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Converting Motor RPM into a 0-to-360-degree ramp signal

Converting Motor RPM into a 0-to-360-degree ramp signal

Rakesh K Dhawan, Power Electronics Group LLC

Converting Motor RPM into a 0 to 360-degree rampDownload

1.0 Abstract

This article presents a method to convert motor rotational speed (RPM) into a continuous ramp signal spanning 0 to 360 degrees, utilizing LTspice for simulation and implementation. The approach starts with foundational mathematical equations that translate mechanical RPM into electrical angular position, incorporating key conversions such as half the electrical speed in radians per second and the rotor’s angular displacement in degrees.

The LTspice implementation leverages behavioral voltage sources and integrators to generate a dynamic ramp signal that accurately reflects rotor position, adapting to positive and negative RPMs. A key insight includes the necessity of halving the electrical speed to align with trigonometric function behaviors, mainly due to the doubling frequency of the tangent function compared to sine and cosine. Simulation results validate the technique with varying RPMs and rotor pole counts, showcasing bidirectional ramp generation suitable for motor control and position tracking systems applications.

2.0 Introduction

Understanding rotor position is fundamental in electric motor control systems, especially for field-oriented control (FOC) applications, sensorless control, and real-time monitoring. One key technique is converting a motor’s rotational speed (RPM) into a continuous ramp signal that spans from 0 to 360 degrees—representing the angular position of the rotor within a single electrical revolution. This article outlines the mathematical approach and LTspice implementation to generate such a ramp, complete with practical examples and simulation results.

3.0 Foundational Mathematical Equations

First, let us look at math. Equations numbered 1 through 6 below illustrate the steps.

                                                                                                                                       … Motor RPM (1)

Motor RPM (n): This is the input mechanical speed of the motor in revolutions per minute (RPM).

                                                                                                                           … (2)

Where p is the number of poles. The electrical speed is proportional to mechanical speed and the number of pole pairs.

                                                                                                  … Half Electrical Speed in rad/s (3)

As explained later, this adjustment plays a critical role due to trigonometric frequency behavior.

                                                             … Intermediate rotor angle in Electrical rad/s (4)

Integrating half the electrical speed gives a linearly increasing (or decreasing) signal over time, essentially a “forever ramp.”

                                                        … Rotor position in Electrical radians (5)

                                                  … Rotor Position in Electrical degrees (6)

This ensures the ramp wraps around at 360 degrees, producing a clean cycle from 0 to 360 and back.

4.0 LTspice Implementation

The above equations are implemented in LTspice using B-sources—behavioral voltage sources capable of defining voltage or current based on mathematical expressions.

Figure 1: The motor speed n is modeled as a voltage source that varies with time. For example, a sinusoidal input mimics acceleration and deceleration.

Figure 2: Implementation of We Half, Half of Electrical Speed in rad/s. A behavioral voltage source calculates half of the electrical speed in rad/s using the motor RPM and the number of poles.

Figure 3: Implementation of the Integral Function to obtain θi, essentially a forever ramp. LTspice integrators accumulate the electrical speed over time, forming a ramp signal representing the rotor angle in electrical radians.

Figure 4: Implementation of θ360 ramp increments positively from 0 to 360 for positive rpm and decrements 360 to 0 for -ve rpm. The final behavioral block uses the Tan function to constrain the ramp between 0 and 360 degrees. The ramp’s direction reflects the motor RPM sign—positive for forward rotation and negative for reverse.

5.0 Why do we calculate We half – Half electrical speed?

A common question arises: Why calculate half of the electrical speed? The answer lies in the behavior of trigonometric functions. We need to look at the Sine, Cosine, and Tangent functions to answer this.

Figure 5: A plot of sine, cosine, and tangent functions reveals that the tangent function completes two cycles in the same period, whereas sine and cosine complete one. This doubling in frequency can lead to distorted position signals when interpreting ramp outputs using tangent-based decoding with We half adjustment. The resulting ramp frequency matches the expected sine/cosine-based waveforms used in most motor control algorithms by halving the electrical speed before integration.

6.0 Simulation Results

Figure 6: Zero-to-360-degree Ramp for Motor Speed of 100 RPM with 22 number of rotor poles

Figure 7: 360-to-Zero-degree ramp with -100 rpm Motor Speed.

Figure 8: Up and Down rotor position ramp with the Motor Speed varying as a Sine with 100 rpm as max speed.

7.0 Applications and Significance

This approach is highly valuable in simulation environments for validating control algorithms, sensorless estimation techniques, and hardware-in-the-loop testing. Engineers can use the 0-to-360-degree ramp as a reference input or internal signal in motor control strategies. Additionally, the modularity of the LTspice implementation allows easy adaptation to different pole counts and motor types.

8.0 Conclusion

The conversion of motor RPM into a 0-to-360-degree rotor position ramp using LTspice provides a robust and insightful method for modeling motor behavior. By leveraging a sound mathematical foundation and behavioral modeling, the approach supports accurate and dynamic simulation of electrical angle tracking. This forms a crucial building block in developing and validating modern electric motor control systems.

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Understanding Permanent Magnet Motors

Let us assume we have a 5-phase motor we are trying to analyze. This motor has the following characteristics.

Figure 1 – 5-Phase Motor with 22 Magnets and 25 Slots. OD of 200mm and Stack of 25mm.

Motor Characteristics:
Input Voltage = 48V
Max Phase Current = 40A
Phase Resistance = 0.22 Ohms
Phase Inductance = 1.5mH

The motor’s backEMF is shown below at 100 RPM. It is slightly trapezoidal compared to the Sinusoidal representation.

5-Phase Motor BackEMF at 100 rpm

Problem Statement: Given the above information, can you develop

  1. an approximate torque-speed curve and
  2. A field weakening plot of Torque vs. Phase Angle and
  3. A field weakening plot of Motor Speed Vs. Phase Angle.

What tools and methods will you use to develop an answer?

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Minimizing Air Gap and Slot Width: Balancing Performance and Manufacturability

Rakesh Dhawan, BTech, MSEE, MBA

In brushless permanent magnet (PM) motors, the air gap is crucial in determining motor efficiency, torque production, and overall electromagnetic performance. Ideally, a smaller air gap is preferred because it results in higher magnetic flux density, stronger coupling between rotor and stator, improved efficiency, and reduced weight. However, in practical applications, manufacturing limitations and mechanical constraints prevent us from reducing the air gap beyond a specific limit.

Similarly, the slot width directly impacts the fringing effect, which occurs when magnetic flux bulges outward at the slot openings before crossing the air gap. The wider the slot opening, the more significant the fringing impact, which increases the effective air gap length and introduces additional reluctance to the magnetic circuit. This leads to flux leakage, reduced torque production, and increased harmonics in the back EMF waveform.

Challenges in Minimizing the Air Gap

  1. Manufacturing Tolerances
    • Achieving a minimal air gap requires high-precision machining and tighter assembly tolerances.
    • Even minor misalignments in the rotor-stator assembly can cause uneven air gaps, leading to localized flux variations and torque ripple.
  2. Mechanical Stability and Thermal Expansion
    • A minimal air gap makes the motor more susceptible to rotor eccentricity and thermal expansion, leading to unwanted physical contact between the rotor and stator.
    • To prevent this, designers must allow for a manufacturing tolerance in the air gap, balancing performance with mechanical reliability.
  3. Vibration and Noise Considerations
    • Reducing the air gap increases magnetic attraction forces between the rotor and stator teeth, leading to higher cogging torque, vibration, and acoustic noise.
    • This requires additional design optimizations like skewing the stator slots or using non-uniform tooth designs.

Importance of Minimizing Slot Width

While reducing the air gap is limited by mechanical factors, minimizing slot width is a practical approach to reducing the fringing effect. Narrower slot openings result in:

  1. Lower Effective Air Gap
    • A narrower slot opening means that flux lines do not need to bend as much, reducing the bulging and fringing effect and maintaining a more uniform field distribution across the air gap.
  2. Reduced Harmonics and Torque Ripple
    • Wide slot openings cause flux pulsations and introduce harmonics, contributing to torque ripple and motor noise.
    • A smaller slot width results in smoother flux transitions, improving torque stability.
  3. Higher Flux Linkage and Efficiency
    • When slot openings are narrow, more flux is directed into the rotor rather than leaking outward.
    • This improves flux linkage and ensures that more magnetic energy is converted into proper torque.

Practical Trade-offs in Slot Design

  • If the slot width is too narrow, winding the stator becomes challenging, which can lead to difficulties in inserting and cooling the copper coils unless one uses a segmented design.
  • If the slot width is too wide, flux leakage increases, requiring Carter’s coefficient correction to adjust for increased air gap reluctance.

Conclusion

While a smaller air gap is ideal for optimal motor performance, manufacturing constraints, and mechanical considerations set practical limits. To compensate for this, reducing slot width effectively minimizes fringing effects and ensures efficient flux utilization. Proper design trade-offs, including optimized slot geometry, precision machining, and skewing techniques, are essential to achieving a high-performance brushless PM motor.

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Analytical Methods for Brushless Permanent Magnet Motors – Slot Modeling

Rakesh Dhawan, BTech, MSEE, MBA

In brushless permanent magnet (PM) motor design, accurate modeling of the air gap is critical for predicting magnetic field distribution and optimizing motor performance. One of the key challenges in slot modeling is the effect of slot openings on the effective air gap. Due to the presence of stator slots, the magnetic field distribution in the air gap is not uniform, and flux tends to bulge outward before entering the rotor. This phenomenon, known as the fringing or slotting effect, increases the reluctance of the air gap and alters the motor’s magnetic characteristics. Carter’s coefficient corrects this non-uniform flux distribution and determines the effective air gap length, directly influencing torque production, efficiency, and inductance calculations.

Looking at the image above, you can tell that the flux has to travel a longer path in the slot openings. Intuitively, the effective air gap is increased, and we can also expect distortion of the flux distribution at the slot opening boundaries. This is inside the motor.
Looking at the image above, you can tell that the flux has to travel a longer path in the slot openings. Intuitively, the effective air gap is increased, and we can also expect distortion of the flux distribution at the slot opening boundaries. This is inside the motor.
Looking at the motor from a side view also indicated flux leakage and distortion due to the slot opening and magnet structure.
Looking at the motor from a side view also indicated flux leakage and distortion due to the slot opening and magnet structure.

Carter’s coefficient (kc​) is a correction factor that accounts for the influence of slot openings on the air gap reluctance inside the motor. It does not take into account the flux leakage, as shown above in the side view of the motor. Additional correction factors may need to be considered because of the 3-D geometry.

Carter’s coefficient (kc​) is given by:

kc=g \geff​

Where:

  • g = actual physical air gap,
  • geff​ = effective air gap larger than g due to slotting effects.

The value of kc​ depends on the ratio of slot opening width to slot pitch and the relative permeability of the iron core. A larger slot opening increases kck_ckc​, effectively increasing the air gap reluctance and reducing flux linkage. This impacts motor performance by decreasing torque and increasing harmonics in the back electromotive force (EMF). We use Carter’s coefficient to adjust the motor’s magnetic circuit model, ensuring more accurate predictions of inductance, air gap flux density, and overall efficiency. By correctly accounting for slot effects, we can optimize slot geometry, improve flux distribution, and achieve better control over motor performance.

Slot Modeling in an Exterior Rotor Permanent Magnet Motor.
Slot Modeling in an Exterior Rotor Permanent Magnet Motor.
Front View of the Electromagnetic Architecture defining Slot Width, Tooth Width, Slot Pitch, etc. for Slot Modeling.
Front View of the Electromagnetic Architecture defining Slot Width, Tooth Width, Slot Pitch, etc. for Slot Modeling.

Conformal Mapping Technique for Slot Modeling by Carter

The conformal mapping technique is a mathematical transformation method used to model the influence of stator slots in electrical machines. It plays a crucial role in calculating the effective air gap length in slot modeling for brushless permanent magnet (PM) motors. Carter’s Method, which applies conformal mapping, corrects for the impact of slot openings on the motor’s magnetic circuit by transforming the complex slot geometry into a simplified equivalent form, making analytical calculations more feasible.

Concept of Conformal Mapping in Slot Modeling

Conformal mapping preserves angles and transforms complex geometries into more manageable shapes while maintaining the relative proportions of the electromagnetic field. In slot modeling, the technique helps in:

  • Converting the actual slotted air gap into an equivalent smooth air gap.
  • Correcting for flux bulging and fringing at the slot openings to estimate magnetic reluctance.
  • Improving the accuracy of air gap permeance calculations.

The conformal mapping transformation modifies the shape of the slot into an equivalent smooth surface, allowing the air gap field distribution to be analyzed without complex numerical methods.

Application in Brushless PM Motors

  • Accurate Magnetic Field Distribution: By modeling the actual effect of slots, designers can predict the precise flux distribution in the air gap, reducing errors in torque and inductance calculations.
  • Reduction of Slot Harmonics: The fringing effect caused by slot openings introduces harmonics in the air gap flux. Conformal mapping helps in optimizing slot shapes to minimize these harmonics.
  • Performance Optimization: This technique allows us to design optimal slot geometries that reduce unwanted losses and improve motor efficiency.

In summary, Carter’s conformal mapping technique allows us to correct slot effects in brushless PM motors, ensuring accurate modeling of air gap behavior and improved performance predictions.

Simplified Geometry of a Complex Electromagnetic Architecture to Analyze Air Gap Flux Distribution.
Simplified Geometry of a Complex Electromagnetic Architecture to Analyze Air Gap Flux Distribution.

Flux Crossing the Gap Over the Slot: Increased Path Length and Its Implications

In brushless permanent magnet (PM) motors, the presence of stator slots introduces a discontinuity in the air gap, affecting the way magnetic flux travels across the gap. Unlike flux crossing the air gap directly over solid iron surfaces, the flux that crosses over a slot opening follows a longer, more resistive path before reaching the highly permeable material on the other side. This is due to the slotting effect, which causes magnetic flux to bulge outward (fringing effect), increasing the effective air gap length and thereby impacting motor performance.

In conclusion, the effective air gap is always more significant than the actual air gap as Kc > 1.

This fundamental equation allows us to determine the contribution to magnetic permeance due to slot openings.
This fundamental equation allows us to determine the contribution to magnetic permeance due to slot openings.
Carter presented three analytical expressions.
Carter presented three analytical expressions.
The above plot has the x-axis as the ratio of air gap and slot pitch and plots Kc1, Kc2, and Kc3. For smaller air gaps, the fringing flux is significant, reducing the effective air gap by up to 9%.
The above plot has the x-axis as the ratio of air gap and slot pitch and plots Kc1, Kc2, and Kc3. For smaller air gaps, the fringing flux is significant, reducing the effective air gap by up to 9%.

Let us consider an example as follows:

g = 1 mm
Ws = 3 mm
Wt = 19.5 mm
Ts = 22.5 mm

The Air Gap is varied while keeping the slot width and pitch constant. Smaller air gaps contribute more to magnetic permeance.
The Air Gap is varied while keeping the slot width and pitch constant. Smaller air gaps contribute more to magnetic permeance.
Permeance contribution is related to the variation of the air gap.
Permeance contribution is related to the variation of the air gap.
The air gap is kept constant as we vary the slot width. As slot width increases, the magnetic permeance contribution increases.
The air gap is kept constant as we vary the slot width. As slot width increases, the magnetic permeance contribution increases.
Permeance contribution as slot width is varied and magnetic permeance is kept constant.
Permeance contribution as slot width is varied and magnetic permeance is kept constant.

Conclusion: Ideally, we want the smallest possible air gap. However, manufacturing considerations prevent us from doing so. Having the smallest possible slot width helps us minimize the slot width’s fringing effect. See a more detailed conclusion here.

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Effects of a Large Air Gap in Thin Stack Motors

Rakesh Dhawan, BTech, MSEE, MBA

Think stack motors are rarely encountered. However, they do exist. BionX, an erstwhile Canadian Company, launched one of the known thin-stack motors in the field of electric bicycles. The large diameter motor with a 12mm stack height had some unusual characteristics. I will discuss that design in a separate post.

Some of the concerns below are about thin stack motors.

  1. Increased Magnetizing Current
    • A larger air gap increases the reluctance of the magnetic circuit.
    • This requires a higher magnetizing current to maintain the same flux density, leading to higher copper losses and reduced efficiency.
  2. Reduced Flux Density & Torque Production
    • The air gap is where the magnetic field transfers between the rotor and stator. A larger gap weakens this field, reducing torque production per ampere.
    • This forces designers to compensate by increasing current, which raises I²R losses and decreases efficiency.
  3. Increased Leakage Flux
    • More flux escapes into unintended paths, leading to poor power factor and additional losses.
    • This can also result in weaker electromagnetic coupling between the stator and the rotor.
  4. Eddy Current Losses in Thin Laminations
    • Thin stack designs rely on laminations to minimize eddy current losses, but a large air gap increases the fringing effect (flux spreading), which can induce additional losses in the edges of the laminations.
    • This can cause localized heating and performance degradation over time.
  5. Structural & Mechanical Stability
    • A large air gap can make the motor mechanically unstable, leading to vibrations and noise.
    • It also demands tighter machining tolerances to maintain uniformity, increasing manufacturing complexity.
  6. Torque Harmonics
    • Because of the non-linearities due to saturations in the laminations, the backEMF is no longer sinusoidal, introducing severe harmonics during torque production.

Balancing Stack Height vs. Air Gap

To optimize motor performance while maintaining thin stacks, designers must strike a balance between stack height and air gap:

  1. Increase Stack Height to Compensate for Air Gap Losses
    • A taller stator stack provides more magnetic material, reducing the reluctance of the core and improving flux linkage.
    • This helps recover lost torque due to an increased air gap.
  2. Optimize Air Gap Size
    • A smaller air gap is preferable for efficiency, but practical manufacturing constraints (mechanical tolerances, rotor movement, cooling needs) must be considered.
    • Using advanced high-permeability materials (e.g., silicon steel laminations) can help minimize the impact of air gap reluctance.
  3. Use High Energy Permanent Magnets (for PM Motors)
    • In permanent magnet (PM) motors, stronger magnets (e.g., NdFeB) help counteract the effect of a larger air gap by maintaining sufficient flux levels.
  4. Improve Slot and Tooth Geometry
    • Adjusting stator slot dimensions and tooth shape can help concentrate the flux density, making the motor more efficient even with a moderate air gap.
  5. Consider Air Gap Shape Optimization (or Flux Focus techniques)
    • A graded or tapered air gap or flux focus technique (instead of uniform spacing) can help direct flux more efficiently, reducing unwanted leakage.

Conclusion

A large air gap in a motor with thin stacks leads to higher losses, lower torque, and efficiency issues. The optimal design requires balancing stack height and air gap size by:

  • Increasing stack height to compensate for reluctance,
  • Using high-energy magnetic materials,
  • Optimizing slot, tooth, and air gap geometries,
  • Keeping air gap tolerances tight while allowing for mechanical stability.

By carefully designing these factors, motor efficiency can be maximized without excessive material or energy loss.

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Analytical Methods for Brushless Permanent Magnet Motors – Air Gap Modeling

Rakesh Dhawan, BTech, MSEE, MBA

Abstract

Due to their efficiency and reliability, Brushless Permanent Magnet (PM) Motors are widely used in high-performance applications. This paper explores analytical methods for modeling and designing such motors. It discusses key aspects like air gap modeling, slot modeling, core loss analysis, and permanent magnet circuit modeling. These analytical techniques help optimize motor performance and improve design efficiency. The study also addresses critical design implications such as air gap corrections, slot width considerations, and the impact of permanent magnets on motor operation.

1. Introduction

Brushless PM motors offer power density, efficiency, and control precision advantages. However, their design complexity requires robust analytical techniques. This paper provides a detailed study of fundamental analytical methods for designing and optimizing these motors. The key focus areas include air gap modeling, slot modeling, and the magnetic circuit representation of PM materials.

1.1 Importance of Analytical Methods in PM Motor Design

Analytical modeling provides insight into the motor’s electromagnetic behavior, reducing reliance on extensive finite element simulations. This enables quick design iteration, leading to more efficient and cost-effective development.

2. Analytical Methods for Brushless PM Motors

2.1 Magnetic Circuit Concepts

The design of brushless PM motors relies on understanding the fundamental properties of magnetic circuits. The governing principles include:

  • Magnetic flux paths
  • Permeance variations
  • Magnetic reluctance calculations

2.2 Air Gap Modeling

Permeance of an Air Gap measures the ease with which a magnetic flux can pass through an air gap in a magnetic circuit. It is the reciprocal of reluctance and is given by:

P=μ0A/g​ … Equation 1

where:

  • P = Permeance (measured in Henries, H)
  • μ0 = Permeability of free space (4π×10−7 H/m)
  • A = Cross-sectional area of the air gap (m²)
  • g = Length of the air gap (m)

Since air has a much lower permeability than ferromagnetic materials, the air gap introduces a significant reluctance in the magnetic circuit, which affects the overall magnetic performance of devices like transformers, inductors, and electric motors.

The air gap is critical in defining the motor’s magnetic field distribution. The air gap permeance is determined using the same equation as above:

Pg​=μ0​A​/g … Equation 2

Where Pg​ is the air gap permeance, μ0​ is the permeability of free space, A is the cross-sectional area, and g is the air gap length.

Here are the permeance values for different air gap lengths, assuming a cross-sectional area of 100 mm² (0.0001 m²):

  • 1 mm air gap → 1.26×10−7H
  • 2 mm air gap → 6.28×10−8 H
  • 3 mm air gap → 4.19×10−8 H

As expected, the permeance decreases as the air gap increases, reducing the ease of magnetic flux flow.

What happens in a transformer with an air gap?

Figure 1 – This is an illustration of a transformer core with an air gap highlighting the magnetic flux paths. The laminated iron core is shown in green, with a small air gap in the middle, depicted as a thin separation between the core sections.

In Fig. 1, our primary focus is on the leakage flux around the air gap. If we define a leakage radius of x at the end of the air gap, the permeance for a differential segment dx can be calculated. The effective length of the flux path becomes g + πx, while the additional effective area to consider is L·dx. Pf represents the additional contribution to the total permeance due to the leakage flux.

Let us consider an example:

L = 12 mm
g = 2mm
A = 50 mm2
Pg = 3.14*10-05 H

If we account for x in the leakage flux, we can use the above equation to determine Pf, representing the additional permeance the leakage flux contributed. The graph at the top (burgundy) shows the percentage contribution, and the graph at the bottom (sky blue) shows the actual value of the contribution. 50% contribution value is achieved at x= 15mm

Effects of Higher Permeance Due to Leakage Flux on Transformer Performance

When higher permeance is caused by leakage flux, it introduces several adverse effects on transformer performance:

  1. Reduced Magnetic Coupling
    • Leakage flux does not effectively link both primary and secondary windings, leading to weaker electromagnetic coupling.
    • This results in reduced energy transfer efficiency and increased losses.
  2. Increased Leakage Inductance
    • Higher leakage permeance leads to increased leakage inductance, which opposes rapid changes in current.
    • This can cause voltage spikes and transients, affecting the performance of power electronics circuits.
  3. Poor Voltage Regulation
    • With increased leakage inductance, the output voltage drops significantly under load conditions.
    • This makes the transformerless effective in applications requiring stable voltage output.
  4. Higher Core Losses & Heating
    • More leakage flux results in additional eddy current and hysteresis losses, leading to excessive heating.
    • Increased temperature can reduce the lifespan of the transformer and degrade insulation materials.
  5. Reduced Power Transfer Efficiency
    • Since leakage flux does not contribute to power transfer, some magnetic energy is wasted.
    • This decreases the overall efficiency of the transformer.
  6. Potential Electromagnetic Interference (EMI)
    • Stray magnetic fields from leakage flux can interfere with nearby electronic components.
    • This is especially problematic in high-frequency transformers used in power electronics.

Key takeaways:

  1. As we move further from the air gap, the contribution of differential permeances decreases.
  2. The exact values chosen are not that critical.
  3. As x increases beyond 10g, the total air gap permeance changes little.
  4. Higher permeance due to leakage flux negatively impacts transformer performance by increasing losses, reducing voltage regulation, and decreasing efficiency.
  5. To mitigate these effects, we need to control and optimize the leakage flux using better winding arrangements, magnetic shielding, or air gaps.

DISCUSSION: Discuss the implications of large air gaps concerning the motor design with thin stacks. How do you balance stack Height vs. air Gap? See the answer here.

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Understanding Feasibility Studies: Turning Ideas into Reality

Every great innovation starts with an idea—but how do you determine whether that idea can be transformed into an actual, functional product? This is where a feasibility study comes into play. A feasibility study is a structured approach to evaluating whether an idea is viable, focusing on technical know-how, proof of concept, and feasibility demonstration.

1. What is a Feasibility Study?

A feasibility study answers the question: Can this idea be turned into a product? It is the first step in the innovation process, analyzing whether a concept can move from theory to reality.

For example, imagine you have an idea for a car that can achieve 500 miles per gallon. While the concept sounds exciting, the key question is: Is it possible? A feasibility study provides a structured method to evaluate such ambitious ideas.

The study primarily focuses on three critical aspects:

  • Existing Knowledge and Technology
  • Demonstration of Concept
  • Building a Crude Prototype

2. Evaluating Existing Knowledge and Technology

The first step in a feasibility study is assessing whether the existing technology supports your idea. This involves:

  • Researching journal papers, patents, and technical literature to see if similar concepts have been explored.
  • Identify previous attempts and understand their successes or limitations.
  • Determining whether advancements in materials, engineering, or physics make today’s idea feasible.

This theoretical exercise helps establish whether the idea has a scientific or technological basis. If similar work exists, it provides confidence that the idea might be achievable.

3. Demonstrating the Concept

Once research indicates an idea might be possible, the next step is to move beyond theory and prove it through demonstration. This is different from creating a full-fledged product—at this stage, the goal is to show that the technology can work.

A demonstration involves:

  • Developing a crude prototype—a simplified product version that proves the core technology functions.
  • Testing whether the concept can produce expected results under controlled conditions.
  • Focusing on technical feasibility rather than manufacturability or cost-effectiveness.

For instance, in the case of the 500-mpg car, this phase might involve building a small-scale engine prototype that demonstrates the potential for extreme fuel efficiency.

4. Building a Crude Prototype

A crude prototype is an early-stage experimental model designed to verify the feasibility of an idea. It is different from a fully functional prototype because:

  • It does not need to be cost-effective.
  • It does not need to be production-ready.
  • It only needs to prove that the idea works.

This stage is critical because it bridges the gap between theory and reality. If a crude prototype successfully demonstrates the core functionality, the next step would be refining it into a more sophisticated prototype for further testing.

In a Nut Shell

A feasibility study is the foundation of product innovation. It helps innovators determine whether their idea can transition from a concept to a real-world application by:

  1. Assessing existing technology and research.
  2. Demonstrating a working concept through tests.
  3. Building a crude prototype to validate the core technology.

By following these steps, innovators can minimize risk, validate ideas early, and ensure resources are invested in projects with real potential. Whether developing cutting-edge electric vehicles, medical devices, or breakthrough engineering solutions, feasibility studies remain an essential first step in technological advancement.

QUESTION: How would you use the 80/20 principle during your feasibility study? Tell me your answer at Rakesh. Dhawan at Power Electronics Group dot com. or write a comment below.

Also, check out NASA’s nine levels of Technology Readiness, which are very useful for recording a concept’s progress. This is a good framework but not entirely applicable to commercializing a technology that must include first articles, pre-production, and production release activities. Also, in the commercial world, TRL1, 2, and 3 can be combined into a single stage, whereas NASA has to follow a three-stage approach because of the much greater risk and uncertainty of its pursuits of the missions.

NASA’s Technology Readiness Levels (TRLs) provide a systematic framework to assess the maturity of a technology, guiding its progression from conceptualization to operational deployment. This nine-level scale assists in evaluating the development stage of a technology, ensuring it meets the necessary criteria before integration into missions or systems. Below is an overview of each TRL:

TRL 1: Basic Principles Observed and Reported

  • Description: Initial scientific research begins, focusing on the fundamental principles of the technology.
  • Example: Observing and reporting basic properties of materials or phenomena.

TRL 2: Technology Concept and/or Application Formulated

  • Description: Practical applications of the basic principles are identified, though they remain speculative without experimental proof.
  • Example: Formulating potential uses for a newly observed material property.

TRL 3: Analytical and Experimental Critical Function and/or Characteristic Proof-of-Concept

  • Description: Active research and development commence, including analytical studies and laboratory experiments to validate the feasibility of the technology concept.
  • Example: Conducting experiments to demonstrate that a new material can function as a semiconductor.

TRL 4: Component and/or Breadboard Validation in Laboratory Environment

  • Description: Basic technological components are integrated to assess their compatibility and functionality in a controlled environment.
  • Example: Testing a prototype sensor in a laboratory setting to ensure it operates as intended.

TRL 5: Component and/or Breadboard Validation in Relevant Environment

  • Description: The technology is tested in an environment that simulates real-world conditions, providing more rigorous validation.
  • Example: Evaluating the performance of a satellite component in a thermal vacuum chamber that mimics space conditions.

TRL 6: System/Subsystem Model or Prototype Demonstration in a Relevant Environment

  • Description: A high-fidelity prototype is developed and demonstrated in an environment resembling the operational setting.
  • Example: Testing a robotic lander in a simulated Martian terrain to assess its performance.

TRL 7: System Prototype Demonstration in an Operational Environment

  • Description: The prototype is tested in the actual operational environment for which it is intended.
  • Example: Deploying a prototype Earth-observing instrument on an aircraft to collect atmospheric data.

TRL 8: Actual System Completed and “Flight Qualified” Through Test and Demonstration

  • Description: The technology has been proven to work in its final form and under expected conditions.
  • Example: A satellite instrument that has completed all ground testing and is certified for launch.

TRL 9: Actual System “Flight Proven” Through Successful Mission Operations

  • Description: The technology has been successfully integrated into a mission and has demonstrated reliable performance in an operational setting.
  • Example: A spacecraft component that has operated successfully during a space mission.

Understanding and utilizing TRLs enables NASA and its partners to manage technological development effectively, ensuring that innovations are sufficiently mature before being incorporated into critical missions.

Source: NASA Technology Readiness Levels

QUESTION: How should NASA use the 80/20 principle during the nine stages of Technology Readiness Levels? Tell me your answer at Rakesh. Dhawan at Power Electronics Group dot com or write a comment below.

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Rules to Optimize Five-Phase Permanent Magnet Synchronous Motor Laminations

Optimizing five-phase Permanent Magnet Synchronous Motor (PMSM) stator laminations is essential for achieving high efficiency, low weight, and superior performance. The five-phase configuration provides lower torque ripple, better fault tolerance, and smoother operation than traditional three-phase motors. Key design considerations include minimizing magnetic saturation, reducing flux leakage, and balancing lamination and copper weight. This article outlines the essential rules for optimizing laminations in five-phase PMSM stators to enhance motor efficiency and reliability.

1. Minimize Lamination Weight While Maintaining Magnetic Performance

Reducing the weight of the stator laminations improves the power-to-weight ratio while maintaining magnetic performance.

A. Core Geometry Optimization

  • Increase Yoke Thickness: Prevents local saturation while keeping iron losses low.
  • Optimize Tooth Width: Ensures proper flux distribution and prevents over-saturation in the core.
  • Slot/Tooth Ratio Adjustment: Balancing slot openings and stator teeth improves flux flow efficiency.

B. Material Selection for Low Core Losses

  • Use high-grade electrical steel (e.g., M350-50A, NO20, or Hiperco 50) for improved magnetic efficiency.
  • Thinner laminations (≤0.5mm) reduce eddy current losses, improving motor efficiency.
  • Consider higher permeability materials to handle higher flux densities without saturation.

2. Reduce Copper Weight Without Compromising Performance

Optimizing copper winding design in five-phase PMSMs reduces weight and losses while maintaining efficiency.

A. Improve Slot Utilization

  • Use trapezoidal or semi-closed slots for higher slot fill factor and reduced excess copper usage.
  • Opt for Litz wire or rectangular conductors to minimize skin effect losses.
  • Reduce end winding length to lower resistance and heat dissipation.

B. Optimize Winding Parameters

  • Adjust turns per phase and wire gauge to balance ampere-turns, efficiency, and weight.
  • Ensure shorter end windings to minimize copper losses.

3. Magnetic Saturation Considerations in Stator Design

Magnetic saturation occurs when the stator core reaches its flux density limit, leading to excessive core losses and heating.

A. Understanding Magnetic Saturation

  • Five-phase PMSMs distribute flux more evenly, but excessive saturation still causes losses and efficiency drops.
  • Most electrical steels (e.g., M350-50A) saturate around 1.8–2.0T.
  • Excessive flux density increases iron losses, torque ripple, and heat generation.

B. Strategies to Prevent Magnetic Saturation

  1. Increase Yoke Thickness to distribute flux more evenly.
  2. Use High-Permeability Materials to handle higher flux densities.
  3. Adjust Winding MMF to prevent over-excitation and excessive core flux.
  4. Improve Magnetic Circuit Balance by using flux guides or auxiliary slots.

4. Flux Leakage Issues for Smaller Stack Lengths

Flux leakage occurs when magnetic flux does not fully link the stator teeth and rotor magnets, reducing motor efficiency. This issue is more severe in shorter stack lengths due to higher end effects and flux path disruptions.

A. Consequences of Flux Leakage

  • Reduced Torque Output: Less flux links with the rotor, leading to lower power.
  • Higher Core Losses: Uncontrolled leakage flux increases eddy current and hysteresis losses.
  • Lower Power Factor: Leakage reactance negatively impacts efficiency.
  • Uneven Magnetic Fields: Causes torque ripple and cogging issues.

B. Strategies to Minimize Flux Leakage

  1. Increase Stator Stack Length (if weight permits).
  2. Optimize Air Gap and Magnetic Path for better flux linkage.
  3. Improve Winding Distribution using fractional-slot or concentrated windings.
  4. Modify Rotor Design (e.g., skewed rotors or optimized magnet positioning) to guide flux effectively.

5. Balancing Saturation, Flux Leakage, and Weight

  • Increasing yoke thickness reduces saturation but adds weight.
  • Extending stack length improves flux linkage but increases weight and cost.
  • Optimizing slot and winding geometry enhances efficiency without adding unnecessary material.

Conclusion

By following these rules for five-phase PMSM stator optimization, engineers can enhance motor efficiency, reduce weight, and improve overall performance. The five-phase configuration already provides lower torque ripple and better efficiency. Still, carefully managing magnetic saturation, flux leakage, and material selection is key to designing high-performance motors with superior power-to-weight ratios.

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Five-Phase Permanent Magnet Motor Design

A five-phase permanent magnet (PM) motor is an advanced electric motor configuration that offers superior performance to traditional three-phase motors. These motors are used in applications requiring higher torque density, smoother operation, and greater fault tolerance. Below is a patent for a typical five phase motor with 25-slots and 22-magnets.

1. Advantages of a Five-Phase PM Motor

Higher Torque Density

  • Five-phase motors reduce torque ripple, providing a smoother power output.
  • More frequent torque production cycles reduce pulsation.

Improved Fault Tolerance

  • If one phase fails, the motor can still operate with reduced performance.
  • This is critical in high-reliability applications like aerospace and defense.

Reduced Harmonics & Better Efficiency

  • Higher phase counts reduce lower-order harmonics, improving efficiency.
  • Less reliance on additional filtering and compensation techniques.

Lower Current per Phase

  • Each phase carries a lower current than a three-phase motor for the same power level.
  • This leads to reduced losses and improved thermal performance.

Enhanced Control Possibilities

  • Five-phase motors allow more control flexibility, including advanced vector control and field-oriented control (FOC).

2. Motor Topology and Design Considerations

Stator Design

  • Five-phase stators are similar to three-phase stators but have five slots per pole per phase for better winding distribution.
  • Standard stator winding configurations:
    • Star (Y)
    • Pentagon
    • Polygonal

Rotor Design

  • Uses permanent magnets embedded or surface-mounted.
  • Interior Permanent Magnet (IPM) designs offer improved saliency and reluctance torque contribution.

Slot-Pole Combinations

  • A popular choice is 25/22 (stator slots per rotor poles), ensuring good flux linkage and minimal cogging torque.

Magnet Material

  • High-performance NdFeB (Neodymium-Iron-Boron) magnets are typically used to maximize efficiency and torque density.

3. Control Strategies for Five-Phase PM Motors

Scalar or Sinusoidal Control

Requires five-phase inverters and controllers with Scalar or Sinusoidal Control with Sinusoidal pulse width modulation.

Vector Control (Field-Oriented Control – FOC)

  • Separates torque and flux control, improving dynamic response.
  • Requires five-phase inverters and controllers with advanced algorithms.

    Space Vector Pulse Width Modulation (SVPWM)

    • More efficient than traditional PWM.
    • Enhances voltage utilization for better efficiency.

    Fault-Tolerant Control

    • Advanced algorithms can detect phase failures and reconfigure control to maintain operation.

    4. Applications of Five-Phase PM Motors

    Electric Vehicles (EVs)

    • Higher efficiency and fault tolerance make them ideal for electric drivetrains.

    Aerospace & Defense

    • Used in unmanned aerial vehicles (UAVs), space applications, and military systems.

    Renewable Energy (Wind & Wave Energy)

    • Provides improved power conversion efficiency in wind turbines and ocean wave generators.

    Industrial Robotics

    • Precise torque control and smooth operation benefit automation and robotic arms.

    Medical Equipment

    • Low torque ripple and smooth motion improve MRI machines, ventilators, and precision medical devices.

    5. Challenges in Five-Phase PM Motor Design

    Inverter Complexity

    • Requires five-phase inverters, which are more complex and expensive than three-phase systems.

    Control Algorithm Complexity

    • Advanced DSPs (Digital Signal Processors) or FPGAs are needed for high-speed computations.

    Cost Considerations

    • More phases mean more copper windings and switching devices, increasing cost.

    Availability of Components

    • Fewer commercial drivers and controllers are designed for five-phase motors compared to three-phase systems.

    Comparison of Three-Phase vs. Five-Phase Permanent Magnet Motors

    FeatureThree-Phase PM MotorFive-Phase PM Motor
    Number of Phases35
    Torque RippleHigher torque ripple due to fewer torque production cyclesLower torque ripple, smoother operation
    Fault ToleranceIf one phase fails, motor stops workingCan operate with reduced performance if one phase fails
    EfficiencyModerate efficiency due to higher harmonic lossesHigher efficiency due to reduced harmonics
    Power DensityModerate power densityHigher power density for the same size
    Control ComplexityEasier to control, widely available controllersRequires advanced control algorithms and specialized controllers
    Inverter ComplexityStandard three-phase inverters widely availableRequires a five-phase inverter, which is more complex and costly
    Magnetic LossesHigher harmonic content leads to greater core and eddy current lossesReduced harmonics lower core losses, improving efficiency
    CostLower cost due to mass production and availabilityHigher cost due to specialized components and design complexity
    Application AreasIndustrial drives, electric vehicles, renewable energyHigh-reliability applications like aerospace, military, and robotics
    Motor Size and Winding DensityStandard size with conventional windingsRequires optimized slot-pole combinations for winding efficiency
    Noise and VibrationMore noticeable noise and vibration due to lower phase countQuieter operation due to smoother torque profile

    Key Takeaways

    1. Three-phase motors are cheaper, simpler, and widely available, making them the standard for most industrial applications.
    2. Five-phase motors excel in efficiency, torque smoothness, and fault tolerance, making them ideal for critical applications.
    3. Five-phase motors’ higher cost and inverter complexity limit their widespread adoption, but they are superior for high-performance applications like aerospace, robotics, and electric mobility.
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    Flux Density Distribution Plots

    The principles behind the operation of electric motors are a tremendous gift of nature. Uncovering those principles and focusing on their precise and accurate applications makes for an elegant and beautifully designed electric motor. I love the electric motor design, and today, I wanted to share this beautiful plot of the flux density distribution of a new IPM motor.

    IPM Motor with Flux Density Contours

    There’s something almost magical about how flux density distributes inside an electric motor, especially when they’re as elegantly engineered as Interior Permanent Magnet (IPM) motors.

    If you’ve ever wondered why your electric car zips around so quietly or how industrial machines deliver such reliable power, IPM motors often play a key role. Here’s a quick rundown of why these motors are unique and what you’re seeing in that eye-catching color plot of flux density contours.

    What Is an IPM Motor?

    “IPM” stands for “Interior Permanent Magnet.” Unlike other motor types where the magnets might be placed on the outer surface of the rotor, IPM motors embed the permanent magnets inside the rotor. This gives them a few advantages:

    • Enhanced Efficiency: By placing magnets within the rotor, the motor can harness magnetic and something called reluctance torque, helping it deliver higher efficiency under various speeds and loads.
    • Robust Construction: Tucking magnets inside offers better mechanical protection (applicable at high rotation speeds or in demanding environments).
    • Improved Performance at High Speeds: IPM motors often excel at delivering torque effectively at higher RPMs—one of the reasons they’re a big deal in electric vehicle applications.

    Understanding the Flux Density Contours

    The colorful image is a snapshot of the “flux density” distribution. Flux density (measured in Teslas) tells us how concentrated the magnetic field is at each point in the motor. Here’s the gist of the color-coded zones:

    • Blue Regions: Typically show lower flux density. These areas might be where the field passes through less magnetic material or experiences more air gaps.
    • Green to Yellow Zones: Indicate higher flux density, meaning the magnetic field is stronger there. These zones often show how the magnetic field routes through the rotor and stator teeth.
    • Bright or High-Intensity Colors: If you see reds or bright yellows, those areas have powerful magnetic fields—often around the magnets or stator teeth tips.

    Why It Matters

    It is crucial for engineers to see how the magnetic field flows because it helps optimize the motor’s design. By tweaking magnet placement, rotor geometry, or even the materials used, designers can:

    1. Maximize Torque Output: Ensuring the magnetic circuit is efficient.
    2. Minimize Losses: Reduce heat and ensure you get more power for every watt of electricity going into the motor.
    3. Improve Reliability: Avoiding “hot spots” or regions of mechanical stress that could lead to premature failure.

    A Future of Quiet, Efficient Power

    IPM motors aren’t just for cars; they pop up in everything from drones to washing machines. Their blend of efficiency, power density, and durability makes them a popular choice in modern motor-driven systems. As battery and power electronics technologies advance, IPM motors will likely become even more integral to everyday life—giving us smoother, quieter, and more energy-efficient ways to move and make things.