Design of a hydrostatic symmetric-pad bearing with the membrane-type restrictor

Transcription

1 Design of a hydrostatic symmetric-pad bearing with the membrane-type restrictor Professor: Shih-Chieh Lin Manufacturing and Production System Lab Dept. of Power Mechanical Engineering, National Tsing Hua University sclin@pme.nthu.edu.tw 1

2 Design of a hydrostatic symmetric-pad bearing with the membrane-type restrictor 2

3 Advantages can be characterized for hydrostatic bearings Low friction (low speeds) Infinite life (wear free) Zero static friction (no stick slip) High damping capacity (squeeze film) High stiffness (membrane compensation) 3

4 Most of compensation mechanisms for hydrostatic bearing use a fluid resisting placed in series with each bearing recess. Pumping driver (Supply pressure ps) When the bearing gap close > resistance goes up > dropping the flow rate through the restrictor > reducing the pressure drop across the restrictor > increasing the recess pressure Restrictor Rr Single pad bearing (Recess pressure p ) 4

5 A membrane restrictor differs from many other variable restrictors in that the flow is regulated by a metal diaphragm. (also called diaphragm controlled restrictor, DCR) r2 r1 W z Membrane l0 r Bearing x Single pad bearing (Recess pressure p ) h Pumping driver (Supply pressure ps) 5

6 The flow rate model of the single-pad configuration p p Q p p p R R p r, s Where R is the flow resistance of the bearing, which is inversely proportional to the cube of the clearance h. Pumping driver (Supply pressure ps) Restrictor Rr R R 3 h * Single pad bearing (Recess pressure p ) 6

7 For the hydrostatic bearing with infinite static stiffness, the flow rate Q provided by the restrictor should be linearly proportional to the recess pressure P. (i.e. R(h) will be a constant) Pumping driver (Supply pressure ps) Recess pressure Restrictor resistance Bearing resistance Restrictor Rr Pumping driver ps Rr p R Atmosphere Single pad bearing (Recess pressure p ) h 7

8 Analytical consideration for infinite stiffness 8

9 When the supply pressure p s is known, the recesses pressure can be expressed as a function of the resistance ratio R r /R. ps p 1 R R r According to a cubic law of the flow resistance, deformationpressure relationship of the restrictor can be obtained: p 1 R R ri p s Where ξ is the deformation ratio of the membrane (x/l 0 ) 9

10 For a membrane, the corresponding stiffness can be described as d r Kr Ar ps p p dx 0 d A d A r is the effective area of the restricting plane (considering as a circular pad) r ' Ar r, r ' 2 ln 1 ' r r2 r r2 r1 Membrane Restricting Plane l0 x r Single pad bearing (Recess pressure p ) 10

11 The corresponding stiffness of the ideal membrane for hydrostatic bearing with infinite stiffness should be K p A s r 2 s r * r, i 3 1 Kr, i p A Where λ is denoted as the design restriction ratio of the restrictor R R 1 6 r, R ln R R r ri ri 2 ri 3 0 r

12 Where To find a K* membrane r,i is denoted to perfectly as the dimensionless satisfy the dimensionless ideal corresponding stiffness stiffness required for of achieving the restrictor the infinite bearing stiffness is difficult. * 2 1 Kri, =

13 The stiffness of the membrane can generally be assumed as a constant K r by the theory of plates and shells. Krieger, S. (1959). Theory of Plates and Shells (2 ed.). New York: Mcgraw-Hill College. 13

14 It was found that K r =1.33, λ=0.25 make the deformation-load relationship of the membrane almost compliance with the ideal trend. Lai TH, Chang TY, Yang YL, Lin SC, Parameters design of a membrane-type restrictor with single-pad hydrostatic bearing to achieve high static stiffness, Tribology International, 107(2017), pp

15 For the single-pad configuration, the clearance of the bearing can be h 1 WW 1 1 h W W K * r 10 WW 0 and the stiffness of the bearing is K W 1 3 WW 3 h 1 W W K 1 1W W 0 * 0 r

16 Analytical Results and Experiments 16

17 When λ = 0.25, K r = 1.33, the bearing will perform very high stiffness at a designed clearance h 0. 17

18 Similar characteristics will observed with different K r, and the clearance ratio will decrease when λ is increased. 18

19 Curves for physical membrane with a dimensionless stiffness of 1.33 can achieving the very high bearing stiffness around the region for the dimensionless loading between 0.2 to

20 A very great stiffness could be obtained when K r = 1.33, but more consideration is required to avoid the negative bearing stiffness. (when K r < 1.33) Negative stiffness Negative stiffness In the case K r = 1.0, the bearing will function with the negative stiffness within the load range W A e p s = 0~

21 Experiment system diagram Pressure sensor signal conditioning Particular filiter(s) Acc. Pressure sensor P0 Pressure sensor P1 Pressure sensor P2 Pumping driver Bypass Flow meter Pressure Regulator Eddy current sensor Displacement sensor signal conditioning Data acquisition devices Matlab P1 Bearing fluid supply tank/ recovery tank Strainer Hydrostatic linear bearing system Heater P2 21

22 Parameters used in the experiment Supply pressure p s 2.0 Bar Reference pressure ratio β Lubricant Viscosity η Diameters of restrictor r 1, r 2, r 3 Designed clearance of restrictor l 0 Young s modulus of membrane E Poisson ratio of membrane v 0.3 Thickness of membrane t Applied load W Size of bearing pad B,C Radius of the inner fillet of bearing pad r i Width of the land of bearing pad ω Reference clearance of bearing pad h PaSec 6, 10, 15 mm 32 μm 210 GPa 0.5 mm 27, 36, 45, 54, 63, 72 Kg 80,200 mm 5 mm 30 mm 20 μm Chang TY, Yang YL, Liu FR, Lin SC. Analysis on Parameters and Design of Membrane-type Restrictor. Proc of the Int Conf on Engineering and Natural Science - Summer Session; Kyoto; 2016; p

23 Max experiment error: -11.8% Avg experiment error: -10.3% Chang TY, Yang YL, Liu FR, Lin SC. Analysis on Parameters and Design of Membrane-type Restrictor. Proc of the Int Conf on Engineering and Natural Science - Summer Session; Kyoto; 2016; p

24 Symmetric-pad bearing with the membrane-type restrictor 24

25 In order to get the wider load range and the isolating contaminants capability, the bearing is often designed as a close form structure made up of a certain number of opposed pads. Single pad bearing Opposed pad bearing 25

26 For a opposed-pad bearing, the upper pad and lower pad are equally designed >> A symmetric-pad configuration A sketch plot for a hydrostatic symmetric-pad bearing 26

27 The electrical network analogy of the bearing Upper recess pressure Upper restrictor resistance Upper bearing land resistance Pumping driver ps Rr1 p1 R1 Rr2 R2 p2 Recess pressure modulates the restrictor Lower bearing land resistance 27

28 Analytical Results and Discussions 28

29 The effects of membrane stiffness on the symmetric-pad bearing were evaluated with the parameter sets listed in the following table Designation Values K r1 = K r2 1.33, 1.50, 2.00, 5.00, Inf << Be equally designed λ 0.05, 0.1, 0.25, 0.5, 1.0 ε 0 ~ 1.0 K r1 = K r2 29

30 Four obvious performance measures were adopt to give the grad of the bearing (ranged from 0.1~0.8 W/A e p s ) H avg : Average clearance H dev : Deviation of the clearance H dvr : Deviation ratio of the clearance H min : Minimum clearance W/A e p s 30

31 For the case K r1 = K r2 = 1.33 λ H avg H dev H dvr H min Avg

32 Conclusions 1. The result shows that the membrane-type restrictor has greater static stiffness than traditional ones (i.e. capillary) not only for single-pad cases but also for symmetric-pad configurations. 2. It is recommend to choice K r1 =K r2 =1.33 and λ=0.25 for the membrane restrictor in a symmetric-pad bearing for light-load design. 3. The minimal deviation of the bearing clearance will appear when K r1 =K r2 =1.33 and λ=1.0 (i. e. R ri = R 0 ). The combination of the design parameters is recommend for heavy-load design. 32

33 4. The membrane restrictor will perform as a capillary restrictor when the stiffness of the membrane K r > It is similar to the single-pad case that the static stiffness of the opposed-pad bearing is inversely proportional to the nominal clearance of the bearing. The thinner nominal clearance is, the greater the stiffness and the smaller the power losses will be. (greater manufacturing accuracy will be required) 6. The bearing clearance will be maintained in most application range without any negative stiffness phenomena when both design parameter are properly chosen. 33

34 About our lab 34

35 Manufacturing and Production System Lab (MAPS) Dept. of Power Mechanical Engineering, National Tsing Hua University 101, Sec. 2, Kuang Fu Road, Hsinchu 30013, Taiwan, R.O.C. Mail: Tel: #33789 Professor: Lin, Shih-Chieh Research Hydrostatic Bearing Hydrostatic guideway Hydrostatic journal bearing Hydrostatic spindle Hydrostatic rotary table Auto-scraping System Scraping Mechanism Machine Vision Image Processing 35

36 Thanks for listening ~ 36