Optical encoders are usually the most reliable equipment for precise measurement and motion control. Due to their high accuracy, high resolution, and repeatability, as well as their ability to work under different environmental conditions and relatively low prices, they are used in various applications. For example, manually controlled machine tools and CNC machine tools, robots, service systems, monitoring and fault diagnosis systems, tracking systems, linear and rotary positioning tables, and other precision positioning applications.

 

 

The overall accuracy and precision of a linear encoder mainly depend on the quality of the measurement scale and nonlinear subdivision error (SDE) within a signal cycle. High accuracy and resolution are crucial for applications that require precise positioning and good repeatability. In some applications, electronic encoders are not only used for position estimation but also provide feedback for speed control.

 

SDE (also known as interpolation error) is a cycle that occurs during each period of encoder rotation, depending on the quality of the main measurement scale of the generated electrical signal. This error occurs during the interpolation process because the distorted analog electronic signal of the encoder prevents it from forming a new quadrilateral signal. In practice, SDEd will not cause any problems until its amplitude reaches the size of the measurement step. In other words, the size of SDE is the limit of the highest resolution. If the positioning error is large, the minimum measurable increment step is meaningless. This is particularly important for applications that require precise positioning and repeatability. In machines where the feed axis or rotary table is directly driven, nonlinear interpolation errors not only cause positioning errors, but also cause loud noise, additional heating, and speed reduction.

 

The quality of an electrical signal largely depends on different aspects, such as the principle of optical scanning, the design of the reading head, and its ability to withstand various deformations, mechanical vibrations, or temperature changes. In order to improve signal quality and make the encoder more robust, manufacturers use advanced optical scanning methods such as single field or interferometric scanning principles, or they implement specially configured multi track analyzer gratings to eliminate high-order harmonic signals. Unfortunately, all of these improvements require more complex encoder configurations and expensive optical components. Non equivalent signal parameters, such as relative amplitude, DCo set, phase shift, and non sine wave shape, must be corrected before the interpolation process. Many research methods to address this issue involve using digital correction and prospect tables or creating different algorithms for line and dynamic compensation. Due to the short range of SDE, which has repetitions in each cycle, its compensation is a difficult task.

 

It is very important to understand the functional limits of the displacement measurement encoder used so that the application can work smoothly and make appropriate adjustments. SDE is one of the parameters that should be investigated first, especially if the encoder's electrical signal is not corrected or compensated before the interpolation process. The method introduced in this article can estimate the magnitude of interpolation error and its trend over a period. Experimental investigations on interpolation errors of specific standard encoders at different scanning speeds have shown that the magnitude of this low-frequency error largely depends on the traversal speed of the encoder reading head. In addition, detailed harmonic analysis of SDE can provide a clearer understanding of the physical properties of errors and improve the performance of encoders and the entire application.

 

 

Use different types of optical scanning principles for photodiodes (such as Talbot e ff ect, Lau e ff ect, Moir é e ff ect, generalized grating imaging, and interferometric) Generate electronic output signals to determine precise positions. Based on the electronic devices used later, optical encoders can have different interfaces to ensure reliable information exchange. One of the most widely used interfaces for incremental position measurement is two analogs near sinusoidal voltage signals (Figure 1). Signals A and B are shifted by 90 degrees, with an amplitude typically of 1Vpp:

 

Among them, Xposition is the relative position between the measuring scale and the reading head; p. The period of the main ruler; SA, SB, the period of the values of output signals A and B at a certain position; SA and SB, respectively, are the values of output signals A and B at a certain position.

 

Figure 1. Definition of Differential Optical Encoder Signal 1 Vpp Interface

 

This process is called interpolation and is directly related to the quality of the signal. The 1Vpp interface is mainly used for applications where interpolation and analog signal digitization processes are executed by subsequent electronic devices of terminal devices.

 

It is very comfortable to observe and track the quality and accuracy of the encoder by combining the simulated encoder signal on the X-axis and Y-axis of the oscilloscope. Unfortunately, in practical applications, the signal output by the encoder is distorted due to imperfections in manufacturing, assembly, and optical scanning operations, as well as negative impacts due to changes in environmental conditions. Signal distortion leads to SDE, which repeats within each cycle of the encoder grating. The change in signal background level (UA_o ff, UB_o ff) is usually caused by defects or pollutants in the encoder's measurement scale. This distortion leads to distortion centered around the Lissajou curve, as shown in Figure 2a. The inconsistent amplitude (UA, UB) between the peaks of signals A and B may be due to uneven or inconsistent illumination of the photodetector. Figure 2c shows that a 90 degree phase shift causes a change in the curve. The main reason for this error is the tilt between the scanning mesh cover and the main measuring scale. All higher harmonics caused by optoelectronics and electronics make the signal not a perfect sine wave. This type of error forms a non circular Lissajous curve, as shown in Figure 2d.

 

Figure 2. Lissajous curve of optical encoder signal with relative subdivision error (SDE): (a) setting error; (b) Amplitude error; (c) Phase shifter error; (d) Signal shape error.

 

 

The magnetic force of the normal form SDE is usually determined by using a reference encoder and a laser interferometer. The difference between the independent position information from the reference device and the latest linear encoder reading is considered an error.

 

Another method implemented in this paper is based on constant speed testing. The encoder reading head being tested is driven at a constant speed and its power output signal is recorded using a digital oscilloscope. Due to the high sampling frequency, the signal of the analog encoder is represented as a set of discrete points. Claiming that the scanning speed is constant and knowing that the number of samples used must be selected by considering Nyquist Shannon sampling, this means combining theoretically reasonable position values at these points. For example, if the scanning speed is 100mm/s, the grating period of the test encoder is 20 µ m, and the sampling frequency is 250MHz, then there are 50000 sampling points per cycle. The first point corresponds to the position value of the laser, and the last point (50000) corresponds to 20 µ m. In order to obtain statistically reliable results, this program must repeat several cycles and several different measurement values, and the average evaluation method must be used.

 

We chose a standard optical (4-field scanning) encoder as the experimental research object. A mobile translation platform based on direct drive technology is used to test the high accuracy and low friction of the encoder's reading head at various constant speeds.

 

Figure 3. Designed experimental setup. The test line encoder is connected to the direct drive line translation bracket through a mounting bracket.

 

The 3-phase iron wire brush servo motor in the translation stage is controlled by an ACS servo motion controller with a built-in driver. In the translation phase, an integrated non-contact linear optical encoder is used as a feedback system for high-resolution positioning and smooth motion control. Use a digital oscilloscope to sample and record electrical signals. The schematic diagram of the experimental device is shown in Figure 4.

 

Figure 4. Schematic diagram of experimental setup

 

 

1. Motion controller: Servo motion controller with built-in driver ACS motion control SPiiPlusCMnt.

 

2. Linear translation platform: Electric direct drive linear translation platform "STANDA" 8MTL1401-300.

 

3. Tested linear encoder: PrecizikaMetrologyL18 optical (4-grating scanning) linear encoder (measuring length=300mm, grating period=20 µ m).

 

4. Data acquisition and processing equipment: a digital oscilloscope PicoScope3000 and a laptop equipped with appropriate software.

 

In order to analyze the properties of these errors at different speeds, the Fast Fourier Transform (FFT) algorithm was used. Since these errors are cyclic, their harmonic analysis helps to identify new signal defects that cause these errors. Third and higher-order harmonics are caused by higher-order distortion of electrical signals. Usually, they are caused by the birefringence effect during the optical modulation process. Therefore, the error composed of harmonics can be represented by the following formula:

 

among δ (x) Represents the SDE of the encoder grating within one cycle, Ai and ji represent the amplitude and phase of harmonics, and x represents the relative position within one cycle p.

 

 

Firstly, we checked the performance of the test line encoder at different speeds, and the encoder supplier specified a maximum traversal speed of 100500, and 1000mm/s. Figure 5 shows the Lissajous curves for several signal cycles at 100, 500, and 1000 mm/s.

 

Figure 5. Lissajous curves for various signal periods at speeds of 100, 500, and 1000 millimeters per second.

 

From these charts, it can be seen that the performance of the encoder begins to decline. As the scanning speed increases, the size and shape of the Lissajou curve change, and higher SDE is introduced. For a more detailed investigation, the reading head of the test encoder was driven to move within a speed range of 100 to 1100 millimeters per second, with a speed of 100 millimeters per second. Record the output electrical signal using a sampling frequency of 250MHz and determine the SDE according to the method described in the previous section. As an example, when the reading head is driven at a speed of 300 millimeters per second, the graphical representation of electronic signals and their combination in the X-Y diagram are shown in Figure 6.

 

Figure 6. Electronic signals and their performance in the X-Y diagram. The encoder operates at a lateral speed of 300 millimeters. The average SDE calculated at this speed is shown in Figure 7.

 

FFT analysis shows that the first, second, and third harmonics have the greatest impact on the error amplitude. Therefore, all three first harmonics are displayed in the same graph to show the impact of each harmonic. The total amplitude of the error is ± 0.185 µ m. The second harmonic, repeated twice per cycle, produces the maximum error value.

 

Figure 7. Average SDE and its decomposition in three first harmonics, when the can speed is 300 mm/s.

 

Similar data processing was performed at the speed of all tests. The calculated total error margin is plotted on a graph, as shown in Figure 8.

 

The results show a strong linear relationship between scanning speed and total SDE. More than 85% of the error value determined by the experiment can be mathematically related to the continuously improving speed of the encoder (R-squared=0.8581). The most severe error is ± 0.52 µ m at 1100mm/s, and there is a significant difference in the linear relationship between the two errors of 900 and 1000mm/s.

 

Figure 8. Dependence of total SDE on scanning speed. Data points and the first statistical parameter.

 

In order to understand the physical meaning of errors that occur during the scanning process, we analyzed the size and behavior of the first three error harmonics, and their dependence on the scanning speed of the test encoder is shown in Figure 9.

 

Figure 9. The third harmonic of the determined SDEs at different speeds.

 

The maximum part of SDE at each speed is caused by the second harmonic. This harmonic shows a strong linear relationship with the crossing velocity (R-square=0.96). Its size increases proportionally with increasing speed. This error behavior is the result of signal amplitude changes, phase shifts, or a combination of them

 

The first harmonic of the error shows a non-linear relationship. The amplitude value begins to increase when the encoder speed reaches 500 millimeters per second or more. Within the range of 900 to 1000 millimeters per second, note that the extreme jumps in values are within the range of 900 to 1000 millimeters per second. In this region, the amplitude decreases relatively from 0.26 microns to 0.01 microns. This harmonic is the result of the electrical signal being shifted from zero horizontally.

 

The change in the meaning of the third harmonic is not significant compared to others. Its amplitude reaches the highest value of 0.06 µ m. This amplitude was observed at a scanning speed of 900 millimeters per second, just like the first harmonic. Usually, this third harmonic is the result of changes during the optical scanning process.

 

 

• At each speed, the largest portion of the SDE budget forms a second harmonic. This is directly related to the increased speed. This means that the difference in signal amplitude or phase shift increases with increasing speed. Amplitude The "o" set or phase error may be caused by the physics of optical scanning principles, as well as dynamic behavior and improper adjustment. Electronic components (such as photodiodes, used processing chips, or analog amplifiers) Or the quality and other impacts of the cables used. Not only do we need to pay attention to these aspects during the design process, but we also need to pay attention to these aspects when selecting the appropriate encoder for specific applications. For example, the working principle of the tested encoder is based on the four field scanning method. If the application requires higher stability of scanning speed or the possibility of measuring scale contamination increases, an optical encoder based on the single field scanning principle must be selected.
• The total SDE values calculated at speeds of 900 and 1000 millimeters per second differ from the determined linear relationship. When analyzing the first harmonic map, when the speed exceeds 500 mm/s, the setting error of the encoder signal begins to show significant changes. The reading head is a complex mechanical part that includes optical and electronic components, as well as spring based suspension. Therefore, even the smallest translation, distance change, tilt, or relative position change between the scanning mesh and the measurement system may be generated by resonance frequency, friction, or other forces.
• FFT analysis shows that the main part of SDE is only composed of a few first harmonics. This means that by using a simple equation containing only three first harmonic (n=3) information, the trend of SDE can be approached quite accurately.