1 Introduction

Way back in 1920, the British scientist Griffith concluded that the inadequate strength of an isotropic solid body is due to the impaired continuity of the material (defects), with the general sizes of the gaps exceeding the intermolecular distances present in the material [1]. According to Griffith, the effective strength of construction materials would be 10 to 20 times higher if the defects were eliminated. However, these defects cannot be eliminated at this stage in the development of the science. They are introduced both in the process of obtaining the workpieces (metallurgical defects) and in the production process for the details from the respective workpieces. The defects in the surface layer of the machine parts and structural components are particularly dangerous. It is well known that the surface layer is loaded most heavily during exploitation; it comes into contact with the surfaces of other components and is subjected to ambience impacts. Accordingly, the state of the surface layer in terms of its microstructure, residual stresses, and its depth of distribution, microhardness and roughness is crucial for the fatigue strength and life of the corresponding component. The control of these properties during the process of surface layer formation is the main reason for increased resistance to fatigue failure. The complex set of surface layer qualities is known as the surface integrity. Increasing the fatigue strength of the component requires a relevant technology for treating the surface layers, whereby the required set of properties for these layers is achieved: grain refinement microstructure, residual compressive stress, maximum depth of the compressive zone, increased microhardness and minimum roughness.

The residual stresses introduced by cutting are usually tensile in nature [2]. Moreover, the cutting is accompanied by the local destruction of the surface layers: For plastic materials, this destruction is preceded by significant plastic strains; for brittle material, a typical brittle destruction is observed. Therefore, the surfaces processed by cutting contain a plurality of micro-defects (dislocations) in the polycrystals within their microstructures. This plurality of dislocation configurations results in micro-cracks due to plastic deformations at the micro level and large micro-stresses. Upon the impact of an external load, these micro-cracks converge, and a single fatigue macro-crack with a relative size of 100 μm is formed. When the load is static, equalization of the stresses in the adjacent grains (stress redistribution) occurs, and the destruction is of the tough plastic type due to the increasing static load. When the stresses are variable, such equalization does not occur, and the macro-crack grows until the complete destruction of the respective component occurs. This process is very dangerous because the reduction in the cross section of the elements is not visible from the outside. Fatigue destruction is the most brittle destruction of the material under the given conditions. It should be noted that some cutting conditions provide residual compressive stresses in the machined layer and thus a longer fatigue life for the machined components can be obtained [3]. Actually, the plastic deformation behaviour of the surface layers of metal component is also observed in other mechanical treatments such as high-efficiency and heavy-load grinding of aerospace difficult-to-cut metallic materials: nickel-based superalloys [4,5,6], titanium matrix composites [7] and Ti2AlNb intermetalics [8].

To improve the fatigue and tribological behaviour as well as the corrosion resistance of structural components, it is necessary to modify the set of topographic, mechanical, chemical and metallurgical properties comprising the surface integrity (SI), of their surface layers. Surface engineering processes are used to modify the SI. They differ according to their corresponding impacts and consist of the mechanical surface treatment (MST) process (no alteration in the chemical composition), surface heat treatment (SHT) process (annealing, hardening, tempering), thermochemical diffusion (TMD) process (carburising, carbonitriding, nitriding) and combinations of these three processes. On the one hand, the SHT and TCD processes are costly, time-consuming and non-ecological, and, on the other hand, these processes are not sufficiently effective with respect to the fatigue behaviour of the metal components. Thus, SHT and TCD are used primarily to increase the hardness and wear resistance of the surface layers. In order to prevent destruction via fatigue effectively, the surface layers must be modified to decrease roughness, increase micro-hardness, increase residual compressive stresses and produce a refined microstructure; all of which can be accomplished in a cost-effective manner through MST.

The essence of MST is the plastic deformation of the surface peaks created by the sliding friction or rolling contact between a deforming element and the surface being treated. The peaks of the relief are plastically deformed, as the metal flows to the free valleys. As a result, the material undergoes strain hardening. At the same time, the contact between the deforming element and the surface being treated increases, the stresses decrease and the metal increases its resistance against further deformation. Thus, the plastic deformation is terminated at a certain depth below the surface, and the deformations are elastic only below this level. Due to differential material hardening, it is never possible to fill the valleys completely. The greater the tendency of a metal to harden, the less the valleys will fill and vice versa—for metals with plasticity close to the ideal value of one, maximal filling of the valleys is observed. The plastically deformed layer of the metal increases its volume. After termination of the contact with the deforming element, the elastically deformed, lower-lying layers seek to regain their original condition. The plastically deformed surface and subsurface layers that have increased their volume due to yielding to the deformation oppose this aspiration. Thus, the surface and subsurface layers are ‘pressed’ and the lower layers are ‘stretched’. In other words, useful residual compressive stresses are introduced into the surface and sub-surface layers, resulting in the increased fatigue strength of the treated material. At the same time, the deformed surface layers have increased micro-hardness and wear resistance.

Compared with finishing machining methods, MST has the following advantages:

  • Greater productivity

  • The material’s fibre integrity is stored

  • Abrasive particles are missing on the treated surface

  • There is less heating of the treated surface

  • The roughness relief and its parameters have a more favourable effect on the operational properties of the surface

  • The microstructure and hardening are more uniform, as the hardening is at a greater depth

  • The residual stresses in the surface and the sub-surface layers are compressive

The methods used to implement MST are of two types: dynamic and static. An advantage of dynamic methods (such as shot peening, laser peening, water cavitation peening) is that they can be applied to the processing of complex surfaces without limitation. Chronologically, the dynamic methods precede the static methods. In 1871, Tilgham invented the sand blast process, which was the precursor of present-day shot peening [9]. The static methods are suitable for treating rotational surfaces. These static methods are known under the common name burnishing methods. One of the first patents involving these methods was published in 1916 [10]. In any static methods, the deforming element (or elements) is (1) a roller or ball, when the contact with the surface being treated is a rolling contact (in the case of a hydrostatic sphere [11], the sphere rotates around a instantaneous axis of rotation according to the Smallest Resistance Law); (2) spherical or cylindrical when the contact with the surface being treated is a sliding friction contact; (3) a ball whose contact with the surface being treated can be rolling contact at some moments in time and sliding friction in others; or (4) a roller whose contact with the surface being treated is both rolling and sliding friction contact.

In 1929, Föppl established the correlation between MST and the increased fatigue strength of the treated specimens for the first time [12]. In the 1930s, Thum studied the relation of roller burnishing with fatigue strength, corrosion fatigue and fretting fatigue [12]. As a result of the improved SI through MST, the fatigue strength of the respective structural component was increased significantly. The surveys of the burnishing methods’ effects on fatigue strength continue to this day [13,14,15]. Many researchers have demonstrated experimentally that the MST increases surface wear resistance [16,17,18,19,20,21,22,23]. It has also been proven experimentally that MST increases the corrosion resistance of treated surfaces [24, 25].

An analysis of the literature on burnishing methods shows that there is no consensus among researchers on a number of concepts. For instance, the ‘roller/ball’ (burnishing) term is often used in the literature; it refers to the deforming element’s shape and does not take the type of contact into account. Yet, even diamond burnishing, carried out via a spherically ended deforming diamond, is included in the ball-burnishing category, which is very confusing. Even when the shape of the deforming element is the same, if the contact is different (rolling, sliding, respectively), different processes will be realized, and, as a result the SIs will have different indicators.

Often, in the literature, the same concept (for example, roller burnishing) is mentioned as a method and then as a process. For example, on the one hand, there is a roller-burnishing method, and, on the other hand, there is Ecoroll’s roller-burnishing process. Of course, this concept can be used as both a method and a process, but such usage must be consistent with the meaning of the corresponding ratiocination. A burnishing method is a coherent time-space arrangement of two bodies (a deforming component and a treated surface) in the mechanical sense, with defined geometry, physical and chemical properties. Further, a burnishing process is an energy and mass exchange resulting from the coherent interaction between two bodies with clearly defined quantitative characteristics. Using the same method, but with different quantitative parameters, many deforming processes can be realized, and, as a result, the processed components will have, for example, different fatigue behaviours.

Slide burnishing (SB) is a static MST method. The method is implemented with simple devices and tools, which is its main advantage. SB is the common name for burnishing, which is implemented via sliding friction contact. When the deforming element is made of diamond (artificial or natural), the method is referred to as diamond burnishing (DB) or slide diamond burnishing (SDB). General Electric first introduced DB in 1962 in order to improve the SI of the treated components [26].

The purpose of this article is to create a united classification system for the static MST methods, i.e. burnishing methods and, on this basis, to outline the place, role and significance of SB within this system, review of the state of SB, and outline the prospects for its development.

2 Classification of burnishing methods

Classifications depending on the various burnishing method signs are known:

  1. 1.

    Depending on the shape of the deforming element, i.e. roller or ball: roller burnishing (Fig. 1) or ball burnishing (Fig. 2), respectively. Obviously, classification under this sign is incomplete, as, for example, conducting SB with a cylindrical-ended deforming element (Fig. 3a) cannot fit into this classification. The classification under this sign is inadequate in terms of method of contact as well. For instance, both SB conducted through a spherical-ended deforming diamond (Fig. 3b) and burnishing with a hydrostatic sphere (Fig. 4) are classified as ball burnishing, regardless of their different contact methods (sliding friction versus rolling friction), which is the reason why different SIs are obtained. The misunderstandings can be minimized if the concept ‘ball burnishing’ is considered to ball burnishing with a hydrostatic sphere (rolling contact), while the first method given in the last example is completely recognizable under the SDB (or DB) name.

  2. 2.

    Depending on the type of the contact between the deforming element (roller or ball) and the surface being treated: (a) When the deforming element performs clean (without slipping) rolling with respect to the surface being treated, then the contact is rolling friction and the methods are, respectively, roller/ball burnishing; (b) if the contact is sliding friction, the method is SB.

  3. 3.

    Depending on the desired SI. Ecoroll uses the terms ‘roller burnishing’ and ‘deep rolling’ processes [11]. The main objective of the first is to produce smoothing, wherein the roughness is reduced considerably. The other attributes of the surface layer (increased micro-hardness, compressive residual stresses) inherent in the MST also exist but are rather concomitant and not significant. Deep rolling aims to produce three effects simultaneously: burnishing, cold work and compressive residual stresses with maximum magnitude in absolute value and of considerable depth. Lambda Research invented the low-plasticity burnishing process [27,28,29,30], which was intended to create a compressive zone with large absolute values of the residual stresses at great depth, whereby the magnitude of the equivalent plastic strain (cold work) is automatically controlled in order not to exceed the set limit. This control ensures the performance of the structural components that are subjected to overloading or high temperatures. In fact, the first Ecoroll process is implemented through the roller burnishing method. Deep rolling and low-plasticity burnishing processes are conducted by one and the same method—ball burnishing with a hydrostatic sphere. Obviously, different quantitative values of the characteristics of a given method lead to the realization of different processes. As can be seen, there is no universal classification of the burnishing methods. The differential-morphological method (DMM) allows not only a universal classification of the existing burnishing methods using a variety of signs but also of the new burnishing methods and tools to be synthesized. Y. N. Kuznetsov developed DMM [31] based on the morphological method proposed by the Swiss astronomer Fritz Zwicky [32]. In the present study, DMM is used for the classification and synthesis of burnishing methods. The method is ‘open’, i.e. the morphological signs of the object can always be expanded with new features according to the researcher’s preferences. The structure of the generalized burnishing method, shown in Fig. 5, consists of the following elements: 1, workpiece element; 2, deforming element; and 3 and 4, the elastic and viscous elements, respectively, for setting the burnishing force. For each element, the signs and the sub-signs can be defined in arbitrary order.

Fig. 1
figure 1

Scheme of single roller burnishing

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Fig. 2
figure 2

Scheme of multiple ball burnishing

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Fig. 3
figure 3

Scheme of slide burnishing a with cylindrical-ended tool and b with spherical-ended tool

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Fig. 4
figure 4

Ball burnishing with a hydrostatic sphere

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Fig. 5
figure 5

Structure of generalized burnishing method: 1 workpiece; 2 deforming element; 3 and 4 elements, respectively elastic and viscous, for setting burnishing force

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Table 1 contains the morphological signs and sub-signs to the second order for the elements in Fig. 5. On the basis of the morphological sub-signs from second order, the so-called morphological matrix has been arranged:

Table 1 Differential-morphological table
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\( \left[M\right]=\left[\begin{array}{ccccccccc}\mathrm{1.1.1}& \mathrm{1.2.1}& \mathrm{2.1.1}& \mathrm{2.2.1}& \mathrm{2.3.1}& \mathrm{3.1.1}& \mathrm{3.2.1}& \mathrm{4.1.1}& \mathrm{5.1.1}\\ {}\mathrm{1.1.2}& \mathrm{1.2.2}& \mathrm{2.1.2}& \mathrm{2.2.2}& \mathrm{2.3.2}& \mathrm{3.1.2}& \mathrm{3.2.2}& \mathrm{4.1.2}& \mathrm{5.1.2}\\ {}\mathrm{1.1.3}& \mathrm{1.2.3}& \mathrm{2.1.3}& \mathrm{2.2.3}& \mathrm{2.3.3}& 0& \mathrm{3.2.3}& 0& \mathrm{5.1.3}\\ {}\mathrm{1.1.4}& \mathrm{1.2.4}& \mathrm{2.1.4}& \mathrm{2.2.4}& \mathrm{2.3.4}& 0& \mathrm{3.2.4}& 0& \mathrm{5.2.1}\\ {}\mathrm{1.1.5}& \mathrm{1.2.5}& \mathrm{2.1.5}& \mathrm{2.2.5}& \mathrm{2.3.5}& 0& 0& 0& \mathrm{5.2.2}\\ {}\mathrm{1.1.6}& \mathrm{1.2.6}& \mathrm{2.1.6}& 0& \mathrm{2.3.6}& 0& 0& 0& 0\\ {}0& \mathrm{1.2.7}& 0& 0& \mathrm{2.3.7}& 0& 0& 0& 0\end{array}\right] \)

The matrix contains the last column of Table 1. Therefore, the number of columns of the matrix should be equal to the number of morphological signs. In the given example, the number of columns is smaller by one unit, because the combinations of sub-signs of 5.1 on one side and of 5.2 on the other hand are incompatible.

In order to synthesize a burnishing method, it is necessary to make a combination containing one element (with a number other than zero) from each column. Each element of the first column is combined with one element from the other columns. Each (compatible) combination corresponds to one burnishing method. Of course, there are also incompatible combinations. For example, some of the known methods are a combination of the following:

  • [1.1.1 1.2.3 2.1.1 2.2.5 2.3.6 3.1.2 3.2.4 4.1.1  5.2.2] corresponds to the ball burnishing with a hydrostatic sphere of the outer cylindrical surfaces (see Fig. 4).

  • \( \left[\mathrm{1.1.1}\kern0.5em \mathrm{1.2.3}\kern0.5em \mathrm{2.1.2}\kern0.5em \mathrm{2.2.4}\kern0.5em \mathrm{2.3.5}\kern0.5em \mathrm{3.1.1}\kern0.5em \mathrm{3.2.1}\kern0.5em \mathrm{4.1.2}\kern0.36em \mathrm{5.1.1}\right] \) corresponds to the roller burnishing of the outer cylindrical surfaces (see Fig. 1).

  • \( \left[\mathrm{1.1.2}\kern0.5em \mathrm{1.2.3}\kern0.5em \mathrm{2.1.1}\kern0.5em \mathrm{2.2.2}\kern0.5em \mathrm{2.3.2}\kern0.5em \mathrm{3.1.1}\kern0.5em \mathrm{3.2.1}\kern0.5em \mathrm{4.1.2}\kern0.36em \mathrm{5.1.1}\right] \) corresponds to the SDB with spherical-ended tool of the holes.

  • \( \left[\mathrm{1.1.1}\kern0.5em \mathrm{1.2.3}\kern0.5em \mathrm{2.1.2}\kern0.5em \mathrm{2.2.2}\kern0.5em \mathrm{2.3.2}\kern0.5em \mathrm{3.1.1}\kern0.5em \mathrm{3.2.1}\kern0.5em \mathrm{4.1.2}\kern0.36em \mathrm{5.1.3}\right] \) corresponds to the SDB with a cylindrical-ended tool of the outer cylindrical surfaces (see Fig. 3a).

  • \( \left[\mathrm{1.1.1}\kern0.5em \mathrm{1.2.3}\kern0.5em \mathrm{2.1.5}\kern0.5em \mathrm{2.2.4}\kern0.5em \mathrm{2.3.5}\kern0.5em \mathrm{3.1.2}\kern0.5em \mathrm{3.2.4}\kern0.5em \mathrm{4.1.2}\kern0.36em \mathrm{5.1.2}\right] \) corresponds to the spherical motion burnishing (SMB) of the shafts (Fig. 6a).

  • \( \left[\mathrm{1.1.2}\kern0.5em \mathrm{1.2.1}\kern0.5em \mathrm{2.1.1}\kern0.5em \mathrm{2.2.4}\kern0.5em \mathrm{2.3.6}\kern0.5em \mathrm{3.1.2}\kern0.5em \mathrm{3.2.4}\kern0.5em \mathrm{4.1.2}\kern0.36em \mathrm{5.1.2}\right] \) corresponds to the SMB of the holes (Fig. 6b) and so on.

Fig. 6
figure 6

Scheme of spherical motion burnishing a of shafts and b of holes

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The method implemented with a deforming ball with undefined motion occupies an intermediate position between SB and ball burnishing. This method is implemented with devices in which the deforming ball is supported by other balls or a rigid plane surface (Fig. 7) [33,34,35,36,37,38,39,40]. For a given burnishing device construction (a given support configuration), the type of contact between the deforming ball and the treated surface (rolling friction or sliding friction) depends on the friction coefficients between the deforming ball and the surface being burnishing, on the one hand, and between the deforming ball and the supports, on the other hand. This method is defined by the following combination:

Fig. 7
figure 7

Ball burnishing with undefined ball motion

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\( \left[\mathrm{1.1.1}\kern0.5em \mathrm{1.2.3}\kern0.5em \mathrm{2.1.1}\kern0.5em \mathrm{2.2.4}\kern0.5em \mathrm{2.3.7}\kern0.5em \mathrm{3.1.2}\kern0.5em \mathrm{3.2.4}\kern0.5em \mathrm{4.1.2}\kern0.36em \mathrm{5.2.2}\right] \)

A burnishing method (Fig. 8) that achieves rolling and sliding effects simultaneously on the burnishing point of the workpiece is also known [41, 42]. The aim of the method is to accomplish a finish with superior SI. This method is defined by the following combination:

Fig. 8
figure 8

Scheme of the burnishing that achieves simultaneously rolling and sliding effects

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\( \left[\mathrm{1.1.1}\kern0.5em \mathrm{1.2.3}\kern0.5em \mathrm{2.1.2}\kern0.5em \mathrm{2.2.4}\kern0.5em \mathrm{2.3.5}\kern0.5em \mathrm{3.1.1}\kern0.5em \mathrm{3.2.1}\kern0.5em \mathrm{4.1.2}\kern0.5em \mathrm{5.1.3}\right] \)

The proposed morphological matrix, which can be expanded and supplemented, contains not only the existing burnishing methods, but it also contains combinations that can be the basis for the synthesis of new burnishing methods and burnishing tools.

3 Essence of SB

The most important feature of SB is the sliding friction contact between the deforming element and the surface being treated. SB is kinematically similar to turning but, instead of a cutting tool blade, a spherical-ended (most frequently) or cylindrical-ended deforming element is moved under pressure over the work surface, causing plastic deformation on the surface and subsurface layers (Fig. 9). SB is especially suited for shafts and large bores but can be implemented on flat-face surfaces, as well. The method can be implemented in one of two ways: (1) The deforming element can be pressed elastically against the surface being treated (as shown in Fig. 9), and (2) without the aid of an elastic element (rigid fixing). The second variant is applied to short-length surfaces, where the shape accuracy is improved by one or two classes. When the deforming element is supported elastically, the shape accuracy is not improved—such improvement must be ensured via pre-treatment. The basic governing factors of the SB process are the sphere radius of the deforming element r, mm, burnishing force Fb, N, feed rate f, mm/rev, and burnishing velocity v, m/min. The number of passes, working scheme and lubricant used are additional factors. SB devices and tools are compatible with every conventional and CNC-controlled lathe or CNC turning centre. Therefore, a workpiece can be slide burnished in one setting directly after machining. The deforming element is most often a diamond—usually a polycrystalline synthetic diamond. The deforming element may also be made of sintered carbide or hardened tool steel. A diamond deforming element has the following advantages: high hardness, high wear resistance (abrasive and adhesive), high compressive strength and a low friction sliding coefficient. Since SB is conducted under sliding friction conditions, the above properties protect the treated material from temperature overloading, enable the SB of the hardest steels and alloys, and prolong the lifetime of the deforming tool. SB is a very economical method for producing mirror-like surface finishes on a wide range of ferrous and nonferrous machined surfaces. Since set up and operation is relatively simple and cycle times are short, no special operator skills are required.

Fig. 9
figure 9

Kinematics of SB

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4 Literary survey of SB and discussion

As noted in Sect. 1, General Electric invented SDB in the middle of the last century. A little later, the method spread to the machinery industry in the former Soviet Union, resulting in a massive number of studies performed by Russian researchers in the third quarter of the last century. Hundreds of publications from this period were devoted to both the SI of diamond-burnished specimens and the study of the process physics: generated heat, wear on the deforming diamond during operation and properties of the lubricants. Quite a few publications of this period refer to the synthesis and study of the physical properties of synthetic diamonds. A comparatively complete bibliographic reference for the Soviet researchers’ publications from this period is contained in the famous book by Yatsenko et al. [43]. Since that time, researchers around the world have investigated the SB process extensively. In terms of modern researchers, Korzynski [44] has made a significant contribution to the development of SB. Additional research groups contributing to SB include CIT, Rzeszow, Poland [44,45,46,47,48,49,50,51,52,53]; IAMT, Cracow, Poland [54,55,56,57]; KSU, Kurgan, Russia [58]; ZNTU, Zaporozhe, Ukraine [59]; Aalto University, Espoo, Finland [60, 61]; Kecskemet College, Hungary [62, 63]; SMSE, China [64,65,66,67]; NITK, Surathkal, India [68,69,70]; and the Technical University of Gabrovo, Bulgaria [71,72,73,74,75,76,77,78,79,80,81,82,83]. Some experimental studies by other researchers have also been reported worldwide [84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119].

The investigations concerning SB can be classified according to several indicators, as shown in Table 2. Figure 10 shows that most publications are devoted to SI resulting from SB. The exploitation properties of the slide-burnished surfaces are significantly less studied. The physical nature of the process is studied least—only 5% of the publications are dedicated to this problem. The nature of SB differs from that of burnishing with a rolling contact (roller/ball burnishing). In SB, the tangential contact between the deforming element and the surface being treated is one of sliding friction. Regardless of the low friction coefficient obtained in the case of using a synthetic diamond as a deforming element, the friction forces work is significant and dissipates into heat. Therefore, the deforming process in SB has a thermo-mechanical nature and the heat generated is the reason thermoplastic deformations emerge. Thus, all of the major effects of SB (smoothing, cold work, introducing residual compressive stresses) depend on the heat generated due to the softening effect of the surface layer. The temperature gradient in terms of the depth is very large—the temperature decreases sharply with depth. When the ‘deforming element-workpiece’ system is fully determined via geometry and physical-mechanical properties, the generated heat depends on the burnishing force, the burnishing speed and the friction coefficient. Due to the very short impact time of the deforming element at a given point on the surface being treated, the very small contact area, and the very high temperature gradient, the experimental determination of the temperature is very difficult. The formation and redistribution of the residual stress field in real-time is practically impossible to determine with an experimental study. These difficulties can be overcome through a FEM simulation of the thermo-mechanical deforming process in SB. For example, a sliding friction coefficient was found in a single publication [78] for a particular combination of materials of the deforming element and the surface being treated. This friction coefficient is an important component in an adequate FE model of the SB, and its precise definition is a prerequisite for more reliable FE results. Thus, the lack of information on the sliding friction coefficient automatically limits the possibility of reliable FE analyses. Information on deforming element wear [86] and heat generated [82] due to friction is also scarce—only one publication is dedicated to the relevant problem (Fig. 11). The heat generated causes a reduction in the surface residual stresses, but this important problem is illuminated in only two publications [80, 82].

Table 2 Classification of the investigations on SB
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Fig. 10
figure 10

Percentage share of the study objects

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Fig. 11
figure 11

Percentage share of the SB process physical nature

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In terms of the SI elements, the greatest attention is paid to the roughness obtained (Fig. 12), followed by the microhardness, residual stresses and microstructure of the surface layers. The methods used for the determination of the residual stresses are shown in Table 3. With six exceptions, experimental methods have been used (destructive and non-destructive), and non-destructive X-ray diffraction is the most commonly used method. The least-studied problem is related to the nanostructuring of the surface layers (see Fig. 12). However, this direction is promising because the nanostructured layers provide great micro-hardness, wear resistance and large low-cycle fatigue strength.

Fig. 12
figure 12

Percentage share of the SI components

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Table 3 Methods used for determination of the residual stresses
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Figure 13 shows that the fatigue behaviour is the most commonly investigated operational property (OP), followed by wear resistance. The integral approach (through S-N curves) is most commonly used to study the fatigue behaviour, while very little attention is devoted to the mechanism of delaying the formation and propagation of fatigue macro-cracking. Corrosion cracking resistance has been studied least, but this is a current problem in engineering practice.

Fig. 13
figure 13

Percentage share of the OP components

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More than three quarters of the studies are devoted to SDB (Fig. 14), i.e. diamond deforming elements. Obviously, the application of a sintered carbid as a deforming element is used considerably less, and the hardened steel is used least. Table 4 shows that the synthetic PCD is the most commonly used diamond. A single-crystal diamond is used considerably less. When considering the group of sintered carbides, the wolfram carbides are most often used (Table 5). The working surface of the deforming element (see Table 2) most often has a spherical form (84%). The effect of using a cylindrical shape is examined considerably less (11%). The toroidal form (5%) is applied only to the SMB of shafts.

Fig. 14
figure 14

Percentage share of the deforming element material

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Table 4 Type of the diamond used
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Table 5 Type of the sintered carbides used
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Figure 15 shows that the purely experimental approach is preferred most by researchers (74%). The analytic + experiment and FE analysis + experiment combinations occupy, respectively, second and third places. The analytical and the FE approaches are rather exceptions. The impression is that FEM is used significantly less for SB analysis than for the analysis of roller/ball burnishing.

Fig. 15
figure 15

Percentage share of the methods of study

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Considerably more research is devoted to SB of steels (65%) compared to SB of nonferrous materials (35%) of the studies (Fig. 16). Information about SB of cast iron is missing. The majority of the nonferrous materials investigated are aluminium alloys and aluminium composites. The impression is that SB of 2024-T3 Al alloy, titanium and magnesium alloys (typical for the aerospace industry) is relatively poorly studied. The probable reason for this neglect is the imposed belief that SB is only used for smoothing, i.e. that the application of SB is aimed primarily at obtaining mirror-like surfaces. On the other hand, the beneficial effect on the fatigue strength is associated largely with Ecoroll’s deep rolling process. In fact, SB has great potential in terms of the being able to create a zone with residual compressive stresses due to the small contact area between the deforming element and the surface being treated. The studies conducted in [76, 77] have shown that SB of 2024-T3 Al alloy not only provides roughness on the order of Ra = 0.05μm but also increases the fatigue life dramatically (hundreds of times). Moreover, the fatigue behaviour of the corresponding component can be controlled by appropriate selection of the SB process parameters. Therefore, SB can be implemented as mixed burnishing [120]. Tables 6 and 7 contain generalized information regarding the treated material—the specific type of material and results obtained for roughness, micro-hardness and residual stresses. It appears that full information exists only for AISI 316Ti, while, for other materials, there is no information on the three characteristics.

Fig. 16
figure 16

Percentage share of the treated material

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Table 6 Summary of SB of steels
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Table 7 Summary of SB of nonferrous materials
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Figure 17 shows that three-quarters of the studies are devoted to the SB of outer cylindrical surfaces, while the SB of holes is covered by only 6% of the studies. It appears that the SB of planar surfaces makes up a significant share of these studies (16%), which somewhat disproves the opinion that SB ‘is also possible in terms of treating flat and shaped surfaces, but it is not used in practice’ [44].

Fig. 17
figure 17

Percentage share of the type of the treated surface

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The percentage shares of the SB process parameters studied are shown in Fig. 18. The most commonly studied parameters are feed rate and burnishing force (which is directly correlated with the burnishing depth). The additional process parameters (lubricant used, number of passes and working schemes) have been studied considerably less. The importance of the additional parameters should not be underestimated, as they have a significant effect on the fatigue life of the slide-burnished components, as found in [77].

Fig. 18
figure 18

Percentage share of the SB process parameters studied

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5 Conclusions and directions for future investigations

Based on the analysis, the following conclusions can be made:

  1. 1.

    The majority of SB studies are focused on the study of SI, where the attention is focused mostly on the roughness and microhardness. Significantly less attention is paid to wear resistance and fatigue strength. The publications that examine the roughness, microhardness and residual stresses for a given material simultaneously are very few in number.

  2. 2.

    A very small percentage of the publications are aimed at optimizing the SB process according to the maximum fatigue strength criterion. In fact, only one publication is devoted to increasing the crack resistance of holes processed by SB.

  3. 3.

    The question concerning the use of SB in combination with TCD processes (for example, nitriding and cementation) is relatively weakly affected.

  4. 4.

    The application of SB for the treatment of holes is poorly studied.

  5. 5.

    The wear on the types of diamond deforming elements and the impact of that wear on the surface quality obtained have been insufficiently studied.

  6. 6.

    FEM is insufficiently used for a complete analysis of both the thermo-mechanical nature of the process and the effect of SB on SI.

  7. 7.

    The following SB governing factors are most often defined: the radius of the spherical-ended deforming element, burnishing force, feed rate, burnishing velocity and number of passes. However, experience has shown that a combination of these factors achieves a different SI results, for different workpiece diameters (10 mm versus 100 mm). The reason for these different results is the different contact area between the deforming element and the surface being treated. Therefore, another control parameter is needed to take the large-scale factor into account.

  8. 8.

    The sliding friction coefficient between the deforming element and the material to be treated is poorly studied.

  9. 9.

    Comprehensive studies comparing SB and roller/ball burnishing in terms of SI are practically absent (with the exception of Hamadache et al. [116]).

  10. 10.

    The possibility of processing non-metallic materials through SB has not been investigated. Recently, Babic et al. demonstrated the use of ball burnishing to process wooden components and showed that the microhardness of the surface layer increased more than seven times [121].

  11. 11.

    The proposed morphological matrix, which can be expanded and supplemented, is a basis for the synthesis of new burnishing methods and tools, including those needed for special applications.

  12. 12.

    Based on the conclusions, the following directions for future investigations are proposed:

  1. (a)

    Conducting extensive research to supplement the missing information in Tables 6 and 7

  2. (b)

    Optimization of the SB process of various metals and alloys using maximum fatigue strength criterion

  3. (c)

    Synthesis of super-hard alloys as deforming elements and the study of their wear resistance

  4. (d)

    Study of the efficiency of SB in combination with SHT and TCD processes

  5. (e)

    Creation of an adequate thermo-mechanical KE model with which to study the thermo-mechanical nature of SB and the effect of the SB process on SI

  6. (f)

    Comprehensive studies comparing SB and roller/ball burnishing in terms of SI

  7. (g)

    Investigation of the possibility of the SB of cast iron and non-metallic materials

  8. (h)

    Synthesis of new burnishing methods and burnishing tools on the basis of the proposed morphological matrix, which can be expanded and supplemented