xxx PROJECT
CASE STUDY: STEEL CAPTURE ELECTROMAGNET
TROLLEY
TROLLEY XXX
STRUCTURAL VERIFICATION
XXX
B
Client Approval
A
Internal coordination
REV.
DATE
ISSUED FOR
PREPARED BY
CHECKED
BY
APPROVED BY
Polimin SPA
POLIMIN W.O: 5874
APPROBED BY
APPROBED
BY
FLS
CONTENT
1.
1.1
2.
2.1
3.
4.
5.
6.
7.
7.1
7.1.1
7.1.2
7.2
8.
9.
9.1
9.1.1
9.1.2
9.1.3
9.2
9.2.1
9.2.2
9.2.3
10.
INTRODUCTION ............................................................................................................ 4
Objective ....................................................................................................................... 4
SCOPE OF THE ANALYSIS .......................................................................................... 5
Exceptions .................................................................................................................... 5
BACKGROUND / REFERENCES .................................................................................. 5
CODES ANS STANDARDS ........................................................................................... 5
GENERAL SITE CONDITIONS ...................................................................................... 6
DESIGN .......................................................................................................................... 7
DESIGN CRITERIA ........................................................................................................ 8
Load Combinations ...................................................................................................... 9
Load Distribution of Electromagnet in chassis: case 1 ........................................... 11
Load Distribution of Electromagnet in chassis: case 2 ........................................... 11
Materials ...................................................................................................................... 11
BOUNDARY CONDITIONS .......................................................................................... 13
RESULTS ..................................................................................................................... 14
Case 1: Normal operation scenario ........................................................................... 14
Chassis behavior analysis, case 1 ............................................................................ 14
Bogie analysis, case 1 ................................................................................................ 15
Bolted connection analysis, case 1. .......................................................................... 16
Case 2: Critical eventuality scenario ......................................................................... 18
Chassis behavior analysis, case 2 ............................................................................ 18
Bogie analysis, case 2 ................................................................................................ 19
Bolted connection analysis, case 2. .......................................................................... 21
CONCLUSIONS ........................................................................................................... 22
Page 2 of 22
TABLES
Table 3-1: Document and plane references .............................................................................................. 5
Table 5-1: Site Conditions .......................................................................................................................... 6
Table 7-1: Trolley – Main Weights ............................................................................................................. 9
Table 7-2: Load distribution in shackle holes, case 1 ........................................................................... 11
Table 7-2: Load distribution in shackle holes, case 2 ........................................................................... 11
Table 7-3: Materials- Mechanical properties ........................................................................................... 12
Table 9-1: Maximum stress evaluation on chassis, case 1 ................................................................... 14
Table 9-2: Maximum stress evaluation on Bogie elements, case 1 ..................................................... 16
Table 9-3: Bolt resistance evaluation, case 1 ......................................................................................... 17
Table 9-4: Maximum stress evaluation on chassis, case 2 ................................................................... 19
Table 9-5: Maximum stress evaluation on Bogie elements, case 2 ..................................................... 20
Table 9-6: Bolt resistance evaluation, case 1 ......................................................................................... 21
FIGURES
Figure 6-1: Trolley, constituted of Chassis and Bogies (Bogie Connector bolts not showed) ........... 7
Figure 7-1: Force diagram for trolley evaluation in normal operation scenario. a) trolley and
electromagnet image, b) model equivalence for analysis. .................................................. 9
Figure 7-2: Force diagram for trolley evaluation in critical eventuality scenario. a) trolley and
electromagnet image, b) model equivalence for analysis. ................................................ 10
Figure 8-1: Boundary conditions in chassis (Nastran) .......................................................................... 13
Figure 8-2: Boundary conditions in bogie (Inventor) ............................................................................ 13
Figure 9-1: von Mises stress in chassis, case 1 .................................................................................... 14
Figure 9-2: Maximum von Mises Stress in Bogie, case 1, a) steel module, b) bogie connector
shaft, c) driven wheel. ........................................................................................................... 15
Figure 9-3: von mises stress on bolts, case 1 ........................................................................................ 16
Figure 9-4: von mises stress verification in chassis, a) general, b) maximum stress view .............. 18
Figure 9-5: von Mises stress in Bogie, case 2, a) general, b) Bogie shaft, c) hub shaft on steel
plate ......................................................................................................................................... 20
Figure 9-6: von mises stress on bolts, case 2 ........................................................................................ 21
Page 3 of 22
1.
INTRODUCTION
xxx, as part of xx project, requires a metal capture system for a belt conveyor feeder TAG
xxx. From the above, xxx has been requested for a new electromagnetic equipment (xxxx)
and the detailed design engineering for a new transfer system (xxx)
xxxx, part of xxx joint venture in xxx, is located 470 km by roadway xxx
1.1
Objective
The purpose of this document is to present a resultant stress analysis of the Trolley xxx by
the action of the electromagnet load and their own weight, the above is calculated with the
Finite Element Method (FEM) on a commercial software. Parts and components are in
solidarity with the structure, by welded or bolted connection. Their stresses Will be limited to
the allowable stress (base on yield stress). Other secondary calculations Will be complete on
analytic calculations.
Page 4 of 22
2.
SCOPE OF THE ANALYSIS
The analysis is developed by allowable stress design (yield stress), which is based on elastic
strain-stress behavior. it means that the structure doesn’t compromise a plastic behavior
(permanent strain) under normal operation or a risk event.
The scope of the analysis is limited to the weight loads on the Trolley and the stresses on the
components and parts are in solidarity with the chassis during operation. The above are
represented by the following:
2.1
•
Chassis
•
Bogies
Exceptions
This document doesn’t study lifting components neither bearing.
3.
BACKGROUND / REFERENCES
Document and planes used as references are in last revision, unless otherwise specified.
Table 3-1: Document and plane references
N°
4.
DOCUMENT NUMBER
TITLE
1
xxx
xxx
2
xxx
xxx
CODES ANS STANDARDS
National codes and international standards used as references are listened in their last
revision, unless otherwise specified.
•
NCh. 3171.Of2010
•
"xxx
•
American Welding Society (AWS), Standard Welding Code
•
Crosby Catalog, Jaw-Jaw tensor and Shackle
•
ASME BTH-1-2017
xx
Design of Below-the-Hook Lifting Devices
Page 5 of 22
5.
GENERAL SITE CONDITIONS
the site conditions are the following:
Table 5-1: Site Conditions
UTM
Coordinates
xxx
Environmental conditions
Noisy work areas, dirty and dusty
Environment
environment, some areas with corrosive
gases and vapors
Elevation
4200 m.(above sea level)
Atmospheric Pressure
600 mbar
Air Density
~0.7 kg/m3
Maximum Ambient Temperature12 °C
Minimum Ambient Temperature-0.1 °C
Average Relative Humidity
70 %
Maximum Humidity
41 %
Minimum Humidity
24 %
Site Class (Peruvian seismic code E030)
Zone 3
Page 6 of 22
6.
DESIGN
o
The Beam Trolley are design to withstand the electromagnet and their own weight, their
movement with the electromagnet hanged, displaces on each side of the bottom flange
of a beam (two beams are required), the model analyzed consist of two parts: Bogie:
Framework who carries a wheelset, who allows displacement on the bottom flange of a
beam used as rail, two bogies for each rail.
o
Chassis: main structure of Trolley, framework that assembles with Bogies.
Bogies and Chassis are connected by the Bogie Connector,
Each Bogie is attached with an electric motor, coupled on a single wheel for each Bogie.
Bogies
Chassis
Bogie
Connector
Shackle
holes
Figure 6-1: Trolley, constituted of Chassis and Bogies (Bogie Connector bolts not showed)
Page 7 of 22
7.
DESIGN CRITERIA
This design criteria are based on recommendation from ASME BTH-1
The Trolley are calculated under allowable stress design, which limits the stress of a material
𝜎
under elastic behavior with a safety factor given. The safety factor expressed as 𝑆. 𝐹. = 𝜎 0
𝑉𝑀
define the relation between yield stress 𝜎0 and maximum stress on a material, the maximum
stress is given by von Mises yield criterion 𝜎𝑉𝑀 ..
As referenced by ASME BTH-1, this trolley complies for Design Category A, which
establishes a design factor 𝐹. 𝑆 = 2 due to predictable variation of loads and load period
lesser than 20,000 cycles in their service class life (Class 0). The above only be valid for the
suspended electromagnet in their four shackle holes.
In addition, this document presents a critical eventuality case, higher than the recommended
for ASME, ASME BTH-1 establishes an increase value of 1.5 times the load in the four
shackle connections. This critical scenario establishes an increase value of 1.5 times the
load but in two shackle holes, higher than the proposed of ASME. This allows to decrease
the factor in 50% of the original design factor to 𝑆. 𝐹. .𝑒𝑣𝑒𝑛𝑡𝑢𝑎𝑙 = 1,5. Nevertheless, the design
factor must compromise an elastic behavior of the trolley.
Finite element calculation is developed in Autodesk Inventor and Inventor Nastran software.
Page 8 of 22
7.1
Load Combinations
Load combinations are related to a normal operation scenario in which the trolley operates
and an eventuality scenario occurred by an accident that compromise the integrity of the
equipment and the operators.
The loads are detailed in Table 7-1: .
Table 7-1: Trolley – Main Weights
Concept
(A) Electromagnet equipment weight (mechanism included)
(B) Chassis Weight
(C) magnetic metal captured weight
Value
45,000 𝑘𝑔𝑓
16,600 𝑘𝑔𝑓
220 𝑘𝑔𝑓
Load combinations are the following:
Case 1.Normal operation scenario: equivalent to the electromagnet weight and the
captured metal weight:
(𝐴) + (𝐶) = 45,220 𝑘𝑔𝑓.
The load is distributed in the trolley in the four shackle holes (see Figure 7-1).
The distribution load is analyzed analytically on item 7.1.1.
a)
b)
Figure 7-1: Force diagram for trolley evaluation in normal operation scenario. a) trolley and
electromagnet image, b) model equivalence for analysis.
Case 2.-
critical eventually scenario (accident): equivalent to 1.5times electromagnet
weight.
Page 9 of 22
1.5(𝐴) = 67,500 𝑘𝑔𝑓.
The load is distributed proportionally between two shackle holes (see Figure
7-2). The distribution load is analyzed analytically on item 7.1.2
a)
b)
Figure 7-2: Force diagram for trolley evaluation in critical eventuality scenario. a) trolley and
electromagnet image, b) model equivalence for analysis.
Trolley weight are incorporate by default on calculation software.
Page 10 of 22
7.1.1
Load Distribution of Electromagnet in chassis: case 1
On the normal operation scenario, the electromagnet is supported on four shackles in the
trolley chassis. The force reactions on electromagnet, in order to prevent a hyperstatic
behavior (due to is tridimensional body are supported on four lugs) a 2D front view
representation is taken to simplify the reaction on the shackle holes. On Table 7-2 AA and
BB output values are used in software model and are used in addition to analytical
calculations of mechanical elements.
Table 7-2: Load distribution in shackle holes, case 1
Item
LT
1.650 𝑚𝑚
LA
814 𝑚𝑚
Peso (A+C)
7.1.2
Value
Image
45,220 𝑘𝑔𝑓
𝛼
1.3°
𝛽
2°
𝛾
80°
AA
224,700 𝑁
BB
218,900 𝑁
Load Distribution of Electromagnet in chassis: case 2
As described on item 7.1.1, in this case the load applies directly on vertical direction on two
shackle holes (see Table 7-3).
Table 7-3: Load distribution in shackle holes, case 2
Item
0 𝑚𝑚
LA
0𝑚𝑚
Peso (A+C)
7.2
Value
LT
Image
45,000 𝑘𝑔𝑓
𝛼
0°
𝛽
−
𝛾
−
AA
441,450 𝑁
BB
−
Materials
For structure and structural components, ASTM A36 steel is used.
Page 11 of 22
wheel and pin shaft are made of SAE 4340 steel.
Wheels are made of SAE 1045 steel.
For welded elements, pre-calculations are developed to determine weld thickness on shackle
holes, E6010 electrode type is used.
The bolt used are a special design of 41mm diameter ASTM A354 BC.
Table 7-4: Materials- Mechanical properties
Concept
Density
Yield Stress
Ultimate strength
Young Modulus
Poisson Coefficient
Unit
𝑘𝑔/𝑚3
𝑀𝑃𝑎
𝑀𝑃𝑎
𝐺𝑃𝑎
−
ASTM
A36
7,850
250
420
200
0.3
SAE
4340
7,850
470
745
200
0.3
SAE
1045
7,850
310
565
200
0.3
E6010
7,850
343
427
200
0.3
ASTM
A354 BC
7,850
724
862
200
0.3
Page 12 of 22
8.
BOUNDARY CONDITIONS
The study is separated in two models, for each model a boundary condition is associated.
One of the studies verifies the chassis and bogie-connector (modelled in Nastran) and the
other study verifies the Bogie part (modelled in Inventor). These restrictions differ on each
other: on the chassis study, those restrictions are applied at the hole of the bogie-connector
and the load are applied on shackle holes (see Figure 8-1), in the bogie study, the
restrictions are applied at the bogie wheels with the complete model but without bolted
connections, the load also area applied on shackle holes (see Figure 8-2). In case 2,
restrictions are applied as same as case one but only with two shackles.
Figure 8-1: Boundary conditions in chassis (Nastran)
Figure 8-2: Boundary conditions in bogie (Inventor)
Page 13 of 22
9.
9.1
RESULTS
Case 1: Normal operation scenario
9.1.1
Chassis behavior analysis, case 1
With an electromagnet weight of 45,220 𝑘𝑔𝑓 is applied on the trolley, it notices a good
behavior on chassis, the higher stresses are located on contact union of bolted connections
as shown on Figure 9-1.
Figure 9-1: von Mises stress in chassis, case 1
A maximum stress on chassis of 52,4 𝑀𝑃𝑎, is in bogie-connector, a part made of A36 steel,
safety factor is calculated.
Table 9-1: Maximum stress evaluation on chassis, case 1
Item
von Mises max. stress: 𝜎𝑉𝑀
Value
52.4
Unit
𝑀𝑃𝑎
Safety Factor: 𝑆. 𝐹.
2
Yield stress (A36)
250
𝑀𝑃𝑎
allowable stress: 𝜎𝑎𝑑𝑚
125
𝑀𝑃𝑎
S.F. calculated: 𝑆. 𝐹.𝑐𝑎𝑙𝑐
4.77
𝑆. 𝐹. < 𝑆. 𝐹.𝑐𝑎𝑙𝑐
OK
-
-
The shown on Table 9-1 concludes that the maximum stress is lower than the allowable
stress.
Page 14 of 22
9.1.2
Bogie analysis, case 1
In relation to the bogie analysis, a maximum stress in their drive wheel with his drive shaft
(see Figure 9-2c and Table 9-2) that high stress concentration is local and in general the
average stress is up to 138.3 𝑀𝑃𝑎, this interaction between shaft and wheel is due to the
drive shaft, the bogie-connector shaft of SAE1045 material has a value of 36,8 𝑀𝑃𝑎 (see
Figure 9-2b).
a)
b)
c)
Figure 9-2: Maximum von Mises Stress in Bogie, case 1, a) steel module, b) bogie connector shaft, c)
driven wheel.
Page 15 of 22
Table 9-2: Maximum stress evaluation on Bogie elements, case 1
Item
Component 1
von Mises max. stress: 𝜎𝑉𝑀
Steel Module
(A36)
76.16
Safety Factor: 𝑆. 𝐹.
Element 2
Unit
Wheel
(AISI 1045)
138.3
𝑀𝑃𝑎
2
2
2
-
Yield stress
250
310
310
𝑀𝑃𝑎
allowable stress: 𝜎𝑎𝑑𝑚
125
155
155
𝑀𝑃𝑎
S.F. calculated: 𝑆. 𝐹.𝑐𝑎𝑙𝑐
3.2
8.42
2.2
-
OK
OK
OK
𝑆. 𝐹. < 𝑆. 𝐹.𝑐𝑎𝑙𝑐
9.1.3
Element 1
Shaft
(AISI 1045)
36.8
Bolted connection analysis, case 1.
Nastran software calculates with von Mises stress with a maximum value of 17.98 𝑀𝑃𝑎, the
safety factor is calculated and shown in 3.
Figure 9-3: von mises stress on bolts, case 1
Page 16 of 22
Table 9-3: Bolt resistance evaluation, case 1
Element
Item
Bolt diameter
von Mises max. stress: 𝜎𝑉𝑀
Unit
Bolt ASTM
A354
41
𝑚𝑚
17.98
𝑀𝑃𝑎
Safety Factor: 𝑆. 𝐹.
2
Yield stress (A36)
724
𝑀𝑃𝑎
allowable stress: 𝜎𝑎𝑑𝑚
362
𝑀𝑃𝑎
S.F. calculated: 𝑆. 𝐹.𝑐𝑎𝑙𝑐
40
𝑆. 𝐹. < 𝑆. 𝐹.𝑐𝑎𝑙𝑐
-
-
OK
As shown in 3, connection bolts comply with load request by electromagnet acting forces.
Page 17 of 22
9.2
Case 2: Critical eventuality scenario
9.2.1
Chassis behavior analysis, case 2
With an electromagnet weight of 67,500 𝑘𝑔𝑓, product of an eventuality scenario is applied in
the trolley, the model it also shows a good behavior on chassis, the higher stresses are
located shackle holes connections as shown on Figure 9-4.
a)
b)
Figure 9-4: von mises stress verification in chassis, a) general, b) maximum stress view
The model shows a maximum stress of 88.4 𝑀𝑃𝑎 located in one of the shackle holes, that
connector is made of A36 steel, safety factor is calculated.
Page 18 of 22
Table 9-4: Maximum stress evaluation on chassis, case 2
Item
von Mises max. stress: 𝜎𝑉𝑀
Value
88.4
Unit
𝑀𝑃𝑎
Safety Factor: 𝑆. 𝐹.
1.5
Yield stress (A36)
250
𝑀𝑃𝑎
allowable stress: 𝜎𝑎𝑑𝑚
166
𝑀𝑃𝑎
S.F. calculated: 𝑆. 𝐹.𝑐𝑎𝑙𝑐
2.82
𝑆. 𝐹. < 𝑆. 𝐹.𝑐𝑎𝑙𝑐
OK
-
-
From Table 9-4 it concludes the maximum stress is lower than the allowable stress.
9.2.2
Bogie analysis, case 2
In relation to the bogie analysis in an eventuality scenario, a maximum stress in the bogie
shaft (see Figure 9-5 and Table 9-5) with the hub (attached to the steel plate), that high
stress concentration is local with a stress of 206 𝑀𝑃𝑎, this interaction is due to the bogie
shaft, the bogie-connector shaft of SAE1045 material has a value of 50.3 𝑀𝑃𝑎 (see Figure
9-2b).
The high stress due to the shaft into the hub is close to the allowable stress and could lead to
failure, however, this is a one-time event without cyclic events related, the high stress it is
Hertz stress will not compromise the bogie, the allowance of a 50% of the safety factor will
guarantee a stress without yield.
a)
Page 19 of 22
b)
c)
Figure 9-5: von Mises stress in Bogie, case 2, a) general, b) Bogie shaft, c) hub shaft on steel plate
Table 9-5: Maximum stress evaluation on Bogie elements, case 2
Item
von Mises max. stress: 𝜎𝑉𝑀
Element 1
Component 1
Shaft (AISI 1045)
Hub (AISI 1045)
206
50
Unit
𝑀𝑃𝑎
Safety Factor reduced 50%:
𝑆. 𝐹.𝑒𝑣𝑒𝑛𝑡𝑢𝑎𝑙
Yield stress
1,5
1,5
-
310
310
𝑀𝑃𝑎
allowable stress: 𝜎𝑎𝑑𝑚
207
207
𝑀𝑃𝑎
S.F. calculated: 𝑆. 𝐹.𝑐𝑎𝑙𝑐
6.2
1.51
-
OK
OK
𝑆. 𝐹. < 𝑆. 𝐹.𝑐𝑎𝑙𝑐
Page 20 of 22
9.2.3
Bolted connection analysis, case 2.
Nastran software calculates with von Mises stress with a maximum value of 77.2 𝑀𝑃𝑎, the
safety factor is calculated and shown in Table 9-6.
Figure 9-6: von mises stress on bolts, case 2
Table 9-6: Bolt resistance evaluation, case 1
Element
Item
Unit
ASTM A354
Bolt diameter
von Mises max. stress: 𝜎𝑉𝑀
Safety Factor: 𝑆. 𝐹.
41
𝑚𝑚
77,2
𝑀𝑃𝑎
2
Yield stress
724
allowable stress: 𝜎𝑎𝑑𝑚
362
S.F. calculated: 𝑆. 𝐹.𝑐𝑎𝑙𝑐
9,4
𝑆. 𝐹. < 𝑆. 𝐹.𝑐𝑎𝑙𝑐
𝑀𝑃𝑎
𝑀𝑃𝑎
-
OK
As shown in Table 9-6, connection bolts comply with load request by electromagnet acting
forces on a critical eventuality scenario.
Page 21 of 22
10.
CONCLUSIONS
The beam trolley design proposal, complies with the criteria condition imposed, not only for
the normal operation scenario, but also the critical eventuality scenario. the bolted
connections complies with the load requirements for both scenarios.
Page 22 of 22