This month's measurement column features answers to frequently asked questions received by our customer support center.
Our photoelectric rotation detectors, such as the LG-9200 and LG-930, can be used in combination with digital rotation indicators like the TM-3100 series to detect the rotational speed of rotating objects such as motors.
It's Sa.
The specifications include an item called "maximum response speed." This defines the upper limit of the rotational speed that can be detected.
Photoelectric rotation detector LG-930
specification
Detection method: Visible light photoelectric reflection method
Detection distance: 70–200 mm (when using the dedicated 12 mm square reflective mark)
Detected object: Reflective mark
Maximum response speed: 25 m/s (when using dedicated 12 mm square reflective marks and spacing them 48 mm apart)
Why is the specified value for a sensor used to detect rotational speed "maximum response speed" and not "maximum rotational speed"?
In photoelectric rotation detectors, light emitted from the sensor itself is directed at a reflective mark attached to the object being measured. The reflected light is then converted into an electrical signal, which is used to output a signal for detecting rotational speed. To convert light into an electrical signal, the reflected light needs to be continuously detected for a certain period of time, so the "time the reflective mark crosses in front of the photoelectric detector" is important. This time is determined by the speed of the reflective mark, but the speed of the reflective mark attached to the rotating object is not determined solely by the rotational speed, but is also affected by the size of the object being measured (the distance from the center of rotation to the reflective mark).
When measuring rotational speed, it is necessary to calculate and confirm in advance whether the desired rotational speed can be measured with this sensor.
[Calculation method]
If the distance from the center of rotation to the reflective mark is r (m) and the rotational speed is n (r/min), then the speed of movement V (m/s) at the location where the reflective mark is placed is:
V = 2πr × n/60 (m/s)
It can be expressed as follows.
If this value is less than or equal to the LG-930's maximum response speed of 25 m/s, a signal that can be measured by a pulse counter or rotation speed indicator can be obtained.
Let's actually calculate the maximum rotational speed that the LG-930 can measure if a reflective mark is placed approximately 10 cm from the center of rotation.
The following relationship holds between the speed V at which an object passes in front of the LG-930 and its rotational speed n:
V = 2πr × n ÷ 60
The LG-930 has a maximum speed of 25 m/s, so it must satisfy equation ①.
V = 2πr × n ÷ 60 ≤ 25
……………①
If you actually input a number and calculate n
n ≤ 25 × 60 ÷ (2π * 0.1) ………………②
n ≤ 2,387
We calculated that it is possible to measure rotational speeds up to 2,387 r/min.
Is there any way to measure the rotational speed up to 4,000 r/min?
When the rotational speed is 4,000 r/min, the moving speed V is
V = 2π×0.1×4,000/60 ≒ 42 m/s
Since this significantly exceeds 25 m/s, the rotation signal cannot be detected in this state.
There are two ways to increase the upper limit of the rotation speed:
In equation ①, in order for V to remain unchanged even when n is increased, it is necessary to decrease r.
For example, as shown in Figure 2(i), if the reflective mark is placed closer to the center of the rotating body, to half its original position of 5 cm, the result of equation ② becomes n ≤ 4,775, and a rotational speed of 4,000 r/min can be measured.
Part 2
As shown in Figure 2ii, this can also be addressed by arranging and applying multiple reflective marks in the direction of rotation.
The success or failure of detection is limited by the "time the reflective mark crosses," so if you make the reflective mark longer...
This will also increase the passage time. By attaching two reflective marks together, the passage time will double even at the same speed, allowing you to measure up to twice the speed (twice the rotational speed). (Attaching three marks will allow you to measure up to three times the rotational speed.)
The upper limit of the rotational speed cannot be increased indefinitely. For example, as shown in Figure 3, if the distance from the center of rotation is short (1/2r) and the reflective mark is continuously applied over 3/4 of the circumference, the rotational speed calculated from equation ① can reach approximately 90,000 r/min. or more. However, this speed cannot be measured.
The area without the reflective markings is too small, so it all ends up looking like a single continuous signal.
The caveat in the product specifications, "when the spacing between stickers is 48 mm," refers to the conditions under which the sensor can distinguish between the presence or absence of reflective marks.
specification
Detection method: Visible light photoelectric reflection method
Detection distance: 70–200 mm (when using the dedicated 12 mm square reflective mark)
Detected object: Reflective mark
Maximum response speed: 25 m/s (when using dedicated 12 mm square reflective marks and spacing them 48 mm apart)
For the LG-930, the reflective markings must be applied such that the ratio of the area without the reflective markings to the length of the reflective markings is 3 or more.
To improve response speed, if you apply multiple reflective markers, please note that you will need at least three times as many areas without reflective markers.
example
When detecting the rotational speed of a φ20 rotating shaft by attaching reflective marks to its outer circumference, the maximum rotational speed n that can be measured with a single reflective mark is:
n ≦25×60/(2π×0.02)≒11,900 r/min
To measure a faster rotation speed, if we attach another reflective mark (12 mm square), the shaft circumference becomes approximately 63 mm, resulting in a reflective mark-to-gap ratio of 24:39, which does not satisfy the previous condition. The condition of a 1:3 ratio between the width of the reflective mark and the gap is satisfied only if the width of the reflective mark is at most slightly less than 16 mm. Compared to using one reflective mark, the measurable rotation speed increases by about 30%, but this is the limit for this shaft size.
Photoelectric rotation detectors have different response speeds depending on the product, and therefore the maximum measurable rotation speed also varies. You need to select a product that combines the rotation speed you want to measure (expected), the size of the object to be measured (distance from the center of rotation to the measurement point), and the detector's response speed.
(Excerpt from the email newsletter issued on July 20, 2022)
