ME2050 Dynamics and Control Rotor balancing lab and design exercise

Solution.pdf

OBJECTIVE 

• Appreciate the need and recognises the applications for rotor balancing. 

• Understand not necessarily the dynamically basic theories balanced. of static balancing and able to prove a statically balanced system is • Understand and able to statically and dynamically balance multiple-mass system. 

• Understand the mathematical theory behind dynamic rotor balancing. 

• Understand and able to experimentally determine moments of balances. 

• Able to apply theory and measurement to determine the angles and positions for balances. 

• Conduct literature research to understand vibration measurement for imbalanced rotors. 

• Using background research, theory and experiment to advise design. 

DESIGN EXERCISE BRIEF 

Unbalanced mass on a rotational system will cause the manifestation of a centrifugal force. This force is related to the rotational velocity of the rotary system. An unbalanced rotational system might result in vibrations on the entire system. Hence, while imbalances are insignificant for applications where rotational velocities are low, the thus induced vibrations in fast rotating systems can be catastrophic. Therefore, it is important for engineers working with rotational systems such as wheels of vehicles and rotating parts in motors, to understand the principles behind rotor balancing. 

CLIENT REQUIREMENT (to be completed in own time as part of report, after timetabled session) 

An automotive maker wants to introduce a wireless pressure sensor into the tyre of automobile wheels. For an 18-inch diameter wheel, assuming the pressure sensor, weighing 50 grams, is mounted at a radial position of 8 inch from centre. A transmitter also needs to be introduced to the wheel, weighing 120 grams, mounted at a radial position of 4 inches from centre and a relative angular position of 0.3 radians from the sensor. The sensor and the transmitter are position 1 cm apart from each other along the shaft axis. Calculate and design a single counterbalance for the wheel to ensure dynamically balanced rotor. 

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ME2050 Dynamics and Control Rotor balancing lab and design exercise 

STATIC AND DYNAMIC ROTOR BALANCING: PART I (You should aim to complete part I within 1 hour) 

THEORY 

Figure 1.1: 2-mass system. 

For two masses shown above, one mass attemps to induce a clockwise turn while the otherwise mass tries to result in a counter-clockwise turn. When the moments of both are balanced, static equilibrium is achieved as shown in the below equation. 

(1) 

However, this system is NOT dynamically balanced (as you will see, experimentally). 

The same principle applies for three mass systems and four mass systems as shown below. 

(2) 

(3) 

Figure 1.2: Graphical representation. 

The angle can also be determined by vector diagrams. Therefore, for a 4-mass system, if two of the vectors are known, the angle of the other two can be graphically determined if we know the moments (vector magnitude) of the third and fourth balances (using compass). 

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ME2050 Dynamics and Control Rotor balancing lab and design exercise 

Figure 1.3: Vector diagram method. 

EQUIPMENT 

A base holds the test unit. A shaft is attached to a rotor at its end. For dynamic tests, a small motor turns the rotor through a rubber belt. The motor will not operate when the protective dome is not in place. Up to 4 balance blocks can be added to the shaft. Circular blocks with different hole sizes (and therefore, different masses) can be add/removed from the rectangular blocks by a small stud. Take care not to misplace the small studs and Allen keys. The assembly includes a horizontal scale and a slider for accurately positioning of the balance blocks, which can be tightened to position by a large Allen key. A protractor on the pulley/rotor helps to determine the angular position of the balance blocks. An extension pulley and a short shaft is also included for measuring the moment of each balance block. When hanger is used with the extension pulley, vertical clearance is required (hanging off the side of the table). Two locking clamps are to be used during static balancing (when motor not running) in order to fix the platform; and the two locking clamps loosened during dynamic tests in order to allow the platform to vibrate. Do not run the unbalanced rotor for extended periods of time, or vibration can start to wear the apparatus. 

Figure 1.4: Rotor balancing experimetnal kit. 

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ME2050 Dynamics and Control Rotor balancing lab and design exercise 

EXPERIMENT PART I – TWO MASS SYSTEM 

• Remove the protective dome. 

• Remove care on not all misplacing balances from all components the shaft and including remove the the different studs. circular masses from the blocks. Take • Fix locking clamps for static tests and remove the rubber belt. 

• Use horizontally the shaft/rotor. glider, horizontal apart You and will 180 scale find degrees and the shaft protractor relative always to on turn each the back apparatus other. to When one to position. fix just 2 one balance mass masses is fixed, at try 120 to turn mm • When now statically both masses balanced. are fixed, note that the shaft will remain in position at any angle. The system is • Undo the locking clamps, turn them away from the assembly and retighten them. 

• Refit the rubber belt and place the protective dome; and activate the motor for a brief period. 

• Observe being statically that vibration balanced, can the be system seen in is the not system, dynamically denoting balanced. dynamic imbalance. Therefore, despite • However, changing the relative the it horizontal is relative possible angle distance to dynamically between to zero. the two balance blocks this (still system 180 degrees with the at two odds balances with each given. other), Without bring EXPERIMENT PART II – THREE MASS SYSTEM 

• Repeat brought the together above to procedures act as 1 large for the single below mass). three-mass configuration (note, two masses are • Because the centre block has two times the mass, the sum of moments still balances out. 

Figure 1.5: 3-mass system. 

• • Remove platform the The platform above locking not configuration to to vibration be clamps fixed by to (if is be locking both unbalanced). used statically during clamps and static during dynamically balancing dynamic test balanced testing (as the (when (no base vibration). using is not motor) strictly to firm) allow and EXPERIMENT PART III – FOUR MASS SYSTEM 

• Now, based on knowledge learned so far, arrange a four-mass system which is 

o Statically and dynamically balanced 

o Statically balanced but dynamically imbalanced 

• It can be noted that all dynamically balanced systems are statically balanced, but the vice versa is not necessarily true. 

By the end of the experiment, please replace all components of the apparatus, including refitting the circular mass (with different holes) back into the rectangular blocks. 

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ME2050 Dynamics and Control Rotor balancing lab and design exercise 

STATIC AND DYNAMIC ROTOR BALANCING: PART II (You should aim to complete part II within 2.5 hours) 

INTRODUCTION 

For a given unbalanced rotational system, it is typical to either add or remove masses at precise angles and positions in order to balance the rotational system. While it is tempting to use trial and error to determine the unbalance and adjust the balances to compensate for simple systems; it is virtually impossible for more complicated systems in the real world. 

Therefore, a good understanding and ability to apply theory to an unbalanced rotor, can help to predict the precise angle and position required for the balances. Building upon the introduction to rotor balancing in the previous lab (Simple Rotor Balancing), this lab intends to introduce the theoretical basis for experimentally measuring and then calculating the angles and positions of balances. 

THEORY 

A two mass system below can be statically balanced, but not dynamically balanced. 

Figure 2.1: 2-mass system. 

Although the moments of the two masses can be balanced statically, the additional twisting moment induced during rotation cannot be balanced. 

The centrifugal forces: 

(1) 

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ME2050 Dynamics and Control Rotor balancing lab and design exercise 

Three mass system on the other hand, is possible to be both statically and dynamically balanced. 

Figure 2.2: 3-mass system 

Taking moments in respect to mass 1: 

(2) 

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ME2050 Dynamics and Control Rotor balancing lab and design exercise 

For four mass systems: 

Figure 2.3: 4-mass system 

Again, moments in respect to mass 1: 

Horziontally (3) 

Vertically (4) 

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ME2050 Dynamics and Control Rotor balancing lab and design exercise 

The moments are directly portional to the centrifugal forces. In the experiment, the parameters are designed so that values for these two are equaly. Therefore, 

Horizontally (5) 

Vertically (6) 

By finding moments of each balance, drawing vector diagrams and using above equations, the angular positoon and the horizontal position of the balances can be determined to achieve dynamic balance. 

EQUIPMENT 

The equipment is same as that used in the previous experiment (Simple rotor balancing). However, in this experiment, the circular mass blocks are to be used. Therefore, all four blocks are of different masses. Additionally, the pulley extension, weight hanger and weights are to be used. The weight hanger itself weighs 10 g. Weights of 10 g and 1 g can be found. 

Figure 2.5: Mesauring moment. 

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ME2050 Dynamics and Control Rotor balancing lab and design exercise 

PROCEDURE 

Figure 2.5: Results table 1 

• Experimentaly determine and fill the values in the above table. 

o Insert the extension pulley and hang weight from the cord. 

o Tighten 1 block to the shaft at precisely 0 degree. 

o Hang weights from the pulley until the block reaches equilibrium at 90 degrees. (remember 

to use the 1 g weights too) 

o Adding 1 g in addition to the equilibrium will result in the free fall of the weight from the 

pulley. 

o Repeat the same for each weight (one at a time), until all moments are determined. 

• From the table below, initial angles and positions for blocks 1 and 2 are given. 

Figure 2.6: Results table 2 

• Use the theory to calculate and predict the angle and position for blocks 3 and 4. (note, depending on position of the block relative from block 1, value can be negative; which implies that block is on the left-hand side of block 1. Therefore, the order of the blocks is not necessarily in numerical order 1, 2, 3 and 4. 

• Hint: use the vector diagrams learned from the theory in the previous lab. 

• Experimentally fix the blocks with your calculated prediction and validate if the system is balanced. 

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ME2050 Dynamics and Control Rotor balancing lab and design exercise 

VIBRATION DURING ROTOR BALANCING (literature review exercise as part of report, in own time after timetabled session) 

Throughout the experiment, the reference for observing if the system is dynamically balanced is through visual inspection and detection of vibration. However, this is not a scientific way of measuring vibration. 

For the report, conduct a background literature review of various types vibration measurement sensors and analysis techniques in order to help more scientifically determine the vibrational levels of imbalanced rotors. Consider how to distinguish background vibrational noise from genuine imbalanced induced vibration signal. 

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