SDSS COUNTERWEIGHT SYSTEM

                            DESIGN CALCULATIONS

                                                                Jim Domanus

                                                             August 7, 1997

SDSS COUNTERWEIGHT

The counterweight system on the telescope is used to maintain telescope
balance under different instrument configurations. During normal operations
the counterweights are in a forward or up position. During an instrument
change, the counterweights are moved to the rear or down position keep the
telescope "bottom heavy" while the lens is removed. This counterweight
movement takes place with the telescope in the vertical position. Figure I
shows the counterweight assembly.

The positioning table that is being used for the counterweights is a
LinTech Series 100000, 4 bearing slide. The load ratings are as following;

                                 DYNAMIC                  STATIC

 HORIZONTAL (Ibs)           3100 (635/bearing)      4720 (1190/bearing)

 ROLL MOMENT (ft- lbs)             280                      415

 PITCH MOMENT (ft-Ibs)             240                      365

The values shown are for 2 million inches of travel life, which corresponds
to 42,000 cycles of the counterweight. All values were found in the LinTech
Catalog and the Thomson Linear Bearing Catalog.

Bearing Results

Calculations for the slide were done with the telescope in the vertical
position, horizontal position, and at a 45 degree angle. In the case of the
SDSS counterweight system all dynamic loading occurs with the telescope in
the vertical position. The calculated equivalent force acting on the
bearings in this position was determined to be 95 pounds per bearing
assembly. This value gives the bearing a factor of safety of 6.5. The
equivalent moment loading in this position was calculated to be 33 ft-lbs.
It should be noted that the weight was designed to keep the center of
gravity close to the center surface of the slide plate, thus reducing the
moment loading on the system.

The counterweight system was also checked with the telescope in the
horizontal position and at a 45 degree angle. The maximum force acting on a
bearing was 136 pounds for the horizontal and 174 pounds at 45 degrees. The
static load rating is 1190 pounds per bearing. This value gives a factor of
safety of 8.8 and 6.8 respectively for the slide.

The results show the minimum factor of safety to be 6.5 while the slide is
in the vertical position. (see calculations for more detail)

Mounting Screws

The counterweight is attached to the linear slide with four 8-32 UNC allen
head cap screws. The cap screws are SAE Grade 8 alloy steel with a minimum
proof strength of 120,000 psi. The loading on the screws was checked with
the telescope in the vertical position, horizontal position, and at a 45
degree angle. The maximum stress on a screw was determined to be 11,950 psi
while positioned at a 45 degree angle. This value corresponds to a minimum
safety factor of 10. (see calculations for more detail)

Safety Cable

In the event of a failure, a safety system was designed to assure that the
weight would not fall to the ground. This consists of a wire rope that runs
through a guide on the weight and is attached to the main body of the
telescope. The wire rope is 3/16 diameter, 7 x 19 strand core, nylon
coated, with a breaking strength of 3700 pounds. The guide is attached to
the counterweight with two 3/8-16 UNC allen head cap screws. The cable is
attached to the main body of the telescope with the cable holder. The cable
is wrapped around a 1/4" diameter dowel pin in the holder and is clamped
using two forged cable clamps per end. The cable holder is attached to the
telescope with two 1/4-28 UNF flat head cap screws. The minimum factor of
safety on this system is 10 through the cable. (see calculations for more
detail)

Conclusion

The results show that the worse case loading on the counterweight system is
on the bearing assembly with the telescope in the vertical position. The
loading in this position is dynamic and gives a factor of safety of 6.5. It
should be noted that the load ratings for the bearings are given for two
million inches of travel life. Therefore the actual life expectancy of the
counterweight system should be greater than two million inches of travel
life.

[Image]

SDSS COUNTERWEIGHT SLIDE CALCULATIONS

TELESCOPE IN THE VERTICAL POSITION

SLIDE BEARING CALCULATIONS

BEARING LOADING

                                  [Image]

                        Figure 2. Vertical Position

[Image]

Where; W = 350 lbs

d4 + dr =.375 in + .75 in = 1.125 in

d2 = 2.088 in

[Image]

Dynamic Load Rating = 635 lbs for 2 million inch travel life.

Factor of Safety = 635 lbs/94.3 lbs = 6.7

MOMENT LOADING

Moment from load = 1.125 in (350 lbs) = 394 in-lbs = 33 ft-lbs

Rated Moment = 240 ft-lbs for 2 million inch travel life

TELESCOPE IN THE HORIZONTAL POSITION

SLIDE BEARING CALCULATIONS

BEARING LOADING

                                  [Image]

WY= 350 lbs (sin45) = 247.5 lbs

WX = 350 lbs (cos45) = 247.5 lbs

Sm3 = 0 = (247.5 lbs)(1.188 in) + (247.5 lbs)(1.125 in) - FX1(2.375 in)

FX1 = 241 lbs = 120.51 lbs/ bearing

SFX = 0 = WX - FX1 - FX3 = 247.5 lbs- FX3 - 241 lbs

FX3 = 6.5 lbs = 3.25 lbs / bearing

SFY =0=WY -FY1 - FY3

FY1 = FY3

2FY1 = WY = 247.5 lbs

FY1 = 123.75 lbs = 62 lbs / bearing

Static Load Rating = 1190 lbs / bearing

Factor of Safety = [Image]= 8.75

TELESCOPE IN THE 45 DEGREE POSITION

SLIDE BEARING CALCULATIONS

BEARING LOADING

                                  [Image]

Figure 4 shows the plate position when the telescope is at 45 degrees. To
simplify the calculations it was assumed that the bearings were an equal
distance apart with a diagonal distance of 3.5 inches.

S m4 = 0 = (247.5 lbs)(1.125 in) + (247.5 lbs)(1.75 in) - FX23(l.75 in) -
FX1 (3.5 in)

Assume FX23 = 1/2 FX1

FX1 = 163 lbs

SFY = 0 = WY - FY1 - FY4

Assume FY1 - FY23 = FY4

WY = 4FY = 247.5 lbs

FY1 = 62 lbs

F1 = [FX12 + FY12] = [163 lbs2 + 62 lbs2]1/2

F1 = 174 lbs

Static Load Rating = 1190 lbs / bearing

Factor of Safety =[Image]= 6.8

COUNTERWEIGHT MOUNTING SCREW CALCULATIONS

TELESCOPE IN THE VERTICAL POSITION

SCREW LOADING

                                  [Image]

Tensile Loading

[Image]

FX1 = 0.113FX2

S m0 = 0 = -(.406 in)(FX1) - (3.594 in)(FX2)+(.375 in)(350 lbs)

FX2 = 36 lbs = 18 lbs/screw

Shear Loading

Assume shear loading on screws is equally distributed.

SFY = 0 = 350 lbs - FY1 - FY2

FY1 = FY2

FY2 = 175 lbs = 87.5 lbs / screw

Screw Data

8-32 UNC Socket Head Cap Screw

Grade 8 Alloy Steel

Proof Stress 120,000psi

Stress Area = AS = 0.014 in2

Stress Calculations

[Image]

TELESCOPE IN THE HORIZONTAL POSITION

SCREW LOADING

                                  [Image]

Tensile Loading

[Image]

Shear Loading

Assume shear loading on screws is equally distributed.

[Image]

Screw Data

8-32UNC Socket Head Cap Screw

Grade 8 Alloy Steel

Proof Stress = 120,000 psi

Stress Area= AS = 0.014 in2

Stress Calculations

[Image]

TELESCOPE IN THE 45 DEGREE POSITION

SCREW LOADING

                                  [Image]

Figure 7 shows the plate position when the telescope is at 45 degrees. To
simplify the calculations it was assumed that the screws were an equal
distance apart with a diagonal distance of 3.5 inches.

Tensile Loading

[Image]

Shear Loading

Assume shear loading on screws is equally distributed.

[Image]

Screw Data

8-32UNC Socket Head Cap Screw

Grade 8 Alloy Steel

Proof Stress = 120,000 psi

Stress Area= AS = 0.014 in2

Stress Calculations

[Image]

CABLE GUIDE MOUNTING SCREWS

MOMENT LOADING

                                  [Image]

[Image]

Design Stress = sd = 10,000 psi

Stress Area = As

[Image]

Use minimum of 5/16 Screw (As=.0524 in2)

A 3/8 screw was selected for this application. The following calculations
determine the factor of safety.

Screw Data

3/8-16 LTNC Socket Head Cap Screw

Grade 8 Alloy Steel

Proof Stress = 120,000 psi

Stress Area = (AS =.0775 in2)

[Image]

SHEAR LOADING

                                  [Image]

Slotted hole, therefore use one bolt area for calculation.

[Image]

CABLE HOLDER MOUNTING SCREWS

                                  [Image]

Tensile Loading

[Image]

Shear Loading

Assume shear loading on screws is equally distributed.

[Image]

ALLOWABLE DESIGN STRESS

Maximum Shear Stress = tmax=5000 psi

Maximum Stress = s1 = 10,000 psi

Shear

[Image]

Tensile

[Image]

A 1/4-28 UNF screw was selected for this application. The following
calculations determine the factor of safety.

Screw Data

1/4-28 UNF Flat Head Cap Screw

Grade 8 Alloy Steel

Proof Stress = 120,000 psi

Stress Area = AS = 0.0364 in2

[Image]

CABLE HOLDER DOWEL PIN

Minimum Rated Double Shear Load = 12,800 lbs (Machinery's Handbook 23rd Ed.
Page 1441)

Maximum Load From Weight = 350 lbs

[Image]
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