T E C H N I C A L R E P O R T
W. Gallieni, ADS Italia
301a002c
341A000/B - Rear and front bogies assembly -
341A001/B - Horizontal guide rollers. -
341A002/B - Drive wheel assembly -
341A003/A - Stow pin assembly -
341A004/B - Leg bottom flange connection to bogie -
For the above conditions are summarised the figures taken from the M3 Calculation Sheets, deriving the figures for different wind speed with the rule of pressure being proportional to the square value of the wind speed.
TIPPING TOTAL WIND FORCE - 2388 × (50:90)² = 737 KN
MOMENT at top of rail 54839 × (50:90)² = 16925 KNm
TORSION MOMENT at C/L pier = 0 KNm
TIPPING TOTAL WIND FORCE - 2643 × (50:90)² = 816 KN
MOMENT at top of rail 58794 × (50:90)² = 18146 KNm
TORSION MOMENT at C/L pier 12080 × (50:90)² = 3728 KNm
TIPPING TOTAL WIND FORCE - 1230 KN
MOMENT at top of rail 27309 KNm
TORSION MOMENT at C/L pier 1499 KN.
TIPPING TOTAL WIND FORCE - 1585 KN
MOMENT at top of rail 34468 KNm
TORSION MOMENT at C/L pier 2682 KNm
TIPPING TOTAL WIND FORCE - 3148 KN
MOMENT at top of rail 69910 KNm
TORSION MOMENT at C/L pier 3838 KNm
TIPPING TOTAL WIND FORCE - 4058 KN
MOMENT at top of rail 88237 KNm
TORSION MOMENT at C/L pier 6867 KNm
| Back Bogie | Front Bogie | |
|---|---|---|
| Dead Load | 2530 KN | 4190 KN |
| Astronomers dead load | 167 KN | 324 KN |
| 80 Km / h wind load | ± 667 KN | ± 667 KN |
| ----------- | ----------- | |
| Max. total | 3364 KN | 5181 KN |
| Vertical adopted design Loads | 3435 KN | 5200 KN |
N.B.: the dead load of 13440 KN is the value resulting from the Weight Budget Summary, while the wind overload is an average figure between the 520 KN with wind in perpendicular direction and the 785 KN with the wind at 45 degrees direction.
Similarly, the design horizontal wind force with the telescope in operation is defined in ( 737 + 816 ) / 2 = 776,5 KN -
| Back Bogie | Front Bogie | |
|---|---|---|
| Dead Load | 2530 KN | 4190 KN |
| Astronomers dead load | 167 KN | 324 KN |
| 225 Km / h wind load | ± 3845 KN | ± 3845 KN |
| 50% snow load | 245 KN | 490 KN |
| ----------- | ----------- | |
| Max. total | 6787 KN | 8849 KN |
| Allowable reduction = 75% of load | 5090 KN | 6637 KN |
| Vertical adopted design loads | 5100 KN | 6870 KN |
Total Horizontal wind load 3924 × 0,75 = 2943 KN
Earthquake lateral load 2943 KN
Mt = 3728 KNm
Mt = 2682 KNm
N.B. : Torque smaller than the one in observing conditions with open shutter, so this one is not a critical condition to be verified.
Using the building dimensions of the June 96 Arcetri Meeting version and the masses of the 31 May 1996 Weight Budget Summary of M3, the following figures of moment of Inertia has been calculated :
N.B. : the values have been calculated reducing the assembly to a number of subassemblies of simplified shape, so the values, sure valid for a correct choice of the drives, should be verified with the final FEA model by M3.
Max. angular velocity 1,5 degrees sec¯¹
Max. angular acceleration 0,3 degrees sec¯²
Max. azimuth rotation ± 270 degrees from South
Max. operating wind speed - Shutter open - 80 Km / h
Max. operating wind speed - shutter closed - 120 Km / h
Clearance on telescope rotation ± 2 degrees
Considering the uneven distribution of loads between the front and the rear bogies, to use wheels of the same dimension having approximately the same max. load, has been chosen four wheel bogies for the rear corners and six wheel bogies for the front ones; the rear wheels have a max. load of 3435 / 4 = 858,75 KN and for the front ones the figure is 5200 / 6 = 866,66 KN, with a min. value of 641,6 KN, figures that become the dimensioning for all the bogies.
Pm = ( 2 × Pmax + Pmin ) / 3 = ( 2 × 866,66 + 641,6 ) / 3 = 791,6 KN
Selected wheel diameter D = 100 cm
Selected rail useful width b = 13,4 cm
Mean rail diameter Dr= 23 m
Wheel max. speed at w = 1,5 degrees per second: ( 23 × pi × 0,25 ) / ( 1 × pi ) = 5,75 rpm
Pmed / ( D × b ) < Pamm × c1 × c2
( 791,6 × 1000 ) / ( 100 × 13,4 ) < 650 × 1,16 × 0,8
590 < 603
Wheel with revolving axis, supported by roller bearings, without ribs ( horizontal guide rollers ), has a conservative value of resistance to movement of 3 N / KN -
Fw = 14420 × 3 = 43260 N
The corresponding torque at the rotation axis is :
MtFw = 43260 × 11,5 = 0,49749E6 Nm
w* = 0,3 × ( 2 × pi / 360 ) = 5,24E-3 1/sec²
Mtacc = J × w* = 3,4706E8 × 5,24E-3 = 1,8186E6 Nm
The corresponding tangential force is :
Facc = 1,8186E6 / 11,5 = 158139 N
Mw80 = 3,728E6 Nm
The corresponding tangential force is:
Fw80 = 3,728E6 / 11,5 = 324174 N
The selected design is the one that foresees two driving units for each corner, thus a total of eight gear/motor units that represent the 50% of the rear wheels and the 33% of the front ones, assuring a good safety coefficient when we have to verify the transmissible tangential driving force with a 0,14 friction coefficient between rail and wheel.
To have the possibility of selecting four poles AC motors VFD controlled, we have increased the reduction ratio of the gears ( including one more reduction couple) to 1:315 compared to the 1:200 of the 1994 preliminary design, so that to the max. wheel velocity of 5,75 rpm correspond a motor speed of about 1880 rpm, i.e. the nominal velocity at 60 HZ.
It is not in the scope of this report to select the type of motor - and the relevant drives - to be used, but, both in the case of AC or DC motors, all must be equipped with spring operated disc brakes and very likely with force ventilation to take into account the very low speed to be developed during the tracking, also if shall be introduced the control taking care of the ±2 degrees clearance position respect to the telescope.
For the resistance to movement of the wheels :
CWR = 497490 / (8 × 7245 × 0,88) = 9,75 Nm
For accelerating the inertia with open shutter :
Cacc= 1818600 / (8 × 7245 × 0,88) = 35,65 Nm
For withstanding the 80 Km / h wind :
Cw80= 3728000 / (8 × 7245 × 0,88) = 73,09 Nm
The wind torque is the prevailing factor in defining the size of the motors and gears, much more important than in the previous 1994 evaluation; remaining in the field of AC motors VFD regulated, I should select a 12,5 KW, 4 poles, Cm / Cn = 2,5 controlled with an inverter able to supply at 1 HZ a continuous torque of 86 Nm (about 1,3 the nominal torque), and a peak torque of 120 Nm between 1 an 60 HZ (about 1,8 times the nominal torque).
The gear is requested to transmit the nominal torque, reduced at the low speed shaft - that is the wheel axis -, that is Cn = 66,31 × 315 = 20900 Nm, that become about
27200 Nm when tracking against the 80 Km / h wind and about 37600 Nm when accelerating in the above condition; The previously selected 315 size of our standard supplier has a nominal torque of 40000 Nm in the four gear train configuration, and can be confirmed.
Rollers estimated diameter D = 400 mm
Rollers nominal velocity n = 23 × pi / 0,4 × pi × 0,25= 14,375 rpm
When the building is in movement we consider that the supporting wheels cannot absorb any important transversal force, so the whole wind force is distributed on two couples of opposite rollers, that gives a max. value each roller of :
Hw = 776,5 / 4 = 194 KN
Assuming for the roller the same material of the wheels and considering the
c2 velocity coefficient = 1,1 for the velocity of 14 rpm, fixing the useful contact width in
7,4 cm, we verify :
Pm = 194000 × 2/3 = 129400 N
129400 / (40 × 7,4) < 650 × 1,1 × 0.8
437,16 < 572
The most unfavourable condition is the 225 Km / h wind gusts at 45 degrees to shutters. without the snow surcharge and Astronomers dead load.
We can calculate that the friction between rail and wheels absorbs horizontal forces, assuming a conservative coefficient of friction m=0,2, as follows :
Front bogie in wind direction Fad = 4190 × 0,2 = 838 KN
Front bogie parallel to wind Fad = 4190 × 1/3 × 0,2 + 4190 × 2/3 × 3/1000 = 288 KN
Rear bogie in wind direction Fad = 2530 × 0,2 = 506 KN
Rear bogie parallel to wind Fad = 2530 × 1/2 × 0,2 + 2530 × 1/2 × 3/1000 = 257 KN
Total absorbed lateral force Fad = 1889 KN
The lateral force absorbed by each of the two couples of opposite rollers is :
FL max = (2943 - 1889) / 2 = 527 KN ; having reduced to 75% the wind gusts load
In conclusion, every horizontal roller is to be verified in the survival condition for a max. force of 527/2 = 263,5 KN .
As can be seen on the preliminary assembly drawings enclosed for comments, the difference is small compared to the dimensions of the frame and could be accommodated properly displacing the fixation bolts scheme in each corner, taking into account that has been decided to design both the 4 wheels and the 6 wheels bogies with the interface top plate level at the same figure, so to eliminate differences in length of the enclosure legs.
In our design we have foreseen to compensate the conical wheels semiangle with the machining of the centre connection frame, so that the interface with the building leg is horizontal; in the M3 design we suggest introducing a couple of opposite shimming plates for each flange, so to have the possibility of a final adjustment of the bogie inclination in respect to the vertical.
When in observing condition with open shutter and 80 Km / h wind at 45 degrees, if we consider the four wheels back bogie unloaded by the wind component, we have the following situation :
Vertical load = 2530 + 167 - 667 = 2030 KN
Horizontal load = 776,5 / 2 = 388,25 KN
The bending moment at the interface flange of 388,25 × 2,27 = 881,32 KNm produces a tensile force on the 50% of the bolted joint of 881,32 / 1,5 = 587,5 KN, value still lower than the 50% of the vertical load, so the bolts must transmit the shear load only and do not become in tension.
One vertical flange of the centre connection frame has to transmit a vertical compression load of 2030 / 2 + 587,5 = 1602,5 KN.
In each one of the main symmetry axis of the leg we introduce a bending moment of 881,32 / 2 × sin 45º = 623,2 KNm, moment that reaches their max. value at the level of the machinery floor axis, i.e. about 2,6 m over the interface flange, that means about a value of 1340 KNm.
In the bolts of the half interface flange we must transmit a tensile force of
T = 1017,5 × 2,27 / 1,5 = 1540 KN , that means 1540 / 14 = 110 KN per each bolt to be combined with the shear force.
In each of the main axes of the most stressed section of the building leg we have a bending moment of :
Mf = 1017,5 × 4,87 / 2 × sin 45º = 3504 KNm
Under these extreme conditions it is not only the stress to be verified, but also the horizontal displacement consequent to the legs deflection, to avoid problems in the gaps between enclosure and telescope.
The centre frame of the bogies is foreseen as a single piece U shaped and open at the top, because to easier the construction, machining and assembly of the bogie; the reason is that the closure of the structure can be obtained with the end flange of the building leg.
The shear effort between leg and bogie could be transmitted shaping properly the bottom flange of the leg, either machining it as per the enclosed conceptual sketch, or welding after the correct alignment on site a couple of additional plates.
In the second hypothesis we could increase of 100 mm or more the height of the centre frame to give more free space to easier the welding operation.
When we consider the 6 wheel bogie in the opposite position to the one verified at the point 7.2.1, i.e. the bogie that is overloaded by the vertical component of the wind tipping moment, the lateral force of 1017,5 KN transmitted by shear through the flanges and that is resisted by the rail through the contact of the horizontal rollers, must be increased by the 838 + 506 = 1344 KN transmitted by friction to the rail top surface through the wheel flanges in contact, forces that generate torsion moment and horizontal bending moment in the single bogie frame and that at the end increase the bending moment in the building leg to the figure of :
Mf = 2943 × 2,60 = 7651,8 KNm at the bottom flange
Mf max. leg = 2943 × 4,87 / 2 × sin45 = 10134,5 KNm
The stow pin is not dimensioned for absorbing any fraction of the horizontal lateral load due to wind or earthquake, because all are verified transmitted to the rail by friction or by contact of the horizontal guide rollers. the stow pin is intended to be a safety interlock with the rotation movement when the building is positioned in the auxiliary building direction with the maintenance hatch open.
The stow pin axis is positioned with an offset of 230 mm in respect to the bogie axis, so to have the possibility of locking the building in the direction of the auxiliary building axis avoiding the coincidence with the axis of the runway and rail joint.
For the purpose of a correct final verification of the rotating building weight and to prepare sufficient information for the call for tender for the construction of the units, has been performed an evaluation of the weight of the single components of the mechanism, obtaining the following values :
Four wheel bogie 22220 kg each, total for two units 44440 kg
Six wheel bogie 32870 kg each total for two units 65740 kg
TOTAL WEIGHT OF THE MECHANISM ~ 110 000 kg