#### 5.1.8.1 Magnets transportation, installation and alignment at the tunnel[^1]

{some section number revision is needed here; also cut repetitive
material that's in Sec. 5.1.8 -- hg}

Stage I magnets (LFM) transportation, installation at the tunnel are
discussed below. The LFMs have:

\- length 65 m

\- weight 32.5 tons

\- low cross sectional bending stiffness and torsion stiffness.

Besides, the LFMs transportation, installation and supporting should be
done at the confined VLHC tunnel.

The high field magnets (HFM) have sizes and weights close to, for
example, RHIC magnets. Therefore, it is reasonable to apply the same
methods for HFM transportation, installation and supporting which were
used at RHIC.

The LFMs have complicated design, therefore were accepted reasonable to
minimize number transport operations with the magnets (lifting, shifting
and moving) and decrease any magnet deformations during transportation.

An inexpensive vehicle are described below for the LFMs transportation.

##### 5.1.8.1.1 VLHC tunnel.

The cross sectional view of the 3 meter in diameter VLHC tunnel are
shown on fig.1. The tunnel has flat concrete flow with track way --
simple floor profile for vehicle steering. The 1st stage magnets are
overhead. The HFM are beneath. Also LFM supports with jacks are shown.

Distances between supports at the tunnel are chosen 6 meters in
accordance with calculations.(see below)

![](media/image1.png)Fig.1. Cross sectional view of the VLHC tunnel.

##### 5.1.8.1.2 LFM vehicle.

Longitudinal view of the LFM vehicle are shown in fig. 2.

The vehicle consists of 11 identical transporters with payload up to 3
tons. Distances between transporters are 6 meters. Each transporter has:

-   four inflated tires(to reduce dynamical loads and increase
    transportation speed);

-   two axles: rear -- driving axle; front -- negligible veering axle;

-   DC reversible motor about 10 kW;

-   Lead-acid battery block;

-   A special mechanism to shift LFM during installation procedure. The
    special mechanism and driving axle use single DC motor.

So, the LFM vehicle uses distributed power between the transporters.
Total driving power is about 110kW. It is enough for LFM transportation
at speed up to 5mph and grade up to 4%. Also, it is enough for LFM
shifting during installation procedure.

Cross sectional view of the LFM vehicle are shown in fig.3. The LFM
transportation level is about 6 feet over the floor and 4 inches over
the supports level.

![](media/image2.png)Fig.2. Longitudinal view of the LFM vehicle at the
tunnel.

![](media/image3.png)Fig.3. Cross sectional view of the LFM transporter.

##### 5.1.8.1.3 LFM installation.

The transporters fix its position with special legs before LFM
installation (see fig.4). Then the LFM safely is shifted to the supports
with the transporter's mechanism. The support's jacks accept weight of
the LFM. The telescopic parts of the transporters are removed and the
vehicle rolls out.

![](media/image4.png)Fig.4.LFM Installation on the supports.

##### 5.1.8.1.4 LFM supporting at the tunnel.

LFM will install on the vertical supports. A distance between supports
was chosen 6 meters. A numerical simulations were done in order to
estimate stresses and deformations. The maximal deflection of the LFM
under weight load are between 1.2 -- 2.1 mm. It depends from final
design of the LFM. In case if properly magnet will connect with vacuum
tube with welds, the sag is close to 1.2 mm and maximal stresses are not
exceed 50 -- 60 MPa. Without welding connection between magnet block and
vacuum tube the sag is close to 2.1 mm and maximal stresses reach up to
90 MPa.

![](media/image5.png)

![](media/image6.png)Fig.5. Displacements(at cm) and equivalent
stresses(at kgs/cm^2^) distribution under the weight load when LFM are
on the supports at the tunnel.

##### 5.1.8.1.5 LFM alignment. 

To estimate deformations of the LFM during alignment at the tunnel
numerical 3D simulations were done of the model of 12 meters LFM fixed
on the both ends and are loaded with horizontal force applied to the
central supports of the vacuum tube and distributed weight load. The
properly magnet block moves on about 0.9mm at vacuum tube movement 1mm.
The horizontal force needed to move LFM on 1mm depends from the position
of the alignment point concerning to the ends of the LFM and changes
from 40kgs to 150kgs without taking into account friction force. Taking
into account that each support supports 3 tons of the LFM weight the
friction force may be estimated as about 300kgs.

Difference relative movement iron halves of the properly magnet can
reach 30m at magnet movement 1mm.

More accurate calculations and studying are needed using a fine mesh
taking into account importance alignment problem.

##### 5.1.8.1.6 Movement of the LFM along an arc way

The LFM has the straight axis. When it is transported along the arc way
the LFM is deformed and axis accepts the arc shape.(We can except it at
a first approaching)

There is simple analytical decision for arc deformed beam:

1/R = M/(EJ);

For example, for an estimation we can define allowable radius R of an
arc for cryoline vacuum jacket

R = unknown -- arc radius;

E = 200 Gpa -- steel elastic modulus;

J = D^3^t/8 -- jackets moment of inertia.

M -- bending moment;

Stresses are equal:

= M/W;

W -- section modulus;

So,

M = W.

If we accept allowable static stresses for LFM:

\[\] = 50 MPa;

And

W = D^2^t/4 - cryoline vacuum jacket section modulus;

> D = 0.3m -- jacket external diameter;

t = 0.006m -- jacket thickness.

We will have:

1/R = \[\]W/(EJ) = 2\[\]/DE

R = 1/2DE/\[\] = ½\*0.3\*200000/50 = 600 meters

Unfortunately, LFM has a complicated composed design. And giving correct
decision totally the analytical estimation can not to take into account
local stresses which can dominate. Therefore, we need to use numerical
simulation to get information about local stresses.

As an example, such simulations were done for a case when first
transporter of the LFM transportation vehicle are on the arc with R =
1000meters, the rest are on the straight way. At this case, a difference
between straight line of the LFM and arc with the distance 6 meters is
0.018m(see Fig.6.). Another words, it means one support of the magnet is
vertically moved on 1.8cm.

![](media/image7.png)

Fig.6.

Numerical 3D simulation with Ansys code show that equivalent stresses
exceeds 200 MPa at this case. It should be noted it is result static
calculations. So as dynamic factor is about 2 we can get unallowable
stresses if arc way will have radius about 1000m. The maximal stresses
are at the closest to the supports plates and welds which connect the
properly magnet block and vacuum jacket. Also large stresses more then
100 MPa are at the vacuum jacket at the area closest to the supports.
Take into account that the welds are concentrators of stresses may
conclude we need to decrease stresses at least at 4 times. It means that
arc transportation way should have minimal radius about 4000m. Larger is
better because most of LFMs will have transportation deformations only
one time.

Stresses concentrators(bolts, welds) at the LFM design are required more
accurate studying and more calculations.

[^1]: original source text: [..\\..\\edits\\older
    edits\\5.1.7.1Magnets_transportation_installationVT-021301.doc](../../../edits/older%20edits/5.1.7.1Magnets_transportation_installationVT-021301.doc)