325-midterm-2014W with MC SA answers

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325

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Mechanical Engineering

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Oct 30, 2023

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Page 1 MECH 325 – Midterm Book 1 Tuesday, October 21, 2014 Name: _____________________________________ Student Number: _____________________________ Circle your section Section 101: T1A (11:00am tutorial) T1B (3:30pm tutorial) Section 102: T1C (2:00pm tutorial) T1D (5:00pm tutorial) Signature: ___________________________________ Part 1 MC Mark _____ / 14 Part 1 SA Mark _____ / 16 Part 2 LA Mark _____ / 30 Total _____ / 60 Instructions There are two parts to this exam with different instructions for each. Please read carefully. Part 1 – Closed-Book (30 marks) Multiple choice (14 marks: 1 marks per question) . Complete all 14 questions by marking your response in pencil in the computer score card . Write your name and student number on the computer card and mark your student number in the “ID Field”. Short answer (16 marks: 2 or 4 marks per question). Complete all 6 questions by marking your response in this exam booklet. After you have completed Part 1, hand in your booklet and Scantron scorecard and you will receive a handout for Part 2 and a separate exam booklet for your answers. You may not return to Part 1 after you hand it in. Part 2 – Open-Book (30 marks) Long answer (30 marks) : Complete all parts to the questions for Part 2 by marking your responses in the separate exam booklet. This portion of the exam is open-book and open-notes. Only non-programmable calculators may be used (or programmable calculators with purged memories) .

Page 2 Part 1 A : Multiple Choice Answer all 14 questions. Each is worth 1 mark. Choose the single best response – a given question may have more than one choice that is correct but marks will only be given for the best answer. 1. Which of the following types of gears is appropriate for high-efficiency, smooth (low-noise) transmission of motion between parallel shafts with minimal axial loading on either shaft? a) Bevel b) Spur c) Worm d) Herringbone e) Helical 2. A spur gear has 40 teeth, a 14° pressure angle, and a pitch diameter of 2.0 in. What is the diametral pitch of the gear? a) 0.05 b) 1.42 c) 2.86 d) 7.0 e) 20.0 3. The worm gear shown has a 1” pitch diameter and has two threads. The gear has an 8” pitch diameter and 96 teeth. If the worm turns 24 revolutions in the direction indicated, how far does the gear turn? a) 4 rotations clockwise b) 1 rotation clockwise c) ½ rotation clockwise d) 1 rotation counter-clockwise e) 4 rotations counter-clockwise 4. In the worm from Question 3, the bearing at A is the locating bearing. What direction are the forces from the worm shaft onto bearing A? a) - x + y - z b) + x - y + z c) + x - y - z d) - x - y + z e) - x - y - z 5. A spur gearset has an input gear with 15 teeth and an output gear with 60 teeth. If 4 N·m of torque is supplied to the input gear at 50 rad/sec, approximately how much power is delivered by the output gear to the load? a) 16 W b) 60 W c) 75 W d) 200 W e) 800 W A B x y ( z out of page)

Page 3 6. For the planetary gear train shown, the sun gear rotates at 2000 rpm clockwise and the arm is fixed. How fast does the ring gear rotate and in which direction? a) 4,000 rev/min (clockwise) b) 2,500 rev/min (clockwise) c) 300 rev/min (counter-clockwise) d) 300 rev/min (clockwise) e) 2,500 rev/min (counter-clockwise) 7. Comparing a square vs. an ACME power screw, which of the following is true regarding the use of a split-nut: a) A split nut reduces friction on both types of power screw b) A split nut allows for backlash adjustment on an ACME power screw c) A split nut allows for backlash adjustment on a square power screw d) A split nut is required when using a bushing for a friction collar on both types of power screw e) A split nut is required when an ACME power screw is non-reversing 8. Which of the following components of belt tension present in V-Belts but normally ignored in flat belts that is the main consideration when calculating belt life? a) Initial tension (F i ) b) Bending tension (F b ) c) Centrifugal tension (F c ) d) Tight-side tension (F 1 ) e) Slack-side tension (F 2 ) 9. A V-belt drive has a driving pulley operating at 200 rpm, a drivetrain value of e = 0.25, a nominal power of H nom = .75 hp, a service factor of K s = 2.5, and a design factor of n d = 1.5. TWO belts are to be used in parallel. The following belts are available in the catalogue. Which is the smallest belt that will satisfy the design requirements? a) Allowable power H a = 0.7 hp b) Allowable power H a = 1.1 hp c) Allowable power H a = 1.5 hp d) Allowable power H a = 2.9 hp e) Allowable power H a = 5.7 hp 10. A timing belt has a driving pulley with pitch diameter of 20 cm and 50 teeth, and a driven pulley with 100 teeth. The wrap angle is 130°. During operation, the tight side tension is 130 N, slack side tension is 40 N, and the driving pulley rotation rate is 120 rad/sec. What is the torque transmitted from the motor shaft to the driving pulley? a) 6.0 N·m b) 9.0 N·m c) 60.0 N·m d) 100.0 N·m e) 600 N·m 100T 30T 15T

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Page 4 11. Which of the following design or operating parameters should be increased in order to be able to reduce the required bushing length of a boundary-lubricated bearing in service? (assume all other parameters remain fixed) a) Operating rotation speed, N b) Applied force, F c) Coefficient of friction, f s d) (PV) rating of the bushing e) Wear factor, K 12. A tapered-roller bearing is best suited for: a) Only large radial loads b) Only large axial loads c) Small radial loads, plus large axial loads in both directions d) Large radial loads, plus large axial loads in both directions e) Large radial loads, plus large axial loads in one direction only 13. Which of the following statements is true for the Soderberg, Gerber, Modified Goodman and ASME-elliptic fatigue failure criteria: a) All criteria predict fatigue failure will occur before yielding b) Only the Modified Goodman criterion is valid for tensile stresses c) The zone to the left of each of the fatigue criteria lines represents the design domain where n < 1 d) When σ a = 0, the safety factor n ≥ 1 when σ m ≤ S y for all criteria e) When σ m = 0, the safety factor n = 1 when σ a = 0.5 * S e for all criteria 14. A motor drives a gearbox input shaft (top shaft in figure to right) at 1200 rpm. The gearbox uses a worm gear to drive a constant torque load attached to the output shaft via a flexible coupling. In addition to torsional shear and direct shear due to the worm gearset, the output shaft is subject to stresses best characterized by: a) steady bending stress plus alternating axial stress b) steady bending stress plus steady axial stress c) zero midrange stress and steady axial stress d) partially but not fully-reversed bending stress only e) alternating bending stress in the z -axis only, plus alternating axial stress

Page 5 P art 1B – Short - Answer Questions (16 marks ) Answer all 7 questions in the spaces provided. Each question is worth 2 marks. 15. The larger helical gear shown has a normal pressure angle of 20°, a helix angle ψ of 30°, N = 35 teeth, and a pitch diameter of 5”. What is the normal pitch in inches? Show your calculations. (2 marks) Diametral pitch P = N/d = 35/5” = 7 in -1 P * p = π , so p = π /7 = 0.45” Normal pitch = _0.45”_____ 16. Based on the shaft loading shown in the top diagram, complete the diagrams for axial force, shear force, bending moment and torsion. Notes: The moments shown are oriented along the x-axis. You do not need to indicate values in your diagrams, but they must follow the usual sign convention. (4 marks)

Page 6 17. Given that the total raising torque, T T , for an ACME power screw is given by the sum of the raising torque at the threads ( T R ) and collar friction torque ( T C ): What is the efficiency, e , which is defined as the ratio of the total raising torque when friction has been eliminated divided by the total raising torque? Simplify the expression, and leave the denominator as T T . (2 marks) = F l / (2 π T t ) 18. The shaft shown has a pair of tapered roller bearings, a helical gear, a spur gear, and a cylindrical roller bearing. Power is transmitted to the large helical gear via a smaller pinion gear and runs in one direction only, with smooth torque delivery. Assuming proper shaft accessories, what are the TWO most significant changes you would suggest to this design and why? (2 marks) Change #1. Shorten shaft to increase stiffness and critical speed Change #2. Replace tapered roller bearings with a single angular ball bearing to reduce cost T T = T R + T C = Fd m 2 π fd m sec α + l π d m − fl sec α " # $ $ % & ' ' + Ff c d c 2

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Page 7 19. The diagram shown below is the tension profile for a flat belt. On this diagram, sketch the tension profile for a V-belt belt that is transmitting the same torque, but otherwise has the same linear speed, initial tension, pulley diameters, and belt weight per unit length. (2 marks) 20. A) For synchronous power transmission with a flexible element, what is the principal operating difference between roller chains and timing belts? Exclude materials and secondary effects such as lubrication, dirt, and maximum capacity. (1 mark) B) What is the simplest way to minimize this difference? (1 mark) A: Chordal speed variation B: Increase number of teeth on the sprocket B C D E F A B ∆ F /2 ∆ F /2

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Page 1 MECH 325 – Midterm Book 2 Tuesday, October 21, 2014 Name: _____________________________________ Student Number: _____________________________ Circle your section Section 101: T1A (11:00am tutorial) T1B (3:30pm tutorial) Section 102: T1C (2:00pm tutorial) T1D (5:00pm tutorial) Signature: ___________________________________ Q21 _____ / 4 Q22 _____ / 4 Q23 _____ / 6 Q24 _____ / 8 Q25 _____ / 8 Q26 _____ / 6 (bonus) Total _____/ 30 + 6 Instructions Please read carefully. Part 2 – Open-Book (30 pts) Long answer : Complete all parts to the question by marking your response in the booklet provided. This portion of the exam is open-book and open-notes. At the end of the exam, return this handout with your answers in the booklet. This is a multi-part problem. For each part, use the parameter values given. Do not carry your answers forward from one part to the next except for dimensions on the figure. If you cannot complete one part, you may move on and still receive full marks for subsequent parts. Do not try to back-calculate to previous parts, since the new parameters given are incorrect and contradictory on purpose. Clearly indicate your final answer to each part by drawing a box around it. Separate different parts with a line drawn across the page. Only non-programmable (or purged) calculators may be used.

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Page 2 Long Answer Problem (3 0 marks) NOTE: The non-SI tables required are appended at the back of the handout. SUGGESTION: Remove the handout staple so you can refer to the figure and the questions at the same time.

Page 3 21. The motor connected to shaft (a) delivers a power of H nom = 2.00 kW at a speed of 3000 revolutions per minute in a counter-clockwise direction, as shown in the figure. Spur gears 2 and 3 deliver the power with an efficiency of 97% to shaft (b) at location D. Shafts (a) and (b) are aligned on the y- axis. The V-belt on Pulley 4 at location B has a wrap angle of 180°. Forces F top and F bottom are parallel to the z-axis. Determine the magnitude of the torque on shaft (b) delivered to the V-belt sheave (4) and the linear speed of the V-belt in ft/min, not in m/s. (4 marks) 22. Regardless of the answers to the previous question, assume T b = 4.87 Nm at a rotational speed of 157 rad/sec (=1500 RPM) in a clockwise direction. Assume a “V V’ configuration (V-belt sheaves on driving and driven ends), so K 1 = 1. Assume a length factor of K 2 = 1, a service factor K s = 1.3 and a design factor of 1.5. Determine the smallest type of belt that will suffice from Table 17-12 (from types A through E), and justify your answer. (4 marks) 23. Regardless of the answers to the previous question, assume F top = 400 N and F bottom = 1100 N. The geometry of the shaft is as follows: x1 = 8 cm; x2 = 8 cm; x3 = 4 cm. The pressure angle of the gears is 20°, and W t = 1200 N. The bearings at A and C are self-aligning. Determine the reaction forces on the shaft from bearing A and bearing C in the X-Z plane ONLY. (6 marks) 24. Regardless of the answers to the previous question, assume the bearing reaction force magnitudes are F A = 1600 N and F C = 1100 N. Select a single-row, 02-series, deep-groove bearing from Table 11-2 that will be appropriate for both locations A and C. Use an application factor of 1.2, a life of x =20 and a reliability of R = 0.995. Use these parameters: L 10 = 10 6 x 0 = 0.02 θ = 4.459 b = 1.483 Determine the C 10 value required and the bearing bore diameter at the more critical location of the two (A or C). (8 marks) 25. Regardless of the answers to the previous question, assume the following for a calculation of stresses at B (the pulley): the shaft is made of steel with S ut = 820 MPa and S y = 650 MPa, and it has a fully- corrected endurance limit of S e = 280 MPa at this location. The pulley is restrained to the shaft using a key and keyway (for the keyway, assume q = 0.75, q s = 0.85, K t = 2.2, K ts = 3.0, K f = 1.75, K fs = 2.2,). The following loading information is to be used: the fully-reversed bending moment magnitude at B due to the power transmission forces is 95 Nm. The steady torque T transmitted by the shaft from gear 3 to the pulley is 52 Nm . To assure a factor of safety of 1.8, determine the minimum shaft diameter needed at location B (the pulley) to prevent fatigue failure, based on the Soderberg criterion. (8 marks) 26. BONUS: Regardless of the answers to the previous question, assume a Type “C” V-belt ( K b = 1600 and K c = 1.716), H d = 2 HP at the rotational speed for shaft (b) of 2000 RPM with a pulley diameter of 5”, so V = 2617 ft/min. The belt tension friction coefficient f = 0.5. Find hoop tension F c , belt tensions F top and F bottom , and the minimum initial tension F i . (6 marks)

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