Not-So-Good Vibrations

     The effects of vibration are closely related to those of thermal conditions and noise.  Any combination of these factors can exacerbate effects that may be caused by exposure to any one in the absence of the others.
     Aspects of vibration that are directly related to the generation and transmission of sound were introduced in the “Occupational Soundscapes” series.  There are, however, ramifications of vibration that are unrelated to noise or hearing loss.  It is these non-noise-related concerns to which this standalone entry of “The Third Degree” is dedicated.  In addition to its effects on humans, the effects of vibration on equipment and structures are also explored.  Causes and methods of control are also revisited to facilitate practical management of vibration sources.

Vibration “Defined”
     Even if unable to precisely define it, most people understand, implicitly, what vibration is.  Therefore, a detailed, technical definition is foregone in favor of a simplified description of key characteristics.  For purposes of this presentation, vibration is defined as “continuous, periodic, mechanical oscillations of small amplitude.”  This definition is used to differentiate it from shock, which is episodic and may cause relatively large movements; shock may also induce vibration in a system.  While shock and vibration are closely-related subjects, limiting the scope of this discussion to vibration maintains alignment with objectives of “The Third Degree” and the through-line of recent Safety, Health , and Environment (SHE)-themed material.
     Vibration types can be classified by two contrasting pairs of terms:  free vs. forced and sinusoidal vs. random.  A system’s response to a single energy input, or event, such as an impact, is free vibration.  This is a function of the physical characteristics of the system that define its resonant properties, including its natural frequency.  Free vibration is often associated with shock; thus, explicit discussion of it is limited to differentiating this type from forced vibration.  Similar control methods are applicable to both types, should they be required.
     Forced vibration is caused by a continuous source of energy (“forcing function”), such as that existing in rotating or reciprocating equipment.  It is a common issue in occupational settings in which powered mechanical machines are used and is, therefore, the primary topic of this presentation.
     Sinusoidal vibration results from a special case in which the forcing function is a pure tone (i.e. single frequency).  Industrial practitioners are unlikely to encounter such “pure” vibration, as experimental conditions are usually required to sustain it.  Thus, it adds little to the discussion of practical operational matters and this presentation will not pursue it in detail.
     In contrast, random vibration is the “natural state” of typical workplaces.  Each machine and vehicle in operation, every material transfer, and every activity adds vibration to the environment in which workers are immersed.  Perhaps it should be called the vibescape…

     Vibration can be quantified in several ways.  It involves the physical movement of matter; thus, the fundamental terms of motion apply:  displacement (distance in m, in, or ft), velocity (speed in m/s, in/s, or ft/s), and acceleration (in m/s^2, in/s^2, or ft/s^2).  Values can also be expressed as levels, analogous to the sound power level (Lp or SPL) used in noise surveys.  Vibration acceleration level, La, is calculated using the same logarithmic algebra:
     La = 20 log (a/a0) (dB) ,
where a is the RMS vibration acceleration and a0 is the acceleration reference value (1 μm/s^2 or 39.4 μin/s^2).  Likewise, vibration velocity and force levels can be calculated using, respectively, the reference values v0 = 1 nm/s (3.3x10-9 ft/s) and F0 = 1 μN (2.2x10-7 lbf).  [Note:  sources are less consistent on vibration level reference values than on sound level reference values; verify the reference value used when citing vibration levels.]

     The natural frequency of a system is the frequency at which free vibration results from an energy input (e.g. impact).  If a system is subjected to forced vibration at or near its natural frequency, resonance can cause destructive amplifications of inputs.  Avoiding this condition requires that a system’s natural frequency and forcing functions be known so that one or more can be modified to prevent convergence.
     A system’s natural frequency is a function of its mass and stiffness.  This relationship is modeled as shown in Exhibit 1 for a single degree of freedom (1 DOF = motion in one direction) system, the simplest type.  The general formula for a system’s natural frequency is

where k is spring stiffness (N/m) and m is mass (kg), or

where k is spring stiffness (lb/ft), g is acceleration due to gravity (32.2 ft/s^2), and W is weight (lb).  Natural frequency can also be determined by measuring static deflection, δ.  Substituting, the formula becomes

for deflections measured in centimeters (cm),

and for deflections in inches (in),

Real-world scenarios (i.e. multiple degree of freedom, or MDOF, systems) may require empirical determination of natural frequencies, as properties of complex systems can be difficult to measure.

Effects on Humans
     A wide range of effects may be experienced by vibration-exposed individuals.  An individual’s experience of vibration is influenced by several factors, including frequency, intensity, duration, and posture.  A model of the human body, subjected to whole-body vibration when standing or seated, is shown in Exhibit 2.  Approximate resonant, or natural, frequencies are given for parts of the body in Exhibit 2 (shown as f0) and Exhibit 3; these are to be avoided at all times to prevent serious injury.

     Performance effects include difficulty reading or concentrating and loss of fine motor control, such as that required for handwriting or precise manipulation of materials.  Physiological effects may include motion sickness, increased heart rate and blood pressure, and fatigue; severe exposures can result in tissue damage.
     When vibration is localized in the upper limbs, through contact with power tools, for example, it is called hand-arm vibration.  Extended exposure can result in numbness of the hands or fingers, loss of grip strength, finger blanching and reduced blood flow, tingling, and vascular and nerve disorders known as hand-arm vibration syndrome (HAVS) or Raynaud’s phenomenon (also called vibration-induced white finger, VWF).  Raynaud’s is most-often associated with vibration in the 25 – 150 Hz range; the ranges of frequencies associated with other vibration-induced sensations are shown in Exhibit 4.

     Preventing injury requires monitoring exposure to vibration and enforcing limits in a manner similar to that used for noise.  ACGIH has established guidelines for whole-body and hand-arm vibration to limit exposure to safe levels.  The curves in Exhibit 5 show the Threshold Limit Value (TLV) and Action Limit (AL) for whole-body vibration.  The TLV is the level of exposure that must never be exceeded; exposures below the AL are considered safe.  Exposures represented by the area between the two curves require mitigation efforts be undertaken, as individuals are at elevated risk of injury.  Exhibit 6 provides some discrete TLV and AL values as well as formulas for calculating intermediate values.

     TLV and AL values are weighted vector sums of accelerations along three orthogonal axes.  The coordinate systems used for standing and seated postures are shown in Exhibit 7 (supine, or recumbent position is also shown, but has little application in industry) and the associated frequency weighting curves are shown in Exhibit 8.  The vector sum of weighted whole-body accelerations is

this value can then be used to estimate the duration of exposure permissible before reaching the TLV (TTLV) or AL (TAL):

     The information for hand-arm vibration follows the pattern of whole-body vibration.  TLV and AL curves are shown in Exhibit 9; Exhibit 10 tabulates select values and provides formulas for the relationships between exposure duration and TLV and AL.
     Two coordinate systems for the hand are shown in Exhibit 11.  The basicentric coordinate system is based on a handle gripped by a user; applying accelerometers to a tool grip is a common measurement method.  The biodynamic coordinate system is based on the human skeletal structure, which is much more difficult to instrument.
     A single frequency weighting curve, shown in Exhibit 12, is used for all axes to calculate the vector sum of weighted hand accelerations:

The 8-hour energy equivalent vibration total can then be calculated:

where Tv is the duration of exposure and T0 is the reference duration (8 hours).  Exposures experienced while performing multiple tasks are summed for comparison to the AL and TLV.

Effects on Equipment and Structures
     The effect of vibration on a structure, such as a building, depends on the type of construction.  Crumbling of masonry construction may be accelerated, while a steel structure may resonate, causing intense noise or increased stress in its members.  A structure can also serve as a transmission path that allows vibration to cause problems for people or machines far from its source.
     Like people, equipment is affected by vibration in various ways.  Accuracy and repeatability of machine tools and robots may suffer.  Material transfer systems may be counteracted by vibrational forces, causing jams or other failures.
     Fasteners and electronic components are especially susceptible to failures caused by vibration.  Threaded fasteners, in particular, require special attention when subjected to significant vibration.  Sufficient preload must be attained in a joint to ensure that the fastener does not loosen unintentionally.  Higher preload then increases the risk of failure posed by any stress risers that exist in the fastener.  Strategically placed undercuts or other features that prevent abrupt changes in cross-section can minimize this risk.
     Vibration can break solder joints, causing components to separate from circuit boards.  In severe conditions, the plastic substrate may be overstressed, causing a crack that exposes internal circuitry to potential shorts.  Electronic failures often require extensive testing to identify, as the root cause may not be visible.  A cascade effect is also possible, where a short in one component or area of a board causes failures of connected or adjacent components.
     Vibration can accelerate degradation of equipment causing failures in shorter service intervals than expected.  The propagation of cracks is accelerated by vibration, as it increases the stress in a material.  Accelerated crack propagation could cause any of the types of failure discussed, whether in the smallest component or the largest structure.

Vibration Controls
     Much of the discussion of noise control in the “Occupational Soundscapes” series also applies to non-noise-focused vibration control.  The hierarchy of controls remains the guiding light for prioritization of mitigation efforts.  The source-path-receiver (SPR) model also remains a useful framework for seeking and prioritizing vibration controls.
     Controlling vibration at its source is often a function of equipment maintenance.  Ensuring that rotating equipment is balanced and that shafts are aligned comprise a relatively large portion of vibration control efforts in many facilities.  Verifying that all mounts are securely fastened and moving parts are provided required clearances to prevent collisions are also significant contributors.
     Similarly, vibration caused by reciprocating equipment can be tamed with a proper counterbalance.  However, the ability to add or “tune” a counterbalance is largely a function of a machine’s design.  If the design of reciprocating equipment does not adequately accommodate this provision, modifying it in service to control vibration may be difficult or impractical.
     Isolating equipment with vibration-absorbing mounts or by constructing a divided foundation are common methods for controlling vibration along its path.  Elastomeric mats can also be used to damp vibrations; equipment may be placed on them or walking surfaces covered with them.
     Administrative controls, such as task rotations, are often used to limit a receiver’s vibration “dose,” as discussed above.  Vibration-reducing gloves can be worn, in some situations, to reduce exposure due to use of power tools or similar activity.  Improved design of tool grips, to incorporate damping material, for example, may be possible.  Characteristics of footwear should also be considered; for example, a hard-soled shoe may be undesirable, with respect to whole-body vibration, despite other advantages it may provide.


     This presentation of vibration-related information is far, far from comprehensive; a thorough overview of shock and vibration topics would require a series rivalling – probably surpassing – that created for noise.  It seemed remiss, however, given the interconnected nature of vibration, noise, and heat and cold stresses, to neglect the topic.
     The objectives of this installment are simple:  (1) increase awareness of vibration as an independent and interrelated environmental factor that should be incorporated in an organization’s Safety && Health program, and (2) demonstrate parallels between vibration, noise, and thermal stress (e.g. frequency dependence, TLVs).  Though deficient as a compendium, this presentation will be deemed successful if it prompts further investigation that results in improved health and performance in a workplace.


     For additional guidance or assistance with Safety, Health, and Environmental (SHE) issues, or other Operations challenges, feel free to leave a comment, contact JayWink Solutions, or schedule an appointment.

References
[Link] Human Factors in Technology.  Edward Bennett, James Degan, Joseph Spiegel (eds).  McGraw-Hill Book Company, Inc., 1963.
[Link] Industrial Noise Control Manual (Revised Edition).  National Institute for Occupational Safety and Health (NIOSH); December 1978.
[Link] Compendium of Materials for Noise Control.  National Institute for Occupational Safety and Health (NIOSH); 1980.
[Link] Fundamentals of Industrial Ergonomics, 2ed.  B. Mustafa Pulat.  Waveland Press; 1997.
[Link] “Noise and Vibration.”  Evan Davies in Plant Engineer’s Reference Book, 2ed.  Dennis A. Snow, ed.  Reed Educational and Professional Publishing Ltd.; 2002.
[Link] Shock and Vibration Handbook, 5ed.  Cyril M. Harris, ed.  McGraw-Hill, 2002.
[Link] Kodak's Ergonomic Design for People at Work.  The Eastman Kodak Company (ed).  John Wiley & Sons, Inc., 2004.
[Link] “OSHA Technical Manual (OTM) - Section II: Chapter 3 - Technical Equipment: On-site Measurements.”  Occupational Safety and Health Administration; February 11, 2014.
[Link] The Noise Manual, 6ed.  D.K. Meinke, E.H. Berger, R.L. Neitzel, D.P. Driscoll, and K. Bright, eds.  The American Industrial Hygiene Association (AIHA); 2022.
[Link] “Threshold Limit Values for Chemical Substances and Physical Agents.”  American Conference of Governmental Industrial Hygienists (ACGIH); latest edition.
 
Jody W. Phelps, MSc, PMP®, MBA
Principal Consultant
JayWink Solutions, LLC
[email protected]