Mojtaba Hasanlu's Portfolios in Rotor

1. Portfolios in Rotor
Winter 2021

2. Overview
1. Balance and spin model into SOLIDWORKS(Solid Design)
2. Hall Rail
3. Literature Review (What findings have been researched and
simulated in Compressor System?)
4. Miscellaneous math modeling of rotor
5. ISO 1940, API 610
6. Balance and Spine Machines
7. Test Machines
8. Classification of shaft, drive shaft, clamping plate and tie bolt
9. Current Assignments

5. Balance Test

6. Balance Test

7. Spin Test

8. Balance Test

9. Configurability of Drawing

10. Drive Shaft

11. Shaft

12. Tie Bolt

13. Classification of Components
Aims and Scope
Create Library for future applications by coding
𝑅2
𝑙2
𝑙1
𝑅2
Type R1(mm)- Right R2(mm) - Left L1(mm) L2(mm)
S1 209.65 209.61 40.15 39.75
S2 209.45 209.46 39.9 40.17
S3 221.80 199.81 45.95 48.18
S4 229.8 229.8 39.8 40
S5 209.65 209.61 40.21 39.89
S6 209.69 209.6 40.58 40.19
S7 188.46 188.48 39.87 40.55
S8 154.69 154.71 32.3 31.99
S9 154.7 154.7 32.24 31.93
S10 209.45 209.45 44.81 44.55
S12 168 168 28.3 28.17

14. 𝑙1
𝑙2
𝑅2
𝑅1
Type R1(mm) R2(mm) L1(mm) L2(mm)
S11 200.07 160.13 44.58 44.82
Shaft

15. Tie Bolt
TB 𝑙1(mm) 𝑙2(mm) 𝑙3(mm)
1 100.55 36.94 65.21
2 102.07 37.47 64.45
3 101.98 38.5 63.24
4 136.34 34.19 63.48
5 99.91 31.02 104.49
6 99 32.07 101.04
7 104.89 32.43 97.99
8 104.42 30.48 99.74
9 103.87 29.36 99.32
10 104.38 31.46 98.65
11 104.38 31.64 99.88
12 104.24 31.38 98.27
13 91.2 31.01 187.01
14 102.62 36.42 64.38
15 101.11 35.7 63.91
16 100.25 34.53 64.59
17 54.91 30.73 104.93
18 55.19 28.02 102.8
19 53.95 29.98 104.32
20 54.96 33.85 104.73
21 54.76 31.46 104.85
22 55.5 29.03 104.85
𝑙
1
𝑙
2
𝑙
3

16. Drive Shaft
D
S
t(mm)
t
2r
2r(mm)
1 8.65 199.86
2 9.09 809.12
3 8.95 209.49
4 8.9 229.85
5 9 209.69
6 9.15 221.86
7 9.14 239.86
8 8.88 209.46
9 9.02 209.57
10 9.03 209.48
11 9.05 209.63
12 9.15 209.45
13 8.9 209.65
14 8.83 209.65
15 8.9 209.69
16 8.93 209.66
17 8.63 209.65
18 9.04 160.06
19 8.83 209.84
20 9.04 133.52
21 9.07 209.49
22 8.89 154.74
23 9 154.76
24 8.93 154.72
t
2r

17. Clamping Plate CP t(mm)
1 12.33 200.05
2 11.85 159.93
3 8.99 209.85
4 9.04 209.87
5 12.15 269.92
6 12 255.96
7 12.34 239.95
8 9.37 209.84
9 9.1 209.9
10 9.14 209.85
11 9 209.87
12 9.03 209.88
13 9.2 299.62
14 8.09 188.54
15 8.84 209.86
16 9.36 205.84
17 9 154.85
18 9.54 154.85
19 9.11 154.82
20 7.07 125.01
21 6.93 124.8
22 7.52 124.83
23 7.14 124.66
24 6.83 94.87
25 6.83 104.87
26 6.81 104.72
27 7.37 104.78
28 7.36 104.74
29 7.2 104.89
30 7.26 89.82
31 6.94 89.83
2r
t

18. 𝑙1
𝑙2
𝑙3
𝑙4
𝑙5
𝑙6
𝑙8
𝑙7
𝑙9
r
𝑙10
L
Balance - Spin
BS 𝑙1(mm) 𝑙2(mm) 𝑙3(mm) 𝑙4(mm) 𝑙5(mm) 𝑙6(mm) 𝑙7(mm) 𝑙8(mm) 𝑙9(mm) 𝑙10(mm) L(mm) 2r(mm)
1 46.22 59.7 28.04 36.18 5.85 15.25 150.47 18.4 22.9 3.08 386.09 129.95
2 68.08 61.03 25.11 25.89 7.04 15.36 140.7 18.45 22.87 3.3 387.83 104.89
3 49.1 59.44 36.08 35.69 6.84 14.92 140.56 18.31 22.73 3.33 387 104.9
4 72.86 59.56 21.99 25.25 7.28 15.2 140.46 19.06 22.48 3.26 387.4 104.87
5 59.9 63.58 21.91 17.74 6.36 15.77 148.92 18.71 23 3.13 385.59 94.92
6 54.66 60.57 25.05 8.29 35.87 15.58 141.02 18.41 22.92 3.31 385.68 119.98
7 45.83 59.7 28.05 36.53 6.62 15.21 150.05 18.88 22.45 3.36 385.68 124.83
8 49.88 59.62 46.09 26.49 6.65 15.27 138.97 18.4 22.77 3.42 387.56 104.87
9 47.75 59.57 21.79 19.45 5.48 30.04 184.67 17.88 23.02 3.46 413.11 89.97
10 47.59 60.32 21.97 19.92 6.93 30.6 185.12 18.35 22.99 3.55 417.34 89.95

19. Hall Rail
In this short report, we would present 3 mechanical processes of Hall Rail in ANSYS
Workbench which are including modal, static and harmonic analyses, respectively. Finally,
safety factor of component will be shown as table.

20. Model
Ton/m Static stress(Pa) SF Dynamic Stress(Pa) SF
50 2.38e9 1.55 5.434e7 6.8
80 3.8e8 0.97 8.7e7 4.25
106 5.04e8 0.73 1.15e8 3.21
150 7.14e8 0.51 1.63e8 2.26

21. d= 20 cm
Ton/m Static stress(Pa) SF Dynamic Stress(Pa) SF
50 4.35e7 8.5 7.74e7 4.7
80 6.97e7 5.3 1.23e8 3
106 9.23e7 4 1.64e8 2.2
150 1.3e8 2.84 2.32e8 1.59
Model

22. d= 15 cm
Ton/m Static stress(Pa) SF Dynamic Stress(Pa) SF
50 6.5e7 5.69 3.9e8 0.94
80 1.04e8 3.55 6.2e8 0.59
106 1.4e8 4.64 8.2e8 0.45
150 1.95e8 1.89 1.16e9 0.31
Model

23. d= 10 cm
Ton/m Static stress(Pa) SF Dynamic Stress(Pa) SF
50 2.5e8 1.48 6.66e7 5.55
80 3.97e8 0.93 1.06e8 3.49
106 5.26e8 0.7 1.4e8 2.64
150 7.45e8 0.49 2e8 1.85
Model

24. d= 5 cm
Ton/m Static stress(Pa) SF Dynamic Stress(Pa) SF
50 4.4e7 5.78 7.4e7 5
80 1.02e8 3.62 1.2e8 3
106 1.35e8 2.74 1.57e8 2.35
150 1.91e8 1.93 2.22e8 1.66
Model

25. d= 10 cm
Ton/m Static stress(Pa) SF Dynamic Stress(Pa) SF
50 2.99e7 12.37 3.83e8 0.96
80 4.79e7 7.72 4.1e8 0.9
106 6.34e7 5.83 5.4e8 0.68
150 8.98e7 4.12 7.66e8 0.48
Model

26. d=13 cm
Ton/m Static stress(Pa) SF
106 2.98e8 1.24
109 3.06e8 1.2092
110 3.09e8 1.1974
113 3.18e8 1.1635
116 3.26e8 1.135
119 3.35e8 1.1045
122 3.43e8 1.0787
125 3.51e8 1.0541
128 3.6e8 1.0278
131 3.68e8 1.0054
133 3.75e8 0.98
Model

27. Modal Analysis

28. Modal Analysis

29. Static Structural

30. Harmonic Analysis

31. Static Structural

32. Harmonic Analysis

33. Static Structural

34. Harmonic Analysis

35. Static Structural

36. Harmonic Analysis

37. Safety Factor
Safety Factor (SF) is introduced in which 2 formats are included of ultimate strength and yield
strength as correctly.
SF𝑢 =
𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑢𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
max 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑠𝑡𝑟𝑒𝑠𝑠
SF𝑦 =
𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
max 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑠𝑡𝑟𝑒𝑠𝑠
Force (kN)
Static Harmonic
Max
Stress(MPa)
SFy SFu
Max
Stress(MPa)
SFy SFu
1500 552.17 1.0866 0.6701 128.44 4.6714 2.8807
2400 883.48 0.6791 0.4188 205.51 2.9196 1.8004
3180 1170.6 0.5126 0.3161 272.3 2.2035 1.3588
4500 1656.5 0.3622 0.2234 385.33 1.5571 0.9602
Material properties of component are experimentally followed:
𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑢𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ =600 MPa
𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ =370 MPa

38. SolidWorks
ABAQUS

39. Results
d=13 cm
Ton/m
ANSYS SOLIDWORKS ABAQUS
Static stress(Pa) SF Static stress(Pa) SF Static stress(Pa) SF
106 2.98e8 1.24 2.59e8 1.4286 2.83e8 1.66
109 3.06e8 1.2092 3.199e8 1.1566 3.50e8 1.34
110 3.09e8 1.1974 3.128e8 1.1829 3.53e8 1.33
113 3.18e8 1.1635 3.317e8 1.1155 3.63e8 1.29
116 3.26e8 1.135 3.403e8 1.0873 3.72e8 1.26
119 3.35e8 1.1045 3.491e8 1.0599 3.82e8 1.23
122 3.43e8 1.0787 3.579e8 1.0338 3.92e8 1.19
125 3.51e8 1.0541 3.668e8 1.0087 4.01e8 1.17
128 3.6e8 1.0278 3.755e8 0.9854 4.11e8 1.14
131 3.68e8 1.0054 3.843e8 0.9628 4.21e8 1.11
133 3.75e8 0.98 3.902e8 0.9482 4.27e8 1.10
140 4.49e8 1.04
145 4.66e8 1.00
150 4.82e8 0.97

40. Literature Rearview
 Linearization
 FEM and analytical solution
 Unbalance/stability
 Vibration control
 Modal analysis

41. Literature Rearview
Condition Monitoring
 Fault detection
 Unbalance
 Bearing dynamic
 Crack
 Control by magnetic bearing

42. Literature Rearview
Static and dynamic analysis
Modal analysis (Frequency and
mode shape)
Crack and fracture mechanics
Finite element method

43. Literature Rearview

44. Literature Rearview
 Nonlinear model
 3D-FEM
 Unbalance Response
 Modal analysis
 CFD

45. Balancing Concepts and Standards
Balance vs Unbalance
Axis of Rotation
Balance
Axis of Rotation
Unbalance
𝑈 = 𝑚𝑗𝑟
𝑗
𝑈 = 0 Balance
𝑈 ≠ 0 Unbalance
mj=single unbalance
rj=distance of unbalance mass from mass center
Unbalance
Balance
w
mj
F

46. • Manufacturing process
• Misalignment
• Faults of Bearing
• Material construction
Unbalance
Balance
w
mj
F
 Static unbalance
 Single-unbalance
 Single plane
 Dynamic unbalance
 Coupled-unbalance
 Multi- plane
𝑤 =
2𝜋
60
𝑁(𝑟𝑝𝑚)
𝐹 = 𝑚𝑟𝑤2
Unbalance Causes

47. Reduce load on the bearings (low centrifugal forces)
Long bearing life
Acceptable vibration levels
𝐸 =
𝑈
𝑀
Theoretical
E= mass eccentricity(microns)
U=Unbalance (gr.mm)
M=Rotor Mass(Kg)
𝐸 =
9550
𝑁
𝐺 Experimental
G=2.5
Turbocompressor
High Speed Compressor
Aeronautics compressor
ISO 1940 Procedures
Total acceptable mass eccentricity
𝐸 =
9550
𝑁
𝐺
Totol residual accepted unbalance
𝑈𝑡 = 𝑀. 𝐸
Unbalance for left and right plane
𝑈𝑠 = 𝑈𝑑 =
𝑈𝑡
2
Total residual admitted unbalance(in grams)
𝑀 =
𝑈
𝑅
R=Balance radius
Goals of the balancing
API 610
𝑈 = 6350
𝑊
𝑁
U=admitted residual unbalance referred to the bearing journals(in grams)
W=Static Load on the considered bearing(Kg.f)
N=Maximum speed(rpm)
Acceptable eccentricity mass
𝐸 =
𝑈
𝑊
=
6350
𝑁

48. vibration
𝜏𝑦
𝐹𝑦
Y
𝐹𝑧
𝜏𝑧
Z
X
𝐹𝑥
𝜏𝑥
Transitional
Torsional
X
Y
z
𝜃𝑥
𝜃𝑧
𝜃𝑦
Axial
Lateral (bending, transverse and
flexural)
Mechanical Vibration

49. 𝑀𝑞 + 𝐶𝑞 + 𝐾𝑞 = 𝐹
𝐹 =
𝑓
𝜏
=
𝑓𝑜𝑟𝑐𝑒
𝑡𝑜𝑟𝑞𝑢𝑒
Newton’s Law (2nd)
𝐹 = 0 Free - vibration Modal Analysis Eigen Vector
Eigen Value
𝐹 ≠ 0 Forced - vibration Transient
Harmonic
Random
𝑞 =
𝑥
𝑦
𝑧
𝜃𝑥
𝜃𝑦
𝜃𝑧
Degree of freedom

50. What is the benefit of Eigenvalue?
What is the benefit of Eigenvector?
• Frequency
• Critical speed
• Transitional and rotational vibration(rotary machine)
• Mode shape (mechanical behavior)
• Maximum and minimum displacement
• Effects of degree of freedom
• Effects of boundary conditions

51. Eigenvalue and Eigenvector
𝐾 − 𝑀𝑤2
𝜆 = 0
𝑀𝑞 + 𝐶𝑞 + 𝐾𝑞 = 0
𝑤2
Eigen value
Eigen vector
𝑤 ≅ 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑤 =
𝐾
𝑀
𝜆
Mode shape
Mass
Stiffness

52. How to calculate K and M matrices?
𝑉 =
1
2
𝜎𝜀𝑑𝑉
𝑈 =
1
2
𝜎𝜀𝑑𝑉
𝑈 =
1
2
𝑞𝑇
𝐾𝑞
Stiffness Mass
Potential Energy Kinetic Energy
𝑈 =
1
2
𝑞𝑇𝑀𝑞

53. Node and Element Concepts
𝑁6
𝑁5
𝑁4
𝑁3
𝑁2
𝑁1
x
y
z
𝜃𝑧
𝜃𝑦
𝜃𝑥

54. Critical Speed (rpm) Type
2504.4 𝜃𝑥
2578.26 𝜃𝑦
2594.34 𝜃𝑧
11271.6 𝜃𝑥
11443.2 𝜃𝑦
30756.6 𝜃𝑧
50842.2 𝜃𝑥
51268.8 𝜃𝑦
66960 𝜃𝑧
67188 𝜃𝑥
𝑲 =
∎ ∎ ∎ ∎ ∎ ∎
∎ ∎ ∎ ∎ ∎ ∎
∎
∎
∎
∎
∎
∎
∎
∎
∎
∎
∎
∎
∎
∎
∎
∎
∎ ∎
∎ ∎
∎
∎
∎
∎
x
y
z
𝜽𝒚
𝜽𝒛
𝜽𝒙
x y z 𝜽𝒙 𝜽𝒛
𝜽𝒚
𝐾 =
∎ ∎ ∎
∎ ∎ ∎
∎ ∎ ∎
𝜃𝑥 𝜃𝑦 𝜃𝑧
𝜃𝑥
𝜃𝑦
𝜃𝑧
How to know types of direction angular velocity?

55. Industrial Models
Boundary Conditions

56. Rotor
1
6
9 8 7
3 2
4
5

57. Natural Frequency Rotor (Hz) Critical Speed (rpm)
41.74 2504.4
42.971 2578.26
43.239 2594.34
187.86 11271.6
190.72 11443.2
512.61 30756.6
847.37 50842.2
854.48 51268.8
1116 66960
1119 67188

58. Math Models
MATLAB
ANSYS
ABAQUS
analytical
numerical
linear
nonlinear
Math Models
simplest advanced
Aspects of rotating machine behavior
Lateral vibration Axial Vibration Torsional Vibration
Rotor dynamic response analysis types
Modal analysis Harmonic Transient analysis Instability Rotor unbalance
Shrink-Fitting
Applications of rotating machines
Marine propulsion/turbomachines
Power stations/automobiles
Machine tools/household machines
Aerospace applications

59. Rotor Response
control
Frequency Mode shape Mistuning
Modal analysis
porous Crack
fracture
Strength of material
Modeling
Vibration
Shock
Noise
Stability
Harmonic
Random and stochastic
Aerodynamic
CFD Flutter FSI
Condition monitoring
Diagnoses and fault detection
Unhealthy bearing
Instability
clearance
unbalancing
misalignment
Electrical motor
Static
Dynamic

60. 𝑚𝑑
Bearing
Impeller
Shaft
𝑘1 𝑐1 𝑘2
𝑐2
𝑚𝑑
𝑚𝑠
Model 1
𝑚𝑠𝑦 𝑐1 + 𝑐2 𝑦 + 𝑘1 + 𝑘2 𝑦 = 𝐹 + 𝑚𝑑𝑔 + 𝑚𝑠𝑔
𝐼𝜃 + 𝑘2𝑦 + 𝑐2𝑦 𝐿 + 𝑚𝑑𝑔 + 𝑚𝑠𝑔
𝐿
2
= 𝐹𝑥0 + 𝜏

61. Model 2
𝑀𝑞 + 𝐶 + Ω𝐺 𝑞 + 𝐾𝑞 = 𝐹 + 𝜏
𝑞 =
𝑥
𝑦
y
x

62. Model shaft-Disk
𝑚𝑥 + 𝑐𝑥 + 𝑘𝑥 = 𝑚(𝑢𝜑 sin 𝜑 + 𝑢𝜑2
cos 𝜑)
𝑚𝑦 + 𝑐𝑦 + 𝑘𝑦 = 𝑚(𝑢𝜑2
sin 𝜑 − 𝑢𝜑 cos 𝜑)
𝑚𝜑 + 𝑐𝜑 + 𝑘𝜑 = 𝜏 − 𝑝 = 𝑚 𝑥𝑢 sin 𝜑 − 𝑦𝑢 cos 𝜑

64. Comparison of various types of bearings
Rolling Element Bearing Sliding Bearing Active Magnetic Bearing
Inferior for impact load.
A deep groove/angular
contact and cone roller
bearing, etc., can support
the load both in radial and
thrust directions.
Suitable for impact load
and heavy load.
Acceptable loads are
approximately:
Radial dir.: less than 5MPa
Trust dir.: less than 7 MPa
Most suitable for light load with high speed.
Acceptable load pressure are approximately:
Radial dir.: 0.3 to 0.5 MPa
Thrust dir.: less than 0.8 MPa
Friction Static friction coefficients
as small as 10-3~10-2
Static friction coefficient is
as large as 10-2~10-1
Small
Dynamic friction coefficient is almost the same as 10-3
Speed Limit Depending on centrifugal
force and lubrication. Etc.
DN<2*105 mm rpm
Depending on turbulent
flow transition and
overhanging of oil film.
Generally, V<120 m/s
Depending on strength of AMB rotor material. Generally,
V<200 m/s
Stiffness and
damping
Large stiffness and no
damping
Large stiffness and high
damping
Stiffness and damping are low but widely controllable.
Noise Comparatively large Comparatively small small
Lubricant Grease in general Oil in general Not required
Life and Breakage Life can be estimated
using fatigue strength of
material seizure breakage
may occur at high-speed
rotation.
Infinite life in
hydrodynamic operation.
Seizure and wear are main
causes of breakage.
Flaking may occur due to
high load.
Nearly permanent
Installation Error Comparatively sensitive Comparatively insensitive Insensitive because bearing clearance is large.
Influence
Contamination
Influential on life, wear,
especially noise.
Comparatively less
influential.
Less influential.
Maintenance By using grease/oil
lubrication, maintenance
is easy.
Leakage from lubricant oil
circulating system need to
be checked and stopped.
Maintenance free in general except some electronics parts.
Cost Mass-produced standard
bearing are inexpensive
and interchangeable.
Generally in-house
production. Comparatively
inexpensive. Arbitrary
bearing dimensions.
Expensive because custom-made manufacture is still the
mainstreams

65. Free Lateral Response of Simple Rotor Models
𝑚𝑢 + 𝑘𝑥𝑇𝑢 + 𝑘𝑥𝐶𝜓 = 0
𝑚𝑣 + 𝑘𝑦𝑇𝑣 − 𝑘𝑦𝐶𝜃 = 0
𝐼𝑑𝜃 + 𝐼𝑝Ω𝜓 − 𝑘𝑦𝐶𝑣 + 𝑘𝑦𝑅𝜃 = 0
𝐼𝑑𝜓 − 𝐼𝑝Ω𝜃 + 𝑘𝑥𝐶𝑢 + 𝑘𝑥𝑅𝜓 = 0
Neglecting Gyroscopic Effects

66. Including Gyroscopic Effects
𝑚𝑢 + 𝑘𝑇𝑢 + 𝑘𝐶𝜓 = 0
𝑚𝑣 + 𝑘𝑇𝑣 − 𝑘𝐶𝜃 = 0
𝐼𝑑𝜃 + 𝐼𝑝Ω𝜓 − 𝑘𝐶𝑣 + 𝑘𝑅𝜃 = 0
𝐼𝑑𝜓 − 𝐼𝑝Ω𝜃 + 𝑘𝐶𝑢 + 𝑘𝑅𝜓 = 0

67. Modal Analysis of Shaft-Disc

68. Forced Lateral Response and Critical Speeds
𝐼𝑑𝜃 + 𝐼𝑝Ω𝜓 − 𝑐𝑦𝐶𝑣 + 𝑐𝑦𝑅𝜃 − 𝑘𝑦𝐶𝑣 + 𝑘𝑦𝑅𝜃 = − 𝐼𝑑 − 𝐼𝑝 𝛽Ω2
sin Ω𝑡
𝐼𝑑𝜓 − 𝐼𝑝Ω𝜃 + 𝑐𝑥𝐶𝑢 + 𝑐𝑥𝑅𝜓 − 𝑘𝑥𝐶𝑢 + 𝑘𝑥𝑅𝜓 = 𝐼𝑑 − 𝐼𝑝 𝛽Ω2
cos Ω𝑡
𝑚𝑢 + 𝑐𝑥𝑇𝑢 + 𝑐𝑥𝐶𝜓 + 𝑘𝑥𝑇𝑢 + 𝑘𝑥𝐶𝜓 = 𝑚𝜀Ω2
cos Ω𝑡
𝑚𝑣 + 𝑐𝑦𝑇𝑣 − 𝑐𝑦𝐶𝜃 + 𝑘𝑦𝑇𝑣 − 𝑘𝑦𝐶𝜓 = 𝑚𝜀Ω2
sin Ω𝑡
𝑓 = 𝑚𝜀Ω2
𝑓 = 𝑚0𝜀Ω2
𝜀 =
𝑚0
𝑚
𝑎
Unbalanced effect

70. Finite Element model of Rotor
𝑢𝑒
= 𝑥𝑖 𝑦𝑖 𝑧𝑖 𝜃𝑥𝑖 𝜃𝑦𝑖 𝜃𝑧𝑖 𝑥𝑗 𝑦𝑗 𝑧𝑗 𝜃𝑥𝑗 𝜃𝑦𝑗 𝜃𝑧𝑗
𝑇
𝑀𝑒𝑢𝑒 + 𝐶𝑒 + Ω𝐺𝑒 𝑢𝑒 + 𝐾𝑒𝑢𝑒 = 𝐹𝑒

71. 𝐾𝑒 =
𝐴𝐸
𝐿
0 0 0 0 0
−𝐴𝐸
𝐿
0 0 0 0 0
0 𝑎𝑧 0 0 0 𝑐𝑧 0 −𝑎𝑧 0 0 0 𝑐𝑧
0 0 𝑎𝑦 0 −𝑐𝑦 0 0 0 −𝑎𝑦 0 −𝑐𝑦 0
0 0 0
𝐺𝐽
𝐿
0 0 0 0 0
−𝐺𝐽
𝐿
0 0
0 0 −𝑐𝑦 0 0 0 0 0 𝑐𝑦 0 𝑓𝑦 0
0 𝑐𝑧 0 0 0 0 0 −𝑐𝑧 0 0 0 𝑓𝑧
−𝐴𝐸
𝐿
0 0 0 0 0
𝐴𝐸
𝐿
0 0 0 0 0
0 −𝑎𝑧 0 0 0 −𝑐𝑧 0 𝑎𝑧 0 0 0 −𝑐𝑧
0 0 −𝑎𝑦 0 𝑐𝑦 0 0 0 𝑎𝑦 0 𝑐𝑦 0
0 0 0
−𝐺𝐽
𝐿
0 0 0 0 0
𝐺𝐽
𝐿
0 0
0 0 −𝑐𝑦 0 𝑓𝑦 0 0 0 𝑐𝑦 0 𝑒𝑦 0
0 𝑐𝑧 0 0 0 𝑓𝑧 0 −𝑐𝑧 0 0 0 𝑒𝑧
𝐺𝑒 = 2Ω𝜌𝐴𝐿
0 0 0 0 0 0 0 0 0 0 0 0
0 0 𝑔 0 ℎ 0 0 0 −𝑔 0 ℎ 0
0 −𝑔 0 0 0 ℎ 0 𝑔 0 0 0 ℎ
0 0 0 0 0 0 0 0 0 0 0 0
0 −ℎ 0 0 0 𝑖 0 ℎ 0 0 0 𝑗
0 0 −ℎ 0 −𝑖 0 0 0 ℎ 0 −𝑗 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 −𝑔 0 −ℎ 0 0 0 𝑔 0 −ℎ 0
0 𝑔 0 0 0 −ℎ 0 −𝑔 0 0 0 −ℎ
0 0 0 0 0 0 0 0 0 0 0 0
0 −ℎ 0 0 0 𝑗 0 ℎ 0 0 0 𝑖
0 0 −ℎ 0 −𝑗 0 0 0 ℎ 0 −𝑖 0
𝑀𝑒 = 𝜌𝐴𝐿
1
3
0 0 0 0 0
1
6
0 0 0 0 0
0 𝐴𝑧 0 0 0 𝐶𝑧 0 𝐵𝑧 0 0 0 −𝐷𝑧
0 0 𝐴𝑦 0 −𝐶𝑦 0 0 0 𝐵𝑦 0 𝐷𝑦 0
0 0 0
𝐽
3𝐴
0 0 0 0 0 0
𝐽
6𝐴
0
0 0 −𝐶𝑦 0 𝐸𝑦 0 0 0 −𝐷𝑦 0 𝐹𝑦 0
0 𝐶𝑧 0 0 0 𝐸𝑧 0 𝐷𝑧 0 0 0 𝐹𝑧
1
6
0 0 0 0 0
1
3
0 0 0 0 0
0 𝐵𝑧 0 0 0 𝐷𝑧 0 𝐴𝑧 0 0 0 −𝐶𝑧
0 0 𝐵𝑦 0 −𝐷𝑦 0 0 0 𝐴𝑦 0 𝐶𝑦 0
0 0 0 0 0 0 0 0 0
𝐽
3𝐴
0 0
0 0 𝐷𝑦
𝐽
6𝐴
𝐹𝑦 0 0 0 𝐶𝑦 0 𝐸𝑦 0
0 −𝐷𝑧 0 0 0 𝐹𝑧 0 −𝐶𝑧 0 0 0 𝐸𝑧
𝐶𝑒 = 𝛼𝑀𝑒 + 𝛽𝐾𝑒

72. Disc Element
𝑢𝑖 = 𝑥𝑖 𝑦𝑖 𝑧𝑖 𝜃𝑥𝑖 𝜃𝑦𝑖 𝜃𝑧𝑖
𝑇
𝐾𝑠 = 𝑑𝑖𝑎𝑔 0 𝑘 𝑘 0 0 0 .
𝐶𝑠 = 𝛽𝑠. 𝐾𝑠
𝑀𝑑 = 𝑑𝑖𝑎𝑔 𝑚 𝑚 𝑚 𝐽𝑝 𝐽𝑑 𝐽𝑑

73. Outline
For future our main scopes are including to focus on other challenges that will add them
step by step onto system such as
Fundamental modeling (theoretical shaft, disk and bearing)
Shrink Fits (thermo-elastic behavior such creep)
Mechanical faults (fault diagnosis, unbalance, misalignment, erosion, crack, porous, wear, rubbish,
clearance)
Bearing effects
Residual Stress
Optimal design (performance index, structural)
Control (Passive, active, semi-active, absorber, resonator) this is problem-solving for system.
Condition monitoring and health monitoring
Uncertainties
Nonlinear behavior (stress-strain, vibrations)
Fatigue
Co-simulation between ANSYS – PHYTON-MATLAB
Multi-stage rotor
Multiphysics effective vibration analysis in solid model (thermal, vibration, acoustics, oil and
lubricant)
Practical machine learning (signal processing, image processing, audio processing)
Standard vibration
Stability vs balance
Mechanical engineering design (power transmission shaft, shaft components, deflection and stiffne