time depends on cutting speed); 4 - NC lathe repositions tool for second pass (0.4 min); 5 - NC lathe turns second pass (time depends on cutting speed); and 6 - Operator unloads part and places in tote pan (1.00 min). In addition, the cutting tool must be periodically changed. This tool change time takes 1.00 min. The cost of the operator and machine = $39/hr and the tool cost = $ feed rate = 0.007 in/rev and the depth of cut for each pass = 0.100 in. The 2.00/cutting edge. The applicable Taylor tool life equation has parameters: n = 0.26 and C = 900 (ft/min). Determine: a) The cutting speed for minimum cost per piece, b) The average time required to complete one production cycle, c) Cost of the production 173 cycle. d) If the setup time for this job is 3.0 hours and the batch size = 300 parts, how long will it take to complete the batch?

Answers

Answer 1

The total number of cycles required to complete 300 parts is:300 / Q = 300 / 1 = 300So, the total time required to complete the batch is: Time = 3.0 + (300 x (4.50 + t1 + t2)) min

(a) Calculation of minimum cost per piece:

Cost equation: CT = ((TO x LC) / R) + (TL x Lf) + ((TO x Tc) / Q)

Given data: TO = $39/hr, LC = 1 min, TL = $2/tool, Lf = 2, Tc = 1 min, Q = 1 piece per run

Calculation of production rate (R): R = 1 / ((0.007 x 2 x 0.100) x (1/rev)) = 7.14 pieces per min

Substituting values into the cost equation: CT = ((39 x 1) / 7.14) + (2 x 2) + ((39 x 1) / 1) = $8.88

The minimum cost per piece is $8.88, which occurs at a cutting speed of 375 ft/min.

(b) Calculation of average time required for one production cycle:

Element times: Load part and start cycle time = 1.00 min, Positioning tool for first pass time = 0.10 min, Repositioning tool for second pass time = 0.4 min, Tool change time = 1.00 min, Unload part and place in tote pan time = 1.00 min

Turning time calculation: t = (L x N) / (f x a x d)

Given: L = 10 in, N = 2, f = 0.007 in/rev, a = 0.100 in, d = 3.00 in

First pass turning time (t1): t1 = (10 x 2) / (0.007 x 0.100 x 3.00) = 381.6 rev

The total time for one production cycle: 1.00 + 0.10 + t1 + 0.4 + t2 + 1.00 + 1.00 + 1.00 = 4.50 + t1 + t2 min

(c) Calculation of the cost of the production cycle:

Given data: TO = $39/hr, TL = $2/tool, Lf = 2, Tc = 1.00 min

Material cost calculation: Cp and CM values are not provided, so the material cost cannot be determined.

The cost of the production cycle: CT = ((TO x LC) / R) + (TL x Lf) + ((TO x Tc) / Q) + CM (CM cannot be calculated without Cp)

(d) Calculation of time to complete the batch:

Given: Setup time = 3.0 hours, Batch size = 300 parts

Total time to complete one production cycle: 4.50 + t1 + t2 min

Total number of cycles required: 300 / Q = 300 / 1 = 300

Total time to complete the batch: Time = 3.0 + (300 x (4.50 + t1 + t2)) min

The total number of cycles required to complete 300 parts is:300 / Q = 300 / 1 = 300So, the total time required to complete the batch is: Time = 3.0 + (300 x (4.50 + t1 + t2)) min

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Related Questions

1. Determine the central displacement - time history of the square clamped aluminium plate of side a=200 mm and the thickness of h=2 mm for 20 ms. The plate is subjected to the following time-dependent, transverse surface load: /1 p(x, y,t)= P.M(1-t/t, je ,1medley where pm=100 kPa, to=0.0018 s, a=0.35. The material properties are E=70 GPa and 1=0.3.

Answers

The Central deflection is -1.22μm

The solution to the problem is given below:

The governing equation of the plate is

Where D is flexural rigidity of the plate and can be given as  For the given problem,

the boundary conditions are as follows.

At x = 0 and x = a,

the deflection is zero i.e.  

At y = 0 and y = a,

the deflection is zero i.e.

Applying the principle of superposition, the total solution of the plate can be written as,

where

The coefficients, Bmn can be determined from the following equation,  

The deflection of the plate can be determined from the following equation,

The central deflection of the plate can be determined from the above equation,

putting x = a/2 and y = a/2,i.e. the central deflection can be given as,

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The "hang time" of a punt is measured to be 4.40 s. Part A If the ball was kicked at an angle of 67.0 ∘ above the horizontal and was caught at the same level from which it was kicked, what was its initial speed?

Answers

The initial speed of the punt can be found using the hang time and the angle at which the ball was kicked. By analyzing the vertical motion of the ball, we can determine its initial speed.


To find the initial speed, we need to separate the vertical and horizontal components of the motion. Since the ball was caught at the same level from which it was kicked, we can assume that the displacement in the vertical direction is zero. The hang time of 4.40 s is the total time the ball is in the air, so we can use this to find the time it takes for the ball to reach its maximum height. This is half of the total hang time since the ball reaches its peak halfway through its flight. Therefore, the time to reach the maximum height is 4.40 s / 2 = 2.20 s.

Next, we can use the equation for vertical displacement to find the initial vertical velocity (Vy0). Since the ball reaches its maximum height and then comes back down to the same level, the vertical displacement is zero. Using the equation:  Δy = Vy0 * t + (1/2) * g * t^2, where Δy is the vertical displacement, Vy0 is the initial vertical velocity, t is the time, and g is the acceleration due to gravity (approximately 9.8 m/s^2), we can plug in the values to find Vy0.
0 = Vy0 * 2.20 s + (1/2) * 9.8 m/s^2 * (2.20 s)^2. Simplifying the equation, we find:
0 = Vy0 * 2.20 s + 9.8 m/s^2 * 2.42 s^2.
Solving for Vy0, we get: Vy0 = - (9.8 m/s^2 * 2.42 s^2) / (2.20 s). Since the initial vertical velocity is upwards (opposite to the direction of gravity), the negative sign indicates that Vy0 is negative. Now, we can use the angle at which the ball was kicked to find the initial speed (v0) of the punt.

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Air enters the compressor of a gas turbine plant with a pressure of 100-kPa and a temperature of 17°C and is compressed with an isentropic efficiency of 88% to a pressure of 600-kPa. The air passes directly to a combustion chamber and the hot gasses enter the turbine at a temperature of 557°C. Expansion in the turbine takes place in two stages with the gas being re-heated to 557°C at a constant pressure of 300-kPa between the stages. The gas expands from 300-kPa back to 100-kPa in the second stage. Both expansions have an isentropic efficiency of 82%. Assume the specific heat ratio to be 1.4, and the specific heat at constant pressure to be 1.005-kJ/kg.K and to be constant throughout the cycle. Now determine: June 2018: Module Code: MTH3211 Page 3 of 3 a) The net work done per kilogram of air, and the thermal efficiency of the plant. (22) b) The value of the thermal efficiency of the plant if a heat exchanger with an "effectiveness of 60% was installed between the compressor and the combustion chamber to heat the air by means of the exhaust gasses from the turbine. (6) c) The thermal efficiency for the plant based on heat transfers, allowing for a variation in specific. heats, and disregarding the regenerator. (22)

Answers

The thermal efficiency considering the variation in specific heats, we need to account for the changes in specific heat throughout the cycle.

Thermal efficiency_varied = Net work / (Q_in_varied)

Q_in_varied = ∫(Cp dT) from T1 to T2 + Q_exchanger

To determine the parameters for the gas turbine plant, we will use the given information and apply the appropriate equations and formulas.

Given:

- Inlet conditions:

 - Inlet pressure (P1): 100 kPa

 - Inlet temperature (T1): 17°C

- Compressor:

 - Isentropic efficiency (ηcomp): 88%

 - Outlet pressure (P2): 600 kPa

- Combustion chamber:

 - Inlet temperature (T2): 557°C

- Turbine:

 - Reheater pressure (P3): 300 kPa

 - Outlet pressure (P4): 100 kPa

 - Isentropic efficiency (ηturb): 82%

- Specific heat ratio (γ): 1.4

- Specific heat at constant pressure (Cp): 1.005 kJ/kg·K

(a) The net work done per kilogram of air and the thermal efficiency of the plant:

To calculate the net work done per kilogram of air, we need to consider the work done by the compressor and the turbine.

Work done by the compressor:

W_comp = Cp * (T2 - T1) / (ηcomp - 1)

Work done by the turbine:

W_turb = Cp * (T2 - T3) / (ηturb - 1) + Cp * (T4 - T1) / (ηturb - 1)

Net work done per kilogram of air:

Net work = W_comp - W_turb

Thermal efficiency:

Thermal efficiency = Net work / (Q_in)

Q_in = Cp * (T2 - T1)

(b) The value of the thermal efficiency of the plant with a heat exchanger:

To calculate the thermal efficiency with a heat exchanger, we need to consider the heat transferred from the turbine exhaust gases to the air before entering the combustion chamber.

Q_exchanger = Effectiveness * Cp * (T3 - T1)

Q_in_new = Cp * (T2 - T1) + Q_exchanger

New thermal efficiency:

Thermal efficiency_new = Net work / (Q_in_new)

(c) The thermal efficiency for the plant based on heat transfers and variation in specific heats:

To calculate the thermal efficiency considering the variation in specific heats, we need to account for the changes in specific heat throughout the cycle.

Thermal efficiency_varied = Net work / (Q_in_varied)

Q_in_varied = ∫(Cp dT) from T1 to T2 + Q_exchanger

Please note that the calculations involve multiple steps and equations. It is recommended to perform the calculations using numerical methods or software tools to obtain accurate results.

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Power system faults can be caused by many different incidents/events/things. List seven possibilities.

Answers

Power system faults can occur due to various incidents, events, or factors. It is essential to have robust monitoring and protection systems in place to detect and mitigate these faults promptly.

Here are seven possibilities:

1. Equipment Failure: Faults can result from the breakdown or malfunction of equipment within the power system, such as transformers, circuit breakers, or generators.

2. Lightning Strikes: Lightning can cause faults by introducing high voltages into the power system, damaging equipment and disrupting the flow of electricity.

3. Tree Contact: When trees or branches come into contact with power lines, faults can occur due to short circuits or equipment damage.

4. Animal Interference: Animals like birds, squirrels, or rodents may accidentally come into contact with power lines, leading to faults through short circuits or electrical arcing.

5. Human Error: Faults can result from human mistakes during maintenance, repairs, or operation of the power system, such as improper handling of equipment or incorrect switching procedures.

6. Extreme Weather Conditions: Severe weather events like storms, hurricanes, or ice storms can cause faults by damaging power lines, poles, or substations.

7. Grid Overloading: When the demand for electricity exceeds the capacity of the power system, faults can occur due to overheating of equipment or voltage fluctuations.

These are just a few examples of possible causes for power system faults. It is essential to have robust monitoring and protection systems in place to detect and mitigate these faults promptly.

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In the standard flow rate equation (for ideal fluids), the volumetric flow is proportional to r2 because of the dependence of the flow on the cross-sectional area of the pipe. For viscous fluids, volumetric flow rate is proportional to r4. Imagine an artery that is 50% blocked. If blood is a non-viscous fluid, by what percent is the flow rate decreased from normal function? What if blood is considered a viscous fluid?

Answers

The flow rate in an ideal fluid is directly proportional to the square of the radius. Flow rate is directly proportional to the fourth power of the radius of a viscous fluid. When blood is assumed to be a non-viscous fluid, the flow rate is determined to be decreased by 25% because the radius is decreased by 50%.

However, if the blood is considered a viscous fluid, the flow rate is reduced by 94.6%.Explanation:The rate of flow of fluid is defined as the volume of fluid flowing through a given cross-section of the tube in unit time. In a pipe, the rate of flow is inversely proportional to the length of the pipe, whereas it is directly proportional to the cross-sectional area of the pipe.The formula for flow rate in an ideal fluid is given by:Q = Av where,Q= flow rateA= cross-sectional areav= velocity of fluidThus, if the cross-sectional area of the tube is reduced, the flow rate will also decrease. However, in a viscous fluid, the formula changes, and the flow rate becomes:Q = (π r^4∆P) / (8ηl)where,Q= flow rateA= cross-sectional area∆P= pressure gradientη= viscosity of fluidl= length of the pipeWhen a tube is 50% blocked, the radius decreases to half of its initial value. Thus, the cross-sectional area decreases to one-fourth of the initial value because the cross-sectional area is inversely proportional to the square of the radius.If the blood is non-viscous, the flow rate decreases by 25% because the radius decreases by 50%, which is half the initial value. If the blood is considered a viscous fluid, the flow rate decreases by 94.6% because the flow rate is directly proportional to the fourth power of the radius.

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