A large antenna mount weighing 12 000 lb is to be supported on three hydrostatic bearings such that each bearing pad carries 4000 lb. A positive displacement pump will be used to deliver oil at a pressure up to 500 psi. Design the hydrostatic bearings.

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We will choose the circular pad design for which the performance coefficients are available in Figure 16–13. The results of the design will specify the dimensions of the pads, the required oil pressure in the recess of each pad, the type of oil required and its temperature, the thickness of the film of oil when the bearings are supporting the load, the flow rate of oil required, and the pumping power required.
Step 1. From Figure 16–13, the minimum power required for a circular pad bearing would occur with the ratio [latex]R_r/R[/latex] of approximately 0.50. For that ratio, the value of the load coefficient is [latex]a_f = 0.55[/latex].
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. Let’s design for a recess pressure of approximately 400 psi. Then, from Equation (16–10), [latex]F = a_fA_pp_r[/latex]

[latex]A_p=\frac{F}{a_fp_r}=\frac{4000 lb}{0.55(400 lb/in^2)}18.2in^2[/latex]

But [latex]A_p = πD^2/4[/latex]. Then the required pad diameter is

[latex]D=\sqrt{4A_p/\pi}=\sqrt{4(18.2)/\pi}= 4.81[/latex] in
For convenience, let’s specify [latex]D = 5.00[/latex] in. Then the actual pad area will be

[latex]A_p = πD^2/4 = (π)(5.00 in)^2/4 = 19.6 in^2[/latex]
The required recess pressure is then

[latex]P_r=\frac{F}{a_fA_p}=\frac{4000lb}{0.55(19.6in^2)}=370lb/in^2[/latex]

Also,
[latex]R = D/2 = 5.00[/latex] in/2 = 2.50 in
[latex]R_r = 0.50R = 0.50(2.50[/latex] in) = 1.25 in

Step 2. Specify the design value of the film thickness, [latex]h[/latex]. It is recommended that [latex]h[/latex] be between 0.001 and 0.010 in. Let’s use [latex]h[/latex] = 0.005 in.

Step 3. Specify the lubricant and the operating temperature. Let’s select SAE 30 oil and assume that the maximum oil temperature in the oil film will be 120°F. A method of estimating the actual film temperature during operation can be found by consulting Reference 12. From the viscosity/temperature curves, Figure 16–7, the viscosity is approximately [latex]8.3 × 10^{-6}[/latex] reyn (lb . s/in[latex]{}^2[/latex]).

Step 4. Compute the oil flow through the bearing from Equation (16–11) ([latex]Q=q_f\frac{F}{A_p}{}\frac{h^3}{\mu}[/latex]). The value of [latex]q_f = 1.4[/latex] can be found from Figure 16–13:

[latex]Q=q_f\frac{F}{A_p}{}\frac{h^3}{\mu}=1.4\frac{4000 lb}{19.6 in^2}{}\frac{(0.005 in)^3}{8.3 × 10^{-6} lb . s/in^2}[/latex]

[latex]Q = 4.30 in^3/s[/latex]

Step 5. Compute the pumping power required from Equation (16–12) ([latex]P=p_rQ=H_f(\frac{F}{A_p})^2\frac{h^3}{\mu}[/latex]). The value of [latex]H_f = 2.6[/latex] can be found from Figure 16–13:

[latex]P=p_rQ=H_f(\frac{F}{A_p})^2\frac{h^3}{\mu}=2.6(\frac{4000}{19.6})^2\frac{(0.005 in)^3}{8.3 × 10^{-6}}= 1631 lb . in/s[/latex]

For convenience, we can convert this to horsepower:

[latex]P=\frac{1631lb.in}{s}\frac{1.0ft}{12in}\frac{1.0hp}{550lp.ft/s}=0.247hp[/latex]

Question 16.5: A large antenna mount weighing 12 000 lb is to be supported ...

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