Metal matrix composites (MMCs) are systematic combinations of two or more materials (one of the materials is a metal) engineered to achieve tailored properties (1). Thus, engineered MMCs have two or more chemically and physically distinct phases that are suitably distributed to provide properties not attainable with either of the individual phases (2). AMMCs exhibit better mechanical and physical properties than the aluminium-matrix alloy (3–5). The hardness and strength of AMMCs are significantly higher than that of the aluminium-matrix alloy, leading to improved wear resistance (6). AMMCs have found applications in aerospace, automotive, nuclear, telecommunications (7) and marine industries (6). The applications of AMMCs in the automotive and aerospace industry sectors can reduce fuel usage by replacing steel and cast-iron parts with lighter AMMCs. Some of these applications include pistons, piston rings, cylinder liners, connecting rods (1), cylinder blocks, driveshafts and brake drums (6). The tribological behaviour of particle reinforced AMMCs has been regularly reported. However, most of the studies have analysed the tribological behaviour of composites reinforced with SiC and Al₂O₃ particles. Besides these conventional reinforcement particles, aluminium alloys also can be reinforced with h-BN (8), TiC (9), TiO₂ (10), ZrO₂ (10) and B₄C (11) to impart wear resistance. Studies on AMMCs reinforced with B₄C particles have been limited mainly due to the higher cost of B₄C particles than SiC and Al₂O₃ particles (12). Al-B₄C composites are commonly used in automotive, sports (7) and neutron shielding applications (13).

B₄C possesses excellent properties such as high hardness, low density, high melting point, chemical inertness and wear resistance, making it suitable for many high-performance applications (14). The hardness of B₄C (Vickers Hardness under the load of 0.981 N (HV0.1) = 3200) is far superior to the hardness of conventional reinforcement particles, SiC (HV0.1 = 2500) and Al₂O₃ particles (HV0.1 = 1900) (15). The density of B₄C (2.52 g cm^–3) (16) is less than the density of solid aluminium (2.70 g cm^–3) (17), which significantly improves specific properties. The densities of SiC, Al₂O₃ and B₄C are 3.21 g cm^–3, 3.92 g cm^–3 and 2.52 g cm^–3, respectively. The density of molten aluminium is 2.38 g cm^–3 (17). Hence, it is evident that the difference in density between molten aluminium and B₄C is lower when compared to the difference in density between molten aluminium and conventional reinforcement phases (SiC and Al₂O₃). This phenomenon minimises the sedimentation of B₄C particles at the crucible bottom during stir casting (12). The abrasive resistance of B₄C (0.4–0.422 (expressed in arbitrary units)) is higher than that of SiC (0.314 (expressed in arbitrary units)) due to its high hardness and strength (18).

This overview aims to discuss the microstructural characteristics, mechanical properties and tribological behaviour of Al-B₄C composites. The different properties and microstructural characteristics of Al-B₄C, Al-SiC and Al-Al₂O₃ composites are compared. Furthermore, the statistical significance of physical parameters (applied load, sliding speed and sliding distance) on the tribological behaviour of the composites is analysed. However, the literature that compares the microstructural characteristics, mechanical properties and tribological behaviour of Al-B₄C, Al-SiC and Al-Al₂O₃ composites are insufficient. The literature on the statistical analysis of the tribological behaviour of Al-B₄C composites is also sparse. Despite these shortcomings, this overview discusses the mechanical and tribological properties of the composites mentioned above. Section 2 gives a brief insight into the fabrication of Al-B₄C composites through the stir casting technique. Section 3 compares the microstructural characteristics of Al-B₄C, Al-SiC and Al-Al₂O₃ composites. Section 4 analyses the tribological behaviour of Al-B₄C composites. The tribological properties of Al-B₄C and Al-SiC composites are also compared in Section 4.

Many methods are available to fabricate MMCs, and the commonly used two primary processes are: (a) solid-state processes; and (b) liquid state processes (6). Liquid state processes include infiltration techniques (pressure infiltration and squeeze casting) and dispersion techniques (stir casting and compocasting). The stir casting (vortex addition) technique has been the most studied method for producing AMMCs due to its simplicity, flexibility, commercial viability and ease of processing (19, 20). The core requirement of the stir casting of MMCs is close contact and bonding between the ceramic phase and the molten alloy. The wettability of the ceramic particles to molten melt is inherently weak. Thus, intimate contact and bonding between them are enhanced by artificially inducing wettability or using an external force to weaken the thermodynamic surface energy barrier. One of the commonly used methods to incorporate, wet and uniformly distribute the ceramic particles is to add the particles to a vigorously stirred molten melt. The stirring action (external force) enhances wetting and ensures homogenous dispersion of reinforcement particles through the matrix. Wettability is also induced artificially by modifying the chemical composition of the matrix alloy: small quantities of reactive elements, such as magnesium, calcium, lithium or sodium, are added (20). The addition of magnesium improves the wettability of Al₂O₃ and SiC particles to the alloy matrix, which increases the wear resistance of Al-Al₂O₃-SiC hybrid composites (21).

Lashgari et al. (22) reported that during stir casting, the addition of magnesium improved wettability between the matrix (A356) and reinforcement particles (B₄C). The reinforcement particles were preheated to enhance the wettability of the ceramic particles with the metal matrix. Details of the stir casting technique and the particle size of B₄C particles are shown in Table I. Mahesh et al. (23) preheated the reinforcement particles to remove impurities and to enhance the wetting characteristics. Canakci et al. (24) observed that the vortex formed due to stirring holds the reinforcement particles dispersed in the melt, which ensured their uniform distribution. After particle addition, the composite melt is poured into a permanent mould. Kalaiselvan et al. (25) fabricated AA6061-B₄C composites reinforced with 4 wt%, 6 wt%, 8 wt%, 10 wt% and 12 wt% B₄C particles through the stir casting process. Uniform distribution of reinforcement particles was observed at all weight percent additions. Furthermore, X-ray diffraction (XRD) analysis of the composites revealed that there is no reaction of the AA6061 matrix with the B₄C particles. This phenomenon shows the thermodynamic stability of B₄C particles at the temperature (920°C) used for the stir casting of AA6061-B₄C composites. The parameters used by Lashgari et al. (22), Mahesh et al. (23), Canakci et al. (24), Kalaiselvan et al. (25), Toptan et al. (26), Mazahery and Shabani (27), Toptan et al. (28) and Baradeswaran and Perumal (29) for the stir casting of Al-B₄C composites are listed in Table I.

Shorowordi et al. (30) studied the matrix-reinforcement interface of Al-20 vol% SiC (Figure 1(a)), Al-20 vol% Al₂O₃ (Figure 1(b)) and Al-13 vol% B₄C (Figure 1(c)) composites produced through the stir casting technique.

Fig. 1.

The microstructure and interfacial characteristics of Al-SiC, Al-Al₂O₃ and Al-B₄C composite are extensively reported in this study. The interfacial reaction product is not observed for the Al-B₄C composite, unlike the Al-SiC composite, which revealed an apparent interfacial reaction. Furthermore, it was observed from the fracture surfaces that Al-B₄C composite exhibited the strongest bonding at the matrix-reinforcement interface, and the bonding of Al-SiC composite is weak due to the low adherence of aluminium matrix to the SiC particles. In Al-Al₂O₃ composites, voids and microvoids are observed at the interface, indicating poor bonding. Moreover, particle distribution is found to be better for Al-B₄C composite when compared to Al-SiC and Al-Al₂O₃ composites.

The mechanical properties of spray-cast Al 6061-15 vol% B₄C and aluminium 6061-15 vol% SiC composites have been reported (31). The B₄C reinforced composite exhibited significantly greater strength, strain to failure in tension and strain hardening compared to the SiC reinforced ones, due to strong bonding at the Al-6061-B₄C interface (31). The strong bonding at the interface is ascribed to the chemical stability of B₄C particles, the absence of interfacial reaction products and the excellent wetting of the particles by the matrix alloy. The wetting characteristics of the Al-6061-SiC composite are weaker than that of the Al-6061-B₄C composite.

3.1 Influence of Boron Carbide Particles Addition on Hardness

An overview of the literature on the tribological properties of Al-B₄C composites is provided in the following subsections. The tribological properties are controlled by the physical parameters (applied load, sliding speed and sliding distance) and material parameters (the type of reinforcement and volume fraction) (35). Hence, the overview is focused on analysing the influence of physical and material parameters on the dry sliding tribological behaviour of the composites. The relevant details of sliding wear studies are shown in Table II.

4.1 Effect of Variation of Applied Load

4.2 Effect of Variation of Sliding Distance and Sliding Speed

4.3 Influence of Mechanically Mixed Layer

4.4 Beneficial Effects of Boron Carbide Particles Addition

4.5 Comparison of Tribological Properties of Aluminium-Boron Carbide and Aluminium-Silicon Carbide Composites

4.6 Inferences Obtained from the Statistical Analysis

The fabrication and tribological properties of Al-B₄C composites are discussed in this overview. The Al-B₄C composites exhibited better particle distribution than Al-SiC or Al-Al₂O₃ composites. The bonding at the matrix-reinforcement interface is also strong, and the interface is free of the interfacial reaction product, which is not the case with Al-SiC and Al-Al₂O₃ composites. The presence of a brittle phase at the matrix-reinforcement interface reduced the wear resistance of Al-SiC composites. The friction coefficient of Al-B₄C composites is lower than that of Al-SiC composites due to the presence of oxidised boron on the contact surfaces. The better tribological properties of Al-B₄C composites compared to those of pure aluminium are due to the abrasion resistance imparted by the B₄C particles. The wear mechanisms induced during wear studies of Al-B₄C composites are plastic deformation, adhesion, abrasion and delamination. Statistical analysis revealed that the influence of physical and material factors and their interaction on the tribological behaviour is statistically significant.

To summarise, Al-B₄C composites exhibit better microstructural characteristics than aluminium-matrix composites reinforced with SiC and Al₂O₃ particles. The tribological properties of Al-B₄C composites are better than those of aluminium and Al-SiC composites; thus, these composites may be considered as a potential candidate for different tribologically crucial applications.

In this research, desized, 100% cotton fabrics (warp/weft yarn density of 34/17 yarns per centimetre) were used. Mikrathermic^® P PCM capsules were provided by Devan Chemicals, Belgium. For the coating process, Mikracat B as a cross linker and L Mikrasoftener as a softener were supplied from Devan Chemicals. RUCO^®-COAT PU 1110 polyurethane coating material was used for coating process and supplied from Rudolf Duraner, Turkey. EDOLAN^® MR polyurethane binder was used for the impregnation method and provided by Tanatex, Switzerland to bond the microcapsules to the fabric. All other auxiliary chemicals used in the study were of laboratory-reagent grade.

The application of the capsules to the cotton fabrics was carried out by impregnation and coating methods. Fabrics were conditioned in accordance with ISO 139:2005 (43) at standard atmospheric conditions (20°C±2 and 65% RH±4) for 24 h. Capsule transfer prescriptions were made according to Tables I and II and in the same ratio to compare the application processes. Polyurethane was selected as binder and each experiment was repeated three times.

The capsules were impregnated in a solution bath containing capsules (125 g l⁻¹) and binding agent (30 g l⁻¹), and then squeezed between rollers to 90% wet pick-up. Achieving long lasting effect, the fabric was exposed to drying for 10 min at 80°C and fixation process for 3 min at 140°C in a laboratory stenter (Table I).

Viscosities of the coating pastes were measured using a DV-II+Pro viscometer (AMETEK Brookfield, USA) and the viscosity of the coating paste was determined to be 9000 cps. Cotton base fabrics were coated with the above mentioned coating pastes using a laboratory type blade coating machine, as two layers of coating. It was subjected to intermediate drying at 100°C for 2 min between each layer. Coated samples were cured at 140°C for 3 min.

SEM images were taken to obtain the existence of capsules on the textile surface from both coated and impregnated samples. Samples were gold-coated (15 mA, 2 min) to assure electrical conductivity. The measurements were taken at 2 kV accelerating voltage. The images were taken at 250× and 1000× magnification.

Thermal properties of the fabrics, such as melting and crystallising temperatures and enthalpies, were measured by DSC performed using a PYRIS^TM Diamond differential scanning calorimeter (PerkinElmer Inc, USA) to distinguish the capsules on the fabric with the help of characteristic endothermic or exothermic peaks. The samples were cooled down to −20°C and then heated up to 40°C at a constant rate of 10°C min⁻¹ under a nitrogen flow rate of 60 ml min⁻¹.

In order to examine the efficiency of the transferred capsules, the surface temperature of the raw fabric samples containing PCM was measured at a certain time interval by thermal camera as shown in Figure 1. Measurements in the system were made in an insulated box. Before measurement, the inner temperature of the box was heated to a constant temperature of 40°C and the test was carried out at this temperature. The inner temperature of the box was kept constant by means of a thermostat. Before measurement, the fabrics were conditioned for 12 h and placed in the box as quickly as possible. Once the fabric was placed in the box, the surface temperature was measured from a fixed point for 15 min. A thermal camera (Fluke Ti100 Thermal Imager, Fluke, USA; emission value 0.94) was used in the measurements and the temperature was recorded every 30 s.

Fig. 1.

When an interface exists between a liquid and a solid, the angle between the surface of the liquid and the outline of the contact surface is described as the contact angle θ (lower case theta). The contact angle (wetting angle) is a measure of the wettability of a solid by a liquid. In order to examine the hydrophilicity of the fabrics, the contact angle was examined. The measurements were carried out at 25°C using the Theta Lite T101 (Biolin Scientific, Sweden) model contact angle device. An image of approximately 5 μl of water droplet dropped onto the surface to be measured was recorded for 10 s by the device camera. Using the device software, an average of 200 data were recorded for 10 s for each sample and the arithmetic mean was taken.

Water vapour permeability is related to breathability of fabrics. Water vapour permeability of samples was determined by using M261 (SDL Atlas International, USA) model water vapour permeability tester according to BS 3424-34:1992-Method 37 (44). The amount of water vapour passed through the samples was determined after 24 h and permeability values were calculated. The test was repeated three times for each sample type.

SEM images of the Mikrathermic^® P PCM capsule are shown in Figure 2. Mikrathermic^® P was around 3 μm and had a spherical shape as expected. SEM images of the PCM capsules transferred to cotton fabrics by coating and impregnation methods, enlarged 250 times and 1000 times, are given in Table III.

Fig. 2.

Table III

SEM Photomicrographs of Fabrics Treated with PCM Capsules

Fabric	250×	1000×
Coated
Impregnated

When the images were examined morphologically, it was observed that the capsules transferred by the impregnation method preserved their spherical form. PCMs transferred by coating remain under the coating polymer and were homogeneously distributed over the entire surface. These images showed that capsule application was successful for both impregnation and coating methods. It was observed that capsules were covered with the binder and fixed onto the textile surface of the cotton fabrics.

The DSC diagrams of coated and impregnated fabrics are given in Figure 3. The heat storage capacity of the Mikrathermic^® P PCM microcapsule is 140 J g⁻¹ according to the literature (45–47). From the DSC curve given in Figure 3 and from Table IV, the amount of heat stored and emitted by the fabrics from the area under the endothermic and exothermic melting and solidification peaks and the temperatures at which heat storage and emission begins can be seen. According to the DSC analysis, similar values were obtained for coated and impregnated fabrics. The values are provided in Table IV in detail.

Fig. 3.

The melting process in fabrics coated with Mikrathermic^® P microcapsules occurred between 25.83°C–31.04°C and the amount of heat energy stored by the cotton fabric during the melting period was measured as 2.70 J g⁻¹. For the Mikrathermic^® P microcapsule, the crystallisation process occurred in the range of 25.70°C–23.45°C and the cotton fabric released −1.45 J g⁻¹ heat during crystallisation. Impregnated fabric absorbed 2.70 J g⁻¹ at 25.72°C during melting and released −1.39 J g⁻¹ at 25.61°C during crystallisation.

Thermal conductivity measures the capacity of temperature exchange between heat and cold passing through a material mass. Decreased thermal conductivity allows for a faster rate of heat transfer in a PCM, increasing the time required for the PCM to undergo a complete charge or discharge. The major shortcoming of PCM is its limited ability to exchange heat effectively due to low thermal conductivity. This suppresses the amount of heat that can be exchanged during melting processes and a lower thermal conductivity of solidification will occur at low temperatures. The effective thermal conductivity of PCM can be increased by many mechanisms such as inserting fins and adding a dispersion of high thermal conductivity nanoparticles (48, 49).

Although the process temperatures are very close to each other, coated fabrics changed state at higher temperatures compared to impregnated fabrics. The shifting of the process peaks to higher temperatures has been explained in the literature as the lower thermal conductivity of the fabric (50). This situation was interpreted as the lower thermal conductivity value of coated fabrics compared to impregnated fabrics resulting in melting and solidification at higher temperatures. However, considering that these data are very close to each other, it was thought that the capsules can be transferred to the fabrics by the coating method. Encapsulated PCMs which were transferred with coating and impregnation lead to lower thermal conductivity and increased heat capacity of a textile structure. They improve the thermal performance of textile material and therefore may save energy.

Depending on the change in ambient temperature, the fabric surface temperature change caused by PCM capsules was measured. For this purpose, a thermal camera was used to determine the heat regulation properties of fabrics that can store heat. Two measurements were taken from two different points in the fabric samples and their averages are shown in Figure 4.

Fig. 4.

The temperature-time curves are given in Figure 4. It can be seen from the graphs that the fabrics which were brought from a cold environment (4°C±2) to a warm environment (40°C±2) were warmed and the temperatures measured on their surfaces increased. On the other hand, it is observed that the heating time of the fabrics in a hot environment and the maximum temperatures reached were not equal. According to both measurement results, it can be seen that the raw fabric heats up the fastest. Similarly, the maximum surface temperature of the raw fabric was higher than the fabrics containing PCM. The raw fabric warmed to almost maximum temperature (about 42°C) in about 5 min. For fabrics containing PCM, the maximum temperature recorded was lower at the end of the measurement period. The maximum value recorded was 37°C for the fabric in which the PCM capsules were impregnated and 40–41°C for the fabric transferred with the coating. Thermal camera analysis was performed for 15 min. It was determined that the temperature of the fabrics remained at the last point which they reached for an extended period. During the measurement period, it was determined that the temperature measured on the surface of the fabric to which the PCM capsules were impregnated was 3°C to 5°C lower than the raw fabric surface temperature. It was determined that the surface temperature of the fabric to which the PCM capsules were transferred with the coating was 1–3.5°C lower than the raw fabric.

When the analysis results were evaluated, it was seen that the fabric with PCM transferred by the impregnation method has more effective temperature regulation. The impregnated fabric, which has the lowest temperature, absorbed more heat in the cold environment when the PCM structure was applied. It also appears that there was not a big difference between coating and impregnation methods in thermal camera analysis. The thermal camera method demonstrates the heat regulation ability of fabrics, but does not provide information about their performance in end-use areas. Therefore, for fabrics treated with coating and impregnation methods, performance evaluation according to the area of use will give the most accurate results. This shows that PCM capsules can also be transferred by the coating method, depending on the usage areas.

In order to evaluate the hydrophilicity properties of raw fabric and PCM-transferred fabrics with different methods, contact angle measurement was made as shown in Figure 5.

Fig. 5.

The angle between the surface of the liquid and the outline of the contact surface is described as the contact angle θ. The contact angle is a measure of the wettability of a solid by a liquid. In the case of complete wetting, the contact angle is 0°. Between 0° and 90°, the solid is wettable and above 90° it is not wettable. When the analysis results were examined, water was completely absorbed by raw fabric in 5 s and this indicates that the fabric is hydrophilic. When comparing the transfer methods of PCM capsules, contact angle of impregnated and coated fabric was obtained as 42° and 73°, respectively. In general, the coating paste has a more viscous structure and this structure causes a thick layer to form on the fabric. Due to this structure, the surface energy of the fabric decreases and it gains water repellency. In the impregnation method, since a viscous structure is not obtained and a layer is not formed on the fabric surface, the contact angle becomes lower causing the textile material to be more hydrophilic than the coated one. This result, as expected, was that the coated fabric was more hydrophobic than the impregnated fabric.

Water vapour permeability analysis was carried out to examine the comfort properties of the fabrics obtained. Water vapour permeability of samples are tabulated in Table V.

The highest water vapour permeability was obtained from raw fabric with 625 g m⁻² per 24 h permeability value. It was determined that the fabrics with PCM transferred by the impregnation method gave a similar result to the raw fabric. On the other hand, water vapour permeability of coated samples reduced to approximately 50% that of the raw base fabric in parallel with the contact angle results. This was due to the additional polyurethane coating layer which contributed mass transfer limitation through the fabric. Even the most breathable coating polymer applied to the samples would add a resistance to vapour flow by closing the pores and creating an additional layer (51). The water vapour permeability of a material plays an important part in evaluating the physiological wearing comfort of clothing systems or determining the performance characteristics of textile materials used in technical applications. Therefore, it is important to choose the transfer method of PCM capsules considering the area where the fabric will be used.

There are few mathematical breakthroughs that have had as dramatic impact on the scientific process as the Fourier transform. Defined in 1807 in a paper by Jean Baptiste Joseph Fourier (1) to solve a problem in heat conduction, the integral transform, Equation (i):

(i)

and its inverse, Equation (ii):

(ii)

provide the framework to determine the spectral make up of a time varying function g(t) using Equation (i). Conversely, if the frequency domain is understood G(ω), the time signal can be derived using Equation (ii). The same analysis can be applied to spatial functions to yield wave number spectra and is the basis for a significant portion of wave optics, and is used in techniques such as Fourier transform infrared (FTIR) spectroscopy (2).

The transform, which is part of a wider family of integral transforms (3), had a profound impact on the development of much of 19th and 20th century mathematical physics. Previously intractable problems in optics, electromagnetism and acoustics became soluble. The insights these breakthroughs yielded paved the way for quantum mechanics and much of modern science. The famous Heisenberg uncertainty principle is actually just a mathematical property of the Fourier transform in Schrödinger’s wave mechanics (4). Domínguez gives a good overview of this history and some of the mathematical properties of the transform that make it so useful (5).

A significant hurdle with the practical application of the Fourier transform in real-world problems is that it is mathematically challenging to calculate for even the simplest of functions. As a consequence the transform is not taught in the UK until undergraduate level and even then only in mathematically heavy courses such as mathematics, physics and engineering. To make progress in practical problems numerical methods are generally required, meaning the practical application of the Fourier transform can feel like an esoteric part of computer science, rather than the scientific core of the modern world.

Fortunately, the great leaps in understanding that quantum mechanics gave us in electronics has ultimately led to a situation where anyone who wants to, can with a few lines of Python (6) code use sophisticated algorithms that have been developed in the post-World War II period. As such, calculations of the Fourier transform are readily available to those that would like to make use of them.

Unfortunately, the education around how to do practical Fourier analysis has become something of a dark art, which is often picked up in an ad hoc manner in postgraduate studies. The advent of accessible artificial intelligence algorithms has further obscured the basic techniques of Fourier analysis and created a strange scenario where even basic spectral methods are being conducted with inefficient computationally heavy neural network approaches.

In this short article we outline some basic practical steps for successfully conducting Fourier analysis. We will also give a few example Python scripts so the interested reader may apply these techniques to their data.

The first challenge for any numerical method is the digitisation step during which the smooth curves of analytical functions must be turned into discrete numbers. There are two sources of data that are normally digitised:

Discussing these in turn, when an analytic function of time g(t) is evaluated, it is relatively trivial to generate the discretised function with N samples in the time window 0 < t ≤ T (Equations (iii) and (iv)):

(iii)

where

(iv)

The numerical value of δ is of crucial importance in numerical estimates of the Fourier transform. It places limits on what information is lost in the discretisation and plays a fundamental role in how experimental work should be designed. It is more usual to quote its reciprocal, which is the sampling frequency, f_s (Equation (v)):

(v)

It is this frequency that appears in one of the most important results associated with the Fourier transform: Nyquist’s theorem (7). This result states (Equation (vi)):

(vi)

where B is the highest frequency component in the signal in g(t).

Nyquist’s theorem is particularly important as we turn our discussion to sampling experimental data. In theoretical work one can choose, in principle, δ to be as small as is necessary. However, in experimental work this is not an available option; the cost of data loggers increases significantly with the sampling frequency and data storage problems quickly become limiting. Moreover, in nearly all applications where data is recorded by a computer, signals are voltages recorded by an analogue to digital converter (ADC). To conduct scientific work a 12 bit ADC is the standard level. This means that a voltage signal varying between a nominal full-scale deflection ±10 V is recorded to the nearest 5 mV as defined in Equation (vii):

(vii)

When numerical results are compared to experimental results this level of precision must always be borne in mind, as the limitations of the sampling frequency or the voltage level are both likely to be significantly more coarse grain in the experimental work. An example of the effects of this digitisation step is shown in Figure 1. A 5.01 Hz sine wave has been sampled for 1 s, with a sampling frequency of 200 Hz. The blue dots denote the locations of the sampled data and the red curve the analytic form of a sine curve with this frequency.

The popular data analytics tool Jupyter (8) was used to generate the graph shown in Figure 1, this is part of the open-source data analytics bundle Anaconda. The code used is shown in Figure 2. The majority of the code is presentational and associated with plotting the graph using the Python library matplotlib (9). However, the numerical analysis makes use of the versatile NumPy library (10). The key lines for our discussion are lines 17 and 18, which generate two vectors Vs and Vss. The vector Vss is the smooth underlying 5.01 Hz sinusoidal signal and Vs is the signal sampled with a sampling frequency of 200 Hz. It is these two vectors that are manipulated in the sections that follow.

Fig. 1.

Fig. 2.

Having defined the digitised signal, discrete Fourier transform (DFT) can be defined as shown in Equations (viii) and (ix):

(viii)

where

(ix)

The DFT is simple enough to code from first principles that it is often used as an example numerical problem to teach students how to use loops in a given programming language, however it is rarely used in production code because it is computationally inefficient. As the number of samples increases, the number of calculations increases with the square of the number of samples (O(N²)). If this efficiency problem had not been solved in a paper by Cooley and Tukey (11), where they introduced what is known as the fast Fourier transform (FFT), a significant amount of the telecommunications sector would not have been possible. The algorithm they published was actually first discovered by Gauss in 1809 in an unpublished paper and uses a divide and conquer technique. The original time series is split into odd samples and even samples; and then a recursive approach used to construct the Fourier spectrum. This is the reason that many implementations of this algorithm impose the restriction that the number of samples should be a power of two, as this improves the operational efficiency. The efficiency of the FFT scales as O(N log N) opened up the possibility of using Fourier analysis in technical areas that previously would not have been possible.

It is not an exaggeration to say the FFT revolutionised electronic engineering and in turn computer science. Nearly all digital communications rely on the FFT in some form. A measure of how integral to the mathematical sciences the algorithm has become is that improvements to the algorithm continue to the modern day, for example a particularly fast and robust implementation of the FFT called the ‘fastest Fourier transform in the West’ (FFTW) was developed and maintained by academics at the Massachusetts Institute of Technology (MIT), USA (12), and remains an active project. Despite how readily available FFT algorithms have become it is still easy to make mistakes when using them in a real-world example. A raw power spectrum of the time series shown in Figure 1 is shown in Figure 3. The spectrum is shown on a log scale to highlight the detailed features that might otherwise be missed.

Fig. 3.

The first and most important point is that the spectrum plotted is actually a power spectrum. Theoretically this is defined as Equation (x):

(x)

where the G^*_k is the complex conjugate of each Fourier component. The process of finding the power spectrum is lossy, as all phase information in the signal is lost. Despite this, there are many situations where the power spectrum is a much more useful quantity than the raw time series. In this example the large peak at 5.01 Hz, which is seven orders of magnitude above the noise floor, easily identifies the main frequency present in original times series. The code snippet in Figure 4 illustrates how simple using the FFT is with a modern analytics package like Jupyter. Line 2 takes the sampled data Vs from Figure 2, calculates the FFT and converts it into a power spectrum (by taking the absolute value and squaring each component of the vector). Line 3 is simply the calculation of the frequency associated with each bin in the spectrum and is determined by the original sampling frequency fs of the signal. The remainder of the snippet is about presenting the spectrum on a graph.

Fig. 4.

The ideal nature of the original time series used to calculate the power spectrum shown in Figure 3 obfuscates some of the limitations of this naïve brute force use of the FFT. A typical experimental time series has underlying electrical noise and the time digitisation further distorts the signal. In the following sections we shall discuss the best practice that should be followed to get the best estimate of a power spectrum from an experimental signal. We first simulate what a noisy experimental signal might look like by adding Gaussian noise and then splitting the data into 20 different finite levels to simulate the effect of an analogue to digital converter. The three signals are shown in Figure 5. The digitised noisy signal is representative of many experimental signals met in practice.

Fig. 5.

The main challenge with any experimental setup is designing the experiment to give the best answers we can reasonably expect. The processing of a time series to give the most spectral insight is no different. In this section we will attempt to give some basic guidelines that a novice time series analyst should follow, where possible, when conducting spectral analysis.

4.1 Filter High Frequency Signals

Once a low pass filter has been applied to the signal it is sensible to resample the data at the lower frequency to enable more details of the spectrum to be resolved in the region of interest. This process is called downsampling (15) and should only be done if there are no higher frequency components that are likely to interfere with the results. Since we have applied a low pass filter there are no higher components in the time series data, hence downsampling can be applied safely. The reasons for doing this are perhaps not obvious at first sight, but as discussed in the next section, the computational impact of having an oversampled time series can be significant, particularly when fine frequency resolution is required in the power spectrum.

If one considers two notes of frequency f₁ and f₂ which are played at the same time, a third lower frequency can be heard. This is called a beat frequency, f_b (Equation (xi)):

(xi)

If the notes are nearly the same frequency, the beat frequency becomes very small, vanishing to zero when they are identical. Guitarists sometimes use this effect to tune their instruments. This point illustrates that in order to distinguish between two frequencies of slightly different tones, the frequency resolution is limited by the length of the time series recorded. To increase frequency resolution one must record longer time series. The impact of increasing the sampling time frame can be quite dramatic. The power spectrum shown in Figure 8 is what is obtained if 25.8 s of data are used at the 40 Hz sampling frequency (1024 data points). The fundamental peak at 5.01 Hz is much sharper allowing for a better resolution of the frequency.

Fig. 8.

If the downsampling step had not been performed to get the same resolution, the number of data points included in the FFT would need to be increased five-fold for no benefit. It is tempting to simply take very long time series and then calculate the power spectrum with a very large number of data points. However, this can be counter productive, not to say computationally inefficient. The spectrum shown in Figure 8 has 512 different frequency bins for 0 < f < 0. 5f_s, which gives a resolution of Equation (xii):

(xii)

If a frequency resolution finer than this is required then it is reasonable to use longer time series. However, fine resolution bins can lead to difficult-to-interpret noise floors. It is unlikely, for example, that there is a two order of magnitude difference in the power content of two adjacent bins outside of the main harmonics of any time series, yet that is what the blue spectrum shown in Figure 8 indicates. This wildly oscillating noise floor is an artefact of the discretisation, rather than a true reflection of the noise content of the signal.

4.4 Averaging Spectra and Window Functions

The application of the FFT to data is one of the most widespread numerical algorithms. It is integral to a huge amount of fundamental scientific research and engineering. In an industrial setting the power spectrum is used as a noise reduction method on many sensors, in the communication sector information is compressed using the FFT and in the laboratory many measurement techniques intrinsically make use of the FFT.

Many instruments report spectra directly, for example the output of an FTIR spectrometer, but it is always prudent to understand what analysis is being conducted on our behalf. As outlined here many analytical steps are happening and they may not be applicable to the analysis that we wish to conduct. Fortunately, many numerical packages are readily available that we as users can use to undertake our own Fourier analysis. All the graphs presented in this article have been generated from within a Jupyter notebook using the standard Python libraries bundled with Anaconda. These are readily available tools that we can all use if we have the inclination. Moreover, any time series can be analysed using Fourier analysis to reveal any possible underlying periodic behaviour. Atypical examples might be timesheets, holidays and production data.

The first stage of data analysis for nearly all time series data should be to understand the power spectra. The first step for a novice is to download the Anaconda bundle and start up the Jupyter executable, the second step is to search one of the many online tutorials (for example, (19)) in data analysis in Python and start experimenting. We are fortunate to live in an age when data analysis is an exceptionally easy thing to do. Let us all embrace this gift!

In recent years, whenever the subject of digitalisation or digital transformation is brought up for discussion, we normally observe two distinguishing reactions from the attendees: one group is excited and satisfied, the other, interested and worried. Of course, some have a good mixture of both. The former has been from companies, big or small, which have a clear digitalisation strategy in place from which obvious development and benefits have been achieved. For the latter, people are as keen as others on implementing solid steps to realise the long-waited benefit from business digitalisation. However, they are not quite sure where and what to start with, despite the continuously advancing technologies in the market. While still dealing with the COVID-19 pandemic, we were very curious about what the book “Digitalization” (1) would bring to help accelerate digital transformation for various organisations.

Professor Schallmo and Professor Tidd are the editors of “Digitalization” with a list of distinguished researchers on the editorial board. Professor Schallmo is a well-known key researcher focusing on business digitalisation at various stages, and the development and application of the methods to innovate business models. “Digitalization” continues his research focus following his previous book “Digital Transformation Now!” (2).

Besides his professorship of technology and innovation management at University of Sussex, UK, Professor Tidd has worked with numerous technology-based organisations globally on technology and innovation management projects. His view and experience of connecting innovation and digitalisation is always insightful. In conjunction with “Digitalization”, it is worth expanding the reader’s knowledge through his bestselling textbook on managing innovation (3).

The book “Digitalization” is a collection of 25 research-based studies which have been arranged in sections to emphasise five aspects of digitalisation: ‘Digital Drivers’, ‘Digital Maturity’, ‘Digital Strategy’, ‘Digital Transformation’ and ‘Digital Implementation’. This arrangement gives a clear statement of the focus of each part. Throughout the book, the literature review of all subjects is very rich which should give the audience a wide range of further reading if required.

The very early challenges that all organisations face in digital transformation are to discover the right opportunities and initiatives holistically. In the section ‘Digital Drivers’, four articles explore this subject from different angles. Disaster management and future‐led innovation framework, presented by Vettorello (Swinburne University of Technology, Australia) et al., and technology‐oriented future analysis by Urbano (Politecnico di Milano, Italy) et al., aim to provide guidance to organisations on innovation management with fast and accurate decision making within highly dynamic and complex environments. We feel these concepts may also have a place for individual business units within a large organisation where specific needs of that business unit can be addressed to capture local opportunity.

Chiaroni (Politecnico di Milano) et al. present a real example of how a circular business model has been applied in the building industry to realise business transformation from linear to circular by adopting digital technologies. Mutanov and Zhuparova (al-Farabi Kazakh National University, Kazakhstan) in the fourth article explain several fundamental reasons that commodity countries such as Kazakhstan and other post-Soviet countries are falling behind on digital transformation. These findings certainly show the great potential of digitalisation. Among the literature provided by the authors, two popular books written by Cross (4) and Tighe (5) are worthy of extra attention to expand ways of thinking and setting strategy.

‘Digital Maturity’ in Part 2 focuses on discovering digitalisation opportunities from a different angle, by assessing the current digital development status of an organisation and comparing with others within the same business sector or even wider to draw action plans for its own needs. First, a systematic literature review is conducted by Ochoa-Urrego and Peña‐Reyes (Universidad Nacional de Colombia) which includes 22 publications on formal maturity model applications.

The other two studies from Schallmo (Neu-Ulm University of Applied Sciences, Germany) et al. and Pierenkemper and Gausemeier (Heinz Nixdorf Institute, University of Paderborn, Germany) et al. emphasise a digital maturity models assessment of small and medium-sized enterprises (SMEs). It is recognised that the examined digital maturity models cannot provide a comprehensive digitalisation implementation plan for SMEs with an overarching vision like that typically seen at large corporations. Although Pierenkemper and Gausemeier list a few aspects of the presented model that may require further investigation, the study itself shows through examples how SMEs can produce a simple development plan for digitalisation using the model provided.

Once digitalisation objectives are determined, it is natural to move onto ‘Digital Strategy’ as presented in Part 3 on how we can capture the opportunities. The first paper in this part gives a deep dive on how disruptive innovation is used as business strategy or model for digital transformation among 80 companies in Germany. To expand the understanding of disruptive innovation, it is worth exploring relevant resources from the bestselling author (6). It is followed by Hartmann (HTW Berlin – University of Applied Science, Germany) et al. and Gernreich (Ruhr-Universität Bochum, Germany) et al. who separately address the importance of top management or an innovation manager who has the necessary knowledge in digitalisation and can drive to complete the plan for desired productivity and benefits.

Kruft and Gamber (Technische Universität Darmstadt, Germany) in the fourth paper present a critical component of digital transformation: continuous culture change, which often poses an even bigger challenge on the entire journey of digitalisation. All organisations need to recognise the significance of cultural renewal and work closely with their employees to bring them along with progress. It is one of the core strategies to empower people with the right tools, knowledge and communication via digital platforms in the era of ever-changing technology.

The focus in the paper from Koldewey (Heinz Nixdorf Institute, University of Paderborn) et al. falls in the mainstream of digitalisation, i.e., smart services interconnecting products with aftersales service. They demonstrate how they use a design research methodology to develop a smart service strategy through four comprehensive case studies. The last paper in Part 3, from Porté (Ecole Polytechnique Fédérale de Lausanne, Switzerland) et al., draws attention to the potential of using Systemic Enterprise Architecture Methodology (SEAM) to align business and IT perspectives on innovative projects. A project by the Society of Family Doctors (SFD) is used to showcase how we structure a problem based on who sees it and why, instead of the problem itself.

Part 4, ‘Digital Transformation’, expands on the first three parts of the book with papers from governments, universities and other parts of the public sector. Meier (University of Innsbruck, Austria) provides a systematic review of the literature on SME digitalisation. Her discovery agrees with a few other papers in the book on challenges that traditional SMEs face while adopting digitalisation: time, financial, human and technical resource constraints. For the public sector, Bjerke-Busch and Aspelund (Department of Industrial Economics & Technology Management, Norwegian University of Science and Technology) use Norwegian Court Administration (NCA) to explain the barriers for digital transformation in a typical public organisation.

The study from Haslam (Centre for IS Management, Department of Politics and Society, Aalborg University, Denmark) et al. identifies a few key elements of how digital transformation has been accelerated at a Danish university during the pandemic period. Staying connected with the Danish Government, Rosenstand (Aalborg University) shows early work on applying a digital ecosphere canvas for cultivating multiple digital ecosystems at Digital Hub Denmark, a private-public partnership organisation. Jütting (Fraunhofer IAO, Fraunhofer Institute for Industrial Engineering, Center for Responsible Research and Innovation (CeRRI), Germany) et al. introduce the pro-poor digitalisation canvas as a conceptual framework aiming to act as a practical tool to evaluate the potential of digital innovations. The particular interest is to practically turn the objectives of the United Nations Sustainable Development Goals (SDGs) 1 (‘no poverty’) and 10 (‘reduced inequality’) into actions to minimise the digitalisation gap between the advanced and developing world.

Digital implementation, the focus of Part 5, is the step to really make the transformation. Although it is impossible to cover all areas in the implementation stage, the authors have attempted in-depth discussion in several major subjects. Gfrerer (University of Innsbruck) et al. lead the discussion in the composition of digital leadership and gender diversity, particularly targeting female managers and how they envisage their roles and challenges to digitalisation and innovation. Reis and Hunt (Thinkergy Ltd, Hong Kong and Thailand) in the second paper also focus on the effectiveness of leadership in digitalisation. They conclude by highlighting the importance of creative leaders in the success of digitalisation and such leaders can be trained up through selective programmes combining effective methodology and pedagogy.

Schallmo and Williams (Neu-Ulm University of Applied Sciences) bring attention to an integrated theoretical approach to digital implementation which aims to realise digitalisation in four interactive dimensions and five procedural phases. The study presented in the fourth paper by Kruszelnicki (Creative Labs sp. zoo ul, Poland) and Breuer (UXBerlin Innovation Consulting and HMKW University of Applied Sciences for Media, Communication and Management, Germany) is particularly interesting. Three use cases are presented to show how Adobe Kickbox has effectively promoted ‘intrepreneurship’ to unlock innovation opportunities. Haag (TH Köln, Germany) et al. have sustainability at the centre of their research. Their main contribution is to provide the ‘design-to-sustainability matrix’ as a toolkit to address ecological challenges through the life cycle of both new and existing product development.

The last two studies in this part put weight on innovation management. Johnsson (Blekinge Institute of Technology, Sweden) et al. explore the key success factors in evaluating innovation teams. In the last paper Colucci and Forciniti (Evidentia srl, Italy) recount the story of how Ferrari has transformed its business through an innovation management programme which involves management at all levels and processes at different stages.

On completing the book, although the questions we had at the start of this review are not fully answered, we were delighted to see several useful case studies presented throughout the book. When it comes to real implementation, we understand that it is impossible to write down all details due to confidentiality and variations in organisational status and need. The richness of the literature resources in this book provided by all authors is hugely beneficial to the audience to gain a theoretical foundation. There is also wide discussion on how digitalisation is applied to various areas of focus, including SMEs, developing countries, gender diversity, SDGs, high-tech industry leaders and the public sector. Digitalisation practitioners such as management and innovation consultants and organisations would find it useful to navigate through the business models and frameworks presented by several authors at different stages of digitalisation. Readers who are very new to the digital transformation subject may find this book too profound and pre‐study is needed to bridge the knowledge gap. Finally, digital transformation is often bundled with innovation for many good reasons. We highly recommend readers continuously explore ways of innovation (7) to identify and truly drive ideas through to implementation.

Over the last decade, the term ‘digital transformation’ has become prevalent across a wide variety of organisations. It refers to converting existing manual processes to create a more efficient and agile business environment. In 2018, >70% of organisations were reported as having a digital strategy or working to implement one (1). Johnson Matthey has established both key innovation programmes and the Digital Johnson Matthey programme to bridge between IT and the business to deliver ‘digital spearhead’ initiatives to meet this goal.

Digital transformation initiatives are part of a global shift towards so-called Industry 4.0 programmes. Evolving from established industrialisation practices, this future way of working builds upon the foundations of streamlined value-chain operations and automation by embedding data, modern smart technology, artificial intelligence and robotics in a seamless manner.

In order to stay competitive, organisations need to improve their internal processes to deliver faster innovation across research and development (R&D) and manufacturing, while accommodating the shifting needs of customers and macroeconomic factors. Additionally, companies are increasing external collaborations with networks of partnerships and innovation centres, to access new technology and capabilities that complement in-house competencies (2). A modern digital infrastructure can facilitate this by providing effective exchange of information alongside a culture of continuous improvement, with an emphasis on operational agility and experimentation to drive the desired outcomes.

Expected benefits of recognising that data is an asset are operational efficiency gains, with the ability to improve product quality and reduce development time and cost. This directly yields an improved competitive position in the marketplace. Moreover, there may also be opportunities to develop new revenue streams by aligning physical product offerings with ancillary software optimisation applications. The Johnson Matthey Levo^TM application for plant optimisation is a good example of this.

The global impact of COVID-19 was widespread and transformative in its own right, as organisations rapidly adapted. With remote working and a need for business continuity, companies accelerated digitisation of systems supporting all manner of business functions. The response to the pandemic and mitigating actions to ensure business continuity have helped to speed the adoption of digital technologies. Many of these changes are embedded and expected to be long lasting. The value of the digital strategic initiative is recognised: 53% of companies plan to cut or defer capital investments because of COVID-19, but just 9% will make cuts in digital transformation efforts (3).

Data is the new digital fuel that is the heart of the Industry 4.0 initiative. Both legacy and current research data are used to create and power the artificial intelligence algorithms and modelling approaches that lead to break-through product innovations.

Historically, attempts at mining legacy data were challenging because data was often in disparate systems and formats, which took time to find, and transcribing information from paper records was cumbersome and error prone. Across many organisations, there has often been fragmentation of ownership of data across disparate groups, as well as segmentation across the organisation, creating barriers to shared information.

The industry-recognised approach is now for data to adhere to Findable, Accessible, Interoperable and Reusable (FAIR) guidelines. By moving to electronic records and systems that allow for structured data capture, i.e., with well-defined metadata and results fields, data scientists and modellers will have near real-time access to a wealth of research and process engineering records.

As technology plays a more pivotal and crucial role in creating an agile business environment, organisations need to recognise that embracing digital tools and analytics helps to unlock the full potential of data. This in itself requires a shift in mindset, necessitating behavioural changes and learnings to manage data more effectively on a day-to-day basis. The community needs to store data in a meaningful manner, to open data repositories and to apply data governance and agreed practices that make the data accessible and clear for other people to use. This task is not insignificant, and conscious effort is required to align to this new way of working and for people to recognise the opportunities that their data presents.

The transformation process is essentially facilitating communication and exchange between stakeholders i.e., between different research, analytical, development and manufacturing departments, to those that ultimately service the external customer. As an organisation transitions from paper to spreadsheets to smart applications for managing these interactions, there is an opportunity to reconsider how processes are performed and how information is communicated, using digital technology.

As organisations work to overcome obstacles and drive operational efficiencies towards improved competitiveness, it is important to recognise that a digital transformation initiative cannot simply be solved by introducing a suite of new tools and applications. In a 2016 survey, 87% of companies thought that digital would disrupt their industry, while only 44% felt prepared for these potential digital changes, and little has changed since then (4, 5). As such, there needs to be a company-wide shift in thinking and process, alongside training and support. With CEO and senior management encouragement, the culture of change across the entire organisation needs to be prioritised. Importantly, there is also a converse ‘bottom up’ alignment, with engagement from end-users who recognise inefficiencies in current practices and who are enthusiastic and contribute ideas about new ways of working.

The challenges of creating a world that is cleaner and healthier, today and for future generations, will only be solved by engaging with disruptive innovation that is driven by digital transformation. As a result, organisations are rapidly developing, adjusting or accelerating strategies to provide the required technical and business agility. This extends from how their employees work and collaborate to how they engage with partners, suppliers and customers. The technology disruptors of today will help make the workplace a data-driven organisation, leveraging technology and culture change to drive business strategy in ways that help promote growth, spur innovation, reduce costs, streamline operations and create satisfied, loyal customers.