Question

Problem Statement You are the manager of a workshop. You need to turn 1,500 shafts as an intermediate step in a larger manufacturing process. It takes your workshop technician 20 min to machine a single shaft at a cutting speed of 15 m/min and 10 min to set up the blank in the spindle. Since you are turning 1,500 shafts, the technician will certainly change the cutting tool to maintain quality - a tool change would require five minutes. The technician's hourly rate is QAR 350 per hour; your overhead cost is 200%. A local supplier sells you the blanks at the cost of QAR 250 per unit. The process has been traditionally done using a high-speed steel (HSS) cutting tool - these tools are available from a local supplier at the cost of QAR 10 per tool. A HSS cutting tool would provide high quality surface finish for 1 hour of cutting at the cutting speed of 15 m/min and then would need to be changed. However, to make (time and financial) savings, you want to investigate using a carbide cutting tool that the supplier offered to you at QAR 50 per tool. This carbide cutting tool would provide high quality surface finish for 6 hours of cutting at the cutting speed of 15 m/min. 1) Calculate the cost of machining the 1,500 shafts at the nominal cutting speed of 15 m/min for both cutting tools 2) Assuming the same feed rate, how many tools will you use at 17.5 m/min for both the HSS and carbide tools. Notice that a higher cutting speed will lower the tool's life. You can use Taylor's tool life equation: V,7" = V2T to find the tool life at a cutting speed of 17.5 m/min. In this equation, V is the cutting speed, T is the tool life and n = 0.125 for HSS and 0.25 for carbide. 3) Calculate the total cost to your workshop for machining the 1,500 shafts: a) Using the HSS tool at 15 m/min (which is what your technician is doing now) b) Using the HSS tool at 17.5 m/min c) Using the carbide tool at 15 m/min d) Using the carbide tool at 17.5 m/min Tabulate your results so you can present them to the head of your business unit (highlight the biggest savings) HSS at 15 m/min HSS at 17.5 m/min Carbide at 15 m/min Carbide at 17.5 m/min Cost (QAR) Cost % Change) NA Time % Change) NA

Answer 1

1/12 1:39 No. : Date : 1 | Whatever) be culling a basic formulae ? as speed for and total cool life cost is given Total cost a Total cost cost cost overhead coste of labour of material & of tool where . I cost of material : Total no of shafts & - cost per shaft ( cost of tool Total no of shafts sool .. No of shafts with I tool / tool! (ii) cost of labour a Total time required & [Rate por how Total overhead .. overhead wst per hour & Total howls .

Date : Date: TT W 1 1 A case 1 LHSS tool at 15 m/min - cost of 1 (same material for all cases) Total no of shafts x lost hir blank _ 1500 x 250 QAR 3,15,000 QAR - > 0 No of shafts with cloot tools reg for " Moral machining time total Sharad Tool life 1500 shafts . - 1500 x [lime for Ishaft I Tool life • 1500 x [ Time for machining ? Tool life and . 1500 20 mins - 60 mins . Soo too of x cost of I took tool » No of tools a 500 tools x 10 * 5000 QAR 7 @

T il Total time required Total machining time polal tool change time a Tootal set up time • 1500 x 20 mins + (No of tools & Time for ! I change ] - + 10mins & 1500 2 e 30000 minst 500 x 5 + 15000 47,500 mins. Todal time in howrs . 47500 . - 60 I lost of labour Total time x Howlly Mate . 47500 x 350. » 2;77,043.34ARI - 60 22,77,083.33 QUR 1 Total overhead cost = Total time & tos ovelhead и Иоv ovelhead cost per howl e 200% of howlly rate - Too QAR /howe owerhead cost a 41500 x 700 - Total 5,54,166.667 QAR.

Page No. : Date : 17 12. Podal tost 20+@3 + + 250 DAR

Case 2. . Combide tool at 15 m/min Main differences from case 1. Material cost is same. - = From One * 3,15,000 DAR > 0 A : cowo si la - Cost of tool will change since I bouth cost nee tool and total at tools required change. - No of tools required for 1500 shalts 2 Total machining time Tool like WO Tool like a 6 howls - 6 X 60 min. 360 min of tools for 1500 shafts "1500 x 20 min 83.33 tool 360 min 84 tools 1. Lost of tool a Tolal no of tool cost myy 2 84 x 50 - 4200 QARO

- Labour cost will change sinu time for tool change differs. Tolal time. Tofal machining time & C No of tools a Time nor tool change + Time for setup • 1500 x 20 min (84 45 min) & 10x1500 2 45,420 min Cost of labour. Total time in hows & Hourly rate 45,420 x 350 60 2,64,950 QAR - ☺ A ovelhead cost a Total time & - orllhead cost pou howe overhead cost per hour & Toolhowr 2. Todal overhead cost 45,420 700 *00 60 - Total cost 29,29,900.-- © 14 are 344 11,74,050 QAR.

Pank: © ... Hiisis dissa I No of tools for uss. For this we nud cool life Quin Jussat 11.5 mlmin. • Using equation Nut & Nata?! here niso out an Mi a 15 m/min . wil ist es Go minha na 0.125 lor uss 12 2 11.5 mlimin 0. Ta teden L oi 125 0.125 15 x (60) . 115 (10) 0.125" (Te 2 15 proi! ! Go 2 o 1.17.511 U -7%0.125 - T2 Jon Go - ( is ! L 17:51 - son's T !! 60 x [ 15 H.S 2 17.48 min.

L A No of tools for uss Machining Time (Total) Tool like a 1500 x 20 min 21,716:24 17. 48 min ~ 1717 tools No of tools for carbide at H.5 mlmin V. 15 mlmin, T2 360 min V2 -11.5 ml min n. 20.25 for carbi . . .25 0.25 15 ml min x [360] 11.5 x { 1 1 2 11.5 x 1360 17.5 Tous To 360* f is 7 360 % L 17.5 'No of e 194.3 min. tools 1500 x 20min Tool like ( 194.3 2 154.4 tools )

I Part ③ ca - Answer Part 0 First Hall is 2 12,11, 250 QAR |||||||||| co Answe is part 7 Second hall 11,14,050 QAR , I wring uss tool at 11.5 m/min Tofal, material wit '_ 266_ casé o is same as 2 3,15,000 2 DAB as Cost of tool ; 2 No of tools of uss at 17.5 mlmin from Part 2 .-. _ x cost per tool 119 X 10 - 11, 170 QAR.

lost of labour will change since maching time will chang is mlmin it takes 20 min M.S m/min 2 x. ce At AL xx15 2 17.5x20 x - 23.33 min. & Total time bood Time for tool change & Time for setup. e Time for machining 2 No of bools & Time per chinge Time for selup y a (isoo x 23. 33 ) à 10' 1111* 5+ 1500 x 10 + 1500x23.3 2 58,580 min I Labour cost e 2 wst 58, 580 hourly rate - 60 3,41,716: 667 QAR:> ☺ 200% out head 2 2x Labour cost * 6,83, 433. 334. → @ I Total cost for uss at 11.5 m/min 214,17,320

(d) Larbidi tool at od 11.5 m/min. Machining time from (6) in b il" i Part 0 in it 223-33 min Total time Machining time eschp line a inil knit Tool change time sul vosti 150 o x 23. 33 41 Cado a hood 1500x lo ) & (No of fool x 5 min ) totdat No I gostool ove in this is is hall given by eleond of part 2 :%2521500 *={23.33 10] Pluss x 5] 0 000 €125 napon wat one al So, 110 min dod Todal labour costa Soo 170 9 I do !.. . 60 hourly ob 120 50,770 350 60 du! x! 2,96,158.33 QAR Total overhead cost a 2x Tolah labour ! 5,92,316166 -> @

Frege N). Date: of Material Tooded cost 2 cost of bool í 3,75,000 Always some 155 x 50 7750 DAR > Total cost - 0 + © © © . 3.12,71,225 . QAR, Iuss at 15 m/minfuss al H.5m/n) Carbide al 15 m/ Carbide at 19:5 7 lost CQARXL 12, 11, aso [417,320 I 11,74,050 112,11,225 lost (% chans NA +17.01% NA +2 8.2% I am fechoul / AA / B A/NA ( /2 1 Toime T 47,500 min 88,580 45,420 I 5o 770 . 1 % thange worot o so giving what was not mentioned all values numerically