# Selection of Optimal Magnets for Traction Motors to Prevent Demagnetization

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{o}H where μ

_{o}= 4π∙10

^{−7}[N/A

^{2}] is the permeability of vacuum(J ≡ B − µ

_{o}H).

_{r}[6,7,8]. However, operating below the knee point will cause it to return along a parallel path which will reduce the residual flux density to a smaller value B

_{r}

^{′}. This reduction in residual flux density δB

_{r}= B

_{r}− Br′ is known as a demagnetization loss, irreversible loss, or simply loss.

_{r}requires more current to generate the same torque. This increases the copper loss, which increases the magnet temperature further, which in turn degrades the magnet more. The resulting vicious circle can cause a significant loss in the performance of the electric vehicle.

- Classic knee point K;
- Knee endpoint k′.

**Classic knee point K**—The magnet material engineers (who develop/test magnets) use the J(H) curve to define the classic knee point K. They define K as the point on the J(H) curve that permits 10% B

_{r}demagnetization loss. (In the 1960s, up to 20% loss was considered acceptable [11,12]). Their metric for demagnetization is the respective field H

_{K.}

_{K}to indicate magnets with fewer defects [13,14]. A J(H) curve that is closest to the largest rectangle B

_{r}H

_{cJ}is deemed to have the least defects (H

_{cJ}= coercivity on the J(H) curve). They used the ‘loop squareness’ H

_{K}/H

_{cJ}[15,16] as a metric to develop better compositions that yielded magnets with the fewest defects [17,18].

_{K}to define the acceptable limit on the demagnetization loss [19,20,21]. Initially, they presumed that the linear segment of J(H) of rare-earths to be nearly horizontal. Therefore, they defined the classic knee point K as the point on the J(H) curve where it intersects a horizontal line that passes through the 0.9∙B

_{r}point [22,23,24]. However, the linear segment is slightly inclined [25,26]. Therefore, later Gaster [27,28] redefined it as the point on the J(H) where it intersects a parallel inclined line that passes through the 0.9∙B

_{r}point. Both definitions indicate that the material engineers considered the 10% reduction in B

_{r}to be acceptable.

_{cJ}is the metric for the demagnetizability of a magnet. However, in 2008, Trout [29] wrote that the ‘(classic) knee point field H

_{K}may be a better figure of merit’ (than coercivity H

_{cJ}) or better metric for the onset of demagnetization. Since then, all commercial B(H) measurement systems are programmed to list this H

_{K}[30,31,32,33]. Currently, manufacturers use this H

_{K}in purchase specifications as a basis to negotiate the price of the magnets. However, over the past 10 years, tremendous improvements enabled the manufacturers to make superior magnets to tighter tolerances. Modern magnets, therefore, require a better metric with a tighter tolerance than the 10% loss allowed by H

_{K}.

**Knee endpoint k′**—The motor design engineers (who select and size the magnets for traction motors), on the other hand, rely on the Maxwell laws-based magnetic field software for the detailed design of traction motors [34,35,36]. Such software uses the B(H) curve rather than the J(H) curve. Therefore, these engineers rely on the B(H) curve to define the knee endpoint k′. They define it as one where the knee on the B(H) curve starts deviating from a straight line to a curve [37].

_{k′}. Motors subject the magnets to nonuniform fields, so the demagnetized volumes (where the flux density is less than the knee endpoint flux density B

_{k′}) are local at the edges or center of magnets. The motor design engineers rely on B

_{k′}to estimate the demagnetized volume fraction V

_{d}[38,39,40,41,42], which is then used to limit the loss in performance caused by the demagnetization of the magnets.

#### 1.1. Difference between K, k′

_{K}(0.25 T) is ~30% lower than the knee endpoint flux density B

_{k′}(0.37 T). It shows that the classic knee point field H

_{K}(−517.2 kA/m) is numerically 9% higher than that H

_{k′}at the knee endpoint (−475 kA/m).

_{K}at the classic knee point. The higher this H

_{K}, the higher the price. However, Figure 1a demonstrates that, by specifying H

_{K}as the basis to price magnets, a buyer is paying a significant, but spurious 9% higher price for a magnet.

_{K}(−1900 kA/m) is 30% (numerically) smaller than the knee endpoint field H

_{k′}(−2500 kA/m).

_{K}as −6.583 kOe (= −524 kA/m). However, its knee endpoint field H

_{k′}of −495.5 kA/m is 5.4% lower. This again demonstrates that using the classic knee point K to price magnets, a buyer is paying a significant, but spurious 5.4% higher cost for the magnet.

_{K}is 40% lower than the 0.45 T knee endpoint flux density B

_{k′}.

#### 1.2. Manual Method to Locate k′

_{1’}, while another may pick point k

_{2’}. However, their flux densities are 0.21 and 0.31 T, respectively—a 50% error. These examples illustrate that the manual method of locating the knee endpoint k′ is imprecise and prone to significant errors.

#### 1.3. Other Prior Methods to Locate k′

## 2. Knee Point k

#### 2.1. Offset Method

_{r}to a smaller Br′. The reduction δB

_{r}= B

_{r}− Br′ is called demagnetization loss. Alternately, we reformulate it as offset x = δB

_{r}/B

_{r}(expressed as a percentage). Then, defining k amounts to specifying x.

#### 2.2. Options for Offset x

- 10% offset (K). This classic knee point K was proposed in the 1990s by magnet material engineers [20] as one that tolerates 10% B
_{r}loss. However, consider the N40UH grade with B_{r}of 1.29 T. A 10% loss reduces it to Br′ of 1.16 T. Table 1 below shows that this is the B_{r}for N33UH, which is three grades below N40UH. Thus, operating at the classic knee point K degenerates a magnet forever to a lower grade, so is unacceptable. - 5% offset (D). This demagnetization point D was suggested in IEC 60404-8-1 [25,67] as one that tolerates 5% B
_{r}loss. However, consider the N50H magnet with B_{r}of 1.40 T. A 5% loss reduces it to Br′ of 1.33 T. Table 1 shows that this is the B_{r}for N42H, which is three grades below N50H. Thus, operating at the demag point D degenerates a magnet forever to a lower grade, so is unacceptable. - 2% offset. This does not degenerate some magnets (for example, it reduces the 1.25 T B
_{r}of N35UH to 1.226 T. It is larger than the 1.15 T B_{r}for a lower grade N33UH. Therefore, it will not degenerate this magnet). However, consider N52H with B_{r}of 1.42 T B_{r}. The 2% loss reduces it to Br′ of 1.39 T. This is B_{r}for N50H, which is one grade below N52H. Thus, operating at this 2% loss the knee point can degenerate some magnets forever to a lower grade, so is unacceptable. - 0.5% offset. This also does not degenerate a magnet, so it may seem to be acceptable. However, for N28EH with B
_{r}of 1.05 T, it amounts to 0.005 T, which is close to the measurement noise floor. However, at present, manufacturing a grade to such tight tolerances is nearly impossible. Specifying such tight tolerance will only increase their cost. Furthermore, tests by Allcock [68] revealed that most magnets suffer from a 0.4% B_{r}long-term irreversible loss (LTIL). Therefore, specifying a 0.5% offset is unacceptable.

#### 2.3. Rationale for 1% Offset

#### 2.4. Grade Spacing

_{r}of the lowest/highest grade N28/N55 is 1/1.5 T. Therefore, as one changes from the lowest grade to the highest, B

_{r}increases by 0.5 T. Since 10 grades fit into this 0.5 T span, they are spaced at about 0.05 T.

_{r}of 1.5 T. Therefore, x = 1% offset is the best option to define the knee point k that prevents degeneration of a magnet to a lower grade.

#### 2.5. Example

_{r}of 1.247 T to Br′ of 1.234 T. However, this is still greater than the 1.222 T residual flux density of the lower grade N48H. This establishes that operating a magnet up to its knee point k

**will not degenerate**it to a lower grade.

_{r}of 1.247 T to Br′ of 1.122 T. This is less than the 1.134 T residual flux density of N40H. This establishes that operating a magnet up to its classic knee point K

**will degenerate**it to a lower grade.

## 3. Demag Flux Density

_{k}at the knee point k as the demagnetization flux density or simply demag flux density herein. B

_{k}signals the onset of excessive demagnetization of magnets. It is similar to that of yield strength σ

_{y}—which signals the onset of plastic or yielding of metals. Therefore, it is a key property of magnets.

_{r}and the demag flux density B

_{k}define the usable segment (green) of a magnet. It also shows that, with increasing temperature, B

_{k}increases sharply while B

_{r}decreases mildly. Therefore, the rate at which a magnet’s usable range narrows with temperature is defined more by B

_{k}than B

_{r}. This confirms that B

_{k}is a key property of the magnet. Such a clutter-free demagnetization plot often provides a better insight as to how temperature impacts the usable range (conventional demagnetization curves cluster B(H) curves with J(H) curves, obscuring the usable range, see Figure 1, Figure 2 and Figure 3).

_{k}for their magnets. Just as the ASTM E8 spec helped widespread use of ‘yield strength’ σ

_{y}, incorporating the ‘demag flux density’ B

_{k}into international standards will enable its widespread use.

_{r,}B

_{k}) characterize the torque capability and heat resistance of the magnet, respectively. These metrics are valued by a motor designer. Therefore, they form the optimal cost basis for magnets.

_{k′}to compute the demagnetized volume fraction. However, as already shown, such manually read values can be imprecise. Instead, using the demag flux density B

_{k}determined by the 1% offset method proposed herein will avoid such errors, resulting in more precise demagnetized volume fractions.

_{K}(as B changes more rapidly than H in the knee). The eDrive systems by Magna Motors utilize it in their design, thereby resulting in a less expensive and more reliable drive system for future transportation mass market.

_{k,}B

_{k}) of the knee point k for all magnets produced worldwide. The demag flux density B

_{k}included therein simplifies the task of accurate estimation of demagnetized volume fractions to limit performance degradation of electric vehicles.

_{k}varies with temperature and grade. This, in turn, shortens the process of selection of an optimal magnet that meets specific severe-duty performance requirements of electric vehicles.

## 4. Demag Flux Density Map

_{k}of all grades and temperatures. Figure 7 shows such a map for a specific manufacturer, over 120 to 180 °C. The grade corresponding to a point can be read off from Table 1. For example, the N33M-N52M curve has 9 points ranging from N33M to N52M, the 7th point refers to N48M, and its B

_{k}at 120 and 150 °C is 0.7 and 0.85 T. Note that some curves are non-monotonic. This may be due to irregular grade spacing, inherent measurement noise, manufacturer variations, etc., which will be investigated in the future.

_{k}requirement is met by the N48M grade at 120 °C or the N35M grade at 150 °C.

_{k}of 0.38 T, which indicates that both deliver the same severe-duty performance. Therefore, this plot demonstrates how cooling a magnet can save significant costs of magnets.

## 5. Conclusions

_{r}. We showed herein that operating above such knee point k protects it from degenerating to a lower grade forever. The paper, therefore, recommends using this newly defined knee point k to prevent the degradation of magnets to a lower grade when simulating the severe-duty short circuit performance of traction motors. Data on this knee point k are available in the comprehensive PMAG database recently developed by MagWeb.

_{k}is a key property of a magnet that signals the onset of excessive demagnetization. Listing it by manufacturers or incorporating it into international standards will help engineers better protect the magnets from degrading to a lower grade during the operation. Moreover, it helps them discover the right manufacturer who offers a better grade (with an optimal demag flux density B

_{k}) for their application and cost reference. This helps in the selection of optimal magnets for traction motors in electric vehicles.

_{K}of a magnet (on a J(H) curve where a magnet can lose 10% Br) is popularly used to negotiate the price of the magnets. This paper, however, shows that this metric can overprice a magnet. Instead, it shows that the demag flux density B

_{k}of a magnet (at the operating temperature) is a better cost metric as it prevents a magnet from degenerating to a lower grade. Using B

_{k}rather than H

_{K}(to price the magnets) would be a milestone for future procurement strategies and the specification of magnets for traction motors in electric vehicles.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) For Arnold’s N38UH, the knee flux densities B

_{k′}, B

_{K}differ by ~50%. (

**b**) For Hitachi’s NMX-S34GH, the knee fields H

_{k′}, H

_{K}differ by 30%. Therefore, the knee endpoint k′ differs significantly from the classic knee point K.

**Figure 2.**For Innuovo’s N48UH grade, the classic knee point K lies inside the nonlinear segment. Therefore, a minute decrease in H can result in a sharp fall in the flux density.

**Figure 4.**(

**a**) Knee point k defined by the 1% offset method prevents the degeneration of a magnet. (

**b**) Yield strength defined by the 0.2% offset method prevents the metal from going plastic.

**Figure 5.**(

**a**) The knee point k will not degenerate the magnet to a lower grade. (

**b**) The classic knee point K will degenerate the magnet to a four grades lower magnet.

B_{r} tesla | 1.05 | 1.10 | 1.15 | 1.20 | 1.25 | 1.29 | 1.32 | 1.35 | 1.38 | 1.40 | 1.42 | 1.45 | 1.49 | Max Temp |

Label | GRADES | deg C | ||||||||||||

AH | 28AH | 30AH | 33AH | 35AH | 38AH | 40AH | 230 | |||||||

EH | 28EH | 30EH | 33EH | 35EH | 38EH | 40EH | 42EH | 45EH | 200 | |||||

UH | 30UH | 33UH | 35UH | 38UH | 40UH | 42UH | 45UH | 48UH | 50UH | 52UH | 54UH | 180 | ||

SH | 30SH | 33SH | 35SH | 38SH | 40SH | 42SH | 45SH | 48SH | 50SH | 52SH | 150 | |||

H | 30H | 33H | 35H | 38H | 40H | 42H | 45H | 48H | 50H | 52H | 120 | |||

M | 30M | 33M | 35M | 38M | 40M | 42M | 45M | 48M | 50M | 52M | 100 | |||

N30 | N33 | N35 | N38 | N40 | N42 | N45 | N48 | N50 | N52 | N54 | N55 | 80 | ||

BHmax | 28 | 30 | 33 | 35 | 38 | 40 | 42 | 45 | 48 | 50 | 52 | 54 | 55 | MGOe |

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## Share and Cite

**MDPI and ACS Style**

Rao, D.; Bagianathan, M.
Selection of Optimal Magnets for Traction Motors to Prevent Demagnetization. *Machines* **2021**, *9*, 124.
https://doi.org/10.3390/machines9060124

**AMA Style**

Rao D, Bagianathan M.
Selection of Optimal Magnets for Traction Motors to Prevent Demagnetization. *Machines*. 2021; 9(6):124.
https://doi.org/10.3390/machines9060124

**Chicago/Turabian Style**

Rao, Dantam, and Madhan Bagianathan.
2021. "Selection of Optimal Magnets for Traction Motors to Prevent Demagnetization" *Machines* 9, no. 6: 124.
https://doi.org/10.3390/machines9060124