Torsional Vibrations

In document Coupling Handbook (Page 60-82)

One class of coupling applications is unique in that a secondary load is transferred through the power transmission system and the equipment connected to the system. That secondary load is torsional vibration. Torsional vibrations are associated with internal combustion engines, reciprocating (piston) type compressors, vane passing frequencies of some centrifugal pumps, grinding mill drives, kiln drives, rolling mill drives, variable speed motors, and the start up of synchronous motors.

Diesel engines represent the most significant unit volume of torsional coupling applications, and will be discussed in separate detail later.

One class of coupling applications is unique in that a secondary load is transferred through the power transmission system and the equipment connected to the system. That secondary load is torsional vibration.

Torsional vibrations are associated with internal combustion engines, reciprocating (piston) type compressors, vane passing frequencies of some centrifugal pumps, grinding mill drives, kiln drives, rolling mill drives, variable speed motors, and the start up of synchronous motors. Diesel engines represent the most significant unit volume of torsional coupling applications, and will be discussed in separate detail later.

Torsional vibrations cause equipment breakdowns such as wear or chatter on loose connections like spline pump shafts, or complete fatigue failure of the shaft or some other element. These harmonic torsional pulses are difficult to detect, because they do not bounce the equipment up and down, as would a lateral vibration. Nor can they be felt by touching the equipment.

Usually, the result of the vibrations is known before the vibration is known. Often something else is blamed.

If the torsional vibratory frequency matches a system torsional natural frequency, the system reaches a harmonic or becomes resonant. That's because the natural frequency is an energy balance point at which additional forces will set off uncontrolled vibration. From a technical standpoint, it is the frequency at which the kinetic energy of spinning inertia blocks is equal to the potential energy of the torsional spring connecting the inertia blocks.

In such systems, inertia blocks can be impellers, pistons, mill rolls, motor rotors or any other device that is mounted on the shaft, which all rotate together as a single wheel. The torsional spring is a combination of the shaft and coupling's flexible element, plus other potentially flexing components such as a spacer or floating shaft.

When the wheel and spring rotate as parts of the same system, the inertia of the spinning wheel is balanced against the windup of the spring. Any additional forward pulsing force on the wheel will cause the spring to windup more and that will in turn react with a reverse force to the wheel. Between pulses, when that additional force is removed the spring unwinds, and the wheel surges forward. When the pulsing force returns, the spring winds up again, reapplying the reverse force to the wheel, etc. That pulsing force which is being applied at some time cycle or frequency at or related to the operating RPM, is

the torsional vibration. If the timing is right, the winding and unwinding of the spring and the energy changes in the wheel resonate back and forth. The point where the timing is right is the system's natural frequency.

Determining the Natural Frequency

All rotating systems have a torsional natural frequency. It is a function of the driven inertia, driver inertia and the torsional stiffness of the shaft, spacer and/or coupling connecting the two. There is a natural frequency for each combination of inertia and spring. Aside from the kinds of torsionally sensitive systems discussed in this section, most systems have torsional natural frequencies so high as to be inconsequential. By itself, the natural frequency is harmless and does not generate torsional vibration, but is simply a sensitive spot along the systems RPM curve. It is a "forcing frequency", i.e. it is not self-initiating or self-sustaining, rather it must be triggered by a vibratory force pulsing at that frequency.

Many systems can be reduced to a two-mass system. For a two-mass system, the frequency can be determined mathematically from the following equation.

CPM= (60/2π) SqRt (Ctdyn x (JA + JL) / (JA x JL))

CPM is the frequency in "cycles per minute".

JA is the polar inertia of the driver JL is the polar inertia of the driven

Ctdyn is the dynamic torsional stiffness of the coupling.

60/2π is a constant.

Reducing a system to a two-mass system is done by lumping inertias connected by torsionally stiff shaft elements. For example the lumped polar moment of inertia of the driver JA and the lumped polar moment of inertia of the driven equipment JL are determined by adding all the individual inertias that are connected by stiff shafts. When a gear reducer or increaser is involved, the downstream inertia must be factored by the square of the gear ratio (speed). It is an inverse function.

A coupling is between the driver and the driven. The coupling stiffness Ctdyn is obtained from the coupling manufacturer. It is called the dynamic torsional stiffness, which is higher than the static torsional stiffness.

Inertia is marked by the symbol "J", the units in the English system are inch-pounds second squared. It is related to WR2 by

"g" the acceleration due to gravity. For a method of calculating the inertia value and the stiffness of connecting pieces refer to AGMA Standard 9004.

In a multi-mass system that includes more than two inertias connected by torsionally soft shafts, couplings, or sections, the natural frequency can be determined using the Holzer method. Refer to a textbook for an example of the Holzer analysis.

As long as the torsional natural frequency is more than 40% above or 30% below (.7 Nc to 1.4 Nc, where Nc is the critical numerical value) the system's operating frequency or idling frequencies (RPM) or associated torsional vibration frequencies (CPM) no resonance problems should occur. If it is in between those values there is a good chance the system vibratory response will cause damage to one or more components. If it is close to any of those frequencies, resonance is likely to occur.5000

Campbell diagrams are graphic plots of operating speeds and pulse frequency. They are used to identify the potential trouble spots where operating or idle RPM is equal to a torsional pulse frequency in CPM, (cycles per minute).

If it is decided to operate the system normally at an RPM above the torsional critical speed, (natural frequency) then the driver must have enough torque available to accelerate the load quickly through the critical speed zone (RPM). Comparing the speed torque capabilities of the driver and the load will determine the system's ability to accelerate through the critical zone quickly enough.

Using the Coupling to Tune Critical Frequency

In the torsionally sensitive system, couplings take on an important extra role beyond the transfer of driving torque and the handling of misalignment. They have the ability to move the natural frequency away from those levels that will be occupied by the torsional vibratory frequency at normal operating or idling speeds. This is called "tuning" the critical frequency. It works as long as the coupling is the controlling element for the critical frequency. That is not the case when long slender shafts are in the torque path. They also can be used to damp the energy of torsional vibration to reduce its potential for damage. The coupling torsional stiffness/softness is an attribute that is important in serving these functions.

Couplings with the highest levels of torsional stiffness are not used here. Those designs primarily serve systems that must transfer motion without windup or backlash, as previously discussed under motion control. Torsionally soft systems have a normal operating speed above the torsional critical speed while torsionally stiff systems have a normal operating speed well below the torsional critical speed. Because the coupling is usually the softest torsional element in either system, the system tends to be stiff when the coupling has a relatively high torsional stiffness and soft when the coupling has relatively high torsional softness.

Stiff couplings have elastomers of the Zytel® and Hytrel® type of plastic or their flex elements are metal. Soft couplings are rubber elastomers in compression or in shear.

Changing to a torsionally stiffer coupling raises the system's natural (critical) frequency, and reduces or eliminates the coupling's capacity to damp vibratory energy.

Using stiffer couplings to drive the critical frequency above the operating speed is as effective on simple systems like a single hydraulic pump driven by a diesel engine as it is on sophisticated high-speed couplings that are found on turbine driven rotating equipment.

When the coupling is used in the regimen of keeping the critical frequency high, it is usually just a matter of making sure the coupling is sufficiently torsionally stiff. That could be accomplished by using a stiff spacer piece with a metallic-element coupling, or by using a very stiff elastomeric element on a flywheel coupling. The coupling manufacturer can provide the necessary information on coupling and spacer piece stiffness.

An exception would occur when a system has a long slender shaft, which usually means the lowest critical frequency would be the result of that shaft. That type of system can become complex because the coupling is no longer the element that controls the stiffness.

The torsionally stiff elastomeric coupling and the torsionally stiff metallic element coupling offer no damping between the driver and the driven equipment. That means torsional vibrations are passed into the driven system. In such stiff systems, loose parts or parts with backlash will vibrate and rattle, and may have wear problems. Typically spline shafts on hydraulic pumps and gears with backlash suffer the wear.

Changing to a torsionally softer coupling lowers the system's natural (critical) frequency, but also may increase the coupling's capacity to damp vibratory energy, so that function and the heat it will generate through hysteresis needs to be considered in the selection. Elastomeric couplings expected to damp torsional energy must be designed to reject the resulting heat to a heat sink. Otherwise the heat will fail the elastomer by melting from the inside out.

Elastomeric torsional couplings can be either compression type or shear types. The more common compression types are of the donut or torus configuration. However, some use elastomer blocks or elastomer cylinders. The compression block types are most often found in the high torque applications. The shear types are shaped to equalize stresses from torque and misalignment.

Torsional softness and torque capabilities are opposite coupling characteristics. A soft coupling tends to have lower torque capabilities than similar sizes of stiff couplings. The softer, lower-torque couplings generally are used on applications that require 100 HP at 2,000 RPM or less. Torque capability increases with torsional stiffness of the flex elements.

The coupling designer must balance the various attributes to achieve the desired coupling for the specific application, or to devise a coupling with broad capabilities as a standard unit that serves many applications. Dual stage torsional couplings can also be obtained. They incorporate two different elements. One is soft for low or idle speed and a stiffer one for high or operational speed.

Some torsional coupling types utilize viscous friction damping This method is found in hydraulic torque converters, which mechanically isolate the driven system from the driver, and transmit torque between them through the motion of a viscous fluid. When a system uses a torque converter, it becomes two separate torsional systems. Torsional vibrations do not pass through the torque converter, except when a lock up device is engaged to mechanically connect the two halves. Hydraulic torque converters are not included in this handbook's discussion of flexible couplings.

Refer to the torsional coupling section and the metallic element section of this handbook for a more detailed description of the couplings used to damp torsional vibration and/or tune critical frequencies. Also refer to the bibliography for more publications on this subject.

Torsionally Sensitive Systems

Torsional vibration problems appear primarily in four types of applications briefly discussed here.

High Speed Machines

High-speed machines have torsional pulses or vibrations at high frequencies, therefore the natural (critical) frequencies must be kept even higher. A discussion about high-speed special purpose couplings and

the associated equipment torsional problems can be found in many of the coupling textbooks. They are a sophisticated coupling application, which is not covered in this handbook.

Variable Frequency Drives

The VFD will produce a torsional pulse at low speeds that is larger than those generated at faster speeds. Keeping the operating speed above 10% of the maximum speed, i.e. no lower than 90% below maximum will alleviate the problem in that type of system.

Synchronous Motors

Synchronous motor start-up is a unique situation. At start-up the motor produces torque pulses at a frequency equal to two times the slip frequency. (Slip frequency is numerically equal to full synchronous speed minus operating speed.) The magnitude of the pulse is related to the torque developed by the motor. As the unit accelerates to full speed, the torque pulses drop in frequency reaching zero at full synchronous speed. The torsional vibrations or vibratory torque ceases at that point. A problem will occur if a torsional natural frequency is less than two times the AC power line frequency, as the start-up torque pulse frequency must then pass through the critical frequency. When going from startup to the running speed the driver must accelerate the load through the critical speed quickly. Acceleration through the critical frequency is a function of the torque available from the motor at starting.

High torque synchronous motors will also have high vibratory pulses that need the damping of torsionally soft couplings, but soft torsional couplings have a high vibratory response when passing through the critical speed, as well as difficulty carrying the high torque loads. The relationship between the two functions therefore must be a compromise. The coupling must be soft enough at startup to dampen some torsional vibration energy, but stiff enough to carry the high torque at running speed.

Reciprocating Internal Combustion Engine Drives

There are three main types of engines in common use. They are gasoline engines, gas engines (natural or LPG or propane or

other), and diesel engines. Gasoline and natural gas engines are spark-ignited low cylinder pressure types as compared to the compression-ignited diesel engine, which requires very high cylinder pressure.

The diesel is the most efficient of the three so it is very popular for continuous duty applications in those regions of the world that have high fuel prices. Gas engines (Natural, LPG or Propane) are most popular where these gases are readily available or where air pollution is a serious problem like the inner cities.

All internal combustion engines generate a torsional vibratory pulse. The magnitude of the pulse is a function of the cylinder pressure, turbo charging, engine's displacement, internal damping, the engine geometry, and whether it is a two or four stroke engine. The diesel drive rotating system accounts for the majority of the torsional vibration problems due to its high cylinder pressures and resulting high magnitude of torsional harmonic pulse compounded by its widespread popularity. The engine itself is designed to tolerate its internally generated forces from torsional vibration and may include some internal damping. The problems start when these harmonic vibrations pass to the driven equipment. Special attention must then be given to selecting couplings that can help reduce these problems

Diesel drives range from the simple low-horsepower single-unit hydraulic pump to a marine installation in which the diesel will drive the propeller and generators through a gear reducer. The preponderance of diesel drive systems can utilize a simple analysis to select the right coupling, however the marine system should be analyzed by an expert in that field.

While the magnitude of the torsional pulse is important, it is also necessary to know the frequency of the pulse. Like magnitude, pulse frequency is dependent on many factors. Those factors can include the number of cylinders, the configuration, such as "V" or inline, the stroke (two or four) and the firing order.

Also note that diesels typically have several torsional pulse frequencies, established at harmonic intervals. A 6-cylinder 4-stroke inline engine will have major harmonic orders of 3 and 6. Pulse frequencies are the RPM multiplied by the order. For example an engine running at 2100 RPM will have pulse frequencies of 6300 and 12600 CPM. If the natural frequency were also 6300 or 12600 CPM, the engine should not be operated at 2100 RPM. Note the frequency in CPM and speed in RPM is the same units in this case.

If any of the torsional frequencies are equal to a natural frequency the system will vibrate at resonance.

Coupling Selection for Torsional Systems

In addition to the damping possibilities, the coupling is selected with three torque values in mind. The first would be the continuous running torque. The coupling should be capable of handling this torque under all environmental conditions of the applications. The second is continuous vibratory torque. The coupling should damp this torque without a meltdown from heat generation. The third is the maximum torque pulse or peak torque. The pulse occurs as a vibratory response torque at critical speed. The coupling rating is a fatigue life in that case. The manufacturer will publish the torque value at 100,000 non-reversing cycles.

Continuous Running Torque

This is the design torque for the system. Usually it is the driver horsepower and operating speed. That value is normally in excess of the load requirements or is tied closely to the load requirements. Since the coupling also will be judged against peak or maximum transients in the system, a service factor is redundant except for high starting torque. Couplings that are oversized by using service factors can also be too stiff. Elastomer couplings may require derate factors on the coupling capabilities for temperature or frequency or speed. A derate factor is not a service factor. For more discussion on the various torque values found in an operating system see the chapter called "Applications ".

Maximum or Peak and Vibratory Torque

It is important when analyzing the torsionally sensitive coupling application to know the value for the generated vibratory torque. That value becomes the forcing torque that puts the natural frequency into critical resonant vibration. In a diesel drive system the torque pulse is a function of cylinder pressure, number of cylinders, use of turbocharging, number of strokes for firing, etc.

Lloyds Register of Shipping publishes a pamphlet that is a good source of harmonic pulse factors used to determine the harmonic vibratory torque of diesel engines. The engine manufacturers could also provide the information. The manufacturers of other drivers or driven equipment should be able to provide the similar forcing torque values for their equipment.

Once the initial pulse torque is known, it is then possible to calculate the values for the vibratory response.

Once the initial pulse torque is known, it is then possible to calculate the values for the vibratory response.

In document Coupling Handbook (Page 60-82)