Frequency Analysis of a Rotating Shaft
AIM:
- To find out the critical or resonant frequencies of a rotating shaft in Solidworks.
- Design the model using solidworks based on any desired dimensions.
Objective:
To create a solid model of a rotating flywheel on a shaft and identify 5 critical frequencies by generating 5 mode shapes using Solidworks Simulation’s Frequency analysis feature.
INTRODUCTION:
Resonant frequency is the oscillation of a system at its natural or unforced resonance. Resonance occurs when a system is able to store and easily transfer energy between different storage modes, such as Kinetic energy or Potential energy as you would find with a simple pendulum.
Resonance - "The increase in amplitude of oscillation of an electric or mechanical system exposed to a periodic force whose frequency is equal or very close to the natural undamped frequency of the system."
Mode:-
The mode is a statistical term that refers to the most frequently occurring number found in a set of numbers. The mode is found by collecting and organizing data in order to count the frequency of each result. The result with the highest count of occurrences is the mode of the set, also referred to as the modal value.
Mode Shapes The deformed shape of the structure at a specific natural frequency of vibration is termed its normal mode of vibration. Some other terms used to describe the normal mode are mode shape, characteristic shape, and fundamental shape. Each mode shape is associated with a specific natural frequency.
Modes are inherent properties of a structure, and are determined by the material properties (mass, damping, and stiffness), and boundary conditions of the structure. Each mode is defined by a natural (modal or resonant) frequency, modal damping, and a mode shape (i.e. the so-called “modal parameters”).
Geometry
Study Properties
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Study name
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Frequency Analysis
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Analysis type
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Frequency
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Mesh type
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Solid Mesh
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Number of frequencies
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5
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Solver type
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FFEPlus
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Soft Spring:
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Off
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Incompatible bonding options
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Automatic
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Thermal option
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Include temperature loads
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Zero strain temperature
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298 Kelvin
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Include fluid pressure effects from SOLIDWORKS Flow Simulation
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Off
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Result folder
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SOLIDWORKS document (C:\Users\SANTANU\Documents\Solidworks FEA)
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Units
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Unit system:
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SI (MKS)
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Length/Displacement
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mm
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Temperature
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Kelvin
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Angular velocity
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Rad/sec
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Pressure/Stress
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N/m^2
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Material Properties
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Model Reference
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Properties
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Components
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| |
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Name:
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Alloy Steel
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Model type:
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Linear Elastic Isotropic
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Default failure criterion:
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Max von Mises Stress
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Yield strength:
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6.20422e+08 N/m^2
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Tensile strength:
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7.23826e+08 N/m^2
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Mass density:
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7,700 kg/m^3
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Elastic modulus:
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2.1e+11 N/m^2
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Poisson's ratio:
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0.28
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Thermal expansion coefficient:
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1.3e-05 /Kelvin
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SolidBody 1(Boss-Extrude4)(Rotating shaft)
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Curve Data:N/A
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Connector Definitions
Pin/Bolt/Bearing Connector
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Model Reference
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Connector Details
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Strength Details
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Bearing Support-1
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Entities:
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1 face(s)
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Type:
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Bearing
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No Data
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Connector ForcesNo Data
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Bearing Support-2
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Entities:
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1 face(s)
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Type:
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Bearing
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No Data
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Connector ForcesNo Data
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Mesh information
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Mesh type
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Solid Mesh
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Mesher Used:
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Standard mesh
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Automatic Transition:
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Off
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Include Mesh Auto Loops:
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Off
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Jacobian points for High quality mesh
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16 Points
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Element Size
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5 mm
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Tolerance
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0.25 mm
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Mesh Quality
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High
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Mesh information - Details
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Total Nodes
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12842
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Total Elements
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7505
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Maximum Aspect Ratio
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4.9355
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% of elements with Aspect Ratio < 3
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99.7
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% of elements with Aspect Ratio > 10
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0
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% of distorted elements(Jacobian)
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0
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Time to complete mesh(hh;mm;ss):
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00:00:02
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Computer name:
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|
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Study Results
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Name
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Type
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Min
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Max
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Amplitude1
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AMPRES: Resultant Amplitude Plot for Mode Shape: 1(Value = 0.0782139 Hz)
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2.404e-03
Node: 1424
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2.471e+00
Node: 8920
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Rotating shaft-Frequency Analysis-Amplitude-Amplitude1
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Name
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Type
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Min
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Max
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Amplitude2
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AMPRES: Resultant Amplitude Plot for Mode Shape: 2(Value = 438.007 Hz)
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7.924e-03
Node: 1802
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1.289e+00
Node: 9136
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Rotating shaft-Frequency Analysis-Amplitude-Amplitude2
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Name
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Type
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Min
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Max
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Amplitude3
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AMPRES: Resultant Amplitude Plot for Mode Shape: 3(Value = 438.071 Hz)
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8.340e-03
Node: 11
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1.289e+00
Node: 9421
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Rotating shaft-Frequency Analysis-Amplitude-Amplitude3
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Name
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Type
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Min
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Max
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Amplitude4
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AMPRES: Resultant Amplitude Plot for Mode Shape: 4(Value = 1,653.51 Hz)
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4.532e-04
Node: 7923
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3.451e+00
Node: 551
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Rotating shaft-Frequency Analysis-Amplitude-Amplitude4
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Name
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Type
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Min
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Max
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Amplitude5
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AMPRES: Resultant Amplitude Plot for Mode Shape: 5(Value = 1,654.1 Hz)
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0.001
Node: 11
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3.446
Node: 576
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Rotating shaft-Frequency Analysis-Amplitude-Amplitude5
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Mode List
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Frequency Number
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Rad/sec
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Hertz
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Seconds
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1
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0.49143
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0.078214
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12.785
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2
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2,752.1
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438.01
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0.0022831
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|
3
|
2,752.5
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438.07
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0.0022827
|
|
4
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10,389
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1,653.5
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0.00060478
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5
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10,393
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1,654.1
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0.00060456
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Mass Participation (Normalized)
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Mode Number
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Frequency(Hertz)
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X direction
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Y direction
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Z direction
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1
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0.078214
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6.849e-10
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3.2173e-10
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1.5506e-33
|
|
2
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438.01
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0.84786
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0.0052583
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2.112e-10
|
|
3
|
438.07
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0.0052579
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0.84787
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1.3106e-12
|
|
4
|
1,653.5
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5.2175e-09
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7.3594e-11
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1.3679e-07
|
|
5
|
1,654.1
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3.4752e-12
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2.5203e-09
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8.8689e-08
|
|
|
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Sum X = 0.85312
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Sum Y = 0.85313
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Sum Z = 2.2569e-07
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RESULTS EXPLANATION
Resnonant frequencies corresponding to different modes of vibration :
CONCLUSION
It must be ensured that system doesnot vibrate with the frequencies tabulated above to avoid failure .