Understanding Polar Plots in Rotor Balancing

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Portable balancer & Vibration analyzer Balanset-1A

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Vibration sensor

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Optical Sensor (Laser Tachometer)

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Balanset-4

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Magnetic Stand Insize-60-kgf

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Reflective tape

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Dynamic balancer “Balanset-1A” OEM

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Definition: What is a Polar Plot?

A polar plot (also called a polar diagram or Nyquist diagram in some contexts) is a circular graphical representation used in rotor balancing that displays vibration data as vectors. Each vector represents both the amplitude (magnitude) and phase angle (direction) of vibration at a specific measurement point. The radial distance from the center represents the vibration amplitude, while the angular position represents the phase angle.

Polar plots are an essential visualization tool in field balancing because they allow technicians to see at a glance how vibration vectors change during the balancing process and to perform graphical vector addition and subtraction operations.

How to Read a Polar Plot

Understanding the components of a polar plot is essential for effective balancing work:

The Coordinate System

• Origin (Center Point): Represents zero vibration. The closer a vector is to the center, the lower the vibration amplitude.
• Radial Distance: The length of a vector from the origin represents the vibration amplitude. Concentric circles mark amplitude scales (e.g., 1 mm/s, 2 mm/s, 3 mm/s).
• Angular Position: The angle of a vector represents the phase. By convention, 0° is typically placed at the right (3 o’clock position), and angles increase counterclockwise (90° at top, 180° at left, 270° at bottom).
• Phase Reference: The phase angle is measured relative to a once-per-revolution reference mark on the rotor, typically detected by a tachometer or keyphasor.

Reading Vector Data

Each vector plotted on the polar diagram contains complete information about the vibration at a specific instant or condition:

• A vector pointing at 45° with a length of 5 mm/s indicates vibration with an amplitude of 5 mm/s occurring at 45° after the reference mark passes the sensor.
• Multiple vectors can be plotted on the same diagram to show how vibration changes throughout the balancing procedure.

Use of Polar Plots in Balancing Procedures

Polar plots are instrumental in visualizing each step of the balancing process:

1. Plotting Initial Vibration

The first vector plotted represents the initial unbalance condition. This “O” vector (for “Original”) shows both the magnitude and angular location of the unbalance-induced vibration.

2. Adding Trial Weight Effect

When a trial weight is added and a test run is performed, a second vector “O+T” is plotted, representing the combined effect of the original unbalance plus the trial weight. By performing vector subtraction (O+T – O), the isolated effect of the trial weight “T” can be visualized as a separate vector.

3. Calculating Correction Weight

The correction weight needed is one that will produce a vibration vector exactly opposite (180° phase shift) and equal in magnitude to the original vibration “O”. This opposing vector, when added to O, results in a vector sum at or near the origin (zero vibration). The polar plot makes this relationship visually clear.

4. Verification

After the correction weight is installed, the final verification run produces a new vector plotted on the same diagram. If the balancing was successful, this residual vector will be very close to the origin, indicating low vibration.

Vector Addition on Polar Plots

One of the powerful features of polar plots is the ability to perform vector addition graphically using the “tip-to-tail” method:

• To add two vectors, place the tail of the second vector at the tip of the first vector.
• The resultant vector is drawn from the tail of the first vector to the tip of the second vector.
• This graphical method allows for quick visualization of how different unbalance sources combine or cancel each other.

Vector subtraction is performed by reversing the direction of the vector being subtracted (rotating it 180°) and then adding it to the other vector.

Advantages of Polar Plot Visualization

Polar plots provide several important benefits in balancing work:

• Intuitive Representation: The circular format naturally represents rotational phenomena, making it easier to visualize the angular relationships between unbalance and correction.
• Complete Information: Both amplitude and phase are shown in a single, compact diagram, eliminating the need for separate charts.
• Visual Quality Check: Anomalies or errors in data collection are often immediately apparent when vectors are plotted. For example, if a trial weight produces almost no change in vibration, this will be visible as two nearly overlapping vectors.
• Documentation: A well-labeled polar plot serves as an excellent record of the balancing procedure, showing the progression from initial unbalance to final corrected state.
• Troubleshooting: When balancing does not achieve expected results, the polar plot can reveal issues such as non-linear system behavior, soft foot problems, or measurement errors.

Modern Balancing Instruments and Polar Plots

Contemporary portable balancing instruments and software automatically generate polar plots in real-time during the balancing procedure. The instrument:

• Automatically plots each measurement as a vector.
• Performs all vector mathematics internally.
• Displays both the graphical polar plot and numerical results simultaneously.
• Allows the technician to zoom, pan, and annotate the plot for documentation.

Despite this automation, understanding how to read and interpret polar plots remains an essential skill for balancing professionals, as it provides insight into the underlying physics and allows for verification of instrument calculations.

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