Speed Control Motor/Brushless Motor Stopping Accuracy of Brushless Motors
Stepper motors and servo motors with excellent stopping accuracy are commonly used when performing high-precision positioning operation.
However, depending on the operating conditions and usage, even a brushless motor can stop with an overrun of a few millimeters.
In this section, we will show how to calculate stopping accuracy using the overrun characteristics (representative values) of brushless motors, and how to use them effectively to improve stopping accuracy.
What is Stopping Accuracy?
Stopping accuracy refers to the "error of the stop position relative to the target position," and can be thought of as "stopping accuracy = overrun + variance."
There are 3 main factors that affect stopping accuracy, and "Overrun + Variance" will be smaller for states in the red frame in the table below.
Now, we will focus on the rotation speed that can be adjusted by the motor, and calculate the stopping accuracy of the brushless motor.
| Primary Factor | Stopping Accuracy (Overrun + Variance) |
|
|---|---|---|
| Speed | Fast | Large |
| Slow | Small | |
| Load Inertia | Large | Large |
| Small | Small | |
| Frictional Load | Large | Small |
| Small | Large | |
Calculation Conditions
- Application
- Belt conveyor
- Belt Speed
- VL = 0.05~1 [m/s]
- Motor Power Supply
- Single-Phase 100 VAC
- Roller Diameter
- D = 0.1 [m]
- Roller Mass
- m2 = 1 [kg]
- Total Mass of Belt and Load
- m1 = 7 [kg]
- External Force
- FA = 0 [N]
- Friction Coefficient of Sliding Surface
- μ = 0.3
- Belt and Roller Efficiency
- η = 0.9
As the preliminary selection calculations confirmed that a 120 W motor + gearhead with a gear ratio of 15 can transport loads, we recommend looking at the BLE2 Series "Product Name: BLM5120HPK+5H15S+BLE2D120-A."
1. Calculation of Stopping Accuracy: NM = 3,000 r/min
Use overrun characteristics (representative value).
Refer to here
- *The overrun characteristics (representative values) of brushless motors BMU Series, BLE2 Series, BXII Series, and BLH Series are shown on the details page for each product. For other series, please contact the Customer Support Center.
1) Motor Shaft Conversion
Since the graph shows values for the motor alone, convert the rotation speed and load inertia of the gearhead shaft obtained from the selection calculations to the motor shaft.
- [1]
- Motor Shaft Speed
NM = NG × i = 191 x 15 = 2,865 [r/min]
Use the black dash line curve of 3,000 r/min for approximation.
- [2]
- Motor Shaft Load Inertia
JM = JG ÷ i 2 = 200 × 10-4 ÷152 ≒ 0.9 × 10-4 [kg·m2]
- [3]
- Motor Shaft Overrun
When reading the overrun (vertical axis) value from [1] (black dash line curve) and [2] (horizontal axis), it is found that it is about 0.9 ± 0.2 [Rev].
2) Gearhead Shaft Conversion
Convert the overrun obtained in 1) to a gearhead shaft.
ORG = ORM ÷ i = (0.9 ± 0.2) ÷ 15 ≒ 0.06 ± 0.013 [Rev]
3) Belt Conveyor Shaft Conversion
Convert the overrun obtained in 2) to the belt conveyor shaft.
ORC = D × π × ORG = 100 × 3.14 × (0.06 ± 0.013) ≒ 19 ± 4 [mm]
Based on the above, the stopping accuracy can be inferred that the overrun of the belt conveyor is 19 mm and the variation is about ±4 mm.
2-1. Improvement of Stopping Accuracy: Deceleration Stop (NM = 3,000 r/min → 1,000 r/min → stop)
As can be seen from the overrun characteristics, the overrun becomes smaller as the rotation speed decreases.
Here, we calculate the overrun when stopping after decelerating.
Follow the same procedure as in "1. Calculation of Stopping Accuracy."
Reading overrun value (vertical axis) from 1,000 r/min (blue dash line curve) and 0.9 × 10-4 [kg·m2] (horizontal axis) shows that it is about 0.2 ± 0.1 [Rev].
Convert this value to a gearhead shaft.
ORG = ORM ÷ i = (0.2 ± 0.1) ÷ 15 ≒ 0.013 ± 0.007 [Rev]
Finally convert to the belt conveyor shaft.
ORC = D × π × ORG = 100 × 3.14 × (0.013 ± 0.007) ≒ 4 ± 2 [mm]
Based on the above, the stopping accuracy when deceleration stop can be inferred that the overrun is 4 mm and the variation is about ±2 mm.
(In this case, a sensor is required at the deceleration point in addition to the sensor at the stop position.)
2-2. Improvement of Stopping Accuracy: Increase Gear Ratio (i = 15 → 30)
As mentioned, the overrun of the gearhead shaft is the value of the motor shaft divided by the gear ratio.
Therefore, by increasing the gear ratio, overrun can be minimized.
Here, we will calculate overrun when the gear ratio is increased.
(In this case, the speed of the belt is also halved to Max 0.5 [m/s].)
1) Motor Shaft Conversion
- [1]
- Motor Shaft Speed
To comply with the same conditions in "1. Calculation of Stopping Accuracy: NM = 3,000 r/min," use the black dash line curve of 3,000 r/min.
- [2]
- Motor Shaft Load Inertia
JM = JG ÷ i 2 = 200 × 10-4 ÷ 302 ≒ 0.2 × 10-4 [kg·m2]
- [3]
- Motor Shaft Overrun
Reading overrun value (vertical axis) from [1] (black dash line curve) and [2] (horizontal axis) shows that it is about 0.6 ± 0.2 [Rev].
2) Gearhead Shaft Conversion
Convert the overrun obtained in 1) to a gearhead shaft.
ORG = ORM ÷ i = (0.6 ± 0.2) ÷ 30 ≒ 0.02 ± 0.007 [Rev]
3) Belt Conveyor Shaft Conversion
Convert the overrun obtained in 2) to the belt conveyor shaft.
ORC = D × π × ORG = 100 × 3.14 × (0.02 ± 0.007) ≒ 6 ± 2 [mm]
Based on the above, the stopping accuracy can be inferred that the overrun is 6 mm and the variation is about ±2 mm when the gear ratio is increased from 1/15 to 1/30.
4. Summary
We described how to determine stop accuracy as well as other methods to effectively improve stopping accuracy of brushless motors.
| Motor Shaft Speed [r/min] | Gear Ratio | Belt Speed [m/s] | Stopping Accuracy | |
|---|---|---|---|---|
| Overrun [mm] | Variation [mm] | |||
| 3,000 | 15 | 1) | 19 | ±4 |
| 3,000 → 1,000 | 15 | 1 → 0.35 | 4 | ±2 |
| 3,000 | 30 | 0.5 | 6 | ±2 |
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