CN103822783A - Precision transmission device dynamic precision measuring system, and detection method - Google Patents

Abstract

The invention discloses a dynamic accuracy measurement system and detection method of a precision transmission device. The system includes a servo drive unit for providing power, a dynamic loading unit for loading, a data acquisition unit for collecting transmission data, and a control processing unit for obtaining accuracy data. Comprehensive and accurate acquisition of input and output data and equipment operating status data, precise control and high correlation between input and output, can detect transmission accuracy indicators of precision transmission devices with high precision, and can be dynamically loaded and the loading process corresponds to the drive , to comprehensively test and evaluate the performance, reliability and life of the precision transmission device under various conditions; it can effectively detect the quality of the precision transmission device before use to ensure a high pass rate when the product is used. Install new products to ensure their reliability and provide inspection standards.

Description

Dynamic accuracy measurement system and detection method of precision transmission device

technical field

The invention relates to a detection system for a precision rotating device and a detection method using the detection system.

Background technique

Precision transmission devices (such as RV reducers, new types of small tooth difference reducers, harmonic reducers, etc.) have been widely used in the fields of aerospace, robot joints, and control systems of various precision instruments and equipment, and the transmission accuracy of the devices The tests in the field often use static theory to deal with dynamic problems, which leads to the fact that the experimental test results cannot reflect the actual working conditions.

In the prior art, the accuracy of the parameters obtained during the loading process and the driving process is low, and the loading process has no necessary connection with the driving, resulting in low reference value of the obtained data; however, in the application field of precision transmission devices, it is necessary to carry out a The detection with higher precision provides a more authoritative reference for its subsequent use.

Therefore, there is a need for a precision transmission device dynamic accuracy measurement system, which can detect the transmission accuracy index of the precision transmission device with high precision, and can be dynamically loaded and the loading process corresponds to the drive, so as to ensure a high pass rate when the product is used , At the same time, it provides inspection standards for the development of new products of precision transmission devices to ensure their reliability.

Contents of the invention

In view of this, the present invention provides a precision transmission device dynamic accuracy measurement system and detection method, which can detect the transmission accuracy index of the precision transmission device with high precision, and can be dynamically loaded and the loading process corresponds to the drive, ensuring the use of the product At the same time, it has a high pass rate, and at the same time, it provides an inspection standard for the development of new products of precision transmission devices to ensure their reliability.

The dynamic accuracy measurement system of the precision transmission device of the present invention includes:

The servo drive unit is used to transmit power to the power input end of the detected workpiece;

The dynamic loading unit is used to dynamically load the power output end of the detected workpiece;

The data acquisition unit includes an input data acquisition system and an output data acquisition system, respectively acquiring the input torque and input speed data input from the servo drive unit to the detected workpiece, and the output torque and output speed data output from the detected workpiece to the dynamic loading unit ;

The control processing unit is used to receive the data signal of the data acquisition unit and calculate and acquire the transmission accuracy data of the detected workpiece according to the data, and is used to control the operation status of the servo drive unit and the dynamic loading unit.

Further, the control processing unit includes a motion control card I and a data acquisition and processing system, the motion control card I is used to issue control commands to the servo drive unit and feed back the operating parameters of the servo drive unit to the data acquisition and processing system; the data acquisition and processing system Send a control command to the dynamic loading unit according to the operating parameters of the servo drive unit; the data acquisition and processing system is used to receive the data information of the input data acquisition system and the output data acquisition system to calculate and obtain the transmission accuracy data of the detected workpiece;

Further, the servo driving unit is a driving servo motor with a driving servo controller, and the driving servo controller is electrically connected to the motion control card I; the dynamic loading unit is a dynamometer with a driver, and the driver is connected to the data Acquisition and processing system is electrically connected; 4. the precision transmission device dynamic precision measurement system according to claim 2, is characterized in that:

Further, the servo drive unit is a drive servo motor with a drive servo controller, and the drive servo controller is electrically connected to the motion control card I; the dynamic loading unit is a load servo motor with a load servo controller, The drive servo controller is electrically connected to the data acquisition and processing system through the motion control card II.

Further, the input data acquisition system includes an input torque sensor and an input grating ruler; the loading end data acquisition system includes an output torque sensor and an output grating ruler;

Further, the servo drive unit and the dynamic loading unit are provided with automatic protection against overvoltage, overcurrent and overload.

The invention also discloses a detection method using the dynamic accuracy measurement system of the precision transmission device, which includes the following steps:

a. Start the servo drive unit to drive the detected workpiece to rotate in a transmission manner, and obtain the operating parameters of the servo drive unit;

b. According to the operating parameters of the servo drive unit in step a, send a command signal to the dynamic loading unit to form dynamic loading on the detected workpiece:

c. During steps a and b, the input torque and the input speed signal of the detected workpiece input by the servo drive unit are obtained, and the output torque and output speed signal of the detected workpiece output to the dynamic loading unit are obtained;

d. Using the input torque, input rotational speed, output torque and output rotational speed in step c, calculate the transmission accuracy data of the detected workpiece.

Further, in step d, the transmission accuracy data of the detected workpiece includes transmission efficiency, transmission error and repeat positioning accuracy;

Further, in step d, the transmission efficiency is $\mathrm{\η}=\frac{P_o}{P_i}\×100\%=\frac{{\mathrm{no}}_o\×T_o}{{\mathrm{no}}_i\×T_i}=\frac{{\mathrm{no}}_o\×T_o}{{\mathrm{no}}_o\×i\×T_i}=\frac{T_o}{i\×T_i}\×100\%,$ P _o and P _i are the output power and input power of the detected workpiece, T _o and T _i are the output torque and input torque of the detected workpiece, i is the transmission ratio of the detected workpiece, n _o and _ni are the output speed of the detected workpiece and input speed;

为输入端实际转角，

为输出端实际转角；The transmission error is

is the actual rotation angle at the input end,

is the actual rotation angle of the output terminal;

Repeat positioning accuracy is ${\mathrm{\θ}}^{\′}=\frac{\max (\mathrm{\Δ}{\mathrm{\θ}}_1,\mathrm{\Δ}{\mathrm{\θ}}_2,...,\mathrm{\Δ\θn})-\min (\mathrm{\Δ}{\mathrm{\θ}}_1,\mathrm{\Δ}{\mathrm{\θ}}_2,...,\mathrm{\Δ}{\mathrm{\θ}}_{\mathrm{no}})}{2},$ Δθ ₁ ,Δθ ₂ ,...,Δθn is the difference between the theoretical output rotation angle θ ₀₁ ,θ ₀₂ ...,θ _0n and the actual output rotation angle θ ₁₁ ,θ ₁₂ ...,θ _1n , n is the detected workpiece Output the fraction divided evenly over a lap.

Beneficial effects of the present invention: In the dynamic accuracy measurement system and detection method of the precision transmission device of the present invention, the measurement system adopts a servo drive unit, a dynamic loading unit, a control processing unit and an input and output data detection unit to obtain input and output data comprehensively and accurately And equipment operating status data, precise control and high correlation between input and output, can detect the transmission accuracy index of the precision transmission device with high precision, and can be dynamically loaded and the loading process corresponds to the drive, comprehensively test and evaluate the precision transmission device in Performance, reliability and service life under various conditions; can effectively test the quality of precision transmission devices before use to ensure a high pass rate when the product is in use. At the same time, for the development of new precision transmission products, especially RV reducers, New type less tooth difference reducer, harmonic reducer, etc., to ensure their reliability and provide inspection standards.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

Fig. 1 is a schematic block diagram of the present invention;

Fig. 2 is a schematic block diagram of another structure of the present invention.

Detailed ways

Fig. 1 is a block diagram of the principle of the present invention, the solid line arrow represents the transmission direction, and the dotted line arrow represents data and control, as shown in the figure: the precision transmission device dynamic accuracy measurement system of the present embodiment includes:

The servo drive unit is used to transmit power to the power input end of the detected workpiece. The servo drive unit can be used to drive a servo motor or even a permanent magnet AC drive servo motor. The control accuracy is high and it is simple and convenient;

The dynamic loading unit is used to dynamically load the power output end of the detected workpiece; the dynamic loading unit can use the existing controllable servo motor to load or the dynamometer or even the hysteresis dynamometer;

The data acquisition unit includes an input data acquisition system and an output data acquisition system, respectively acquiring the input torque and input speed data input from the servo drive unit to the detected workpiece, and the output torque and output speed data output from the detected workpiece to the dynamic loading unit ; The input data acquisition system is used to detect the input torque and the input speed data can be realized by a variety of sensors, for example, the input speed data can use an angle sensor (grating scale) or a normal speed sensor, and the angle and speed can be converted to each other to achieve different computing purposes;

The control processing unit is used to receive the data signal of the data acquisition unit and calculate and obtain the transmission accuracy data of the detected workpiece according to the data, and is used to control the operation status of the servo drive unit and the dynamic loading unit; the control processing unit can use an ordinary industrial computer And combined with the usual drive servo motor motion control card Ⅰ, such as PMAC motion control card Ⅰ.

In this embodiment, the control processing unit includes a motion control card I and a data acquisition and processing system, and the motion control card I is used to issue control commands to the servo drive unit and feed back the operating parameters of the servo drive unit to the data acquisition and processing system; The acquisition and processing system sends control commands to the dynamic loading unit according to the operating parameters of the servo drive unit; the data acquisition and processing system is used to receive the data information of the input data acquisition system and the output data acquisition system to calculate and obtain the transmission accuracy data of the detected workpiece; the data acquisition The processing system can adopt the existing industrial computer and data acquisition card, etc., and has conversion and amplification functions, which belongs to the prior art and will not be repeated here;

In this embodiment, the servo drive unit is a drive servo motor with a drive servo controller. In this embodiment, a permanent magnet AC drive servo motor is used. The drive servo controller is electrically connected to the motion control card I, and the motion control card I is the PMAC motion control card I; the dynamic loading unit is a dynamometer with a driver, the dynamometer adopts a hysteresis dynamometer, and the driver is electrically connected to the data acquisition and processing system; in this embodiment, the motion control card I Accept the command and control the drive servo motor, and feed back the signal to the data acquisition and processing system. The data acquisition and processing system sends a command signal to the driver according to the signal and adjusts its dynamic loading parameters. Of course, this structure is also suitable for static loading; hysteresis The dynamometer is composed of a stator with toothed poles, a hollow hysteresis cup rotor, an excitation coil, a bracket and a bottom plate. When the internal coil of the hysteresis dynamometer passes current, it generates magnetic lines of force and forms a magnetic circuit to generate torque and change the excitation. The current can change the load torque, while the excitation current is dynamically controlled by the dynamometer controller. At the same time, the PMAC motion control card I will also send control signals to the drive of the hysteresis dynamometer through the industrial computer (data acquisition and processing system), so that Realize dynamic torque loading on the detected workpiece.

In this embodiment, the input data acquisition system includes an input torque sensor and an input grating ruler; the loading end data acquisition system includes an output torque sensor and an output grating ruler; this structure makes the measurement system use direct displacement for the measurement of the dynamic accuracy of the precision transmission device The measurement method can realize the dynamic and static measurement of the transmission error and the real-time measurement of the hysteresis. It has good adaptability. The grating ruler has a high measurement resolution and is suitable for occasions that require high precision; the grating ruler can be obtained directly Rotation angle position data, so as to obtain the angular displacement information of the detected workpiece, and through the PMAC motion control card Ⅰ, the signal of the grating scale can be processed into speed information, which is used to measure the input and output shaft rotation angle and speed of the precision reducer, and the data It is transmitted to the data acquisition and processing system through the PMAC motion control card I, and the signal input to the grating scale is used as the feedback signal for driving the servo motor position control.

Fig. 2 is a schematic block diagram of another structure of the present invention, as shown in the figure, the difference between this embodiment and the above-mentioned embodiment is only: the dynamic loading unit of this embodiment is not a dynamometer, but a loading servo motor is used for loading, of course , need to be equipped with a loading servo controller, the driving servo controller is electrically connected to the data acquisition and processing system through the motion control card II; in this embodiment, the motion control card I accepts commands and controls the driving servo motor, and at the same time feeds back signals to Data acquisition and processing system, the data acquisition and processing system sends a command signal to the motion control card II according to the signal and adjusts the dynamic loading parameters of the loading servo motor. Of course, this structure is also suitable for static loading; the load can be changed by changing the loading parameters of the loading servo motor At the same time, PMAC motion control card I will also send control signals to motion control card II, drive servo controller and loading servo motor through industrial computer (data acquisition and processing system), so as to realize dynamic torque loading on the detected workpiece.

In this embodiment, both the servo drive unit and the dynamic loading unit are provided with automatic protection against overvoltage, overcurrent and overload.

In the present invention, the above-mentioned equipment can be installed on a test bench, which has better integrity, and will not be described in detail here; the position or speed of the driving servo motor is controlled in real time through the PMAC motion control card I, and the data acquisition adopts high-speed ADLINK data acquisition The card is used for synchronous collection, and all data collected are processed synchronously in real time and automatically stored; of course, the present invention can also have automatic protection functions for overvoltage, overcurrent, and overload, and is mainly used in servo drive units to avoid damage to equipment. This will not be repeated here.

The invention also discloses a detection method using the dynamic accuracy measurement system of the precision transmission device, which includes the following steps:

a. Start the servo drive unit, drive the detected workpiece to rotate in a transmission mode, and obtain the operating parameters of the servo drive unit; the operating parameters are used as the loading reference of the dynamic loading unit, and have a determined or set proportional relationship;

b. According to the operating parameters of the servo drive unit in step a, send a command signal to the dynamic loading unit to form dynamic loading on the detected workpiece:

c. During steps a and b, the input torque and the input speed signal of the detected workpiece input by the servo drive unit are obtained, and the output torque and output speed signal of the detected workpiece output to the dynamic loading unit are obtained;

d. Using the input torque, input rotational speed, output torque and output rotational speed in step c, calculate the transmission accuracy data of the detected workpiece.

In this embodiment, in step d, the transmission accuracy data of the detected workpiece includes transmission efficiency, transmission error and repeat positioning accuracy; these three parameters can fully reflect the transmission accuracy of the detected workpiece.

In this embodiment, transmission efficiency is an important technical performance of mechanical transmission, and is one of the important indicators for evaluating the performance of precision transmission devices, and it is also the focus of attention in this field; the present invention can measure the The transmission efficiency under ; in step d, the transmission efficiency is $\mathrm{\η}=\frac{P_o}{P_i}\×100\%=\frac{{\mathrm{no}}_o\×T_o}{{\mathrm{no}}_i\×T_i}=\frac{{\mathrm{no}}_o\×T_o}{{\mathrm{no}}_o\×i\×T_i}=\frac{T_o}{i\×T_i}\×100\%,$ P _o and P _i are the output power and input power of the detected workpiece, T _o and T _i are the output torque and input torque of the detected workpiece, i is the transmission ratio of the detected workpiece, n _o and _ni are the output speed of the detected workpiece and input speed; in fact, the input and output torque values under 25%, 50%, 75%, and 100% of the rated load (through the hysteresis dynamometer at the output end) can be tested at different speeds respectively. Draw a curve; for a specific speed, take the ordinate as the efficiency value and the abscissa as the time, so that the transmission efficiency of the precision transmission device can be drawn;

为输入端实际转角，为输出端实际转角；本实施例中，设

如果将输出的实际转角

与输出的理论转角

之差值中最大与最小值之差作为试验件的传动误差，即本系统所测试的传动误差；也就是如果在精密传动装置输出轴的一转内取60个测试点(即输出轴每转6°取一个值)，则对于输出轴分别有60个理论转角

和实际转角则可以求出60个实际转角与理论转角之间的差值

输出轴运动误差可表示为：Transmission error is the most important technical index of precision mechanical transmission accuracy and one of the indicators to measure transmission accuracy. The greater the transmission error, the greater the change in the transmission ratio of the transmission device, and the lower the transmission accuracy, otherwise the higher the transmission accuracy; when the speed is not high, it only affects the motion accuracy; when the speed is high, it not only affects the motion accuracy , will also disrupt the stability of the work. The measuring system adopts the direct displacement measurement method to measure the transmission error, which can realize the dynamic and static measurement of the transmission error and the real-time measurement of the hysteresis. It has good adaptability, and its measurement resolution is guaranteed by the circular grating used in the test bench; The error is

is the actual rotation angle at the input end, is the actual rotation angle of the output terminal; in this embodiment, set

If the actual rotation angle of the output

Theoretical corner with output

The difference between the maximum and minimum value of the difference is taken as the transmission error of the test piece, that is, the transmission error tested by this system; that is, if 60 test points are taken within one revolution of the output shaft of the precision transmission device (that is, each revolution of the output shaft 6° to take a value), then there are 60 theoretical rotation angles for the output shaft

and the actual corner Then the difference between 60 actual rotation angles and theoretical rotation angles can be obtained

The output shaft motion error can be expressed as:

The repeated positioning accuracy is a test relative to the output end of the drive servo motor; the repeated positioning accuracy is ${\mathrm{\θ}}^{\′}=\frac{\max (\mathrm{\Δ}{\mathrm{\θ}}_1,\mathrm{\Δ}{\mathrm{\θ}}_2,...,\mathrm{\Δ\θn})-\min (\mathrm{\Δ}{\mathrm{\θ}}_1,\mathrm{\Δ}{\mathrm{\θ}}_2,...,\mathrm{\Δ}{\mathrm{\θ}}_{\mathrm{no}})}{2},$ Δθ ₁ ,Δθ ₂ ,...,Δθn is the difference between the theoretical output rotation angle θ ₀₁ ,θ ₀₂ ...,θ _0n and the actual output rotation angle θ ₁₁ ,θ ₁₂ ...,θ _1n , n is the detected workpiece Output the score of the average division on a circle, and this embodiment adopts 60;

That is, 60 test points are taken within one revolution of the motor output end (that is, a value is taken every 6° of the output shaft), and there are 60 theoretical rotation angles θ ₀₁ , θ ₀₂ ..., θ ₀₆₀ and actual rotation angles for the output shaft θ ₁₁ , θ ₁₂ ..., θ ₁₆₀ , then the difference between 60 actual rotation angles and theoretical rotation angles can be obtained from the calculation formula of the rotation angle deviation Δθ ₁ , Δθ ₂ ,..., Δθ ₆₀ , so the repeat positioning accuracy for

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 60</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 60</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span>$

For the above system and method, the servo drive is adopted and the dynamic loading is realized under the control of the drive. Combined with the characteristics of the servo drive, it has a relatively accurate transmission precision response, and is suitable for RV reducers, new type reducers with less tooth difference, and harmonic reducers. High-precision transmission devices such as gears and other transmission devices.

Finally, it is noted that the above embodiments are only used to illustrate the technical solutions of the present invention without limitation. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be carried out Modifications or equivalent replacements without departing from the spirit and scope of the technical solution of the present invention shall be covered by the claims of the present invention.

Claims (8)

1. A precision transmission device dynamic accuracy measurement system, characterized in that: comprising: The servo drive unit is used to transmit power to the power input end of the detected workpiece; The dynamic loading unit is used to dynamically load the power output end of the detected workpiece; The data acquisition unit includes an input data acquisition system and an output data acquisition system, respectively acquiring the input torque and input speed data input from the servo drive unit to the detected workpiece, and the output torque and output speed data output from the detected workpiece to the dynamic loading unit ; The control processing unit is used to receive the data signal of the data acquisition unit and calculate and acquire the transmission accuracy data of the detected workpiece according to the data, and is used to control the operation status of the servo drive unit and the dynamic loading unit. 2. The dynamic accuracy measurement system for precision transmission devices according to claim 1, wherein the control processing unit includes a motion control card I and a data acquisition and processing system, and the motion control card I is used to send Control commands and feed back the operating parameters of the servo drive unit to the data acquisition and processing system; the data acquisition and processing system sends control commands to the dynamic loading unit according to the operating parameters of the servo drive unit; the data acquisition and processing system is used for receiving input data acquisition systems and output data acquisition The data information of the system is calculated to obtain the transmission accuracy data of the detected workpiece. 3. The dynamic accuracy measurement system of precision transmission device according to claim 2, characterized in that: the servo drive unit is a drive servo motor with a drive servo controller, and the drive servo controller is connected to the motion control card I electronically. connection; the dynamic loading unit is a dynamometer with a driver, and the driver is electrically connected with the data acquisition and processing system. 4. The dynamic accuracy measurement system of precision transmission device according to claim 2, characterized in that: the servo drive unit is a drive servo motor with a drive servo controller, and the drive servo controller is connected to the motion control card I electronically connection; the dynamic loading unit is a loading servo motor with a loading servo controller, and the driving servo controller is electrically connected to the data acquisition and processing system through the motion control card II. 5. The dynamic accuracy measurement system of precision transmission device according to claim 3 or 4, characterized in that: the input data acquisition system includes an input torque sensor and an input grating scale; the loading end data acquisition system includes an output torque sensor and an output grating scale. 6. The dynamic accuracy measuring system of precision transmission device according to claim 4, characterized in that: the servo drive unit and the dynamic loading unit are equipped with automatic protections for overvoltage, overcurrent and overload. 7. A detection method utilizing a precision transmission device dynamic precision measurement system, characterized in that: comprising the following steps: a. Start the servo drive unit to drive the detected workpiece to rotate in a transmission manner, and obtain the operating parameters of the servo drive unit; b. According to the operating parameters of the servo drive unit in step a, send a command signal to the dynamic loading unit to form dynamic loading on the detected workpiece: c. During steps a and b, the input torque and input speed signal of the detected workpiece input by the servo drive unit are obtained, and the output torque and output speed signal of the detected workpiece output to the dynamic loading unit are obtained; d. Using the input torque, input rotational speed, output torque and output rotational speed in step c, calculate the transmission accuracy data of the detected workpiece. 8. The detection method according to claim 7, characterized in that in step d, the transmission accuracy data of the detected workpiece includes transmission efficiency, transmission error and repeat positioning accuracy. 8. detection method according to claim 7 is characterized in that: in step d, transmission efficiency is $\mathrm{\&eta;}=\frac{P_o}{P_i}\&times;100\%=\frac{{\mathrm{no}}_o\&times;T_o}{{\mathrm{no}}_i\&times;T_i}=\frac{{\mathrm{no}}_o\&times;T_o}{{\mathrm{no}}_o\&times;i\&times;T_i}=\frac{T_o}{i\&times;T_i}\&times;100\%,$ P _o and P _i are the output power and input power of the detected workpiece, T _o and T _i are the output torque and input torque of the detected workpiece, i is the transmission ratio of the detected workpiece, n _o and _ni are the output speed of the detected workpiece and input speed; The transmission error is

is the actual rotation angle at the input end,

is the actual rotation angle of the output terminal; Repeat positioning accuracy is ${\mathrm{\&theta;}}^{\&prime;}=\frac{\max (\mathrm{\&Delta;}{\mathrm{\&theta;}}_1,\mathrm{\&Delta;}{\mathrm{\&theta;}}_2,...,\mathrm{\&Delta;\&theta;n})-\min (\mathrm{\&Delta;}{\mathrm{\&theta;}}_1,\mathrm{\&Delta;}{\mathrm{\&theta;}}_2,...,\mathrm{\&Delta;}{\mathrm{\&theta;}}_{\mathrm{no}})}{2},$ Δθ ₁ , Δθ ₂ ,...,Δθn are the differences between input rotation angles θ ₀₁ ,θ ₀₂ ...,θ _0n and output rotation angles θ ₁₁ ,θ ₁₂ ...,θ _1n .

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