Shaft alignment for rotary machines using wireless power transfer process: Foundations and design approach

Abstract

The aim of this paper is to present the fundamentals of an original method of shaft alignment for rotating machines based on the principle of wireless power transfer (WPT) process. WPT alignment of shafts in rotating machinery is simple and more accurate than existing methods (conventional mechanical methods or Laser-optical method) and can result in reduced power consumption and minimized mean time between failures. Shaft alignment is an important factor in the proper functioning and longevity of machinery. Proper shaft alignment ensures that the rotating shafts of a machine are in a straight line and rotate on the same axis. This contributes to reducing the wear and tear on the bearings and other components of the machine, leading to improved reliability and longer service life. A high precision WPT alignment system has been designed with the primary coil placed in the driver machine, as an electrical motor, and the secondary coil placed in the driven machine, as a pump. The calculation of the magnetic interactions between both coils (primary and secondary coils), in particular the mutual inductance and coupling coefficient, perfectly explains deviations in the shaft (angular misalignment and parallel offset) and aligns entirely with measurement results, with a difference of approximately 4%. This new alignment method with magnetic interactions has proven effective in designing and implementing actual shaft alignment. WPT alignment offers precise shaft alignment tools for proper alignment of shafts and reduces troubleshooting issues.

Keywords

Coupling coefficient magnetic interactions mutual inductance shaft alignment wireless power transfer

1. Introduction

The industry invests significant time and resources in the precision alignment of rotating machinery to ensure a reliable maintenance program. This involves expenses such as alignment equipment, personnel training, labor costs, and machinery downtime. Proper shaft alignment is a critical maintenance procedure for ensuring the longevity and optimal performance of machinery, including pumps, motors, compressors and turbines [1]. It plays a vital role in reducing excessive axial and radial forces exerted on vulnerable components bearings, seals, rotors, crankshafts, and couplings [2]. This reduction in forces results in several key benefits, including lower levels of noise and vibration, decreased operating temperatures, minimized mechanical wear and tear, and a reduced risk of downtime due to equipment breakage [3,4]. However, during operation, several factors can cause shaft misalignment in motors, such as thermal distortion of housing supports of bearings, differential thermal growth of machine parts, piping forces due to pressure and temperature variations, movement of the foundation, aging of the installation, etc. Ultimately, regular maintenance and proper alignment extend the lifespan of the machinery, making it more reliable over time [5–7].

Shaft misalignment typically manifests as a combination of parallel and angular misalignment, as seen in Fig. 1. Parallel misalignment occurs when the centerlines of both shafts run parallel but are offset, while angular misalignment occurs when the shafts intersect at an angle. In the process of alignment, it is crucial to bring both these misalignments within specified tolerances, ideally aiming for zero misalignments. Adjustment takes place in two planes: vertical and horizontal mounted equipment, and “Back-Front” and “Left-Right” for vertically mounted units, as specified in [8–10].

Fig. 1.

Different types of misalignment: a) Offset, b) Angular.

The method for shaft alignment can be classified into two categories based on the specific requirements of the machinery: the level of precision required and the available resources. The first category includes traditional methods such as the rule method, dial indicator method, bubble level method, feeler gauge method, and graphical alignment tools, which retain relevance in certain applications [11–13]. The second category comprises laser alignment methods, which are gaining popularity due to their speed and enhanced precision. Both categories represent a balance between improved alignment precision, ease of use, and cost-effectiveness. However, a significant drawback of both methods is the need to halt machine operations during the alignment process [14,15].

The aim of this work is to propose a novel method based on the principle of wireless power transfer (WPT) process, called the WPT alignment method for aligning the shafts of rotating machinery. This method enables real-time monitoring of alignment with high precision and can be automated, thus reducing reliance on operator expertise.

Firstly, the foundations and principles of this method are introduced, elucidating how the mechanical challenge of aligning two shafts in rotating machinery can be transformed into a problem involving contactless energy transfer of magnetic energy between two coils (the primary and secondary coils). The voltage induced in the secondary coil, following Faraday’s general law, represents an electrical quantity that is both measurable and capable of accurately depicting the various types of shaft misalignments shown in Fig. 1. Subsequently, analytical expressions will be formulated to compute the magnetic interactions between the two coils. The calculated mutual inductance and magnetic coupling coefficient between two coils mirror the changes in induced voltage at the secondary coil, which are influenced by three specific offsets and the misalignment of the two aligned shafts. The results of the conducted tests and simulation processes unequivocally confirm that the induced voltage in the secondary coil, along with mutual inductances and the magnetic coupling coefficient between primary and secondary coils, reach their maximum values when there are no displacements in the x, y and z directions, and there is no inclination between the two shafts.

2. Wireless power transfer shaft alignment process

The measurement principle of the wireless power transfer shaft alignment system is based on the calculation of the magnetic interaction between primary and secondary coils, as shown in Fig. 2. This system uses wireless power transfer technology to transfer power and data between the primary and secondary coils, which are mounted on the rotating shafts of the machinery being aligned. The primary coil is typically mounted on a stationary part of the machinery, while the secondary coil is mounted on the rotating part. The magnitude and phase of the induced current are used to determine the relative position and angle of the two coils. By analyzing the data from the primary and secondary coils, the alignment software can calculate the misalignment between the shafts and provide feedback to the operator. The software can also calculate the required adjustments needed to achieve proper alignment and provide real-time feedback to the operator during the alignment process.

Fig. 2.

Principle of shaft alignment using the wireless power transfer method.

The mechanism of wireless inductive power transfer can be explained using Faraday’s law of induction. This law states that any spatial or temporal change in the magnetic environment of a coil of wire will induce a voltage. This change in WPT systems based on magnetic coupling is produced by a time varying current in another coil that is present in the vicinity. Figure 2 presents the two coils for magnetically inducing a voltage. A primary coil, placed on the driver shaft and powered by a high frequency AC power source serves as the transmitter, while a secondary coil functions as a receiver. Typically, an inductive WPT system consists of three parts: transmitter, inductive coupler, and receiver, as seen in Fig. 3. The system can be considered static when the distance between the transmitting and receiving coil is constant and dynamic when the distance and the load vary.

Fig. 3.

Schematic diagram of the inductive wireless power transfer.

3. Mathematic model

The mathematical formulae developed in [16,17] are used to calculate the magnetic interactions between two inclined elementary parallelepipedic conductors n and m, as shown in Fig. 4.

Fig. 4.

System of two elementary parallelepipedic conductors.

The mutual inductance between the two elementary conductors n and m can be defined as: $\begin{eqnarray}M_{n,m}=\frac{{\mu}_{0}\overrightarrow{e_{n}}.\overrightarrow{e_{m}}}{4{\pi}S_{n}S_{m}}\int _{V_{n}}\int _{V_{m}}\frac{1}{|\overrightarrow{r_{n}}-\overrightarrow{r_{m}}|}dV_{n}∼dV_{m}\end{eqnarray}$ (1) Where (a_n × b_n × c_n) and (a_m × b_m × c_m) are respectively the dimensions of the elementary conductors n and m. $\overrightarrow{e_{n}}$ and $\overrightarrow{e_{m}}$ are respectively the normal unit of the elementary conductors n and m. S_n and S_m are respectively the normal cross-sectional areas of the elementary conductors n and m. V_n and V_m are respectively the volume of the elementary conductors n and m. $\overrightarrow{r_{n}}$ and $\overrightarrow{r_{m}}$ are respectively the position vectors of the elementary conductors n and m.

After several mathematical procedures, the total mutual inductance between the primary and secondary coil can be expressed as: $\begin{eqnarray}M_{p,s}=\mathop{\sum }_{n=1}^{\mathit{Nsegp}}\mathop{\sum }_{m=1}^{\mathit{Nsegs}}M_{n,m}\end{eqnarray}$ (2) With: $\begin{eqnarray}M_{n,m}=\frac{{\mu}_{0}\overrightarrow{e_{n}}.\overrightarrow{e_{m}}}{4{\pi}S_{n}S_{m}}\mathop{\sum }_{i=0}^{1}\mathop{\sum }_{j=0}^{1}\mathop{\sum }_{k=0}^{1}\mathop{\sum }_{l=0}^{1}\mathop{\sum }_{p=0}^{1}\mathop{\sum }_{q=0}^{1}(-1)^{i+j+k+l+m+n}{\Gamma}\end{eqnarray}$ (3) And $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \hspace{-22.0pt}{\Gamma}=\left(\frac{V^{2}W^{2}}{4}-\frac{V^{4}}{24}-\frac{W^{4}}{24}\right)U\ln \left(\frac{U+r}{\sqrt{V^{2}+W^{2}}}\right)+\left(\frac{W^{2}U^{2}}{4}-\frac{U^{4}}{24}-\frac{W^{4}}{24}\right)V\ln \left(\frac{V+r}{\sqrt{U^{2}+W^{2}}}\right)\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle +\left(\frac{V^{2}U^{2}}{4}-\frac{U^{4}}{24}-\frac{V^{4}}{24}\right)W\ln \left(\frac{W+r}{\sqrt{V^{2}+U^{2}}}\right)\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle +∼\frac{1}{60}(U^{2}+V^{2}+W^{2}-3U^{2}V^{2}-3W^{2}V^{2}-3U^{2}W^{2})r\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle -\frac{UV^{3}W}{6}\tan ^{-1}\left(\frac{UW}{Vr}\right)-\frac{UW^{3}V}{6}\tan ^{-1}\left(\frac{UV}{Wr}\right)-\frac{VU^{3}W}{6}\tan ^{-1}\left(\frac{WV}{Ur}\right)\end{eqnarray}$ (4) Where the auxiliary variables U, V , and W are defined based on the dimensional parameters as: $\begin{eqnarray}\displaystyle U & = & \displaystyle {\delta}_{n,m}+(-1)^{j}a_{m}-(-1)^{i}a_{n}\end{eqnarray}$ (5) $\begin{eqnarray}\displaystyle V & = & \displaystyle {\beta}_{n,m}+(-1)^{l}b_{m}-(-1)^{k}b_{n}\end{eqnarray}$ (6) $\begin{eqnarray}\displaystyle W & = & \displaystyle {\gamma}_{n,m}+(-1)^{q}c_{m}-(-1)^{p}c_{n}\end{eqnarray}$ (7) $\begin{eqnarray}\displaystyle r & = & \displaystyle \sqrt{U^{2}+V^{2}+W^{2}}.\end{eqnarray}$ (8)N_sgp and N_sgs are respectively number of elementary conductors of the primary and secondary coil. 𝛿_{n, m}, 𝛽_{n, m} and 𝛾_{n, m} are respectively the distances between n and m conductors in x, y and z directions.

Here, the basic characteristics of coupling coefficient k and mutual inductance M_{p, s} between primary and secondary coils are confirmed [18–20]. The coupling coefficient is the percentage of coupling set according to primary-side inductance L_p, secondary-side inductance L_s, and mutual inductance M_{p, s}, as shown in Eq. (2). Then, the coupling coefficient is maximal if the mutual inductance is maximal [21–23]: $\begin{eqnarray}K=\frac{M_{p,s}}{\sqrt{L_{p}L_{s}}}.\end{eqnarray}$ (9)

4. Simulation and experiments

To verify the above analysis and test the performance of the proposed formulae in evaluating the interaction magnetic, specifically the coupling coefficient, with respect to the horizontal displacement X, axial tilt angle 𝜃 and vertical displacement Z between two adjacent coil, series of measures and comparisons using some related devices were conducted, which include the impedance analyzer, vertical displacement drive devices, axial angle measurement unit, etc. The characteristics of the model are listed in Table 1.

The model verification process mainly includes two parts: (i) testing the simulation effectiveness of different displacements (horizontal displacement , axial tilt angle and vertical displacement ); (ii) testing the effectiveness of the WPT alignment method (this is conducted mainly by comparing the measured induced voltage and different possible misalignments).

Table 1
Model parameters

Symbol Quantity Value

a _p Outer radius of primary coil 200 mm

b _p Inner radius of primary coil 150 mm

E _p Length of primary coil 50 mm

a _s Outer radius of secondary coil 150 mm

b _s Inner radius of secondary coil 125 mm

E _s Length of secondary coil 25 mm

𝛼 Distance between primary and secondary coil in x-direction Variable

𝛽 Distance between primary and secondary coil in y-direction Variable

𝛾 Distance between primary and secondary coil in z-direction Variable

N ₁ Number of turns of primary coil 200

N ₂ Number of turns of secondary coil 200

Symbol	Quantity	Value
a _p	Outer radius of primary coil	200 mm
b _p	Inner radius of primary coil	150 mm
E _p	Length of primary coil	50 mm
a _s	Outer radius of secondary coil	150 mm
b _s	Inner radius of secondary coil	125 mm
E _s	Length of secondary coil	25 mm
𝛼	Distance between primary and secondary coil in x-direction	Variable
𝛽	Distance between primary and secondary coil in y-direction	Variable
𝛾	Distance between primary and secondary coil in z-direction	Variable
N ₁	Number of turns of primary coil	200
N ₂	Number of turns of secondary coil	200

For further details, we have presented in Table 2 the coupling coefficient values at various selected positions.

Table 2

Comparison of coupling coefficient

Positions (x, z, 𝜃)	Measured value	Calculated value
(0, 0, 0)	0.97	0.93
(0, 0.015, 0)	0.2	0.15
(0, 0, 40)	0.74	0.73

Fig. 5.

Variation of the coupling coefficient between two coils along the x-direction.

Fig. 6.

Coupling coefficient between two coils as a function of the air gap.

Fig. 7.

Inclination effect between two coils on the coupling coefficient.

For comparing the simulation results implemented in the programming language Matlab with measured data, the coupling coefficient between two coils has been calculated when the primary coil is moving over the second in the horizontal displacement, as shown in Fig. 5.

To compare the simulation results with the measured data, the coupling coefficient between two coils has been estimated for the three possible cases of misalignments. This includes when the primary coil moves over the second in the horizontal displacement X, as shown in Fig. 5, when the primary coil moves over the second in the vertical displacement Z (air gap), as shown in Fig. 6, and when the primary coil moves over the second at axial tilt angle 𝜃, as shown in Fig. 7.

The results of the coupling coefficient are in good concordance with both methods (simulation and measurement), as represented by Figs 5, 6 and 7. It is confirmed that the coupling coefficient is maximum if there is no offset in the space between the two magnetic axes of the primary and secondary coil.

The shaft alignment procedure for rotary machines employing the innovative WPT technique involves the meticulous adjustment of the driver shaft connected to the primary coil in the Z direction. This fine-tuning aims at maximizing the induced voltage at the secondary coil, which is linked to the driven shaft. Subsequently, precision adjustments in both X and Y directions are executed to attain a renewed peak in induced voltage. The alignment tests conducted in the alignment laboratory using this method have consistently demonstrated its exceptional relevance and effectiveness.

5. Conclusion

The Wireless Power Transmission (WPT) systems have various applications, such as wireless charging of electronic devices, electric vehicles, medical electronics, wireless lighting, drones, industrial sensors, and more. The general aim of the present study is to apply contactless power transmission systems to solve old problems in heavy mechanics, which have not benefited as much from technological advancements compared to other disciplines such as electronics, telecommunications, and medicine. We have proposed a new method based on wireless power transmission for shaft alignment for rotating machines, named WPT alignment of shafts. This novel technique has several major advantages compared to old existing techniques as the reliability of electrical measurements, the verification of machines in operation and the possibility of verification from the control room. With the developed mathematical model, we translated the shaft alignment problem into a calculation of magnetic interactions between two conductive coils; the primary coil is linked to the driver shaft, while the secondary coil is linked to the driven shaft. Simulation results concord with measurement results and demonstrate that the coupling coefficient accurately represents the various possible misalignments of the shafts. The sensitivity and accuracy of the proposed method are validated in the laboratory through several tests aligning the shafts of rotating machines. Perhaps one day, this method will be implemented and commercialized as a new device for aligning the shafts of rotating machines.

Footnotes

Acknowledgements

This work was supported by the General Direction of Research and Development Technologies, Ministry of Higher Education and Research Sciences, Algeria.

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