4.3 Design of a damper support with a flexible ring
· Bearing outer diameter Do 60 mm;
· Required ring stiffness k = 0.2 x107 N/m;
· Bearing lumped mass m = 15 kg;
· Ring material 40XHMA (Russian standard), Young module E = 0.19x1012 N/m2;
· Overloading coefficient n = 2.5;
· Maximal unbalance of the rotor support (me)d = 20gr cm;
· Dynamic transmissibility coefficient of the shaft vibrations kd = 4.
1. Radial displacement
= 20 x10-5 / 15 = 0.13o10-4 i = 0.013 mm
= (15 x2 / 0.2x107) x 9.81 + 4x0.13o10-4 =
1471.5 o10-7 + 0.52o10-4 = 1.99 o10-4 i = 0.19 mm
2. The ring inner diameter
Usually between the flexible ring and the bearing outer ring there is located a cylindrical bushing. The ring inner diameter is taken out of the table A3.1 as the nearest D1=65mm. Then the bushing thickness is 2.5mm. The ring outer diameter is D2=68mm.
Number of center pedestals n=6 is determined out of the ring displacment limit d0<dmax. The other dimensions are taken out of the table: center pedestals width b1=5mm, milling cutter diameter d=20 mm.
3. The ring width is taken out of design consideration b=14 mm.
4. The ring thickness.
s=(D2-D1) /2 -2 d 0 = 68-65) / 2-2x0.19 =1.5 - 0.38 =1.12 mm
5. The ring stiffness / flexibility
= (65 +68)/2= 66.5 mm
= 1.12+0.19=1.31 mm
= = = 235o10-6 mm/N
Stiffness k = 0.425 x 10 7 N/m
7. St:ress in the ring
= = 420 MPa
8. Fatigue safety factor.
The ring material 40XHMA properties:
s-1 =500MPa; ys =0.3; ks =1.1; =1.1; =1
= 0.85o500=425 MPa
The ring stress is alterating, so
sa =sd /2 = 210 MPa; sm= sd/2 =210 MPa
= (425-0.3x210)/(1.2x210) = 1.436
The fatigue safety factor is to be not smaller than 1.3 to 1.4.
The resulting stiffness is about two (2) times higher than required. It can be corrected by the ring width or by the thickness under the stress limit control.