Frequency Analysis of a rotating shaft

1. AIM

Find out the critical frequencies of a rotating shaft in Solidworks by conductiing frequency analysis.

2. OBJECTIVES

1. Create the model in Solidworks.
2. Conduct a frequency analysis and apply a bearing fixture on the stepped face of the rod at the two ends and perform the analysis.
3. Find out 5 mode shapes and list the resonant frequencies

3. INTRODUCTION

Rotating shafts tend to bow out at certain speeds and whirl in a complicated manner. Whirling is defined as the rotation of the plane made by the bent shaft and the line of centers of the bearings. The phenomenon results from such various causes as mass unbalance, hysteresis damping in the shaft, gyroscopic forces, and fluid friction in bearings. In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear. As the speed of rotation approaches the object's natural frequency, the object begins to resonate, which dramatically increases system vibration. The resulting resonance occurs regardless of orientation. When the rotational speed is equal to the numerical value of the natural vibration, then that speed is referred to as critical speed.

• Natural Frequency: All physical structures have natural frequencies. These are the frequencies at which the structure will tend to vibrate when subjected to certain external forces. These frequencies are dependent on the way mass and stiffness are distributed within the structure.

• Resonance: Resonance is a phenomenon in which a dynamic force drives a structure to vibrate at its natural frequency. When a structure is in resonance, a small force can produce a large vibration response.

4. CAD GEOMETRY

FINITE ELEMENT ANALYSIS (FEA)

Finite Element Analysis is a widely used study which deals with various analysis like thermal, structural etc on the mathematical and engineering model. The main principle of this analysis is to divide the model into various smaller elements and then the analysis are made on each element.

Solver: We use SolidWorks which provides us with two types of solvers:

1. FFEPLUS - It is an iterative solver. An initial solution is assumed and from this solution through iterations, the final solutions can be reached.
2. Direct Sparse - It is a direct solver which does not use any approximations.

Options in Frequency analysis in SolidWorks:

1. Number of frequency: it allows the user to specify the number of mode shapes or natural frequency that is needed to be considered.
2. Frequency closest to: It allows the study to be focused on a particular frequency. It is only available with direct solver.
3. Upper Bound Frequency: It allows the user to set a particular frequency above which the solver will not calculate.

Incompatible Boundary Options: if the body is having several contacts between the parts inside the model, the nodes may not be perfectly matched with each part in order for the force to be transferred.

These problems can arise due to several reasons: 1.The geometric size is not uniform; 2.The mesh size is not uniform throughout.

SolidWorks uses the default mode of surface to surface bonding contact, if results do not converge properly, the node to surface contact is used.

STEPS

1. Model the system using solidworls sketch, boss extrude tool.
2. Activate the solidworks simulation plugin.
3. Create a new study and select the frequency analysis.
4. Apply the material to the beams.
5. Select the face at ends for bearing fixture.
6. Create mesh and use high quality mesh. Set appropriate mesh size.
7. Run the study;
8. Compare the results.

Material Selection

Fixtures

Mesh

6. RESULTS, OBSERVATIONS AND CONCLUSIONS

Mode1

Here the maximum frequency amplitude is at the outer diameter of the the disc and minimum at the shaft.

Mode2

Here the maximum frequency amplitude is at the disc as a whole and minimum at the ends of the bearing fixture.

Mode3

Here the maximum frequency amplitude is at the disc as a whole and minimum at the ends of the bearing fixture.

Mode4

Here the maximum frequency amplitude is at the opposite ends of the disc and and minimum is at at the opposite ends of the disc which is 90deg to the maximum amplitude and also at the ends of the bearing fixture.

Mode5

Here the maximum frequency amplitude is at the opposite ends of the disc and and minimum is at at the opposite ends of the disc which is 90deg to the maximum amplitude and also at the ends of the bearing fixture.

Resonant frequencies

Frequency Number	Rad/sec	Hertz	Seconds
1	0.15218	0.02422	41.288
2	1,633.7	260.01	0.0038461
3	1,633.8	260.03	0.0038457
4	6,105.9	971.78	0.001029
5	6,106.9	971.95	0.0010289

Mass Participation (Normalized)

Mode Number	Frequency(Hertz)	X direction	Y direction	Z direction
1	0.02422	3.9797e-42	8.0737e-14	1.9152e-13
2	260.01	2.6988e-10	0.10099	0.80455
3	260.03	1.0228e-11	0.80455	0.10099
4	971.78	4.3168e-09	1.0639e-10	4.6299e-13
5	971.95	1.6018e-09	2.8443e-11	2.6964e-10
		Sum X = 6.1987e-09	Sum Y = 0.90554	Sum Z = 0.90554

Observation & Conclusions

The frequency analysis is performed on the rotating shaft and the different mode shapes of the rotating shaft is been listed above. When the shaft vibrates at these resonant frequency it will destroy the shafts. Frequency is the one of the factor which cannot be modified. Therefore, this parameter are very important while designing the structures because when body vibrates at thier natural frequency(resonant frequncy) it causes failure in structure of element. Natural frequency is depends upon the two factors stiffness & mass. Natural frequency increases by increasing stiffness or by decreasing the mass. So it is suggested to operate the rotating shaft such that it does not reach the above-mentioned frequencies to prevent the shaft from damage. By doing so, it reduces the damage to the shaft and hence it provides the increase in life period to the rotating shaft. Thus the frequency study is been performed to find out the different mode shapes of the shaft using the simulation in SolidWorks. The natural frequency for different modes has been listed on the table and through graph it is clearly seen that as the mode number increases the frequency of the system changes. This means that the system will have different mode shapes for different frequency. In a few modes we can see that the shaft tends to bow, which is known as whirling of the shaft. The whirling motion is defined as the rotation of the plane enclosed by the bent-up shaft axis and bearing center line about the bearing center line itself.