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Waviness is the measurement of the more widely spaced component of surface texture. It is a broader view of roughness because it is more strictly defined as "the irregularities whose spacing is greater than the roughness sampling length". It can occur from machine or work deflections, chatter, residual stress, vibrations, or heat treatment. [1] [2] Waviness should also be distinguished from flatness, both by its shorter spacing and its characteristic of being typically periodic in nature.

Surface roughness component of surface texture

Surface roughness often shortened to roughness, is a component of surface texture. It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. If these deviations are large, the surface is rough; if they are small, the surface is smooth. In surface metrology, roughness is typically considered to be the high-frequency, short-wavelength component of a measured surface. However, in practice it is often necessary to know both the amplitude and frequency to ensure that a surface is fit for a purpose.

In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.

Residual stress

Residual stresses are stresses that remain in a solid material after the original cause of the stresses has been removed. Residual stress may be desirable or undesirable. For example, laser peening imparts deep beneficial compressive residual stresses into metal components such as turbine engine fan blades, and it is used in toughened glass to allow for large, thin, crack- and scratch-resistant glass displays on smartphones. However, unintended residual stress in a designed structure may cause it to fail prematurely.



There are several parameters for expressing waviness height, the most common being Wa & Wt, for average waviness and total waviness, respectively. [3] In the lateral direction along the surface, the waviness spacing, Wsm, is another parameter that describes the mean spacing between periodic waviness peaks. There are numerous measurement settings which influence these resultant parameter values, which are mentioned below. One of the most important is the waviness evaluation length, which is the length in which the waviness parameters are determined. Within this length the waviness profile is determined. This is a surface texture profile that has the shorter roughness characteristics filtered out, or removed; it also does not include any profile changes due to changes in workpiece geometry that are either unintentional (flatness) or intentional (form).

Waviness is included in the ISO standards ISO 4287 [3] and ISO 16610-21 [4] as well as the U.S. standard ASME B46.1, [5] and it is part of the surface texture symbol used in engineering drawings. [6]

ISO 16610: Geometrical product specifications (GPS) – Filtration is a standard series on filters for surface texture, and provides guidance on the use of these filters in various applications. Filters are used in surface texture in order reduce the bandwidth of analysis in order to obtain functional correlation with physical phenomena such as friction, wear, adhesion, etc. For example, filters are used to separate roughness and waviness from the primary profile, or to create a multiscale decomposition in order to identify the scale at which a phenomenon occurs. Historically, the first roughness measuring instruments - stylus profilometer - used to have electronic filters made of capacitors and resistors that filtered out low frequencies in order to retain frequencies that represent roughness. Later, digital filters replaced analog filters and international standards such as ISO 11562 for the Gaussian filter were published.

An engineering drawing, a type of technical drawing, is used to fully and clearly define requirements for engineered items.


The measurement of the waviness can be done with a variety of instruments, including both surface finish profilometers and roundness instruments. The nature of these instruments is continually progressing and now includes both stylus-based contact instruments as well as optical & laser-based non-contact instruments. In earlier instruments, the measurement output was inherently linked to the instrument itself, whereas there is now emerging some divergence between the instrument that collects the surface profile data and the analytical software that is able to evaluate this data.

Examples of two earlier generation instruments are the waveometer or a microtopographer. A waveometer uses a plastic tip that is connected to an electronic pickup which then measures the surface variations. The measurement is recorded as an electronic signal which is amplified and split into two signals: a high band and a low band. For measuring a ball bearing, the low band signal records variations that occur every four to seventeen times per revolution and the high band signal records variations that occur seventeen to 330 times per revolution; the low band is the waviness. These bands are transmitted to an oscilloscope for analysis. [7] [8]

Amplifier electronic device that can increase the power of a signal

An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It is a two-port electronic circuit that uses electric power from a power supply to increase the amplitude of a signal applied to its input terminals, producing a proportionally greater amplitude signal at its output. The amount of amplification provided by an amplifier is measured by its gain: the ratio of output voltage, current, or power to input. An amplifier is a circuit that has a power gain greater than one.

Ball bearing type of rolling-element bearing that uses balls to maintain the separation between the bearing races.The purpose of a ball bearing is to reduce rotational friction and support radial and axial loads

A ball bearing is a type of rolling-element bearing that uses balls to maintain the separation between the bearing races.

Oscilloscope type of electronic test instrument

An oscilloscope, previously called an oscillograph, and informally known as a scope or o-scope, CRO, or DSO, is a type of electronic test instrument that graphically displays varying signal voltages, usually as a two-dimensional plot of one or more signals as a function of time. Other signals can be converted to voltages and displayed.


Waviness measurements are not as common as roughness measurement however there are important applications. For example, waviness in bearing balls and bearing races is one of the reasons for vibrations and noise in ball bearings. Other application examples are waviness in flat milled sealing surfaces, "orange peel" on painted surfaces, and chatter on round shaft surfaces. [9] [10] [11]

Bearing balls are special highly spherical and smooth balls, most commonly used in ball bearings, but also used as components in things like freewheel mechanisms. The balls come in many different grades. These grades are defined by bodies such as the American Bearing Manufacturers Association (ABMA), a body which sets standards for the precision of bearing balls. They are manufactured in machines designed specially for the job.

Race (bearing) track in a bearing along which the rolling elements ride

The rolling-elements of a rolling-element bearing ride on races. The large race that goes into a bore is called the outer race, and the small race that the shaft rides in is called the inner race.

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Geometric dimensioning and tolerancing standardized code for engineers to specify parts for manufacturing

Geometric dimensioning and tolerancing (GD&T) is a system for defining and communicating engineering tolerances. It uses a symbolic language on engineering drawings and computer-generated three-dimensional solid models that explicitly describe nominal geometry and its allowable variation. It tells the manufacturing staff and machines what degree of accuracy and precision is needed on each controlled feature of the part. GD&T is used to define the nominal geometry of parts and assemblies, to define the allowable variation in form and possible size of individual features, and to define the allowable variation between features.

Broaching is a machining process that uses a toothed tool, called a broach, to remove material. There are two main types of broaching: linear and rotary. In linear broaching, which is the more common process, the broach is run linearly against a surface of the workpiece to effect the cut. Linear broaches are used in a broaching machine, which is also sometimes shortened to broach. In rotary broaching, the broach is rotated and pressed into the workpiece to cut an axisymmetric shape. A rotary broach is used in a lathe or screw machine. In both processes the cut is performed in one pass of the broach, which makes it very efficient.

Surface plate

A surface plate is a solid, flat plate used as the main horizontal reference plane for precision inspection, marking out (layout), and tooling setup. The surface plate is often used as the baseline for all measurements to a workpiece, therefore one primary surface is finished extremely flat with tolerances below 11.5 μm or 0.0115 mm per 2960 mm for a grade 0 plate. Surface plates are a very common tool in the manufacturing industry and are often permanently attached to robotic-type inspection devices such as a coordinate-measuring machine. Plates are typically square or rectangular.

Surface metrology is the measurement of small-scale features on surfaces, and is a branch of metrology. Surface primary form, surface fractality and surface roughness are the parameters most commonly associated with the field. It is important to many disciplines and is mostly known for the machining of precision parts and assemblies which contain mating surfaces or which must operate with high internal pressures.

Condition monitoring is the process of monitoring a parameter of condition in machinery, in order to identify a significant change which is indicative of a developing fault. It is a major component of predictive maintenance. The use of condition monitoring allows maintenance to be scheduled, or other actions to be taken to prevent consequential damages and avoid its consequences. Condition monitoring has a unique benefit in that conditions that would shorten normal lifespan can be addressed before they develop into a major failure. Condition monitoring techniques are normally used on rotating equipment, auxiliary systems and other machinery, while periodic inspection using non-destructive testing (NDT) techniques and fit for service (FFS) evaluation are used for static plant equipment such as steam boilers, piping and heat exchangers.

Rolling (metalworking) metalworking process

In metalworking, rolling is a metal forming process in which metal stock is passed through one or more pairs of rolls to reduce the thickness and to make the thickness uniform. The concept is similar to the rolling of dough. Rolling is classified according to the temperature of the metal rolled. If the temperature of the metal is above its recrystallization temperature, then the process is known as hot rolling. If the temperature of the metal is below its recrystallization temperature, the process is known as cold rolling. In terms of usage, hot rolling processes more tonnage than any other manufacturing process, and cold rolling processes the most tonnage out of all cold working processes. Roll stands holding pairs of rolls are grouped together into rolling mills that can quickly process metal, typically steel, into products such as structural steel, bar stock, and rails. Most steel mills have rolling mill divisions that convert the semi-finished casting products into finished products.

Orange peel (effect)

Orange peel is a certain kind of finish that may develop on painted and cast surfaces, even screen protectors. The texture resembles the surface of the skin of an orange. Gloss paint sprayed on a smooth surface should also dry into a smooth surface. However, various factors can cause it to dry into a bumpy surface resembling the texture of an orange peel. The orange peel phenomenon can then be smoothed out with ultra-fine sandpaper, but it can be prevented altogether by changing the painting technique or the materials used. Orange peel is typically the result of improper painting technique, and is caused by the quick evaporation of thinner, incorrect spray gun setup, spraying the paint at an angle other than perpendicular, or applying excessive paint.

Surface finish, also known as surface texture or surface topography, is the nature of a surface as defined by the three characteristics of lay, surface roughness, and waviness. It comprises the small, local deviations of a surface from the perfectly flat ideal.

Roundness is the measure of how closely the shape of an object approaches that of a mathematically perfect circle. Roundness applies in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft or a cylindrical roller for a bearing. In geometric dimensioning and tolerancing, control of a cylinder can also include its fidelity to the longitudinal axis, yielding cylindricity. The analogue of roundness in three dimensions is sphericity.

ISO 25178: Geometric Product Specifications (GPS) – Surface texture: areal is an International Organisation for Standardisation collection of international standards relating to the analysis of 3D areal surface texture.

Laser beam profiler

A laser beam profiler captures, displays, and records the spatial intensity profile of a laser beam at a particular plane transverse to the beam propagation path. Since there are many types of lasers — ultraviolet, visible, infrared, continuous wave, pulsed, high-power, low-power — there is an assortment of instrumentation for measuring laser beam profiles. No single laser beam profiler can handle every power level, pulse duration, repetition rate, wavelength, and beam size.

Road surface textures are deviations from a planar and smooth surface, affecting the vehicle/tyre interaction. Pavement texture is divided into: microtexture with wavelengths from 0 mm to 0.5 millimetres (0.020 in), macrotexture with wavelengths from 0.5 millimetres (0.020 in) to 50 millimetres (2.0 in) and megatexture with wavelengths from 50 millimetres (2.0 in) to 500 millimetres (20 in).

Abbott-Firestone curve

The Abbott-Firestone curve or bearing area curve (BAC) describes the surface texture of an object. The curve could be found from a profile trace by drawing lines parallel to the datum and measuring the fraction of the line which lies within the profile.


A spotface or spot face is a machined feature in which a certain region of the workpiece is faced, providing a smooth, flat, accurately located surface. This is especially relevant on workpieces cast or forged, where the spotface's smooth, flat, accurately located surface stands in distinction to the surrounding surface whose roughness, flatness, and location are subject to wider tolerances and thus not assured with a machining level of precision. The most common application of spotfacing is facing the area around a bolt hole where the bolt's head will sit, which is often done by cutting a shallow counterbore, just deep enough "to clean up"—that is, only enough material is removed to get down past any irregularity and thus make the surface flat. Other common applications of spotfacing involve facing a pad onto a boss, creating planar surfaces in known locations that can orient a casting or forging into position in the assembly; allow part marking such as stamping or nameplate riveting; or offer machine-finish visual appeal in spots, without the need for finishing all over (FAO).

Surface integrity is the surface condition of a workpiece after being modified by a manufacturing process. The term was coined by Michael Field and John F. Kahles in 1964.

MountainsMap micro-topography software published by Digital Surf

Mountains is an image analysis and surface metrology software platform published by the company Digital Surf. Its core is micro-topography, the science of studying surface texture and form in 3D at the microscopic scale. The software is dedicated to profilometers, 3D light microscopes ("MountainsMap"), scanning electron microscopes ("MountainsSEM") and scanning probe microscopes ("MountainsSPIP").

Digital Surf is a French software company formed in 1989 mainly known for its Mountains software, that is offered as embedded or optional OEM surface analysis software by the majority of profilometer and microscope manufacturers.

Taylor Hobson is an English company founded in 1886 and located in Leicester, England. Originally a manufacturer of cameras and cine lenses, the company now manufactures precision metrology instruments. In particular, profilometers for the analysis of surface textures and forms.


  1. Oberg et al. 2000 , p. 699.
  2. Oberg et al. 2000 , p. 702.
  3. 1 2 ISO 4287, Geometrical Product Specifications (GPS) -- Surface texture: Profile method -- Terms, definitions and surface texture parameters
  4. ISO 16610, Geometrical product specifications (GPS) -- Filtration -- Part 21: Linear profile filters: Gaussian filters
  5. ASME B46.1, Surface Texture (Surface Roughness, Waviness, and Lay).
  6. Jensen 2001 , p. 86.
  7. Measuring waviness , retrieved 2009-08-20.
  8. Degarmo, Black & Kohser 2003 , p. 225.
  9. Harsha, S.P.; Kankar, P.K. (July 2004), "Stability analysis of a rotor bearing system due to surface waviness and number of balls", International Journal of Mechanical Sciences, 46 (7): 1057–1081, doi:10.1016/j.ijmecsci.2004.07.007 .
  10. Harsha, S. P.; Sandeep, K.; Prakash, R. (July 2004), "Nonlinear Dynamic Response of a Rotor Bearing System Due to Surface Waviness", Nonlinear Dynamics , 37 (2): 91–114, doi:10.1023/B:NODY.0000042916.10351.ff .
  11. Yhland, E. M. (1967), "Waviness measurement—an instrument for quality control in rolling bearing industry", Proceedings of the Institution of Mechanical Engineers, 182 (3K): 438–445, doi:10.1243/PIME_CONF_1967_182_341_02