# Torque Modeling

• Liang Yan
• I-Ming Chen
• Chee Kian Lim
• Guilin Yang
• Kok-Meng Lee
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 4)

## Abstract

By utilizing the analytical magnetic field model, the actuator torque caused by the interaction between current carrying coils and the magnetic field of the PM-pole rotor is formulated based on Lorentz force law. This torque model relates the torque output of the spherical actuator to the current inputs of coils and the rotor orientation, which indicates that the torque output of the PM spherical actuator is orientation dependant. Nonsingularity is one of the important advantages of the PM spherical actuator. Based on the torque model, existence of inverse electromagnetics solution or nonsingularity workspace of the PM spherical actuator is verified through the condition numbers of the torque matrix. In addition, the minimum right-inverse electromagnetics solution is proposed to calculate the required current inputs for desired torque output. This solution can minimize the electric power consumption of the spherical actuator. The linear torque model can facilitate the real-time motion control of the actuator. It can also be used for the spherical actuator design to maximize the actuator torque output.

## Keywords

Condition Number Current Input Torque Output Electric Power Consumption Switch Reluctance Motor
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Liang Yan
• 1
Email author
• I-Ming Chen
• 2
• Chee Kian Lim
• 3
• Guilin Yang
• 4
• Kok-Meng Lee
• 5
1. 1.School of Automation Science and Electrical EngineeringBeihang UniversityBeijingPeople’s Republic of China
2. 2.School of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingaporeSingapore
3. 3.School of Mechanical & Aeronautical EngineeringSingapore PolytechnicSingaporeSingapore
4. 4.Singapore Institute of Manufacturing TechnologyNanyangSingapore
5. 5.Georgia Institute of TechnologyAtlantaUSA