The Elements of Machine Design Volume N . 2

The Elements of Machine Design Volume N . 2

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1920 edition. Excerpt: ...sq. in. on the surface of the cylinder into which it is sprung. The pressure of the ring on the cylinder per unit of length is p b, and the resultant of the uniform pressure from A to B is p b X chord A B, or--p = 2pbrsia6 The moment of this about B is--2 p b r2 sin2 6 Putting this value of the bending moment in the equation above--2 pbrskPO = E I0r (2) But for a rectangular section (I, Table IV, p. 70)--=bfi_ 12 1 1 24 p r2 sin2 6 ' r Ep For 26 = 180, let tx be the thickness of the ring--1 1 24 p r2 Hence, for uniform pressure of ring on cylinder--(3) (4) = sin2 6... (5) h 26= t--100 o-I97 h 200 0-311 400 0-489 600 0630 800 0745 1000 0-837 120 0-908 I40o O960 l600 0-990 1800 1-ooo From which table the thickness at different points in the ring can be calculated when ix is known. Fig. 141 shows a ring drawn from these values. It is found that about two-thirds of the inside curve of the ring agrees very closely with a circle struck from a point c at a distance o c = a from the centre of the outside of the ring. It is easy to show that a = 0-206 ix nearly. The ring can therefore be bored Fig. 141 out to a radius r--0794 th and the points near A then thinned to agree with the proportions above. From Equation (3)---'S(h-7)..,61 The stress in the spring ring at its thickest part is (I, 49)--0 _ M _ 6 M 1 1 = bl? But the bending moment is--V pj 12 V p) Inserting this value--/-Y(H) 'w or, using the value in (6)--r 2 f=TMpn (7a) n h = r/... (8) For instance, for cast-iron let E = 17,000,000; f = 5000 lbs. per sq. in., as the stress is constant and of one kind; p = 3J lbs. per sq. in. Then ti = 0-092 r, and p/r = 1-007. With the same data; except that p = 2 lbs. per sq. in., tx--o-o6g r, and p/r = 1-009. Assuming p/r = 105, e = 17,000,000 and / more

Product details

  • Paperback | 106 pages
  • 189 x 246 x 6mm | 204g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236566777
  • 9781236566775