CHARTS AND TABLES 



25 



26. Effect of the FlexibiUty of Flywheel Spokes on WR^ of Rim.— The effective 

 WR^ of the rim is 



^ 



m 



WR' = 



iWR')' 



{WRyp 



9.775(7 



where (WR^)' = flywheel effect of the rim 



/ = natural torsional frequency of 

 the system of which the fly- 

 wheel is a member, in vibra- 

 tions per sec. 

 C = torque required to move the 

 rim through one radian relative 

 to the hub 



^ _ 12„Eka^bR ( L , R \ 



where g = number of spokes 



E = bending modulus of elasticity of the 



spoke material 

 k = 7r/64 for elliptical, and h = }^2 for 

 rectangular section spokes 

 All dimensions are in inches. 



For cast-iron spokes of elliptical section: 



E = 15 X lO*^ lb. per sq. in. 

 ga'bR XIO'/L . R A Ib.-in. 



C = 



0.1132L2 



(i+!-0 



radians 



Note: It is found by comparative calculations that with spokes of moderate taper very little error is involved in 

 assuming the spoke to be straight and using cross section at mid-point for area calculation. 



Section A-A 



Note: Since the beads at the ends of the spokes comprise 

 but a small part of the flywheel WR', very little error 

 will result in assuming them to be of rectangular cross 

 section. Also, because of the effect of the clamping 

 bolts, the outer hub will be considered a square equal 

 to the diameter. The spokes will be assumed straight 

 and of mid-point cross section. 



Part 

 of fly 

 wheel 



TYPICAL EXAMPLE 



The flywheel shown below is used in a 

 Diesel engine installation. It is required 

 to determine effective WR- for calculation 

 of one of the natural frequencies of tor- 

 sional vibration. The anticipated nat- 

 ural frequency of the system is 56.4 

 vibrations per sec. 



(o) 



(b) 



(r) 



(rf) 



ie) 



if) 



Formula 



IFie= 



2f 



26 



16a 

 neglecting 

 / ir^ + L^ \ 



\ 12 y 



56 



26 



19 



10[(52)^ - (43)^] 

 40.75 



= 955,300 



Total for rim = 1,016,300 Ib.-in. 



squared 



6 X 



5.25 X 2.5 X 11 

 4.90 



V-¥ 



-1-8.5(8.5-1-11) +^^^n =36,800 



2.625[(17)^ - (13)-' 

 39.2 



= 3,700 



TT X 0.250 X 12 



32 



[1.697 X (IS)* 



(6)^] = 13,900 



Total for remainder of flywheel 

 = 54,400 Ib.-in. squared 



From formula (26) 



C = 



6 X (5.25)3 X 2.5 X 19.5 X lOi^ 



\3 X 1 



0.1132 X (11)2 

 19.5 



19.5 "'" 11 



1,970 X 10« 



Ib.-ir 



l) = 2,6, „ ^ .., --y. — 

 / radians 



and WR' 



1,016,300 



1.016,300 X (56.4)' 



-I- 54,400 



9.775 X 2,970 X lO*^ 



= 1,197,000 Ib.-in. squared 



t-:; 



:-iO, 



