PROJECT ON MACHINE DESIGN I LESSON 1

Transcription

1 PROJECT ON MACHINE DESIGN I LESSON 1 Your dein tak will be to dein the power crew mechanim. The coure main objective i to familiarize you with typical calculation of element of machine (therefore, ome dein olution will be impoed) and to teach you to yntheize and ue in the dein proce knowlede from your previou coure: Mechanic, Strenth of Material, Material Science, Manufacturin Technoloy, Workhop, Enineerin Drawin and Metroloy. You will alo need to ue the knowlede iven to you on the concurrent lecture Introduction to Machine Dein I. The contruction tak will conit of two part: calculation documentation and drawin documentation. For dein calculation you mut ue ordinary enineerin calculator (not any computer oftware). Some ketche will alo need to be drawn in the calculation documentation, o pleae brin baic drawin acceorie (pencil, eraer, ruler, etc.) to the clae. Calculation documentation will be prepared ucceively on clae (mainly), therefore, in addition to notebook (you ll have to make ome note on clae), pleae brin looe A4 heet with you. Fi. 1

2 CAR JACK EXAMPLE OF POWER SCREW MACHANISM Fi. 2

3 STRENGHT ANALYSIS The machine or it part durin exploitation are under the influence of external factor, which may lead to detruction, damae or other chane preventin it for further work. The deiner' tak i to chooe the dimenion, hape, material and method of makin individual machine element to minimize the probability of fail or wear. The procedure hould be baed on the analyi of poible fail and damae. Mechanical load can lead to the fail of machine element. We ditinuih between two poible type of fail. Firtly, the fail of an element can occur when a certain limit tre value i exceeded. In cae of tenion it i the o-called ultimate tre R m (determined experimentally; it i the tre value that caue the pecimen to break). Similarly, correpondin tree can be determined for other load pattern: compreion R, bendin R, torion R and hear R t. Secondly, the detruction of an element can arie a a reult of it permanent deformation. In thi cae, the limit value of tre i defined a the yield tre (point) / elatic limit R e or the proof tre / offet yield point R 02 for tenion, Q c for compreion, Q for bendin, Q for torion, or Q t for hear. In material tandard uually can be found only two tre value R ( R ) and m r R e or 02 R ( Q ). Other tre value are determined experimentally. For many material they can be found in the literature. In the abence of precie data, thee value can be determined uin tandard (Tab. 1). Tab. 1 Tenion Compreion Bendin r Torion and hear Material Q r Q c Q Q Carbon teel Q r Q r 1,19 Q r 0,62 Q r Alloy teel Q r Q r 1,10 Q r 0,60 Q r Cat teel Q r 1,35 Q r 1,15 Q r 0,60 Q r Grey cat iron 0,60 R r 1,80 R r 1,20 R r 0,60 R r Malleable cat iron Q r 1,30 Q r 1,10 Q r 0,70 Q r Brae 0,60 R r 0,60 R r 0,65 R r 0,40 R r Bronze 0,60 R r 0,60 R r 0,50 R r 0,34 R r Aluminum alloy 0,60 R r 0,60 R r 0,64 R r 0,40 R r Uin data from the Table 1 one can determine the dein tre k by dividin limit tre Q by the afety factor x : Qr Q Q c Q Qt = ; kc = ; k = ; k = ; kt = (1) x x x x x Typically, for each roup of machine, the rule for ettin the afety factor are determined (e. for car jack the afety factor hould be 6 8). When producin typical part ued in mot machine, the averae afety factor that can be ued are et a in Table 2. c

4 Tab. 2 Safety factor (averae) Material x x z Steel 2 2,3 3,5 4 Cat teel 2 2,3 3,5 4 Grey cat iron 3,5 3 Malleable cat iron 2 2,3 3,5 4 Brae 3 5 Bronze 3,5 4,5 Aluminum alloy 3,9 6 All above concern the cae of contant load. In the cae of variable, fluctuatin load, it i poible another proce of fail, different than at contant load. The fail occur after repeatedly exceedin a certain level of tre. Thi kind of proce i called fatiue. There i a limit value of tre uch that the pecimen under tre with a lower value i not detroyed reardle to the number of load chane. Thi value i called the endurance limit. Endurance limit depend on the type of load variability. It i determined for individual load cae pulatin and revered load. Endurance limit i denoted with a ymbol Z with correpondin indexe: rj pulatin tenion; rc revered tenion/compreion; cj pulatin compreion; j pulatin bendin; o revered bendin; j pulatin torion; o revered torion; tj pulatin hear; to revered hear. A in the cae of contant load, endurance limit can be determined uin tandard (Tab. 3) and dein tre k can be determined by dividin endurance limit Z by the afety factor x z (Tab. 2): Z k = (2) x z

5 Tab. 3 Tenion Compreion Bendin Torion and hear Material Z rj Z rc Z cj Z j Z o Z j, Z tj Z o, Z to Carbon teel 0,56 R r 0,31 R r 0,56 R r 0,76 R r 0,42 R r 0,50Q r 0,25 R r Alloy teel 0,52 R r 0,31 R r 0,52 R r 0,66 R r 0,42 R r 0,46 R r 0,25 R r Cat teel 0,50 R r 0,30 R r 0,68 R r 0,60 R r 0,34 R r 0,40 R r 0,24 R r Grey cat iron 0,44 R r 0,30 R r 1,20 R r 0,80 R r 0,50 R r 0,46 R r 0,35 R r Malleable cat iron 0,50 R r 0,30 R r 0,64 R r 0,56 R r 0,33 R r 0,36 R r 0,21 R r Brae 0,50 R r 0,31 R r 0,50 R r 0,62 R r 0,36 R r 0,36 R r 0,21 R r Bronze 0,44 R r 0,26 R r 0,44 R r 0,54 R r 0,31 R r 0,30 R r 0,17 R r Aluminum alloy 0,48 R r 0,29 R r 0,48 R r 0,60 R r 0,34 R r 0,36 R r 0,20 R r Value of the afe bearin preure followin formula: p dop for tationery connection can be evaluated uin where: p contant load; p j pulatin load; p o revered load. p = 0,8 k ; p = 0,8 k ; p = 0, 4k (3) c j cj o cj Attention! Do not confue p dop with: k d ; k dh (or p doph ) contact tre; f dbh. Havin value of dein tree we can tart dein calculation. In the beinnin we determine the external load carried by the iven machine element. Next we evaluate reaction, determine danerou cro ection of the element and type of tree in them (e.. tenile, bendin), with takin into conideration type of their variability (contant, pulatin revered). The area of ection we evaluate uin the followin formula: tenion compreion Pr σ r = ( j, c ) A (4) Pc σ c = kc ( kcj ) A (5)

6 bendin torion hear bearin preure M σ = k ( k j, k o) (6) W x M τ = k ( k j, k o ) (7) W o Pt τ t = k t ( k tj, k to) A (8) Pn p = p ( p j, po ) A (9) where σ r, σ c, σ denote normal (perpendicular) tre (tenion, compreion, bendin), τ, τ t tanential tre (torion, hear), Pr, Pc, Pt, P n force that caue tenion, compreion, torion and hear, M, M bendin moment and torional moment, A ection area, W, W ection modulu. x o In cae of complex tre we evaluate ubtitute tre and check i it le then dein tre in uniaxial tre tate: σ k ( k, k ) (10) z r c STANDARIZATION In the dein proce very often typical part are bein ued (e.. ear, bearin, crew, nut etc.). Many of thee element are tandardized. Standardization i development and implementation of uniform tandard. It aim i to oranize, implify and unify, amon other: technical markin and vocabulary (e.. rule for enineerin drawin); baic quantitie ued in the machine dein (normal dimenion, tolerance, fit, thread profile, etc.); material (type of teel, cat iron, etc.); typical element (crew, nut, waher, key, etc.). The reat advantae of uin tandardized element in contruction i to reduce the cot of manufacturin and exploitation of machine and device. It reult, amon other thin, from the fact that: tandardized element can be ma produced; the interchaneability of part i thu introduced; the work of the contructor i much more eay.

7 Fi. 3

8 Fi. 4 Fi. 5

9 BUCKLING OF RODS Conider the cae of a rod compreed by axial force P (Fi. 6). If the force i not too bi, after activatin a mall force Q perpendicular to the axi of the rod, the rod will bend, and after it withdrawal it will return to it previou poition. If, however, the force P exceed the appropriate value (the o-called critical force P ), then after intantaneou Q force activation the bar will not return to it previou poition traiht equilibrium, but will take on a new form of permanent equilibrium with a bent axi. Thi tate of curvilinear equilibrium i very danerou, becaue in addition to compreion, we are dealin with bendin, which at any mall increae in force P can lead to lo of tability of the rod. Fi. 6 Bucklin i called the bendin of the rod caued by the critical value bein exceeded by the compreive force. The value of the critical force P (for the compreed traiht rod) can be determined uin the Euler formula: where: P 2 π EJ = (11) l min 2 w E Youn modulu; J min minimum value of rod cro ection moment of inertia (bucklin will occur in a plane perpendicular to thi main axi, in relation to which the moment of inertia i the mallet). l w bucklin lenth, depended on the rod mountin condition (boundary condition) Fi. 7.

10 Fi. 7 Introducin lenderne: i min minimum radiu of cro ection moment of inertia, λ rod i J = (12) A 2 min min we obtain Euler formula : l w λ = (13) i min σ 2 π E = (14) 2 λ which i preented on raph (Fi. 8). Fi. 8

11 Euler formula can be ued only, if train i proportional to tre (Hooke law), i.e. when σ σ. Another word, Euler formula can be ued for rod, which lenderne i rater prop then lenderne limit λ r. E = (15) λr π σ prop For lenderne λ λ empirical curve σ = f ( λ) can be approximated by traiht line r (Tetmajer Jaińki formula) or by parabola (Johnon Otenfeld formula). In practice, the cope of applicability of thee formula i limited we do not ue them for the value of lenderne, below which there i no daner of bucklin, i.e. λ < 25. Rod of thi lenderne are treated a compreed only in trenth calculation.