Educating Homeowners on Everyday Door Safety Practices

An ideal spring acts in accordance with Hooke's law, which states that the force with which the spring pushes back is linearly proportional to the distance from its equilibrium length:

$\displaystyle F=-kx$,

where

$\displaystyle x$ is the displacement vector – the distance from its equilibrium length.

$\displaystyle F$ is the resulting force vector – the magnitude and direction of the restoring force the spring exerts

$\displaystyle k$ is the rate, spring constant or force constant of the spring, a constant that depends on the spring's material and construction. The negative sign indicates that the force the spring exerts is in the opposite direction from its displacement

Most real springs approximately follow Hooke's law if not stretched or compressed beyond their elastic limit.

Coil springs and other common springs typically obey Hooke's law. There are useful springs that don't: springs based on beam bending can for example produce forces that vary nonlinearly with displacement.

If made with constant pitch (wire thickness), conical springs have a variable rate. However, a conical spring can be made to have a constant rate by creating the spring with a variable pitch. A larger pitch in the larger-diameter coils and a smaller pitch in the smaller-diameter coils forces the spring to collapse or extend all the coils at the same rate when deformed.

Since force is equal to mass, m, times acceleration, a, the force equation for a spring obeying Hooke's law looks like:

$\displaystyle F=ma\quad \Rightarrow \quad -kx=ma.\,$

The mass of the spring is small in comparison to the mass of the attached mass and is ignored. Since acceleration is simply the second derivative of x with respect to time,

$\displaystyle -kx=m\frac d^2xdt^2.\,$

This is a second order linear differential equation for the displacement $\displaystyle x$ as a function of time. Rearranging:

$\displaystyle \frac d^2xdt^2+\frac kmx=0,\,$

the solution of which is the sum of a sine and cosine:

$\displaystyle x(t)=A\sin \left(t\sqrt \frac km\right)+B\cos \left(t\sqrt \frac km\right).\,$

$\displaystyle A$ and $\displaystyle B$ are arbitrary constants that may be found by considering the initial displacement and velocity of the mass. The graph of this function with $\displaystyle B=0$ (zero initial position with some positive initial velocity) is displayed in the image on the right.

In simple harmonic motion of a spring-mass system, energy will fluctuate between kinetic energy and potential energy, but the total energy of the system remains the same. A spring that obeys Hooke's law with spring constant k will have a total system energy E of:^[14]

$\displaystyle E=\left(\frac 12\right)kA^2$

Here, A is the amplitude of the wave-like motion that is produced by the oscillating behavior of the spring.

The potential energy U of such a system can be determined through the spring constant k and its displacement x:^[14]

$\displaystyle U=\left(\frac 12\right)kx^2$

The kinetic energy K of an object in simple harmonic motion can be found using the mass of the attached object m and the velocity at which the object oscillates v:^[14]

$\displaystyle K=\left(\frac 12\right)mv^2$

Since there is no energy loss in such a system, energy is always conserved and thus:^[14]

$\displaystyle E=K+U$

The angular frequency ω of an object in simple harmonic motion, given in radians per second, is found using the spring constant k and the mass of the oscillating object m^[15]:

$\displaystyle \omega =\sqrt \frac km$^[14]

The period T, the amount of time for the spring-mass system to complete one full cycle, of such harmonic motion is given by:^[16]

$\displaystyle T=\frac 2\pi \omega =2\pi \sqrt \frac mk$^[14]

The frequency f, the number of oscillations per unit time, of something in simple harmonic motion is found by taking the inverse of the period:^[14]

$\displaystyle f=\frac 1T=\frac \omega 2\pi =\frac 12\pi \sqrt \frac km$^[14]

In classical physics, a spring can be seen as a device that stores potential energy, specifically elastic potential energy, by straining the bonds between the atoms of an elastic material.

Hooke's law of elasticity states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its tension, the force used to stretch it. Similarly, the contraction (negative extension) is proportional to the compression (negative tension).

This law actually holds only approximately, and only when the deformation (extension or contraction) is small compared to the rod's overall length. For deformations beyond the elastic limit, atomic bonds get broken or rearranged, and a spring may snap, buckle, or permanently deform. Many materials have no clearly defined elastic limit, and Hooke's law can not be meaningfully applied to these materials. Moreover, for the superelastic materials, the linear relationship between force and displacement is appropriate only in the low-strain region.

Hooke's law is a mathematical consequence of the fact that the potential energy of the rod is a minimum when it has its relaxed length. Any smooth function of one variable approximates a quadratic function when examined near enough to its minimum point as can be seen by examining the Taylor series. Therefore, the force – which is the derivative of energy with respect to displacement – approximates a linear function.

The force of a fully compressed spring is:

$\displaystyle F_max=\frac Ed^4(L-nd)16(1+\nu )(D-d)^3n\$

where

E – Young's modulus

d – spring wire diameter

L – free length of spring

n – number of active windings

$\displaystyle \nu$ – Poisson ratio

D – spring outer diameter.

Zero-length spring is a term for a specially designed coil spring that would exert zero force if it had zero length. That is, in a line graph of the spring's force versus its length, the line passes through the origin. A real coil spring will not contract to zero length because at some point the coils touch each other. "Length" here is defined as the distance between the axes of the pivots at each end of the spring, regardless of any inelastic portion in-between.

Zero-length springs are made by manufacturing a coil spring with built-in tension (A twist is introduced into the wire as it is coiled during manufacture; this works because a coiled spring unwinds as it stretches), so if it could contract further, the equilibrium point of the spring, the point at which its restoring force is zero, occurs at a length of zero. In practice, the manufacture of springs is typically not accurate enough to produce springs with tension consistent enough for applications that use zero length springs, so they are made by combining a negative length spring, made with even more tension so its equilibrium point would be at a negative length, with a piece of inelastic material of the proper length so the zero force point would occur at zero length.

A zero-length spring can be attached to a mass on a hinged boom in such a way that the force on the mass is almost exactly balanced by the vertical component of the force from the spring, whatever the position of the boom. This creates a horizontal pendulum with very long oscillation period. Long-period pendulums enable seismometers to sense the slowest waves from earthquakes. The LaCoste suspension with zero-length springs is also used in gravimeters because it is very sensitive to changes in gravity. Springs for closing doors are often made to have roughly zero length, so that they exert force even when the door is almost closed, so they can hold it closed firmly.

• Shock absorber
• Slinky, helical spring toy
• Volute spring

• Sclater, Neil. (2011). "Spring and screw devices and mechanisms." Mechanisms and Mechanical Devices Sourcebook. 5th ed. New York: McGraw Hill. pp. 279–299. ISBN 9780071704427. Drawings and designs of various spring and screw mechanisms.
• Parmley, Robert. (2000). "Section 16: Springs." Illustrated Sourcebook of Mechanical Components. New York: McGraw Hill. ISBN 0070486174 Drawings, designs and discussion of various springs and spring mechanisms.
• Warden, Tim. (2021). “Bundy 2 Alto Saxophone.” This saxophone is known for having the strongest tensioned needle springs in existence.

• Paredes, Manuel (2013). "How to design springs". insa de toulouse. Retrieved 13 November 2013.
• Wright, Douglas. "Introduction to Springs". Notes on Design and Analysis of Machine Elements. Department of Mechanical & Material Engineering, University of Western Australia. Retrieved 3 February 2008.
• Silberstein, Dave (2002). "How to make springs". Bazillion. Archived from the original on 18 September 2013. Retrieved 3 February 2008.
• Springs with Dynamically Variable Stiffness (patent)
• Smart Springs and their Combinations (patent)

 

 

The technical meaning of maintenance involves functional checks, servicing, repairing or replacing of necessary devices, equipment, machinery, building infrastructure and supporting utilities in industrial, business, and residential installations.^[1][2] Terms such as "predictive" or "planned" maintenance describe various cost-effective practices aimed at keeping equipment operational; these activities occur either before^[3] or after a potential failure.

Maintenance functions can be defined as maintenance, repair and overhaul (MRO), and MRO is also used for maintenance, repair and operations.^[4] Over time, the terminology of maintenance and MRO has begun to become standardized. The United States Department of Defense uses the following definitions:^[5]

• Any activity—such as tests, measurements, replacements, adjustments, and repairs—intended to retain or restore a functional unit in or to a specified state in which the unit can perform its required functions.^[5]
• All action taken to retain material in a serviceable condition or to restore it to serviceability. It includes inspections, testing, servicing, classification as to serviceability, repair, rebuilding, and reclamation.^[5]
• All supply and repair action taken to keep a force in condition to carry out its mission.^[5]
• The routine recurring work required to keep a facility (plant, building, structure, ground facility, utility system, or other real property) in such condition that it may be continuously used, at its original or designed capacity and efficiency for its intended purpose.^[5]

Maintenance is strictly connected to the utilization stage of the product or technical system, in which the concept of maintainability must be included. In this scenario, maintainability is considered as the ability of an item, under stated conditions of use, to be retained in or restored to a state in which it can perform its required functions, using prescribed procedures and resources.^[6]

In some domains like aircraft maintenance, terms maintenance, repair and overhaul^[7] also include inspection, rebuilding, alteration and the supply of spare parts, accessories, raw materials, adhesives, sealants, coatings and consumables for aircraft maintenance at the utilization stage. In international civil aviation maintenance means:

• The performance of tasks required to ensure the continuing airworthiness of an aircraft, including any one or combination of overhaul, inspection, replacement, defect rectification, and the embodiment of a modification or a repair.^[8]

This definition covers all activities for which aviation regulations require issuance of a maintenance release document (aircraft certificate of return to service – CRS).

The marine and air transportation,^[9] offshore structures,^[10] industrial plant and facility management industries depend on maintenance, repair and overhaul (MRO) including scheduled or preventive paint maintenance programmes to maintain and restore coatings applied to steel in environments subject to attack from erosion, corrosion and environmental pollution.^[10]

The basic types of maintenance falling under MRO include:

• Preventive maintenance, where equipment is checked and serviced in a planned manner (in a scheduled points in time or continuously)
• Corrective maintenance, where equipment is repaired or replaced after wear, malfunction or break down
• Reinforcement^[11]

Architectural conservation employs MRO to preserve, rehabilitate, restore, or reconstruct historical structures with stone, brick, glass, metal, and wood which match the original constituent materials where possible, or with suitable polymer technologies when not.^[12]

Preventive maintenance (PM) is "a routine for periodically inspecting" with the goal of "noticing small problems and fixing them before major ones develop."^[13] Ideally, "nothing breaks down."^[14]

The main goal behind PM is for the equipment to make it from one planned service to the next planned service without any failures caused by fatigue, extreme fluctuation in temperature(such as heat waves^[15]) during seasonal changes, neglect, or normal wear (preventable items), which Planned Maintenance and Condition Based Maintenance help to achieve by replacing worn components before they actually fail. Maintenance activities include partial or complete overhauls at specified periods, oil changes, lubrication, minor adjustments, and so on. In addition, workers can record equipment deterioration so they know to replace or repair worn parts before they cause system failure.

The New York Times gave an example of "machinery that is not lubricated on schedule" that functions "until a bearing burns out." Preventive maintenance contracts are generally a fixed cost, whereas improper maintenance introduces a variable cost: replacement of major equipment.^[13]

Main objective of PM are:

1. Enhance capital equipment productive life.
2. Reduce critical equipment breakdown.
3. Minimize production loss due to equipment failures.

Preventive maintenance or preventative^[16] maintenance (PM) has the following meanings:

• The care and servicing by personnel for the purpose of maintaining equipment in satisfactory operating condition by providing for systematic inspection, detection, and correction of incipient failures either before they occur or before they develop into major defects.
• The work carried out on equipment in order to avoid its breakdown or malfunction. It is a regular and routine action taken on equipment in order to prevent its breakdown.^[17]
• Maintenance, including tests, measurements, adjustments, parts replacement, and cleaning, performed specifically to prevent faults from occurring.

Other terms and abbreviations related to PM are:

• scheduled maintenance^[18]
• planned maintenance,^[19] which may include scheduled downtime for equipment replacement
• planned preventive maintenance (PPM) is another name for PM^[20]
• breakdown maintenance:^[20] fixing things only when they break. This is also known as "a reactive maintenance strategy"^[21] and may involve "consequential damage."^[22]

Planned preventive maintenance (PPM), more commonly referred to as simply planned maintenance (PM) or scheduled maintenance, is any variety of scheduled maintenance to an object or item of equipment. Specifically, planned maintenance is a scheduled service visit carried out by a competent and suitable agent, to ensure that an item of equipment is operating correctly and to therefore avoid any unscheduled breakdown and downtime.^[23]

The key factor as to when and why this work is being done is timing, and involves a service, resource or facility being unavailable.^[18][19] By contrast, condition-based maintenance is not directly based on equipment age.

Planned maintenance is preplanned, and can be date-based, based on equipment running hours, or on distance travelled.

Parts that have scheduled maintenance at fixed intervals, usually due to wearout or a fixed shelf life, are sometimes known as time-change interval, or TCI items.

Predictive maintenance techniques are designed to help determine the condition of in-service equipment in order to estimate when maintenance should be performed. This approach promises cost savings over routine or time-based preventive maintenance, because tasks are performed only when warranted. Thus, it is regarded as condition-based maintenance carried out as suggested by estimations of the degradation state of an item. The main promise of predictive maintenance is to allow convenient scheduling of corrective maintenance, and to prevent unexpected equipment failures.^[3] This maintenance strategy uses sensors to monitor key parameters within a machine or system, and uses this data in conjunction with analysed historical trends to continuously evaluate the system health and predict a breakdown before it happens.^[24] This strategy allows maintenance to be performed more efficiently, since more up-to-date data is obtained about how close the product is to failure.^[25]

Predictive replacement is the replacement of an item that is still functioning properly.^[26] Usually it is a tax-benefit based ^{[citation needed]} replacement policy whereby expensive equipment or batches of individually inexpensive supply items are removed and donated on a predicted/fixed shelf life schedule. These items are given to tax-exempt institutions.^{[27][citation needed]}

Condition-based maintenance (CBM), shortly described, is maintenance when need arises. Albeit chronologically much older, It is considered one section or practice inside the broader and newer predictive maintenance field, where new AI technologies and connectivity abilities are put to action and where the acronym CBM is more often used to describe 'condition Based Monitoring' rather than the maintenance itself. CBM maintenance is performed after one or more indicators show that equipment is going to fail or that equipment performance is deteriorating.

This concept is applicable to mission-critical systems that incorporate active redundancy and fault reporting. It is also applicable to non-mission critical systems that lack redundancy and fault reporting.

Condition-based maintenance was introduced to try to maintain the correct equipment at the right time. CBM is based on using real-time data to prioritize and optimize maintenance resources. Observing the state of the system is known as condition monitoring. Such a system will determine the equipment's health, and act only when maintenance is actually necessary. Developments in recent years have allowed extensive instrumentation of equipment, and together with better tools for analyzing condition data, the maintenance personnel of today is more than ever able to decide what is the right time to perform maintenance on some piece of equipment. Ideally, condition-based maintenance will allow the maintenance personnel to do only the right things, minimizing spare parts cost, system downtime and time spent on maintenance.

Despite its usefulness of equipment, there are several challenges to the use of CBM. First and most important of all, the initial cost of CBM can be high. It requires improved instrumentation of the equipment. Often the cost of sufficient instruments can be quite large, especially on equipment that is already installed. Wireless systems have reduced the initial cost. Therefore, it is important for the installer to decide the importance of the investment before adding CBM to all equipment. A result of this cost is that the first generation of CBM in the oil and gas industry has only focused on vibration in heavy rotating equipment.

Secondly, introducing CBM will invoke a major change in how maintenance is performed, and potentially to the whole maintenance organization in a company. Organizational changes are in general difficult.

Also, the technical side of it is not always as simple. Even if some types of equipment can easily be observed by measuring simple values such as vibration (displacement, velocity or acceleration), temperature or pressure, it is not trivial to turn this measured data into actionable knowledge about the health of the equipment.

As systems get more costly, and instrumentation and information systems tend to become cheaper and more reliable, CBM becomes an important tool for running a plant or factory in an optimal manner. Better operations will lead to lower production cost and lower use of resources. And lower use of resources may be one of the most important differentiators in a future where environmental issues become more important by the day.

Another scenario where value can be created is by monitoring the health of a car motor. Rather than changing parts at predefined intervals, the car itself can tell you when something needs to be changed based on cheap and simple instrumentation.

It is Department of Defense policy that condition-based maintenance (CBM) be "implemented to improve maintenance agility and responsiveness, increase operational availability, and reduce life cycle total ownership costs".^[28]

CBM has some advantages over planned maintenance:

• Improved system reliability
• Decreased maintenance costs
• Decreased number of maintenance operations causes a reduction of human error influences

Its disadvantages are:

• High installation costs, for minor equipment items often more than the value of the equipment
• Unpredictable maintenance periods cause costs to be divided unequally.
• Increased number of parts (the CBM installation itself) that need maintenance and checking.

Today, due to its costs, CBM is not used for less important parts of machinery despite obvious advantages. However it can be found everywhere where increased safety is required, and in future will be applied even more widely.^[29][30]

Corrective maintenance is a type of maintenance used for equipment after equipment break down or malfunction is often most expensive – not only can worn equipment damage other parts and cause multiple damage, but consequential repair and replacement costs and loss of revenues due to down time during overhaul can be significant. Rebuilding and resurfacing of equipment and infrastructure damaged by erosion and corrosion as part of corrective or preventive maintenance programmes involves conventional processes such as welding and metal flame spraying, as well as engineered solutions with thermoset polymeric materials.^[31]

•  This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22. (in support of MIL-STD-188).

• Maintenance Planning, Coordination & Scheduling, by Don Nyman & Joel Levitt Maintenance ISBN 978-0831134181
• The Care of Things. Ethics and Politics of maintenance, by Jérôme Denis & David Pontille, Polity Press ISBN 978-1509562381

• Wu, S.; Zuo, M.J. (2010). "Linear and nonlinear preventive maintenance" (PDF). IEEE Transactions on Reliability. 59 (1): 242–249. doi:10.1109/TR.2010.2041972. S2CID 34832834. Archived (PDF) from the original on 2016-08-18.