Multiple Coil Lift Calculation

Purposes of the Study

To investigate the stress distribution in the MCWF and the lifting device.

To make sure mounting plates and bolted joints are within allowable limits.

Procedures of the Investigate

Finite element analysis was used to evaluate the loading and to calculate the stresses, forces, and reactions.

The geometry of the finite element model for coils and MCWF are based on the Pro/E drawings.

Hand calculation was performed to check the bolted joint capacity.

FEA Model with Lifting Device

Weak spring for stability

3” mounting plate

Swivel hoist ring

Attach 3” plates to the Type B shell by bonded contact elements at the inboard and outboard locations in the mid-plane.

Mount swivel hoist ring to the 3” plate.

Hinged supports at swivel hoist rings

Add a weak spring at edge of Type A shell to assure the stability of the model.

Weak spring for stability

Swivel hoist ring

Swivel hoist ring

Analysis performs Two lifting Positions

Side-Lifting Position Uplifting Position

Load Case and Unit

The only loading is the weight of machine, which can be calculated by specifying the linear accelerations and mass density.

The element mass matrix of the model produces a total weight of 19.8 kips, which is less than the measured weight of 21 kip. Therefore, the gravity acceleration was increasing by 6.07% to yield a total weight of 21 kips.

For possibility of swing during the lifting, a higher safety factor as per ASME-BTH [1] will be used in the design of bolted joint connection.

Two lift positions were considered in the analysis.

The unit of results from the computer plots and output are meter for the displacement, pascal for the stress, and newton for the force.

The nodal coordinate system is No. 16, which is a cylindrical coordinate system with x-axis passing through the inboard and outboard supports and z-axis in the vertical direction.

Vertical Displacements and Reactions for Side-Lifting Position

zx

Y

The plot of vertical displacement (Uy) contour shows slightly weight difference on both sides of x-y plane (x is in the radial direction). The stability was sustained by the weak spring.

The reactions are summarized in RSYS=18:

Reaction: NODE FX (N) FY (N) FZ (N)IB support 102178 0.0 47,578.0 -44.3

OB support 103385 -1.3 45,828.0 44.3Weak link 103461 0.1 0.1 0.0

Total -1.3 93,406.0 0.0

The reactions in Fy are very close between the inboard and outboard supports. The total reaction in Fy is 93,406 N or 21.0 kip.

The reactions in Fx and Fz are negligible.

The reaction on the weak spring is very small.

RSYS=18

von Mises Stress Plot for Side-Lifting Position

Higher stress was found in the shell type B near the inboard and outboard lift locations.

The maximum stress is 25.0 MPa or 3.63 ksi

Reaction force

The maximum compressive stress on the contact surface of the lift plate is 10.3 MPa or 1.50 ksi

The maximum tensile stress on the contact surface of the lift plate is 10.7 MPa or 1.55 ksi.

The actual stress on the contact surface will be the stress as shown plus the stress due to bolt preload.

Normal Pressure on the 3” Lift Plate for Side-Lifting Position

Vertical Displacements and Reactions for Uplifting Position

The plot of vertical displacement contour shows slightly weight difference on the left and right sides of the support. The stability was prevented by the weak spring.

The reactions are summarized in RSYS=0:

yx

z

RSYS=0

The reactions in Fz are very close between the inboard and outboard supports. The total reaction in Fz is 93,408 N or 21.0 kip.

The reactions in Fx and Fy are negligible.

The reaction on the weak spring is very small.

Reaction: NODE FX (N) FY (N) FZ (N)IB support 102178 0.9 -1.6 47,605.0

OB support 103385 -0.9 1.6 45,803.0Weak link 103461 0.0 0.0 0.0

Total 0.0 0.0 93,408.0

von Mises Stress Plot for Uplifting Position

Higher stresses were found in the shell type B near the inboard and outboard lift locations.

The maximum stress is 29.4 MPa or 4.26 ksi

Reaction force

The maximum compressive stress on the contact surface of the lift plate is 8.73 MPa or 1.27 ksi

The maximum tensile stress on the contact surface of the lift plate is 5.53 MPa or 0.80 ksi.

The actual stress after bolt preload on the contact surface will be smaller than the stress in the side-lifting position.

Normal Pressure on the 3” Lift Plate for Uplifting Position

Evaluation of the Bolted Joints

The bolted joint consists of four 1-8 UNC bolts as shown in the right [2].

The grade and material identification of bolt is SAE J429 Grade 8 with min. yield strength of 130 ksi and min. tensile strength of 150 ksi [3]

9"

3"

For bolt group, the side-lifting position with 3” moment arm is the governing case.

Total shear on the bolt group = 47,605 N or 10.70 kip

Total bending moment on contact surface =10.7 x 4.25 = 45.48 k-in

Bolt shear force = 10.70 / 4 = 2.675 kip per bolt

Bolt axial force = 45.48 / 3 / 2 = 7.579 kip per bolt

Bolt thread min. patch diameter (Es min) = 0.910” for class 2A bolt

Tensile stress area of bolt

=

= 0.5937 in2

Assume reusuable connection, the bolt preload Po can be determined from [4]:

Po = 0.75 × At × 0.85 x Sy = 49.20 kip

Evaluation of the Bolted Joints (cont’d)

Assume preload relaxation is 5%

Effective preload = 49.20 x 0.95 = 46.74 kip

For connection design, the factor of safety for design Category A = 2.4 [1]

Assume coefficient of friction between steel surfaces = 0.3

Friction force from preload = 0.3 x 46.74 x 4 = 56.09 kip

Factor of safety for shear = 56.09 / 10.70 = 5.24 > 2.40 OK

Since effective preload (46.74 k) > bolt axial load (7.58 k), there are no possibility of joint separation.

The following calculation checks the engagement length of thread hole [3]:

Tensile strength of bolt = 150 ksi

Tensile strength of stellalloy = 78 ksi

Shear area of bolt thread As = 1.1873 in2,

where:

Shear area of thread hole An = 1.6733 in2,

where:

Evaluation of the Bolted Joints (cont’d)

Engagement length if bolt and hole thread have equal strength Lc = 0.7168 in

where

Relative strength of the external (bolt) and internal (hole) thread is:

J = (As x Su_ext.) / (An x Su_int.) = (1.1873x150) / (1.6733x78) = 1.3645

The required length of thread hole in stellalloy is:

Q = J x Lc = 1.3645 x 0.7168 = 0.9781 in

The provided thread hole engagement length = 2.0 in > 0.9781 in OK

Conclusion:

The axis of swivel hoist ring support is very closed to the mass center of the coil assembly. Additional slings are needed for stability and rotation.

The side-lifting position is the governing case for lifting device.

The lifting forces are about the same for the inboard and the outboard swivel hoist rings.

The stresses in the shell are small.

For SAE J429 Grade 8 bolt, a effective preload of 46.74 will provide a factor of safety of at least 5 for the shear force and joint separation at the bolted joint.

The required thread hole engagement length is 0.978”, smaller than the existing thread hole engagement length of 2”.

References:

1. ASME BTH-1-2005, “design of Below-the-Hook Lifting Devices “

2. NCSX drawing SE141-115, Rev. 10, “Production winding from Type-B”

3. Barrett R. T., “Fastener Design Manual”, NASA Reference Publication 1228, Appendix A, P82, 1990

4. Oberg, E., Jones. F., Horton, H., and Ryffel, H, “Machinery’s Handbook”, 27 th Edition, Industrial Press Inc., New York, 2004