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To discuss the significance of Equation (1) with respect to frequency and its implications for the design of system. Give an overview of the type of system which can be adversely affected by the presence of rotating imbalance and what measures can be adopted to eliminate them.
In simplest terms, vibration in motorized equipment is merely the back and forth movement or oscillation of machines and components, such as drive motors, driven devices (pumps, compressors and so on) and the bearings, shafts, gears, belts and other elements that make up mechanical systems.
Vibration in industrial equipment can be both a sign and a source of trouble. Other times, vibration just "goes with the territory" as a normal part of machine operation, and should not cause undue concern. But how can the plant maintenance professional tell the difference between acceptable, normal vibration, and the kind of vibration that requires immediate attention to service or replace troubled equipment?
With a basic understanding of vibration and its causes the maintenance professional can quickly and reliably determine the cause and severity of most machine vibration and receive recommendations for repair.
Vibration is not always a problem. In some tasks, vibration is essential. Machines such as oscillating sanders and vibratory tumblers use vibration to remove materials and finish surfaces. Vibratory feeders use vibration to move materials. In construction, vibrators are used to help concrete settle into forms and compact fill materials. Vibratory rollers help compress asphalt used in highway paving.
In other cases vibration is inherent in machine design. For instance, some vibration is almost unavoidable in the operation of reciprocating pumps and compressors, internal combustion engines and gear drives. In a well engineered, well maintained machine, such vibration should be no cause for concern.
MOST COMMON CAUSES OF MACHINE VIBRATION
Vibration can result from a number of conditions, acting alone or in combination. Keep in mind that vibration problems may be caused by auxiliary equipment, not just the primary equipment.
These are some of the major causes of vibration.
1. Imbalance - A "heavy spot" in a rotating component will cause vibration when the unbalanced weight rotates around the machine's axis, creating a centrifugal force. Imbalance could be caused by manufacturing defects (machining errors, casting flaws) or maintenance issues (deformed or dirty fan blades, missing balance weights). As machine speed increases the effects of imbalance become greater. Imbalance can severely reduce bearing life as well as cause undue machine vibration.
2. Misalignment/shaft run-out - Vibration can result when machine shafts are out of line. Angular misalignment occurs when the axes of (for example) a motor and pump are not parallel. When the axes are parallel but not exactly aligned, the condition is known as parallel misalignment. Misalignment may be caused during assembly or develop over time, due to thermal expansion, components shifting or improper reassembly after maintenance. The resulting vibration may be radial or axial (in line with the axis of the machine) or both.
3. Wear - As components such as ball or roller bearings, drive belts or gears become worn, they may cause vibration. When a roller bearing race becomes pitted, for instance, the bearing rollers will cause a vibration each time they travel over the damaged area. A gear tooth that is heavily chipped or worn, or a drive belt that is breaking down, can also produce vibration.
4. Looseness - Vibration that might otherwise go unnoticed may become obvious and destructive if the component that is vibrating has loose bearings or is loosely attached to its mounts. Such looseness may or may not be caused by the underlying vibration. Whatever its cause, looseness can allow any vibration present to cause damage, such as further bearing wear, wear and fatigue in equipment mounts and other components.
Unbalance in rotating machines is of a common source of vibration excitation. We consider a spring-mass system constrained to move in the vertical direction and excited by a rotating machine that is unbalanced. The unbalance is represented by an eccentric mass m with eccentricity e that is rotating with angular velocity w. EOM becomes:
The steady-state solution of the previous section can be replaced and reduced into non-dimensional form where Fo is replaced by mew2
Figure 1: - Rotating Unbalance
Figure 2: response and phase angle vs frequency ratio Î©.
SOLUTION OF THE FIRST TASK:
Using excel program and using the equation no. 7 of unbalance rotating the response vs. frequency ration for variable damping ration can be obtained as follow: -
Table 1: detailed calculation of response for the case were Î¾= 0.1 and for various frequency ratio.
Table 1: detailed calculation of response for Î¾= 0.1
[Y / r Î²]
Figure 3: the response vs the normalized frequency plot for Î¾=0.
Table 2: accumulated result for all cases
Figure 4: plot of response vs frequency ratio.
SOLUTION OF THE SECOND TASK:
Discuss the significance of Equation (1) with respect to frequency and its implications for the design of system. Give an overview of the type of system which can be adversely affected by the presence of rotating imbalance and what measures can be adopted to eliminate them.
The centrifugal force (mrÏ‰2) caused by body rotation of is directly proportional to square of the rotation frequency (Ï‰2) and its function change with rotational speed. Where as result of this variation the real solution of it can directly affected with the values of normalized frequency in many cases as resulted into achieved plot were as normalized frequency increased Î© (i.e. Ï‰ become larger than Ï‰n the response behave as follow: -
As body rotation Ï‰ increased but below natural frequency Ï‰n (i.e. Î© less than 1) the response is negligible (Y/rÎ² â‰ˆ 0) with no valuable effect of the damping ratio Î¾.
At resonant (the body rotation Ï‰ equal the natural frequency Ï‰n ) the damping ratio play essential rules of the response.
As body rotation Ï‰ increased above natural frequency Ï‰n (i.e. Î© larger than 1) the response is negligible (Y/rÎ² â‰ˆ 1) with no valuable effect of the damping ratio Î¾.
This implies that system design will be affected in which zone to select the appropriate frequency or in preventive maintenance applications the required damping will be restricted to the measured rotating speed
An overview of the type of system which can be adversely affected by the presence of rotating imbalance
In order to investigate the effect of the rotating unbalance vibration and how to eliminate it we should first know the vibration effect and its characteristics to eliminate it properly.
Effects Of Vibration
The effects of vibration can be severe. Unchecked machine vibration can accelerate rates of wear (i.e. reduce bearing life) and damage equipment. Vibrating machinery can create noise, cause safety problems and lead to degradation in plant working conditions. Vibration can cause machinery to consume excessive power and may damage product quality.
In the worst cases, vibration can damage equipment so severely as to knock it out of service and halt plant production.
Figure 5: Examples of unbalance rotating machines.
Yet there is a positive aspect to machine vibration. Measured and analyzed correctly, vibration can be used in a preventive maintenance program as an indicator of machine condition, and help guide the plant maintenance professional to take remedial action before disaster strikes.
Characteristics Of Vibration
To understand how vibration manifests itself, consider a simple rotating machine like an electric motor. The motor and shaft rotate around the axis of the shaft, which is supported by a bearing at each end.
One key consideration in analyzing vibration is the direction of the vibrating force. In our electric motor, vibration can occur as a force applied in a radial direction (outward from the shaft) or in an axial direction (parallel to the shaft).
An imbalance in the motor, for instance, would most likely cause a radial vibration as the "heavy spot" in the motor rotates, creating a centrifugal force that tugs the motor outward as the shaft rotates through 360 degrees. A shaft misalignment could cause vibration in an axial direction (back and forth along the shaft axis), due to misalignment in a shaft coupling device.
Another key factor in vibration is amplitude, or how much force or severity the vibration has. The farther out of balance our motor is, the greater its amplitude of vibration. Other factors, such as speed of rotation, can also affect vibration amplitude. As rotation rate goes up, the imbalance force increases significantly.
Frequency refers to the oscillation rate of vibration, or how rapidly the machine tends to move back and forth under the force of the condition or conditions causing the vibration. Frequency is commonly expressed in cycles per minute or Hertz (CPM or Hz). One Hz equals one cycle per second or 60 cycles per minute.
Though out motor 'simple,' even this machine can exhibit a complex vibration signature. As it operates it could be vibrating in multiple directions (radially and axially), with several rates of:-
Amplitude and frequency.
Vibration from deteriorating roller bearings.
More all could combine to create a complex vibration spectrum.
Vibration measurements aspect: -
Vibration analyzers can also be used. Several commercial vibration analyzers are available today. They consist of a vibration pick up and an FFT (Fast Fourier Transformation) analyzer, a balancing kit for phase measurement and an inbuilt computer.
The pick up essentially a piezo electric type with a natural frequency of 25 kcps. (KHz). Built in double integration is also available for displacement plots. FFT converts time domain signal to a signal in frequency domain to identify the frequencies of concern.
Sample of vibration measuring devices: -
Vibration pick ups: Seismic Instruments
The commonly used vibration pick ups are called seismic instruments. The basic element of many vibration measuring instrument is a seismic unit which is basically a spring mass-damper system mounted on a vibrating body on which measurements are to be made as shown in Figure 6.
Figure 6: Seismic Unit
To investigate the isolating region from the amplification region transmissibility Vs frequency ratio plot might be obtained from the equation
T = Ff / Fm
Eliminate unbalanced VIBRATION using isolator: -
Vibratory forces generated by machines and other causes are often unavoidable; however, their effects on a dynamical system can be minimized by proper isolator design. The force to be isolated is transmitted through the spring and damper.
Vibration is a characteristic of virtually all industrial machines. When vibration increases beyond normal levels, it may indicate only normal wear-or it may signal the need for further assessment of the underlying causes, or for immediate maintenance action.
To understanding why vibration occurs and how it manifests itself is a key first step toward preventing vibration from causing trouble in the production environment.
The most common mechanical problems of unbalance, looseness, misalignment and bearing failures in a wide variety of mechanical equipment, including motors, fans, blowers, belts and chain drives, gearboxes, couplings, pumps, compressors, closed coupled machines and spindles.