1 Introduction

The transmission error of the machine tool refers to the difference between the actual displacement of the output shaft and the theoretical displacement under the condition that the input shaft of the machine drive chain is driven completely accurately and rigidly. The drive chain for the composite movement required to form the surface of the workpiece on the machine tool - the end-to-end actuators of the "internal connection" drive chain must always maintain a strict motion relationship that meets the specified requirements. The transmission accuracy of the transmission chain refers to the accuracy of the transmission motion, which can be measured by the transmission error. Due to the actual transmission chain error of the machine tool, there is an error in the forming motion path of the workpiece surface, which is finally reflected on the workpiece to be processed, which causes the shape error of the forming surface. Since the machine tool transmission chain is mainly composed of gear pair, worm gear pair, thread pair, etc., the transmission chain error mainly comes from the machining precision and installation accuracy of these transmission components. From a kinematic point of view, all factors that cause the instantaneous gear ratio to deviate from a given transmission requirement are sources of drive chain error.

The measurement of machine tool transmission error is the premise of effective compensation for transmission error. Therefore, the precision measurement of machine tool transmission error has always been an important research topic of mechanical transmission technology. The basic measurement method of machine tool transmission error is to install the sensor in the relevant part of the machine tool. By using the measuring instrument of machine, light and electric principle and applying the error evaluation theory, the error of each link of the machine tool transmission system is measured, analyzed and adjusted. The cause of the error and the law of change.

2. Sensor selection

Correct and reasonable selection and installation of the sensor according to the motion characteristics of the end components of the transmission chain are necessary conditions for accurately measuring the motion accuracy of the transmission chain. According to the working principle, the commonly used sensors for machine tool transmission error measurement can be divided into the following categories:

(1) Grating sensor

The biggest advantage of the grating sensor is that the signal processing method is simple, easy to use, and the measurement accuracy is high (the accuracy of the grating sensor manufactured by famous foreign manufacturers such as Heidenhain of Germany and Fagor of Spain can reach 1 μm/m); the disadvantage is that the grating ruler is expensive. The working environment is relatively high, and the linear expansion coefficient of the glass grating is inconsistent with the machine tool, which is easy to cause measurement error.

(2) Laser sensor

Laser sensors (including single-frequency and dual-frequency lasers) have high measurement accuracy, but the measurement cost is also high. They are sensitive to changes in environmental conditions (such as temperature, airflow, vibration, etc.). Measures must be taken when using them at the production site. Measurement stability and reliability.

(3) Magnetic grid sensor

The magnetic scale can be divided into two types: linear (effective measuring length 3m) and strip shape (effective measuring length up to 30m), which has the advantages of low manufacturing cost, convenient installation and use, and the linear expansion coefficient is the same as that of the machine tool; The measurement accuracy is lower than that of the grating scale, and since the magnetic signal strength is continuously weakened with the use time, it is necessary to re-record the magnet, which is inconvenient for use.

(4) Inductive synchronizer

The advantages of the inductive synchronizer are low manufacturing cost, convenient installation and use, and low requirements on working environment conditions; the disadvantage is that the signal processing method is complicated, and the measurement accuracy is limited by the measurement method (the measurement accuracy of the conventional measurement method is about 2 to 5 μm) .

Sensors can be divided into analog and digital types according to different signal output methods. Digital sensors can be divided into incremental, absolute and signal modulation.

In the computer test system, the output signal of the analog sensor needs to be digitized by analog-to-digital converter (A/D), and the cost of A/D conversion is high at high resolution, and the small analog signal is solved. The anti-interference problem of microvolts is also quite difficult.

In digital sensors, absolute encoders can output parallel digital signals without the need for A/D conversion, making it easy to interface with a computer. However, with the improvement of measurement accuracy, the cost of absolute encoders is also higher and higher, even higher than the cost of high-precision A/D conversion, so it is difficult to be accepted in many practical applications. Incremental sensors and signal-modulated sensors have lower manufacturing costs and stronger anti-interference ability, and can be used to greatly improve the resolution by subdividing without changing the engraving density of the encoder. Therefore, in the accuracy measurement of the transmission chain. These two types of sensors are the most used. Common incremental sensors include grating incremental encoders, magnetic grid sensors, capacitive encoders, etc.; signal modulation sensors are mainly inductive synchronizers, laser interferometers, seismographs, resolvers, and the like.

3. Dynamic measurement method of machine tool transmission error

The basic measurement principle of transmission error: Let θ1 and θ2 be the displacements of the input and output shafts (angular displacement or linear displacement) respectively. The theoretical transmission ratio between input and output is i. If θ1 is used as the reference, the actual displacement of the output shaft. The difference from the theoretical displacement is the transmission chain error δ, ie δ = θ2 - θ1/i. According to the different measurement methods of the displacement signals θ1 and θ2, the transmission error measurement methods can be divided into two types: the phase measurement method and the counting method.

3.1 Machine tool transmission error ratio phase measurement method

The phase relationship between the output signals θ1, θ2 of the two sensors reflects the transmission error of the drive train. When the transmission error TE=0, that is, the transmission ratio is constant, a constant phase relationship is maintained between θ1 and θ2; when the transmission ratio i changes, the phase relationship between θ1 and θ2 also changes. The phase comparison method measures the transmission error TE indirectly by measuring the phase relationship between θ1 and θ2. With the development of digital technology and computer technology, the phase measurement method has experienced the development process from analog phase to digital phase to digital phase to computer digital phase.

(1) Analog phase method

The commonly used trigger phase meter uses the analog phase comparison method. The principle of analog phase comparison: after the two signals are divided, they become the same frequency signal and enter the specific phase meter. The time difference Δt between them depends on the phase difference δ(t) between θ1 and θ2. After being identified by the bistable flip-flop, Δt is converted into an analog quantity Δu corresponding to the duty ratio of the phase rectangular wave, and the change of the duty ratio reflects the transmission error of the transmission chain.

The analog phase measurement system has the following problems: 1δ(t) is a periodic function with a period of 2π and a certain law. Let f be the phase change frequency and ω=2πf be the angular frequency, then δ(t)=δ( Ωt). When the two signals are in phase, the phase measurement is a repeated measurement with a period of 1/f. From the condition 0 ≤ δ(ωt) ≤ 2π, Δu has a linear relationship with δ(t). Since δ(ωt) changes periodically, it is required that the time constant τ of the analog recording head is smaller than the period of the measured change phase difference, that is, τ ≤ 1/f, otherwise, when an accurate reading has not been obtained in the previous phase change period, The latter cycle has begun to repeat, so that the phase difference change cannot be recorded in real time. Therefore, the dynamic measurement performance of the analog phase comparison method is poor, and it cannot meet the dynamic measurement requirements of real-time analysis processing. 2 The measurement resolution and the measurement range are mutually constrained. If the resolution is increased, the range is reduced. To do this, the range selection circuit needs to be configured, and the phase difference of the measured signal must be less than 360°. 3 It is required to enter the same frequency of the two signals than the phase meter, that is, only the same frequency ratio phase can be performed. Therefore, the frequency division/multiplier of the two signals must meet the transmission ratio change requirement, the circuit structure is complex, and the anti-interference ability is poor. The range is small.

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