Figure 1:
![A two-phase HSM, (A) Whole motor, (B) Rotor, and (C) Stator [28]. HSM, hybrid stepper motor.](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_001.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKEPIMAVFE%2F20260317%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260317T004543Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBUaDGV1LWNlbnRyYWwtMSJGMEQCICWDqwuWqBpJVbDRZevrg%2B65p9LKjDa%2FMTO59RVWRrCxAiAjf4wucpSoDvOxhOTuR8WxAiAQolsjiXIbTW%2F5XUa41SrFBQjf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMQ1PV8v2JikvagPh9KpkFTQAwhxuD61QCRt%2Fc%2B8RL%2BR%2B8RU1XdWli%2FrBl8WtzHcxvH%2FXWJvdO2TpkTBgOorRmvY7cCn3Kf1vb6aIYuF%2B6nbyxlZ0MSte%2BogxKGHjCH1t4OYmVAEuXVHRqtIZLZVfIkBoFmDZyGJPx9nCng1s6%2BPeeSYoQV7nXKDOYetVTzqleES%2BMDUGOzv2VEyHH2ePMAbp2TqwbmK5YBTGVlyThsX7W8mbSD3A1hkGtwhrTf7Dse%2FgFQuOilHij%2BVEahxz9CSvCZdEzTIQlJ7JUqsJl9ZVRcrBAV8B2Bw7OivSkpO4pYTkdQtkqSKit5HaXHOLySxuRuPmgTEaWl5uBOuI08y2aHXFzmgRgd6yF1nCrzMCfU2MurZ4FBoSmSk6GKRz1pCDu%2BCLj%2BT1Rw0mBt3e11%2F9I2JABUKBzA2anYh1H3C2RjWnr8wkJH7InEZX%2FuIlf%2FLwVscZYJGQrhcxR0XhIs5P1fhC1SS3fgGN4dYolygowro2cjA8RmrWyasaP%2BwkAi2eJMHohl9jk8tcJX2E1CZ1ckUH59ZNg5CUCWFPDAbakJVMm73qGlz4tnzVirKDSqdbRMJuGPZwF5xK7zrYCGJ9PP%2FoaQJCpy%2Bpc%2FjQ7qCzNJnESjsavR4aQGkUuyjiazE43GP5z9%2BzUNwZeD3%2Fmks2rPZDE7V9K84i5pIszgXjtN5R0uoCIAl0DOspl0wImsmhUYHbE0aQcoHR4GO2GB7utCKqj8iSujqKYk5f5eVSg5oXF51h5T8zjIXP1W6z41Q46pM6pgbXH2yiI9RzUpT4GUAPBVAOXSbca9CL0J%2BYpXDDx3Fr2cwNcdyMiS5gw9hkiaDHlsZd20CjCbnaJrgi8bbwmIVWwMjj%2Fnerug6kYkPm3%2B58vZoAw%2BujhzQY6sgFi3JI0VKq%2FbGPcUY2tEqdjCKLH0f9%2BfC%2Bxfym38U3VT0Mu2%2BFWXYpnqYLZphfPe6tQzgyh6gScEt4oNcR57N%2FulnsVWNqVAS3nAPK9EUh7c3CracTNp3S9YQ30cSp3nMtAfDq6TXW19Ac4v3dOfBhcTmX2SxehanlQnH4o5ePufBsaighRTtNcCpuF0PBHyiXtnOaJhPcxbrG6rAmGQrq8HwR2gwomuNct7TkmqwCyzKEc&X-Amz-Signature=620e2b188a0d04f1e163600c1124b7d0155ed7273bf9e36ddf41aad709dacf91&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 2:
![Stepper motor testbed, (A) Front view, (B) Back view, 1: Stepper motor, 2: Weights carrier arm, 3: Arduino and LCD shield, 4: Load cell, 5: Weights [28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKEPIMAVFE%2F20260317%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260317T004543Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBUaDGV1LWNlbnRyYWwtMSJGMEQCICWDqwuWqBpJVbDRZevrg%2B65p9LKjDa%2FMTO59RVWRrCxAiAjf4wucpSoDvOxhOTuR8WxAiAQolsjiXIbTW%2F5XUa41SrFBQjf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMQ1PV8v2JikvagPh9KpkFTQAwhxuD61QCRt%2Fc%2B8RL%2BR%2B8RU1XdWli%2FrBl8WtzHcxvH%2FXWJvdO2TpkTBgOorRmvY7cCn3Kf1vb6aIYuF%2B6nbyxlZ0MSte%2BogxKGHjCH1t4OYmVAEuXVHRqtIZLZVfIkBoFmDZyGJPx9nCng1s6%2BPeeSYoQV7nXKDOYetVTzqleES%2BMDUGOzv2VEyHH2ePMAbp2TqwbmK5YBTGVlyThsX7W8mbSD3A1hkGtwhrTf7Dse%2FgFQuOilHij%2BVEahxz9CSvCZdEzTIQlJ7JUqsJl9ZVRcrBAV8B2Bw7OivSkpO4pYTkdQtkqSKit5HaXHOLySxuRuPmgTEaWl5uBOuI08y2aHXFzmgRgd6yF1nCrzMCfU2MurZ4FBoSmSk6GKRz1pCDu%2BCLj%2BT1Rw0mBt3e11%2F9I2JABUKBzA2anYh1H3C2RjWnr8wkJH7InEZX%2FuIlf%2FLwVscZYJGQrhcxR0XhIs5P1fhC1SS3fgGN4dYolygowro2cjA8RmrWyasaP%2BwkAi2eJMHohl9jk8tcJX2E1CZ1ckUH59ZNg5CUCWFPDAbakJVMm73qGlz4tnzVirKDSqdbRMJuGPZwF5xK7zrYCGJ9PP%2FoaQJCpy%2Bpc%2FjQ7qCzNJnESjsavR4aQGkUuyjiazE43GP5z9%2BzUNwZeD3%2Fmks2rPZDE7V9K84i5pIszgXjtN5R0uoCIAl0DOspl0wImsmhUYHbE0aQcoHR4GO2GB7utCKqj8iSujqKYk5f5eVSg5oXF51h5T8zjIXP1W6z41Q46pM6pgbXH2yiI9RzUpT4GUAPBVAOXSbca9CL0J%2BYpXDDx3Fr2cwNcdyMiS5gw9hkiaDHlsZd20CjCbnaJrgi8bbwmIVWwMjj%2Fnerug6kYkPm3%2B58vZoAw%2BujhzQY6sgFi3JI0VKq%2FbGPcUY2tEqdjCKLH0f9%2BfC%2Bxfym38U3VT0Mu2%2BFWXYpnqYLZphfPe6tQzgyh6gScEt4oNcR57N%2FulnsVWNqVAS3nAPK9EUh7c3CracTNp3S9YQ30cSp3nMtAfDq6TXW19Ac4v3dOfBhcTmX2SxehanlQnH4o5ePufBsaighRTtNcCpuF0PBHyiXtnOaJhPcxbrG6rAmGQrq8HwR2gwomuNct7TkmqwCyzKEc&X-Amz-Signature=71083d90f8db30af81a518fcdd73643855b2801d6e917797bd49bad03742075e&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 3:
![Real motor and simulated model output torque [28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKEPIMAVFE%2F20260317%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260317T004543Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBUaDGV1LWNlbnRyYWwtMSJGMEQCICWDqwuWqBpJVbDRZevrg%2B65p9LKjDa%2FMTO59RVWRrCxAiAjf4wucpSoDvOxhOTuR8WxAiAQolsjiXIbTW%2F5XUa41SrFBQjf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMQ1PV8v2JikvagPh9KpkFTQAwhxuD61QCRt%2Fc%2B8RL%2BR%2B8RU1XdWli%2FrBl8WtzHcxvH%2FXWJvdO2TpkTBgOorRmvY7cCn3Kf1vb6aIYuF%2B6nbyxlZ0MSte%2BogxKGHjCH1t4OYmVAEuXVHRqtIZLZVfIkBoFmDZyGJPx9nCng1s6%2BPeeSYoQV7nXKDOYetVTzqleES%2BMDUGOzv2VEyHH2ePMAbp2TqwbmK5YBTGVlyThsX7W8mbSD3A1hkGtwhrTf7Dse%2FgFQuOilHij%2BVEahxz9CSvCZdEzTIQlJ7JUqsJl9ZVRcrBAV8B2Bw7OivSkpO4pYTkdQtkqSKit5HaXHOLySxuRuPmgTEaWl5uBOuI08y2aHXFzmgRgd6yF1nCrzMCfU2MurZ4FBoSmSk6GKRz1pCDu%2BCLj%2BT1Rw0mBt3e11%2F9I2JABUKBzA2anYh1H3C2RjWnr8wkJH7InEZX%2FuIlf%2FLwVscZYJGQrhcxR0XhIs5P1fhC1SS3fgGN4dYolygowro2cjA8RmrWyasaP%2BwkAi2eJMHohl9jk8tcJX2E1CZ1ckUH59ZNg5CUCWFPDAbakJVMm73qGlz4tnzVirKDSqdbRMJuGPZwF5xK7zrYCGJ9PP%2FoaQJCpy%2Bpc%2FjQ7qCzNJnESjsavR4aQGkUuyjiazE43GP5z9%2BzUNwZeD3%2Fmks2rPZDE7V9K84i5pIszgXjtN5R0uoCIAl0DOspl0wImsmhUYHbE0aQcoHR4GO2GB7utCKqj8iSujqKYk5f5eVSg5oXF51h5T8zjIXP1W6z41Q46pM6pgbXH2yiI9RzUpT4GUAPBVAOXSbca9CL0J%2BYpXDDx3Fr2cwNcdyMiS5gw9hkiaDHlsZd20CjCbnaJrgi8bbwmIVWwMjj%2Fnerug6kYkPm3%2B58vZoAw%2BujhzQY6sgFi3JI0VKq%2FbGPcUY2tEqdjCKLH0f9%2BfC%2Bxfym38U3VT0Mu2%2BFWXYpnqYLZphfPe6tQzgyh6gScEt4oNcR57N%2FulnsVWNqVAS3nAPK9EUh7c3CracTNp3S9YQ30cSp3nMtAfDq6TXW19Ac4v3dOfBhcTmX2SxehanlQnH4o5ePufBsaighRTtNcCpuF0PBHyiXtnOaJhPcxbrG6rAmGQrq8HwR2gwomuNct7TkmqwCyzKEc&X-Amz-Signature=8462b267bbe65aeee1eb360debf68cb8d931d72a36ef80ffaa146420abaa77c0&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4:

Figure 5:
![Linearized tooth to tooth arrangement and flux tubes [14, 15].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_005.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKEPIMAVFE%2F20260317%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260317T004543Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBUaDGV1LWNlbnRyYWwtMSJGMEQCICWDqwuWqBpJVbDRZevrg%2B65p9LKjDa%2FMTO59RVWRrCxAiAjf4wucpSoDvOxhOTuR8WxAiAQolsjiXIbTW%2F5XUa41SrFBQjf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMQ1PV8v2JikvagPh9KpkFTQAwhxuD61QCRt%2Fc%2B8RL%2BR%2B8RU1XdWli%2FrBl8WtzHcxvH%2FXWJvdO2TpkTBgOorRmvY7cCn3Kf1vb6aIYuF%2B6nbyxlZ0MSte%2BogxKGHjCH1t4OYmVAEuXVHRqtIZLZVfIkBoFmDZyGJPx9nCng1s6%2BPeeSYoQV7nXKDOYetVTzqleES%2BMDUGOzv2VEyHH2ePMAbp2TqwbmK5YBTGVlyThsX7W8mbSD3A1hkGtwhrTf7Dse%2FgFQuOilHij%2BVEahxz9CSvCZdEzTIQlJ7JUqsJl9ZVRcrBAV8B2Bw7OivSkpO4pYTkdQtkqSKit5HaXHOLySxuRuPmgTEaWl5uBOuI08y2aHXFzmgRgd6yF1nCrzMCfU2MurZ4FBoSmSk6GKRz1pCDu%2BCLj%2BT1Rw0mBt3e11%2F9I2JABUKBzA2anYh1H3C2RjWnr8wkJH7InEZX%2FuIlf%2FLwVscZYJGQrhcxR0XhIs5P1fhC1SS3fgGN4dYolygowro2cjA8RmrWyasaP%2BwkAi2eJMHohl9jk8tcJX2E1CZ1ckUH59ZNg5CUCWFPDAbakJVMm73qGlz4tnzVirKDSqdbRMJuGPZwF5xK7zrYCGJ9PP%2FoaQJCpy%2Bpc%2FjQ7qCzNJnESjsavR4aQGkUuyjiazE43GP5z9%2BzUNwZeD3%2Fmks2rPZDE7V9K84i5pIszgXjtN5R0uoCIAl0DOspl0wImsmhUYHbE0aQcoHR4GO2GB7utCKqj8iSujqKYk5f5eVSg5oXF51h5T8zjIXP1W6z41Q46pM6pgbXH2yiI9RzUpT4GUAPBVAOXSbca9CL0J%2BYpXDDx3Fr2cwNcdyMiS5gw9hkiaDHlsZd20CjCbnaJrgi8bbwmIVWwMjj%2Fnerug6kYkPm3%2B58vZoAw%2BujhzQY6sgFi3JI0VKq%2FbGPcUY2tEqdjCKLH0f9%2BfC%2Bxfym38U3VT0Mu2%2BFWXYpnqYLZphfPe6tQzgyh6gScEt4oNcR57N%2FulnsVWNqVAS3nAPK9EUh7c3CracTNp3S9YQ30cSp3nMtAfDq6TXW19Ac4v3dOfBhcTmX2SxehanlQnH4o5ePufBsaighRTtNcCpuF0PBHyiXtnOaJhPcxbrG6rAmGQrq8HwR2gwomuNct7TkmqwCyzKEc&X-Amz-Signature=248a76b0ccac51c0ad9b8e55cf93fbc95df34842a51f1a363265cfe7c88f892a&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 6:
![Construction of a two-phase hybrid stepping motor [14].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_006.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKEPIMAVFE%2F20260317%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260317T004543Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBUaDGV1LWNlbnRyYWwtMSJGMEQCICWDqwuWqBpJVbDRZevrg%2B65p9LKjDa%2FMTO59RVWRrCxAiAjf4wucpSoDvOxhOTuR8WxAiAQolsjiXIbTW%2F5XUa41SrFBQjf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMQ1PV8v2JikvagPh9KpkFTQAwhxuD61QCRt%2Fc%2B8RL%2BR%2B8RU1XdWli%2FrBl8WtzHcxvH%2FXWJvdO2TpkTBgOorRmvY7cCn3Kf1vb6aIYuF%2B6nbyxlZ0MSte%2BogxKGHjCH1t4OYmVAEuXVHRqtIZLZVfIkBoFmDZyGJPx9nCng1s6%2BPeeSYoQV7nXKDOYetVTzqleES%2BMDUGOzv2VEyHH2ePMAbp2TqwbmK5YBTGVlyThsX7W8mbSD3A1hkGtwhrTf7Dse%2FgFQuOilHij%2BVEahxz9CSvCZdEzTIQlJ7JUqsJl9ZVRcrBAV8B2Bw7OivSkpO4pYTkdQtkqSKit5HaXHOLySxuRuPmgTEaWl5uBOuI08y2aHXFzmgRgd6yF1nCrzMCfU2MurZ4FBoSmSk6GKRz1pCDu%2BCLj%2BT1Rw0mBt3e11%2F9I2JABUKBzA2anYh1H3C2RjWnr8wkJH7InEZX%2FuIlf%2FLwVscZYJGQrhcxR0XhIs5P1fhC1SS3fgGN4dYolygowro2cjA8RmrWyasaP%2BwkAi2eJMHohl9jk8tcJX2E1CZ1ckUH59ZNg5CUCWFPDAbakJVMm73qGlz4tnzVirKDSqdbRMJuGPZwF5xK7zrYCGJ9PP%2FoaQJCpy%2Bpc%2FjQ7qCzNJnESjsavR4aQGkUuyjiazE43GP5z9%2BzUNwZeD3%2Fmks2rPZDE7V9K84i5pIszgXjtN5R0uoCIAl0DOspl0wImsmhUYHbE0aQcoHR4GO2GB7utCKqj8iSujqKYk5f5eVSg5oXF51h5T8zjIXP1W6z41Q46pM6pgbXH2yiI9RzUpT4GUAPBVAOXSbca9CL0J%2BYpXDDx3Fr2cwNcdyMiS5gw9hkiaDHlsZd20CjCbnaJrgi8bbwmIVWwMjj%2Fnerug6kYkPm3%2B58vZoAw%2BujhzQY6sgFi3JI0VKq%2FbGPcUY2tEqdjCKLH0f9%2BfC%2Bxfym38U3VT0Mu2%2BFWXYpnqYLZphfPe6tQzgyh6gScEt4oNcR57N%2FulnsVWNqVAS3nAPK9EUh7c3CracTNp3S9YQ30cSp3nMtAfDq6TXW19Ac4v3dOfBhcTmX2SxehanlQnH4o5ePufBsaighRTtNcCpuF0PBHyiXtnOaJhPcxbrG6rAmGQrq8HwR2gwomuNct7TkmqwCyzKEc&X-Amz-Signature=5bfa1511a2e5a15b41413be1fa7711dd8955123c6b88eab269d2d7efd65cbe68&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
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Figure 27:

Stepper motor experiment results [28]
| Current [A] | Weights mass [g] | Torque [mN/m] |
|---|---|---|
| 1.05 | 218 | 130.8 |
| 1.53 | 297 | 178.2 |
| 1.96 | 373 | 223.8 |
| 2.35 | 433 | 259.8 |
| 2.73 | 477 | 286.2 |
Motor specifications [28]
| Motor outer diameter | 56.5 mm |
| Motor body height | 52 mm |
| Stator outer diameter | 54.1 mm |
| Stator inner diameter | 30 mm |
| Number of teeth in each stator pole | 5 |
| Stator teeth depth | 1.25 mm |
| Stator height | 23 mm |
| Air gap | 0.1 mm |
| Rotor outer diameter | 29.8 mm |
| Each half-rotor height | 10 mm |
| Distance between two half-rotors | 3 mm |
| Number of teeth in each half-rotor | 50 |
| Rotor teeth depth | 1.5 mm |
| Magnet diameter | 20.8 mm |
| Magnet height | 13 mm |
| Number of wire-turns per coil | 32 |
| Wire diameter | 0.6 mm |
| Stator and rotor material | Steel 1,008 |
| Magnet material | NdFe35 (1.3 T) |
| Stator and rotors teeth fillet radius | 0.125 mm |
| Maximum nominal current | 3A |
| Angle per step | 1.8° |
| Rotor and stator teeth angle (pitch) | 7.2° |
| Rotor and stator teeth width | 3.6°(0.94 mm) |
| Stator pole thickness | 2 mm |
The motor parameters
| Absolute permeability | μ0 | 4π × 10−7 H/m |
| Slot thickness | t | 0.939 mm |
| Air gap length | g | 0.1 mm |
| Rotor and stator teeth depth | d | 1.375 mm |
| Tooth thickness | s | 0.939 mm |
| Number of teeth per stator pole | Zs | 5 |
| Number of rotor teeth | Zr | 50 |
| Number of wire-turns per stator winding | Ns | 32 |
| Excitation current | i | 1.5 A |
| Rotor height | h | 20 mm |