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Unformatted text preview: MECH 325 Assignment for Module #3: Shafts and Shaft Accessories
.pdf Softcopy due on Vista at 8:00am, November 4, 2010 Hardcopy due to at start of class on November 4, 2010 Scenario
Figure 1 shows a preliminary design of a shaft for a mass‐produced portable wire spooling machine. The shaft is to be supported by Bearings A and C. End D of the shaft is cantilevered such that a removable spool can be fit onto the shaft, wound with wire, and then removed. A flat belt pulley at B is used to drive the system. As shown, the expected placement of Bearing A, Pulley B, and Spool D are known but the position of Bearing C has not yet been determined. In addition, the various diameters along the shaft axis have not yet been specified. Your task is to design a suitable 800 mm long shaft for this application. As the machine is to be mass‐produced and portable, low cost and low weight are desirable. Your objective is therefore to minimize the product of cost and shaft mass. The performance metric is: Performance = (cost ∙ mass)‐1 [($∙kg)‐1] Details on how cost is computed are outline below. Your design must also satisfy the strength and stiffness constraints detailed in the following sections. xc
190 mm Hub A B C Spool D 20 mm 20 mm 20 mm 800 mm 300 mm Figure 1: Driveshaft Geometry. The shaft diameters are not shown to scale, and the shoulder locations and sizes as drawn are arbitrary. The quantity xc is defined by 250 ≤ xc ≤ 450 mm. Application Details
Bearings A and C The bearings have no axial load, and ball bearings are sufficient. Both bearings are self‐aligning. The distance between the centres of the two bearings may be from 250 to 450 mm. The left bearing (A) has a minimum inner bore of 10 mm, the right (C) a minimum inner bore of 20 mm. Larger sizes of bearings are acceptable, with bore sizes available in 2 mm increments. Pulley B and Drive Motor Pulley B connects to a 1.0 kW motor, mounted directly under the pulley. At load, the motor rotates at 1000 rpm and the pulley rotates at 600 rpm. The combined radial load from the belt at Pulley B (i.e. F1 + F2) is 800 N. Assume that the 20 mm wide belt is 94% efficient. Pulley B is shown with a 20 mm hub (for keys or setscrews, for example), and can be right‐ or left‐mounted; alternatively, the pulley be exchanged for a hub‐less version if desired. The pulley is available in bores from 10 mm and higher, in 2 mm increments. The pulley may be secured to the shaft by a key, set screw, spline or tapered shaft with lock‐nut arrangements, or a combination of accessories. Spool D The wire spool is to slide onto the shaft at D using a 4‐tooth, Class B spline. You may assume that each spool will incorporate a steel insert to provide an appropriately sized female spline; you may also assume that an appropriate axial position/retaining system for the spool is in place. The empty wire spool has a mass of 3 kg and holds 47 kg of wire when fully wound. Wire is wound onto the spool beginning at a radius of 8 cm and extending to a radius of 12 cm. During winding, the orientation of the incoming wire is horizontal (i.e. the wire passes out of the page in Figure 1). The wire tension is adjusted during winding in order to maintain a constant shaft rotation rate. Axial forces on the spool due to the wire are negligible. Shaft A-D The shaft is to be made from stock AISI 1050 cold‐drawn steel (assume properties for 30 mm stock apply). The following requirements must be observed in the shaft design: Mounting of the pulley sheave and spool must guarantee proper axial placement to within 0.5 mm. The allowable vertical deflections are 1 mm, with maximum slope of 0.008 rad. Appropriate values for angular misalignment of sealed bearings are to be observed. All sections of the shaft receiving shaft elements must have a machined surface. The shaft is to be designed for fatigue loading using the Modified‐Goodman criterion. Design Cost The goal is to design the shaft with the smallest product of final mass and overall cost. Mass will be based on shaft mass only (i.e. ignore bearings, the pulley, the spool, etc.). To simplify your work, cost is to be determined by the following model: Stock shaft can be bought for $13/kg in diameters of 9 mm and up in increments of 2 mm. Machining costs $50/kg of removed material. To illustrate, for a 3 kg shaft before machining with 0.5 kg machined off, the cost is: $13 / kg 3kg $50 / kg 0.5kg $64 . The machining cost of shaft splines (including the required spline at D for the spool) is based on the local shaft diameter d in mm: $40 $1 d 10mm . The cost for bearings and pulleys will be approximated by a linearly increasing function of local bore diameter D in mm: $15 $1 D 10mm . Other components (keys, set screws, etc.) do not need to be included in the cost estimate. Reporting Requirements
There are three graded elements for this assignment: a report for formal marking (75% of mark), your assessment of the designs of two other teams in the class (15%), and the performance of your design relative to others in the class (10%). Report Each team will submit a report in two formats: A paper (hardcopy) version of the report is due at the beginning of class on Nov 4 A .pdf (softcopy) version of the report is due at 8:00am on Nov 4 to the assignment drop box on Vista Important: you must submit both the hardcopy and the softcopy versions of your report! Your report shall consist of: A title page with the assignment number, your group number, and names and student numbers for all team members. In addition, specify which portions of the assignment each person substantially contributed to (this will only be used for reference unless an irresolvable dispute on iPeer arises). A summary of your approach to the problem, your assumptions and methods, your final design, and the design and performance information requested below. Point‐form writing, tables, and figures are all encouraged. The summary must not exceed 2 pages and text should be computer‐generated. An appendix outlining your detailed calculations. The appendix can be hand‐written or computer‐generated and must not exceed 10 pages. The report must contain the following design and performance information in the summary (supporting calculations must also be provided, either directly in the summary or in the appendix): profile drawing of the designed shaft, showing all lengths, diameters, and features (e.g. keys, grooves, etc.) V, M, |T| diagrams of the shaft (axial forces F are minimal, show torque magnitude |T| only) Identify critical locations. Provide a table that summarizes the following: o maximum bending and shear stresses (MPa), with corresponding safety factors o maximum linear deflection (mm) and angular deflection (slope in rad) A summary of the costs o cost of raw shaft at $13/kg o cost of machining at $50/kg of removed material o cost of machining of splines o cost of components o total cost ($) Mass of finished shaft (kg) Performance metric from Page 1: (cost ∙ mass)‐1 [($∙kg)‐1] Your Assessment of Other Designs The .pdf versions of the reports will be posted to Vista and you will be randomly assigned two teams to review. For each team you review, you should analyze the work in terms of: A critique of overall design and design decisions (e.g. is the overall design a good one or a bad one? Why? Are there errors, omissions, or unreasonable assumptions?) Analysis of the calculations and work (e.g. are the diagrams correct? Do you compute the same shaft stresses and deflections reported?) Each of your assessments should be roughly between a half and a full page. Be sure to identify the numbers of the teams you are evaluating on your assessments. Include a title page with your assessments (with the same information as the report title page) and submit everything as one document at the start of class on Tuesday, November 16. Performance Relative to Class The top performing team (i.e. the team with the design with the highest performance metric that satisfies all design requirements and constraints) will receive the top performance mark on the assignment. Performance marks for the rest of the class will be determined by the instructor using either a linear or non‐linear scaling. A working design will at minimum receive a performance mark of 50%. Addendum After reviewing other teams’ designs, if your team feels that your report could be improved substantially due to oversights, you may submit a 1‐page, 12‐pt font addendum with clarifications and/or amplifications. This can be handed in as a hardcopy to the Mech Office (CEME 2054) or emailed as a .pdf file but must be received by Dr. Ostafichuk no later than 8:00am on Wednesday, November 10. This is not intended as an opportunity for you to completely change your design. Any extra points gain in the addendum will be worth ½ of their value had they been provided in the original report. ...
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