Back to basics: Machine vibration and components to address it

Machine vibration is a normal, and typically unavoidable, result of moving and rotating parts, often caused by standard manufacturing and assembly tolerances that lead to clearances between mating parts or imbalances in rotating parts. And while routine machine wear can cause vibration to increase over time, when a machine experiences a significant or sudden increase or change in vibration, this can be an indicator that something is wrong and the machine or its components are being subjected to increased forces, loss of stiffness, and premature wear.

Although it’s not difficult to detect when vibration is approaching (or has reached) detrimental levels, pinpointing its causes can be challenging, since numerous components and operating factors contribute to a machine’s vibration. But an analysis of the vibration’s frequency and amplitude can help engineers and technicians root out the causes of worrisome vibration and determine its severity.

Machine vibration frequency: Frequency indicates the number of times an object oscillates, or vibrates, per unit of time and is often expressed in either cycles per second (referred to as Hertz, Hz) or cycles per minute (CPM). Frequency is probably the most fundamental parameter in machine vibration analysis. It is especially useful for narrowing down the potential causes of vibration, since every part vibrates at a distinct frequency or frequency range.

Machine vibration amplitude: Amplitude defines the magnitude of the machine’s oscillation and is used to judge the severity of the vibration. Oscillations with large amplitude indicate that the vibratory movements are large, fast, or forceful, resulting in more stress on the machine, components, and structure. Amplitude can be measured and specified for three aspects of oscillation: displacement, velocity, and acceleration.

Displacement amplitude: Displacement amplitude measures the distance the vibrating part travels in one direction from a reference position during oscillations. (Note that the peak-to-peak displacement value, which measures total travel in both directions, is sometimes used.) This vibration measurement is important because vibrations with a high displacement amplitude can cause machine components to exceed their yield point and experience catastrophic failure. Displacement measurements are typically used when vibration frequencies are low.

Velocity amplitude: Velocity amplitude measures the speed of the oscillation. This measurement is typically considered the industry standard for evaluating the condition of a machine based on its vibrations, because it takes into account both vibration frequency and displacement. (Recall that velocity is the rate of change of displacement.) In fact, ISO standards refer to velocity amplitude when specifying the severity of machine vibration. Velocity amplitude can be expressed in terms of peak value or, more often, in terms of the root mean square (RMS) value, which is an indicator of the vibration energy.

Acceleration amplitude: Acceleration amplitude is directly related to the force imparted by the vibration and is especially useful for assessing the likelihood of fracture for equipment that rotates at high speed. The high forces associated with acceleration can also cause lubrication breakdown, which can lead to excessive wear, heat, and premature failure. Acceleration is typically measured in g or multiples of earth’s gravitational acceleration.

HOW FAST FOURIER TRANSFORMS ARE USED IN VIBRATION ANALYSIS

Fast Fourier transforms are mathematical calculations that transform, or convert, a time domain waveform (amplitude versus time) into a series of discrete sine waves in the frequency domain.

Machine vibration is typically analyzed with measurements of the vibration frequency, displacement, velocity, and acceleration. The latter three — displacement, velocity, and acceleration — are time domain measurements, meaning their amplitudes are plotted versus time. But these vibration signals contain useful information, such as noise and harmonic content, that are difficult or impossible to detect when their amplitudes are plotted in the time domain.

However, when displacement, velocity, and acceleration amplitudes are expressed in the frequency domain —that is, amplitude versus frequency — abnormalities, in the form of high amplitudes at certain frequencies, become visible …

… and because many vibration-related issues occur at specific frequencies, the cause and location of the vibration can be narrowed down or identified based on variations in amplitude at certain frequencies.

Note: A time domain plot is referred to as waveform, and a frequency domain plot is referred to as a spectrum.

Every waveform can be expressed as the sum of simple sine waves with varying amplitudes, phases, and frequencies. A Fourier transform is a mathematical process that converts a time domain waveform into these individual sine wave components in the frequency domain — a process often referred to as spectrum analysis or Fourier analysis.

To understand fast Fourier transforms, it’s helpful to first understand the underlying process, known as discrete Fourier transform (DFT). A discrete Fourier transform tests the time domain waveform for discrete, or individual, frequencies based on the length of the signal (N). The number of frequencies, or samples, required is equal the signal length squared (N2). Even for small signals, this can take significant time and computing power. To make the Fourier transform faster and more efficient, a method known as the fast Fourier transform is used.

Fast Fourier transforms (FFT) significantly reduce the number of complex calculations that must be undertaken by assuming that N (the length of the signal) is a multiple of 2. The underlying mathematics of this assumption eliminates redundant calculations and those that have no value (multiplying by 1 for example) which provides significant computational efficiencies and reduces the number of required samples to N·log2(N) — an amount significantly less than N 2 . This allows fast Fourier transforms to provide close approximations of the more timeconsuming discrete Fourier transforms, but with significantly faster computing time.

The sampling rate must be greater than the highest frequency component of the signal to ensure the sampled data accurately represents the input signal, according to the Nyquist sampling theorem.

The instrument for analyzing signals via fast Fourier transforms is the digital signal analyzer (also referred to as a spectrum analyzer). This device captures the vibration signal, samples it, digitizes it, and performs the FFT analysis. The resulting FFT spectrum helps pinpoint the location, cause, and severity of the vibration, based on the amplitude of the displacement, velocity, and frequency spectra.

COMPONENT TYPES USED FOR VIBRATION AND SHOCK MITIGATION

Most shock absorbers common in industry achieve their damping characteristics through the use of hydraulic fluids. The fluid is pushed by a piston and rod through small orifice holes to create damping, and this action compresses some type of gas. This in turn creates a spring force to return the rod back to its starting position when the load is removed.

Shock absorbers and dampers are generally made of high-strength steel to handle the pressures from the internal hydraulic forces. Elastomeric seals prevent the fluid from leaking out of the cylinder, and special plating and coatings keep the units protected from harsh operating environments.

Recent and ongoing developments in sealing technologies and in the internal designs of shock absorbers and dampers have allowed for longer service life and more compact designs. Miniaturization is a growing trend in these devices, as systems require tighter tolerances and smaller machine footprints. In machine automation and robotics, motion stabilization requires the use of hydraulic dampers, particularly microhydraulic designs.

In contrast, most vibration isolation products rely generally on mechanical designs to achieve their isolation characteristics. A spring function provides support for the mounted equipment, while decoupling it from the vibration source. Friction and elastomeric material properties give the isolators their damping characteristics.

Isolators can be made from a variety of materials. Wire rope and spring isolators can be made from carbon steel, stainless steel or aluminum. Elastomeric isolators generally have metallic components that function as mounting brackets, separated by an elastomeric material that provides the stiffness and damping desired. Common elastomeric compounds include natural rubber, neoprene and silicone; however, a vast selection of compounds and compound blends can be used to achieve different characteristics specific to the application.

Air springs are comprised of metallic end fittings coupled by a composite elastomericbased bladder that contains the compressed air used to provide isolation. These single-acting designs are comprised of a pressurized bladder and two end plates. As air is directed into the air bladders, they are expanded linearly.

All of these reusable designs are selfcontained, offering a number of advantages over any other technology that may require outside componentry. For example, hydraulic systems may require plumbing while electrical systems may require wiring and power.

Energy or power dissipation is key when selecting a damper or shock-absorbing device. The size and characteristics of the device are based on these inputs, so it is generally the first consideration to make.

Dynamic spring rate and damping are the two biggest considerations when selecting an isolator. These characteristics will define the natural frequency (sometimes referred to as resonant frequency) of the isolation system and are important in achieving the desired performance.

Gas springs, also called gas dampers, tension springs and gas-pressure springs depending on the setup and context, are compressed-air or oil cylinders that install in motion designs to damp forces and return kinematic linkages and more complicated assemblies to default positions. Gas springs work through a piston on the end of a rod that protrudes from a steel cylinder body; usually compressed gas (often nitrogen) within the cylinder exerts force on this piston to reassume and maintain set positions. Nitrogen is common here because it’s inert and nonflammable. In such designs, oil or grease between the piston and other contacting parts minimize friction. In fact, the small amount of oil in these gas springs serves another function — to further damp and gently decelerate gas springs during full extension or compression. Some setups even include a fine hole in the piston for damping that’s still slower than with other designs; such slow-damper springs are common on safety gates and doors.

In contrast, extended-reach gas springs usually leverage telescoping mechanisms pairing multiple cylinders on one rod; then the smaller cylinder extends from within the larger cylinder. Consider one particularly long-stroke application: Passive heave compensators — systems on ships or offshore oil-rig systems that reduce the effect of waves on engineered structures — use gas springs with strokes to many meters long.

Still other gas-spring applications include those for medical beds and hoists; industrial equipment such as machinetool presses; off-highway and automotive equipment for hatches, hoods, and covers; office equipment and furniture; and general strut and support applications. Fast-acting gas springs find use in weaponry and aerospace design. Specific variations include gas springs with standard or fixed-height cylinders; spindle-only designs; and cable, return, adjustable auto-return, nonrotating, stage, and multi-mode cylinders.

Elastomer and other synthetic and rubber pads can also damp vibration and isolate shock loads. They are available in a number of shapes, including tubes, bushings, blocks, pads and washers. These components are commonly used in heavyduty applications to create strong cushioning plates or foundations in heavy machinery such as cranes, presses, and also for vibration reduction in lab and testing equipment, aerospace, and for pipelines and bridges.

The rubber-like materials with which they are designed allow these padding materials to meet specific requirements, such as natural frequency, load, and area. And because they are soft, they are forgiving in most environments.

Predicting the natural frequency of an application lets material manufacturers target known disturbance frequencies to dissipate energy. The lower the ratio of natural system frequency to disturbance frequency, the more it’s possible to isolate problem vibrations.

These cushioning plates can protect machinery subsystems against impacts and isolate vibration and structure-borne noise. For example, PAD plates from ACE Controls withstand compressive loads to 10,000 psi (69 N/mm 2) depending on plate form and size.

Another custom product called Sorbothane (from a company with the same name) is a thermoset that attenuates shock with near-faultless memory. That means its deformation is elastic and not plastic, so pads of the material reliably return to their original shape. Custom pieces of the material work for vibration damping, acoustic damping and isolation. Sorbothane works by turning mechanical energy into heat as the material is deformed. Molecular friction generates heat energy that translates perpendicularly away from the axis of incidence.

APPLICATION EXAMPLE: HOW AN ARBOR CAN REDUCE MACHINE TOOL VIBRATION

On a typical machine tool, the tool that performs the machining operation (cutting, milling, or boring, for example) is attached to a rotating spindle that drives the tool. But on machines that require long machining lengths, such as milling and boring, the tool is mounted to an arbor. The arbor is driven by the spindle and provides the necessary length for the tool to reach the workpiece in these operations.

Horizontal milling machines are often referred to as “arbor milling machines” because their design requires the use of an arbor to achieve the proper tool position.

In machining processes, vibration can cause poor surface finish and machining accuracy as well as noise and reduced tool life. But machining operations require high forces and high rotational speeds, which naturally induce vibration.

Short of changing the part requirements or modifying the machining setup — unrealistic solutions in most cases — the most common way to reduce vibration in machine tool operations is to slow the machining rate. But a slower machining rate means fewer parts produced in a given amount of time (parts per minute, day, or hour) and lower productivity.

However, one factor that affects the amount of vibration at the tool is relatively easy to modify. This factor is the design of the arbor — particularly its rigidity. The arbor’s rigidity is especially important when the machining length is long and the arbor has a high length-to-diameter (L/d) ratio — also referred to as overhang.

To address the problem of vibration in machine tools, some manufacturers have even developed vibration-damping arbors that significantly reduce vibration, allow longer machining lengths (L/d ratio of 8 or greater), and cut down on machining times.

While each manufacturer uses a proprietary damping technology, most vibration-damping arbors are based on passive tuned mass damping systems — consisting of a mass, a set of springs, and a damper. Multiple springs (or, similarly, several materials with frequencydependent stiffness) are used to address various frequencies that occur during machining.

The frequencies of the tuned mass damping system are designed to match the structural frequencies to be eliminated. So when any of the specified frequencies is excited, the damper resonates out of phase with the structure, absorbing or dissipating the kinetic energy caused by vibrations.

“Connected” versions of vibration-damping arbors have also recently become available. The connected arbor designs have embedded sensors and use Bluetooth or other wireless technology to transmit tool performance data — such as temperature or cutting status — to a dashboard. This insight is especially helpful for internal machining processes that can’t easily be monitored or inspected, such as boring or internal turning.

Manufacturers indicate that machine tool vibration amplitudes are up to 1,000 times lower when using a vibrationdamping arbor versus a standard arbor. This allows machining rates to be increased — leading to significant productivity improvements without sacrificing machining quality or tool life.