The Study of the Balancing Process for Starting Rotors in Heavy-Duty Vehicles: An Industrial Application

Abstract

In the heavy-duty vehicle industry, unbalance in the armature is one of the most common problems affecting starters’ performance and durability. This research presents a comprehensive study to improve the balancing process for starting rotors in heavy-duty vehicles. The complete manufacturing process of armatures was analyzed to understand the contribution of assembly processes to unbalancing. The analysis revealed that the primary factor leading to high unbalance in these parts is the misalignment of conductors within the armature winding. During assembly, these conductors experience axial movements, resulting in non-uniform mass distribution and causing unbalanced values ranging from 150 to 350 g·mm. These values surpass the permissible limit, making rectification during the balancing process at the end of the assembly impossible. Consequently, a novel alignment tool was designed to address this issue, significantly reducing the effect and achieving the maximum allowable unbalance of 100 g·mm. This allowed the balancing machine used in the process to correct the initial unbalance of the reinforcements in a single work cycle, improving operation efficiency by about 15%.

1. Introduction

The analysis of unbalance in the manufacturing process of starting rotors for heavy-duty vehicles is a critical aspect that impacts the efficiency and reliability of these machines. Unbalance in rotors can lead to excessive vibrations, causing mechanical failures and reducing the lifespan of vehicle components. During manufacturing, factors such as machining errors, assembly misalignments, and material inconsistencies contribute to unbalance, making early detection and correction crucial [1].

In this context, it is well known that transportation is a basic global requirement, and internal combustion engines (ICEs) continue to provide high economic benefits to the automotive industry. Its components study continues to be a challenge to improve its performance, efficiency, and emission reduction. One of the main components of ICEs is the starter, which converts electrical energy into mechanical energy to rotate finally the engine flywheel. The steering wheel’s initial spin of the engine is required to obtain the necessary momentum for the internal components of the engine to start moving and thus start the combustion process [2,3,4]. The starter is automatically switched off once the engine has started and runs independently [5]. The initial starting process of the ICE and its operation depends on it, hence its importance.

Because the starter is an essential device for the commissioning of ICEs, as mentioned by Michelotti and Silva [6], each component that is part of them must have an elevated level of quality and performance. The starter motors are constructed with different components that interact in an orderly manner to carry out the operation described above, among which are the solenoid, field coils or stator, housing, impeller arrow shaft and drive, carbons, and rotor (also called armature). Its operation is based on the interaction between a stationary magnetic field and the armature, which contains windings. When current is supplied to the motor, torque is induced, causing the armature to spin. This mechanical motion is transmitted to the flywheel of the ICE, starting it up. The presence of brushes allows for the commutation of current in the rotor, ensuring that torque is applied continuously and enabling smooth and efficient rotation of the starter motor [7].

In the process of starting an internal combustion engine, as described above, the 12 v starter motor generates a maximum power of 7.3 kW within a speed range of 50–150 RPM, where the starting engine armature rotates at high speeds to provide the power necessary to overcome the initial resistance of the engine and put it into operation.

Since its conceptualization, armatures have been designed to have an optimal residual unbalance [8] under international regulatory standards ISO 21940-11:2016 [9]. However, the armatures will inevitably present mechanical unbalances due to the variations allowed in the manufacturing process and the dimensional and geometric tolerances of the materials with which the armatures are manufactured [10]. Therefore, an additional check and a balance correction operation will be necessary for the armatures at the end of their manufacturing process.

To carry out these balancing operations, specialized equipment called balancing machines is required. There are four basic types: static balancing stands, hard-bearing machines, high-speed machines, and soft-bearing machines. Soft-bearing machines, in particular, are one of the best options to have in a manufacturing cell due to their flexibility and finer balance levels for general balancing applications [11].

One of the most common problems in the armature is the unbalance that particularly affects starters’ performance and durability. The disadvantages that an unbalanced armature can generate are diverse and vary in their degree of effect on the final product, e.g., vibrations, friction, harmful loads on ball bearings or bearings, overheating, and variation in magnetic flux [12].

Unbalance is the non-uniform distribution of mass throughout the body of an armature. In the same way, balancing can be conceptualized as a procedure by which the mass distribution of an armature is verified by measuring the vibration generated while it is rotating at a speed similar to its working speed. If necessary, this is corrected to ensure that the residual unbalance is within limits specified by international standards requirements. The latest is achieved by adjusting the masses, adding or removing material in predefined locations of the armature to be balanced, called balancing planes, and thus ensuring smooth and efficient operation, as pointed out by Lawson et al. [13].

In a simplified way, the unbalanced calculation is performed by multiplying the unbalanced mass by the distance from the axis of rotation following international regulatory standards ISO 1940-1:2003 [14].

While there is considerable research about the unbalance phenomenon, most studies show measurement techniques where several instruments and mathematical algorithms are proposed to determine the magnitude and position of the masses causing the unbalance in armatures [15,16,17,18]. However, even with a precise method to measure and correct the unbalance, it is possible to find pieces within the production processes so severe that the correction process is insufficient to balance them. Mainly due to the function they must perform, which makes these parts corrections unfeasible since they could affect their performance and integrity. Lastly, they automatically turn into costly waste. In this context, it is important to note that the balancing process occurs during the final operations of the production line when the armatures are already completely manufactured.

It is essential to carry out studies on the subject that help to determine the possible variables that contribute to increasing the unbalance, which will directly help to reduce the correction process to minimize these unbalances and, as little as possible, affect the integrity of the armatures. Thus, greater stability in the production processes, aside from higher quality and reliability in the performance of starters built with these armatures, is achieved.

This research provides a global study on improving the balancing process for starting rotors. The complete manufacturing armature process is analyzed to identify specific assembly unbalancing contributions. It was found that conductor misalignments were the main unbalancing cause, which could not be corrected at the assembly operation end. This study also proposes improvements to the unbalanced process by designing a novel conductor driver alignment tool to reduce this effect.

2. Methodology

2.1. Armature Manufacturing Procedure

Experimental research was divided into two stages. In the first stage, the objective was to measure the unbalance of a controlled group of parts along the different operations considered process significant. This helped to monitor unbalanced behavior as components were added or executed in production processes, and any relevant changes were taken as a reference for the second stage.

The parts’ unbalance in the second stage was monitored and then analyzed. This allowed the basis determination of the increase in unbalanced factors to implement an improvement in the process.

The flow diagram manufacturing process of the armature can be seen in Figure 1. Eight key operations were selected for this study, highlighted in green, and the balancing operation to which the pieces arrive to be measured and corrected is highlighted in black. These operations presented changes in the unbalanced values due to the addition of a significant mass resulting from assembling the components that make up the armature. Additionally, the geometric characteristics of the armatures are altered, generating a radial displacement that contributes to modifying the unbalance of the armature. Although the components are assembled with high precision, the manufacturing error of each element propagates and accumulates in the assembly process and could eventually affect the quality of the mechanical assembly. Therefore, operations were selected to reflect the most significant changes in unbalance without increasing the amount of data to be analyzed. Finally, these operations were chosen because they can identify the assembly of some components with sufficient mass to modify the part unbalance. According to the literature, these operations have also been recognized as the root cause for the unbalanced increase in similar pieces to those studied in this research [19,20,21].

2.2. Unbalance Measurement Equipment

The armature used in the current balancing experiments is taken from a commercial heavy-duty truck starting motor. It weighs 2950 g and has a length and diameter of 197 mm and 76 mm, respectively. For such armatures, ISO 1940-1:2003 [14] generally specifies a balance grade of G6.3. It should be noted that a 100 g·mm value is the maximum allowed in this study so that the armature can go to the final process and comply with the abovementioned standard.

The semi-automatic balancing equipment was used to measure the unbalance of the armatures, which had previously been prepared and calibrated for the test. Figure 2 shows the supports mounted on the measuring station of the balancing equipment. This unit contains a pair of electrodynamic unbalance detectors for both armature planes (commutator and pinion side), a programmable traction motor, and an angular position sensor.

The rotor unbalance in the considered balancing machine is computed using the influence coefficient method, which means the rotor requirements are satisfied with the next assumptions: (1) the unbalanced rotor vibratory response is proportional to the unbalance amount, and (2) the unbalance amount is negligible compared to the total weight of the rotor, as mentioned by Tseng et al. [22]. An important aspect to consider is that the armature can be regarded as a rigid body because its service speed, when assembled in a starter motor, is far lower than its natural frequency.

Under the context of a manufacturing process and following the guidelines for designing a control chart, Montgomery [23] mentions that to detect moderate to large changes in a process, a relatively small sample size of n = 4, 5, or 6 is required, which yields reasonably effective results, provided that the manufacturing process has low variability. Similarly, the number of resources allocated to the inspection process and the associated costs should also be considered. Based on the above, a representative sample of twelve pieces was chosen. Here, the unbalance of the pieces during key operations (marked in green in Figure 1) is evaluated to identify the primary stage where pieces tend to increase their unbalance significantly. Thus, the main objective is to adjust values that can be corrected during the armature balancing stage (marked in black in Figure 1).

2.3. Unbalance Mathematical Computation

As reported in an earlier study [22], when a rotor with an unbalance rotates on a soft-suspended support, the vibration amplitude correlates with the level of unbalance [24]. Thus, the extent of the unbalance can be determined by evaluating the vibration amplitude. In the balancing system analyzed, the signals from the vibration sensors undergo filtering and amplification, and the vibration’s amplitude and phase angle, Y(t), are subsequently calculated using the Fourier series.

In general, any periodic signal can be represented using a Fourier series expansion as follows [22]:

$$\mathrm{Y}\left(\mathrm{t}\right)=a_0+{{\displaystyle \sum }}_{n=1}^{\infty }\left(a_n\cos n\omega t+b_n\sin n\omega t\right)=a_0+a_1\cos \omega t+b_1\sin \omega t+a_2 \cos 2\omega t+b_2\sin 2\omega t+\cdots ,$$

(1)

where

$$a_n={\displaystyle \frac{1}{\pi }}{{\displaystyle \int }}_{-\pi }^{\pi }\mathrm{Y}\left(\mathrm{t}\right)\cos n\omega tdt, \mathrm{and} b_n={\displaystyle \frac{1}{\pi }}{{\displaystyle \int }}_{-\pi }^{\pi }\mathrm{Y}\left(\mathrm{t}\right)\sin n\omega td$$

(2)

Referring to this application, the fundamental frequency ω in Equations (1) and (2) corresponds to the rotor’s balancing speed. Given that the vibration signals are primarily influenced by the fundamental component, Equation (1) can be simplified as follows [22]:

$$\mathrm{Y}\left(\mathrm{t}\right)\approx a_0+a_1\cos \omega t+b_1\sin \omega$$

(3)

Additionally, because the vibration sensors employed in the proposed balancing system are of the velocity type, $a_0=0$. As a result, it can be demonstrated that Y(t) is expressed as follows [22]:

$$\mathrm{Y}\left(\mathrm{t}\right)=y\cos \left(\omega t-{\varphi }_1\right)=y \angle {\varphi }_1$$

(4)

with $\mathrm{y}=\sqrt{a_1^2+b_1^2, {\varphi }_1=ta{n}^{-1}\left({\displaystyle \frac{b_1}{a_1}}\right), } \mathrm{and} a_1=\left({\displaystyle \frac{1}{\pi }}\right){{\displaystyle \int }}_{-\pi }^{\pi }Y\left(t\right)\cos \omega t dt, b_1=\left({\displaystyle \frac{1}{\pi }}\right){{\displaystyle \int }}_{-\pi }^{\pi }Y\left(t\right)\sin \omega t dt.$ In the balancing process, the rotor speed $\omega$ is predetermined, allowing the amplitude and phase angle of Y(t) to be calculated using Equation (4).

The influence coefficient method is utilized to compute the unbalanced rotor in the balancing system analyzed. Figure 3 displays the basic setup of the starter armature considered in this study. This approach allows for modeling each unbalance on two separate planes of the armature, known as the balancing planes. During the balancing process, vibration data are collected from these planes using two electrodynamic sensors, and a reference point is established from the armature’s positioning at the measurement station to determine the unbalance phase angle.

The vibration measurements $Y_A$ and $Y_B$ taken from planes A and B, respectively (refer to Figure 3), and are considered to be linear combinations of the unknown unbalances $U_A$ and $U_B$ on those planes [22], respectively, i.e.,

$$\left[\begin{array}{c}{\mathrm{Y}}_{\mathrm{A}}\\ {\mathrm{Y}}_{\mathrm{B}}\end{array}\right]=\left[\begin{array}{cc}{\mathsf{\theta }}_{\mathrm{AA}}& {\mathsf{\theta }}_{\mathrm{AB}}\\ {\mathsf{\theta }}_{\mathrm{BA}}& {\mathsf{\theta }}_{\mathrm{BB}}\end{array}\right] \left[\begin{array}{c}{\mathrm{U}}_{\mathrm{A}}\\ {\mathrm{U}}_{\mathrm{B}}\end{array}\right]= \mathsf{\theta }$$

(5)

Here, $\theta$ represents the influence coefficient matrix, with all of its elements being complex numbers. Each element, ${\theta }_{ij}$, in matrix $\theta$ is referred to as an influence coefficient and quantifies the impact of an unbalance in the jth plane on the vibration observed in the ith plane. To calculate these influence coefficients, a trial mass M_j of substantial weight is placed on one plane, and the resulting vibrational response is measured on the corresponding measuring plane. This process is then repeated for the other plane. The influence coefficient is then derived from the obtained measurements [22].

$${\theta }_{ij}={\displaystyle \frac{Y_i^j-Y_j}{M_j}}, \mathrm{with} i,j=\mathrm{A},\mathrm{B},$$

(6)

In this context, $Y_j$ represents the jth vibration reading without the trial mass, $Y_i^j$ denotes the ith vibration reading when the trial mass is placed on the jth balancing plane, and $M_j$ is a complex number that indicates the amplitude and angular position of the trial mass. After constructing the influence coefficient matrix, the unbalances in the armature can be calculated using the resulting equations [22].

$$\mathrm{U}=\left[\begin{array}{c}{\mathrm{U}}_{\mathrm{A}}\\ {\mathrm{U}}_{\mathrm{B}}\end{array}\right]={\left[\begin{array}{cc}{\mathsf{\theta }}_{\mathrm{AA}}& {\mathsf{\theta }}_{\mathrm{AB}}\\ {\mathsf{\theta }}_{\mathrm{BA}}& {\mathsf{\theta }}_{\mathrm{BB}}\end{array}\right]}^{-1}\left[\begin{array}{c}{\mathrm{Y}}_{\mathrm{A}}\\ {\mathrm{Y}}_{\mathrm{B}}\end{array}\right]$$

(7)

As a result, the correction masses that need to be added to planes A and B can be determined by

$$U_c=-U={\left[U_{cA} U_{cB}\right]}^T,$$

(8a)

with

$$U_{cA}={\displaystyle \frac{{\theta }_{BB}{Y}_A-{\theta }_{AB}{Y}_B}{{\theta }_{AA}{\theta }_{BB}-{\theta }_{AB}{\theta }_{BA}}} \mathrm{and} U_{cB}={\displaystyle \frac{{\theta }_{AA}{Y}_B-{\theta }_{BA}{Y}_A}{{\theta }_{AA}{\theta }_{BB}-{\theta }_{AB}{\theta }_{BA}}}.$$

(8b)

When balancing a rotor using the mass addition method, Equation (8b) enables the calculation of the appropriate correction masses values $U_{cA}$ and $U_{cB}$ once the influence coefficient matrix is determined. Equation (7) demonstrates that the influence coefficient matrix connects the unbalance to the vibratory response. While this matrix offers a practical solution for balancing rotors using the mass addition method, an additional relationship is necessary for mass removal techniques to link the material removed from the armature to the milling cutter’s cutting depth. The latest balancing equipment automatically establishes this relationship. A “material removal curve” is generated by making a series of cuts with varying depth and length parameters to measure how the removed material impacts the armature’s unbalance.

This section describes the fundamental process of determining the vibratory response using sensors across multiple planes (A and B) and how this is calculated through variations in mass. In this context, unbalance can be effectively minimized by measuring vibrational signals in both balancing planes and calculating the required correction masses. This approach forms the core operational principle of mass production balancing equipment and is essential for achieving precise and efficient balancing in high-volume production environments.

3. Results and Discussion

3.1. Analysis of Results before the Alignment Tool Implementing

Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 display the piece 3D representation assembled in each operation and their respective unbalanced graph; the CE nomenclature corresponds to Commutator End, and DE corresponds to Drive End, which denotes what plane of the armature belongs to the unbalanced shown in the figures.

Figure 4 exhibits the shaft lamination assembly operation. The unbalanced values ranged from 3.17 to 102.32 g·mm, corresponding to the CE, and 3.08 to 112.69 g·mm, corresponding to the DE. The variation in these values is related to the misalignment between the lamination and the shaft, which is a product of the assembly process, and the natural wear and tear that the equipment accumulates. In this context, Paramasivam et al. [10] determined that the main factor affecting the unbalance of the armatures presented in their study was the misalignment between the shaft and the lamination, which was corrected by an improvement in the equipment design for assembling these two components, thereby achieving a significant reduction in radial and axial deviations, reducing their unbalance. However, in this study, it is considered that the measured values are not determining factors to generate an affectation in the final unbalance of the studied armatures, that although some values are slightly outside the allowed unbalance parameter, are not large enough to prevail or be maximized disproportionately in subsequent operations.

The conductor twisting operation is illustrated in Figure 5, wherein the unbalanced values increased in the CE from 24.39 to 141.78 g·mm and in the DE from 49.06 to 142.68 g·mm. This increase in unbalance is attributed to a couple of factors. Firstly, the assembly of the conductors comprising the armature winding generates mass misalignment. Secondly, twisted conductors lack homogeneity and may experience varying degrees of deformation depending on the bending equipment. Consequently, this leads to a shift in the armature’s center of gravity, resulting in a 30% increase in unbalance compared to the previous step. However, this unbalance will be compensated for by assembling the remaining components of the armature.

Consequently, Figure 6 displays the conductor’s end-cutting operation. The CE unbalanced values range from 20.04 to 373.39 g·mm and DE from 46.62 to 230.28 g·mm. At this point, it is important to mention that the significant increase in unbalanced is due to an uneven cut at the end of the conductors, which causes the removed material to change considerably in mass distribution. Therefore, it tends to unbalance it by up to 265% compared to the previous step. This effect caused by asymmetric windings leading to unbalance is mentioned by Park et al. [25], although the author does not mention the severity of the unbalances generated. In the present study, the measured values are decisive in generating an affectation in the final unbalance of the studied armatures, being this is the operation that most unbalance contributes to the armatures.

Now, the attention shifts to Figure 7, which depicts the commutator insertion operation. The unbalanced values in CE start from 47.30 to 205.84 g·mm and DE from 25.83 to 189.83 g·mm. Here, the operation presents a change in unbalanced maximum values since the significant switch mass assembled tends to redistribute the armature mass considerably. The latest affects the CE to a greater extent, which tends to reduce the unbalanced value by 45% compared to the previous operation, which is an improvement but not significant enough to compensate for the unbalance accumulated until the above operation.

Subsequently, Figure 8 exhibits the band insertion operation. The CE unbalanced values range from 45.43 to 193.37 g·mm and for DE from 6.71 to 177.43 g·mm, which is not considered a significant change in the maximum unbalanced values. The previous sentence is because the reduction compared to the maximum unbalanced values of the previous operation is less than 10% since the bands do not have a significant mass, and their main function is to hold the conductors.

Figure 9 displays the armature varnishing operation. The unbalanced values range from 43.57 to 185.05 g·mm and 5.65 to 205.05 g·mm for CE and DE, respectively. This operation showed a slight increase in the unbalance of the armature because a resin covering the body of the armature (lamination) was added and tended to be concentrated in the DE. Medellin and Mendoza [20] reported that this process stage is considered key in affecting the unbalance due mainly to the amount of control of resin applied. However, for this process, as the measured unbalance data show, this transaction is unimportant as the change in maximum unbalance is around 16% concerning the previous unbalanced values.

The commutator grooving operation is depicted in Figure 10. The unbalanced values range from 42.87 to 182.80 g·mm for CE and 4.90 to 203.39 g·mm for DE. This operation does not contribute significantly to changes in the unbalance, mainly because the material is hardly removed from the commutator. Its effect is less than 1% compared to the previous operation.

Finally, Figure 11 shows the armature machining operation. The unbalanced values range from 27.59 to 109.53 g·mm and 7.14 to 146.47 g·mm for CE and DE, respectively. This operation displayed a significant unbalance reduction by 40% in the maximum values of unbalance measured to the previous operation due to the removal of excess material in three areas of the armature (commutator, lamination diameter, and conductor tips). However, the armature should be adjusted to the optimal parameters at this point, which often becomes impossible due to the large, accumulated unbalance from previous stages.

In this context, it is remarkable to mention that the unbalanced variations presented by the pieces according to the literature were due to the accumulation of dimensional tolerances, the inherent variation in the manufacturing process, the parallelism between components, the assembly of eccentric parts, the precision of machining, and the non-uniformity of materials density, whichever come together as the assembly process progresses causing the initial armature unbalance to be altered [26,27,28]. As this study remarks, to the causes mentioned above, there is an extra factor concerning the accumulated unbalance by all stages previous to armature balancing, mainly attributed to the conductor cutting operation.

3.2. General Analysis of the Armature Unbalanced Process

Based on the above information, Figure 12 shows the unbalanced values in each key operation in the rotor assembly process for the ICE starter.

Although the part’s unbalanced values change each operation as the mass distribution is adjusted, it is in the conductor end-cutting operation (delimited between red dotted vertical lines in Figure 12) where the greatest amount of unbalance is observed. At this point, more than 25% of analyzed pieces exceed the maximum allowed unbalanced value of 100 g·mm, reaching values between 200 and 373 g·mm, as Figure 12 displays by a horizontal dotted red line. The maximum allowed unbalanced value has been reported elsewhere [29] and represents the limit for balancing parts in a single cycle of the production process, thus complying with the unbalance tolerance established by design for these assemblies under ISO 1940-1 [14].

Regarding the above results, it can be remarked that axial misalignment of conductors plays a significant role in the unbalanced variations on an adjustment method to reduce coaxiality and initial unbalance in the rotor assembly [30,31]. This influence is manifested especially after the conductor end-cutting operation, where misalignment in conductors leads to non-uniform material removal, increasing the unbalance on the side corresponding to the CE plane. It is crucial to underline that correcting and optimizing the conductor alignment at this stage is essential to ensure compliance with the unbalanced tolerances required by the product design. Although the following unbalance operations tend to decrease the misalignment due to the incorporation of the final components and the machining operations, the latter are insufficient to reverse such a high unbalance.

3.3. Design of the Alignment Tool

Based on the preliminary results of the study and the analysis of the conductor end-cutting operation, it was determined that there was no adequate support point to provide rigidity and keep the conductors’ alignment that make up the armature winding, mainly due to the limited space available within the assembly equipment. Considering these previous elements, the tool prototype was manufactured with the following characteristics: minimally invasive, easy to assemble, and low-cost implementation (see Figure 13). Figure 14 shows the tool-sectioned view interacting with the armature components in the tips-cutting operation.

The proposed novel tool works as follows: It is assembled by the pinion armature side, matching the tool teeth and armature pinion teeth separations. Once coinciding, the tool is pushed until it meets the lamination isolator and rotates approximately 9°. This way, the tool teeth are below the sprocket teeth, and a rigid position is maintained, providing adequate support to the armature conductors to maintain a uniform position. The tool must be applied from the start of the conductor end-cutting operation and through the following assembly processes up to the band insertion operation, in which, by resistance welding, the conductors are permanently attached to the commutator, eliminating the possibility of any misalignment.

Rotational Dynamics Analysis of the Alignment Tool

The inertia matrix of a rotor describes how the rotor mass is distributed concerning its rotation axes and is crucial in the dynamic analysis of rotating systems. It can be represented in a 3 × 3 matrix form, and its elements are divided into two main categories:

Moments of inertia: Diagonal elements of the matrix represent rotor resistance to rotate around the principal axes. For a rotor, the moments of inertia around the coordinate axes x, y, and z are I_xx, I_yy, and I_zz, respectively.

Products of inertia: These are the off-diagonal elements of the matrix and represent the mass distribution concerning the pairs of axes. The products of inertia $I_{xy}$, $I_{xz}$, and $I_{yz}$ indicate how the mass is distributed concerning the x, y, and z axes.

The general form of the inertia $I$ matrix is as follows [32,33]:

$$I=\left(\begin{array}{ccc}{I}_{xx}& -I_{xy}& -I_{xz}\\ -I_{xy}& I_{yy}& -I_{yz}\\ -I_{xz}& -I_{yz}& I_{zz}\end{array}\right)$$

(9)

This matrix is fundamental for the analysis of rotational dynamics due to its contribution to predicting the behavior of the rotor under different load and rotation conditions.

In this context, Equations (10) and (11) represent the inertia moment values of the armatures presented in Figure 15, with the conductors aligned after using the novel tool (Figure 15a) and without using the alignment tool (Figure 15b).

$$I_{Aligned}=\left(\begin{array}{ccc}1716519.4307& -0.8639& -2.6871\\ -0.8636& 3292663.3243& -1.2295\\ -2.6871& -1.2295& 3292663.3243\end{array}\right)$$

(10)

$$I_{Misaligned}=\left(\begin{array}{ccc}1718819.1977& -2670.6162& 4836.9595\\ -2670.6162& 3303393.7166& -99.4998\\ 4836.9595& -99.4998& 3303033.0662\end{array}\right)$$

(11)

These values were computed by using the software SolidWorks. Misaligned armature shows significantly increased inertia products concerning the correctly assembled armature, of which there are almost zero products of inertia. This last indicates a balanced armature around the main axes. These non-zero inertia products cause cross moments of inertia that affect rotor stability and can generate additional vibrations during operation because high products of inertia introduce additional forces that result in unliked vibrations. Although the main moments of inertia have also changed, the products of inertia are the main cause of the unbalance [34,35]. Differences in moments of inertia are due to non-uniform mass distribution and misalignment, but the predominant effect on unbalance comes from high products of inertia.

3.4. Analysis of Results after the Alignment Tool Implementing

The novel prototype tool was manufactured and implemented in a second set of controlled parts, thus allowing the evaluation of its impact on reducing the unbalanced level. Figure 16 exhibits the unbalanced values in each relevant operation during the armature assembly process. It is important to observe that the novel conductor alignment tool was applied from the conductor end-cutting operation and remained assembled until the band insertion operation.

In contrast to the data obtained from the first group (see Figure 12), Figure 16 reveals that the unbalanced values do not reach the maximum critical level previously achieved when implementing the novel conductor alignment tool during conductor end-cutting operation, improving operation efficiency by about 15%. Rather, data exhibit stable behavior throughout subsequent operations of the assembly process. In this context, the innovative driver alignment tool was designed to maintain the unbalanced values with a tendency to decrease gradually below 100 g·mm. This achievement is significant since it balances the parts in a single cycle within the production process. Thus, it complies with the unbalanced tolerance required by the design and contributes to the assembly process performance improvement and quality of armature for heavy-duty equipment in the automotive industry.

4. Conclusions

The armature manufacturing process has been studied to analyze and identify specific contributions to unbalancing during assembly. A novel driver alignment tool was also designed to evaluate these unbalanced effects. The main conclusions are as follows:

One of the primary factors contributing to the high initial armature unbalances observed in this research is the misalignment of conductors within the armature winding. As a corrective measure, the proposed tool ensures proper conductor positioning during manufacturing operations, thereby minimizing displacement during handling and assembly to prevent adverse effects on the final armature unbalance, improving operation efficiency by about 15%.

Misalignment of conductors during end-cutting operations leads to uneven distribution of armature mass. The previous unbalance might exceed 100 g·mm and, if not corrected before band insertion, may compromise compliance with the required unbalance tolerance specified in the design. By controlling this critical feature, the objective is to reduce the number of armatures exhibiting high levels of unbalance during the manufacturing process, thereby enhancing operational efficiency, reducing scrap associated with highly unbalanced parts, and prolonging tool durability.

The armature with misaligned conductors presents a high imbalance and exhibits an inertia matrix with significantly non-zero products, negatively affecting the dynamics of the armature.

Finally, it is important to note that the design of the conductor alignment tool represents an optimal solution for this research study. Due to its flexibility in armature assembly, minimal interference with manufacturing equipment interactions, and the resources invested, it significantly improves the unbalance resulting from conductor misalignment. Furthermore, this research aims to serve as a reference, providing a precedent to address similar issues. The proposed approach seeks to resolve specific identified problems and aims to establish best practices applicable to the industry, thereby contributing to the advancement and optimization of manufacturing processes for related products.