Analysis of Tesla-Like Induction Motor
David Meeker
04Feb2015
Introduction
The purpose of this note is to analyze an induction motor similar to that used by Tesla Motors. Some geometry information is publicly available from patents and photographs on the web. Other aspects of the machine can be selected based on educated guesses. The result of this note will be a model of a Tesla-like motor and an examination of its performance via the model.
Publicly Available Information
A good place to start is patent US 7,741,750, "Induction Motor with Improved Torque Density". This patent is assigned to Tesla Motors, and the inventor is Yifan Tang, who used to be Principal Motor Technologist at Tesla. The patent shows a cross-section of the motor, shown below as Figure 1.
Figure 1: Tesla Induction Motor Cross-Section from Fig. 1 of US 7,741,750.
Several design attributes are in evidence from the patent:
- 60 Stator Slots
- 74 Rotor Slots
- Full-pitched winding is one preferred embodiment
- Open rotor slots is preferred, though closed rotor slots are also discussed.
- Air gap length is "at least 0.5mm"
- Describes a pretty saturated operating regime.
Although the geometry is shown in detail in the patent is no good scale for the size of the motor. However, there is a picture of the rotor at the Tesla Motors Club site:
Figure 2: Rotor of Tesla Model S IM from the Tesla Motor Club site (Stator also pictured).
By using the 8/5" X 11" sheet of paper next to the rotor in combination with ScanIt, the dimensions of the rotor can be estimated. From this picture, the rotor OD appears to be 5.64". With this scaling, the ID of the rotor appears to be exactly 2", and the stator OD is 9". Although it is difficult to determine the air gap precisely from the relatively grainy patent Figure 1, the machine, as drawn, appears to have a 0.030" (~0.75mm) air gap.
Using the scaling from the picture, the following dimensions were eyeballed from the patent's Figure 1:
- Rotor inner radius = 1.000"
- Rotor tooth root diameter = 2.000"
- Rotor outer radius = 2.820"
- Rotor tooth width = 0.110"
- Rotor tooth tip width = 0.150"
- Rotor tooth edge width = 0.030"
- Stator inner radius = 2.850"
- Stator tooth root radius = 3.57"
- Stator outer radius = 9.000"
- Stator tooth width = 0.134"
- Stator tooth tip width = 0.175"
- Stator tooth edge width = 0.030"
Lastly, it's also clear from http://my.teslamotors.com/roadster/technology/motor that the motor has copper rotor bars rather than aluminum ones.
Photos of the motor mount make it look like there are actually two motors in the Model S (see Figure 3 below).
Figure 3: Motor mount of Model S.
Inferred Features
The lamination material and thickness is not given. However, Figure 2 above says that the maximum speed is 16,000 RPM, which implies a 533Hz fundamental at maximum speed. However, a very small percentage of the machine's operation would be spent at this highest speed, so it wouldn't make sense to design for continuous operation at 533Hz. Instead, it would make sense to use 29 gauge (0.014") M-19 silicon steel, a common choice 400Hz machines. It is reasonable to assume a stacking factor of 0.96 for this material choice, based on stacking factor estimates in the literature.