vb.net barcode reader code Rolling Element, Hydrodynamic and Hydrostatic Bearings in Software

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Rolling Element, Hydrodynamic and Hydrostatic Bearings
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Fig 655: A load-pressure relationship based on a one-dimensional approximation [19]
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Hydrostatic = W a Ps LD
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W L n Cd
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Bearing load Bearing length Rotational speed Diametrical clearance
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D Hydrodynamic = W a n h LD Cd Ps = Control supply pressure D = Bearing diameter h = Dynamic viscosity
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Fig 656: Hydrostatic and hydrodynamic journal bearing characteristics [19]
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supply pressure, bearing length and bearing diameter On the other hand, the load capacity of a hydrodynamic bearing is directly proportional to the rotational speed, dynamic viscosity, bearing length and the cube of the bearing diameter and inversely proportional to the square of the diametrical clearance When hydrodynamic characteristics are introduced into a hydrostatic bearing, it becomes a hybrid bearing
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648 Design of Hydrostatic Bearings
(a) Circular pads According to Mott [14], the three factors characterizing the performance of a hydrostatic bearing are its load-carrying capacity, the flow of oil required and the pumping power required, as indicated by the dimensionless coefficients af, qf and Hf The magnitudes of the coefficients depend on the design of the pad [1, 14]: F = a f A p Pr Q = qf
F h3 Ap
F h3 P = Pr Q = H f Ap where F is the load on the bearing, lb or N; Q the volume flow rate of oil, in3/s or m3/s; P the pumping power, lbin/s or Nm/s (watts); af the = pad load coefficient, dimensionless; qf the pad flow coefficient, dimensionless; Hf the pad power coefficient, dimensionless; Ap the pad area, in2 or m2; Pr the oil pressure in the recess of the pad, psi or Pa; h the film thickness, in or m and is the dynamic viscosity of the oil, lbs/in2 or Pas Figure 657 shows the typical variation of dimensionless coefficients as a function of the pad geometry for a circular pad with a circular recess As the size of the recess (Rr/R) increases, the loadcarrying capacity increases, as indicated by af But at the same time, the flow through the bearing increases, as indicated by qf The increase is gradual up to a value of Rr/R of approximately 07, and then rapid for higher ratios This higher flow rate requires a much higher pumping power, as indicated by the rapidly increasing power coefficient At very low ratios of Rr/R, the load coefficient decreases rapidly The pressure in the recess would have to increase to compensate in order to lift the load The higher pressure requires more pumping power Therefore, the power coefficient is high at
Rolling Element, Hydrodynamic and Hydrostatic Bearings
Fig 657: Dimensionless coefficients for a circular pad hydrostatic bearing [14]
either very small ratios of Rr/R or at high ratios The minimum power is required for ratios between 04 and 06 [14] Example: Circular Pads Hydrostatic Bearings A large antenna mount weighing 12,000 lb is to be supported on three hydrostatic bearings such that each bearing pad carries 4,000 lb A positive displacement pump will be used to deliver oil at a pressure of up to 500 psi We now design the hydrostatic bearings [14]
Precision Engineering
From Figure 659, the minimum power required for a circular pad bearing would occur with a ratio (Rr/R) of approximately 050, for which the value of the load coefficient ar = 055 The pressure at the bearing recess will be somewhat below the maximum available of 500 psi because of the pressure drop in the restrictor placed between the supply manifold and the pad The design is completed for a recess pressure of approximately 400 psi F = af Ap Pr Ap = Ap =
F a f Pr
4000 055  400 
Ap = 182 in2 1174191 mm2 But as Ap = p D 2/4, the required pad diameter is D = D =
4 Ap / 4 (182 ) /
D = 481 in 12217 mm For convenience, the diameter, D, is assumed to be 500 in The actual pad area will then be Ap = pD 2/4 Ap = (p) (5)2/4 1264514 mm Ap = 196 in2 R = D/2 = 500/2 = 250 in Rr = 050 R = 050 (250) = 125 in The required recess pressure is then F Pr = a f Ap Pr =
4000 055 196
Pr = 370 lb/in2 026 kg /mm2 The clearance, h, is recommended to be between 0001 and 001 in Assume h = 0005 in = 0127 mm The viscosity can be obtained from Figure 634 for a given type of lubricant and temperature In this case, it is assumed that viscosity, = 83 10 6 lbs/in2 qf = 14 (Figure 659) Q = qf
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