ROTOR DYNAMICS OF TURBOMACHINERY3.2.2 Evaluation of HD effectiveness by a set of non-dimensional parameters
Usually HDs are designed for operating wihin high dynamic loads range. It can be a range of a critical speed wc or an operating speed w where unbalance loads reach maximal values.
The main HD dimensions which control its damping and stiffness are the damper radius, length and clearance. The damper performances can be approximately evaluated by a set of generalized parameters [ 2,4 ].
Bearing parameter B:
,
here
m - lubricant absolut viscosity, Pa.sec; R - bearing radius, m; L R - squeeze film bearing land length, m; mA - mass lumped at either of the bearing stations, ea; wC - pin-pin critical speed, s-1; d - radial clearance (housing radius - journal radius) , m.
The damper reduced length is calculated for a damper with annular groove:
- for a damper without end seals
.
Li - is a land-width beetween end side and annular groove
- for a damper with end seals, for example with piston ring seals
Here Li - is a land-width beetween ring seals and annular groove i.e. land - width of the operating area.
Gravity parameter - 
, aaa WB =mB g;
Unbalance parameter - U
U = (Fu / mDdw 2) =eu /d,
aaa FU - unbalance force (mDeUw2); mD mass lumped at the rotor mid-span ; eU - unbalance eccentricity.
Frequency ratio - W
W =w /wC
Mass ratio - a
a = mB /mD
For most practical tasks usually only B and W parameters are analysed, the others are not verifyed.
Below are given some results of experimental and analytical investigations of a large number of dampers [ 3 ]. The typical set of the experimental results is listed in Table 2.
Table 2
|
Test |
d, mm |
LR mm |
Oil Type |
Average viscosity Ns/m2 |
Unbalance gm cm |
Maximum Peak-to peak Amplitudes G, mm |
Speed at which Max Amplitude occurs, rpm |
|
A |
0 |
0 |
SAE 30 |
35.98x10-2 |
1.016 |
0.289 |
7248 |
|
A |
0 |
0 |
SAE 30 |
30.10x10-2 |
2.032 |
0.502 |
7243 |
|
1 |
0.0635 |
7.62 |
SAE 30 |
30.10x10-2 |
5.67 |
0.552 |
6950 |
|
2 |
0.0635 |
7.62 |
Turbine 3 |
2.36x10-2 |
5.67 |
0.254 |
6980 |
|
3 |
0.1905 |
15.24 |
SAE 30 |
32.39x10-2 |
17 |
0.590 |
7005 |
|
4 |
0.1270 |
7.62 |
Turbine 3 |
3.13x10-2 |
11.33 |
0.178 |
7008 |
|
5 |
0.1905 |
15.24 |
Turbine 3 |
2.25x10-2 |
17 |
0.266 |
7240 |
Calculated values of the appropriate non-dimensional values are listed in Table 3, below.
Table 3
|
Oano. |
Max. Amplitude Ratio G/d |
Unbalance parameter U |
Bearing parameter B |
Gravity parameter |
Mass ratio a |
|
1 |
8.7 |
0.1 |
8.731 |
0.268 |
0.445 |
|
2 |
4.1 |
0.1 |
0.684 |
0.268 |
0.445 |
|
3 |
3.1 |
0.1 |
2.784 |
0.089 |
0.445 |
|
4 |
1.4 |
0.1 |
0.114 |
0.134 |
0.445 |
|
5 |
1.4 |
0.1 |
0.193 |
0.089 |
0.445 |
Analysis and tests of modelling rotors have shown that the bearing parameter should be kept within range of 0.05<B<4 and for the best results to a value of about 0.1. The gravity parameter W should be kept to a value less than 0.1. Values B < 0.05 produce rotor unstability, at B>4 the dynamic transmissibility t is near to 1.
Investigations of more than 20 dynamically developed engines give the following results ( parameter here is not considered):
· HDs with ring seals have 0.02<B<0.2,
· HDs without ring seals have 0.002<B<0.8 (note much large dispersion).
Considering these values in terms of design usage can be summarised as following:
· not all of the investigated dampers can be considered as optimal;
· good results in vibration amplitude can be obtained within a wide range of B values;
· the dimensions obtained by the non-dimensional parameters can be made more accurate by test and/or analysis.
