CN105300691B - Bevel Gear Transmission error measurement method based on best locating distance - Google Patents
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Abstract
基于最佳安装距的锥齿轮传动误差测量方法，包括步骤：(1)将锥齿轮副以设计安装距安装在测量系统旋转主轴的前端进行单面啮合测量，改变小轮安装距，在多个点位上进行测量，获取锥齿轮副的最佳安装距；(2)在得到锥齿轮副的最佳安装距后，在该位置上进行单面啮合测量并绘制传动误差曲线；(3)在传动误差曲线上通过计算提取到四项基本偏差，并根据精度标准进行精度等级的评定；(4)对传动误差进行快速傅里叶变换、逆快速傅里叶变换等计算，获取其它几条偏差曲线，对齿轮副的传动质量进行进一步分析。本发明对传动误差曲线进行计算、分析，得到多项单项偏差和曲线，能够更加准确地评价锥齿轮副的传动质量。
The method of measuring the bevel gear transmission error based on the optimal installation distance includes the following steps: (1) Install the bevel gear pair at the front end of the rotating main shaft of the measurement system with the designed installation distance for single-sided meshing measurement, change the small wheel installation distance, Measure at the point to obtain the optimal installation distance of the bevel gear pair; (2) After obtaining the optimal installation distance of the bevel gear pair, perform single-sided meshing measurement at this position and draw the transmission error curve; (3) in Four basic deviations are extracted from the transmission error curve through calculation, and the accuracy level is evaluated according to the accuracy standard; (4) Fast Fourier transform, inverse fast Fourier transform and other calculations are performed on the transmission error to obtain other deviations The curve is used to further analyze the transmission quality of the gear pair. The invention calculates and analyzes the transmission error curve, obtains multiple individual deviations and curves, and can more accurately evaluate the transmission quality of the bevel gear pair.
Description
技术领域technical field
本发明涉及精密测试技术与仪器领域，具体涉及一种基于最佳安装距的锥齿轮传动误差测量方法。The invention relates to the field of precision testing technology and instruments, in particular to a method for measuring bevel gear transmission errors based on the optimum installation distance.
背景技术Background technique
锥齿轮传动机构在汽车、直升飞机、机床及电动工具制造业中得到了广泛的应用。锥齿轮副是实现相交轴运动传递的基础元件，其制造精度、质量直接影响机器设备的效率、噪声、运动精度和使用寿命。Bevel gear transmission mechanisms are widely used in automobile, helicopter, machine tool and electric tool manufacturing industries. The bevel gear pair is the basic component to realize the motion transmission of intersecting axes, and its manufacturing accuracy and quality directly affect the efficiency, noise, motion accuracy and service life of the machine equipment.
传动误差是指传动系统输出端的实际位移相对于理论位移的差值。齿轮在加工过程中产生的制造误差、在安装过程中产生的装配误差以及在传动过程中的温度变形和受力弹性变形都将产生传动误差，因此，通过测量传动误差不仅可以评定齿轮传动质量，还可以诊断误差来源。单面啮合测量运动接近于齿轮的使用状态，能够更高效，更精确地对齿轮的传动质量进行检测。The transmission error refers to the difference between the actual displacement of the output end of the transmission system and the theoretical displacement. The manufacturing error generated during the processing of the gear, the assembly error generated during the installation process, and the temperature deformation and force elastic deformation during the transmission process will all produce transmission errors. Therefore, by measuring the transmission error, not only the gear transmission quality can be evaluated, Error sources can also be diagnosed. The single-sided meshing measurement movement is close to the use state of the gear, which can detect the transmission quality of the gear more efficiently and accurately.
采用传统单面啮合法进行传动误差测量时，是采用一个标准齿轮与被测齿轮进行啮合，或是一对锥齿轮副进行啮合。与标准齿轮啮合测量单个锥齿轮或测量一对锥齿轮副时，按照传统方法进行测量是不够精确的。且锥齿轮副的传动平稳性与安装距有很密切的关系，锥齿轮副在最佳安装距的位置进行测量才能得到最准确的测量结果。When using the traditional single-sided meshing method to measure the transmission error, a standard gear is used to mesh with the measured gear, or a pair of bevel gear pairs are meshed. When measuring a single bevel gear meshed with a standard gear, or measuring a pair of bevel gear pairs, traditional methods are not accurate enough. Moreover, the transmission stability of the bevel gear pair is closely related to the installation distance, and the most accurate measurement results can be obtained only when the bevel gear pair is measured at the optimum installation distance.
发明内容Contents of the invention
为解决背景技术中提出的技术问题，本发明提出了一种基于最佳安装距的锥齿轮传动误差测量方法，首先找到锥齿轮副的最佳安装距，然后将锥齿轮副以最佳安装距安装并进行单面啮合测量，得到齿轮副的传动误差信号并进行计算和分析。In order to solve the technical problems raised in the background technology, the present invention proposes a method for measuring the transmission error of bevel gears based on the optimum installation distance. Firstly, the optimum installation distance of the bevel gear pair is found, and then the Install and measure the single-sided meshing, get the transmission error signal of the gear pair, and carry out calculation and analysis.
本发明是采用如下技术手段实现的：The present invention is realized by adopting the following technical means:
基于最佳安装距的锥齿轮传动误差测量方法，其特征在于：包括以下步骤：The bevel gear transmission error measurement method based on the optimum installation distance is characterized in that: comprising the following steps:
1)将锥齿轮副以设计安装距安装在测量系统旋转主轴的前端，在安装距查找的参数设置中对小轮安装距偏移量、查找次数进行设置。然后在设置的各点位上进行单面啮合测量得到锥齿轮副的传动误差曲线，对传动误差曲线进行FFT获取每点传动误差曲线的前三次谐波幅值，再通过对谐波幅值的计算得出锥齿轮副的最佳安装距；1) Install the bevel gear pair at the front end of the rotating main shaft of the measurement system with the designed installation distance, and set the small wheel installation distance offset and search times in the parameter setting of the installation distance search. Then, single-sided meshing measurement is performed on each set point to obtain the transmission error curve of the bevel gear pair, and FFT is performed on the transmission error curve to obtain the first three harmonic amplitudes of the transmission error curve at each point, and then through the harmonic amplitude calculation Calculate the optimal installation distance of the bevel gear pair;
2)在得出锥齿轮副的最佳安装距后，调整两齿轮位置，使齿轮副在最佳安装距啮合，然后进行单面啮合测量，通过安装在旋转主轴上紧邻锥齿轮的圆光栅测得两齿轮的转角值，通过计算得到锥齿轮副的传动误差曲线；2) After obtaining the optimal installation distance of the bevel gear pair, adjust the position of the two gears so that the gear pair meshes at the optimal installation distance, and then carry out single-sided meshing measurement. The rotation angle values of the two gears are obtained, and the transmission error curve of the bevel gear pair is obtained through calculation;
3)对传动误差曲线进行计算，提取出四项单项偏差，分别为齿轮副的切向综合总偏差，齿轮副的一齿切向综合偏差，齿距累积总偏差和单个齿距累积偏差，并进行精度等级评定；3) Calculate the transmission error curve and extract four individual deviations, which are the tangential comprehensive total deviation of the gear pair, the tangential comprehensive deviation of one tooth of the gear pair, the cumulative total deviation of the tooth pitch and the cumulative deviation of a single tooth pitch, and Carry out accuracy grade evaluation;
4)对传动误差曲线进行进一步的计算和分析，得到其它几条偏差曲线，分别为：旋转谐波曲线、齿距累积偏差曲线、平均齿廓误差曲线、长波分量曲线、短波分量曲线、角速度幅值谱、角速度平均误差曲线、角加速度幅值谱、角加速度平均误差曲线。4) Carry out further calculation and analysis on the transmission error curve, and obtain several other deviation curves, which are: rotation harmonic curve, tooth pitch cumulative deviation curve, average tooth profile error curve, long-wave component curve, short-wave component curve, angular velocity amplitude Value spectrum, angular velocity average error curve, angular acceleration magnitude spectrum, angular acceleration average error curve.
所述步骤1)，传动误差的测量要在1)中确定的最佳安装距位置进行。In the step 1), the measurement of the transmission error should be carried out at the optimal installation distance determined in 1).
由于采用了上述技术方案，本发明的有益效果是：Owing to adopted above-mentioned technical scheme, the beneficial effect of the present invention is:
在最佳安装距位置上对锥齿轮副进行测量，为测量结果的准确性提供了有效保证。针对锥齿轮副的传动误差进行单项误差的提取及频域上的分析，能够更精确地对锥齿轮副的传动质量进行评价。The bevel gear pair is measured at the best installation distance position, which provides an effective guarantee for the accuracy of the measurement results. Aiming at the transmission error of the bevel gear pair, the single error extraction and frequency domain analysis can be used to evaluate the transmission quality of the bevel gear pair more accurately.
附图说明Description of drawings
图1锥齿轮传动误差测量方法的流程。Figure 1 Flowchart of the measurement method for bevel gear transmission error.
图2传动误差测量系统框图。Fig. 2 block diagram of transmission error measurement system.
图3传动误差曲线及各单项误差在曲线上的表示。Figure 3 Transmission error curve and the representation of individual errors on the curve.
具体实施方式Detailed ways
为使本发明的目的、技术方案及优点更加清晰，以下结合附图及实施例对本发明做进一步说明。附图说明用于解释本发明方法及实施例。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. The accompanying drawings are used to explain the methods and embodiments of the present invention.
本发明基于最佳安装距的锥齿轮传动误差测量方法的流程如图1所示，本发明的具体实施步骤如下：The present invention is based on the flow process of the bevel gear transmission error measuring method of optimal installation distance as shown in Figure 1, and the specific implementation steps of the present invention are as follows:
首先，参照图2说明本发明的传动误差测量采用的测量系统结构。该测量系统包括一对啮合的锥齿轮副，两个圆光栅测量系统、数据采集卡、驱动装置及控制器。圆光栅测量系统由读数头、DSI接口、细分器相连接组成；驱动装置由主轴电机及驱动器相连接组成；所述一对啮合的锥齿轮副中，小轮由主轴电机驱动，带动与之啮合的大轮转动。两个圆光栅分别测量同轴齿轮的转角值，测得的角度值经读数头、DSI接口和细分器进入数据采集卡中，经过计算得到传动误差的数值。First, referring to FIG. 2 , the structure of the measurement system used in the transmission error measurement of the present invention will be described. The measurement system includes a pair of meshing bevel gear pairs, two circular grating measurement systems, a data acquisition card, a drive device and a controller. The circular grating measurement system is composed of a reading head, a DSI interface, and a subdivider; the driving device is composed of a main shaft motor and a driver; among the pair of meshing bevel gear pairs, the small wheel is driven by the main shaft motor, and drives with it The large wheel that meshes turns. The two circular gratings measure the rotation angle value of the coaxial gear respectively, and the measured angle value enters the data acquisition card through the reading head, DSI interface and subdivider, and the value of the transmission error is obtained through calculation.
第一步，在进行正式的传动误差测量之前，先进行最佳安装距的查找。设置安装距查找的中点、步距和查找点数，在设置的点位按顺序依次进行单面啮合测量，对各点传动误差数据进行FFT，得到每点传动误差幅频谱的前三次齿频谐波幅值，各次谐波幅值均有一个谐波公差值及一个影响因子Q，将各次谐波幅值与谐波公差值相除后乘以相应的Q因子，然后相加，得到齿轮副在该位置的传动质量因数F，将各点的F值进行比较，F值最小的点即为最佳安装距；The first step is to search for the optimum installation distance before conducting formal transmission error measurement. Set the midpoint, step distance and search points of the installation distance search, perform single-sided meshing measurement in sequence at the set points, perform FFT on the transmission error data of each point, and obtain the first three tooth frequency harmonics of the transmission error amplitude spectrum of each point Wave amplitude, each harmonic amplitude has a harmonic tolerance value and an influence factor Q, divide each harmonic amplitude and harmonic tolerance value, multiply by the corresponding Q factor, and then add , get the transmission quality factor F of the gear pair at this position, compare the F values of each point, and the point with the smallest F value is the best installation distance;
第二步，调整锥齿轮副的位置，使大轮、小轮在第一步中找到的最佳安装距位置啮合，进行传动误差的测量。传动误差的测量有两种方式，分别为基于大轮转数的方式和基于啮合整周期的方式。基于大轮转数的方式即为按照参数设置中设置的大轮旋转转数进行传动误差的测量。基于啮合整周期的方式则为大轮小轮都要完成整转的啮合，即旋转转数都为整数，啮合整周期的计算式如下：The second step is to adjust the position of the bevel gear pair so that the large wheel and the small wheel are meshed at the best installation distance found in the first step, and the transmission error is measured. There are two ways to measure the transmission error, one based on the number of revolutions of the large wheel and one based on the full cycle of meshing. The method based on the number of rotations of the large wheel is to measure the transmission error according to the number of rotations of the large wheel set in the parameter setting. The method based on the full meshing cycle is that the large wheel and the small wheel have to complete the meshing of the full rotation, that is, the number of rotations is an integer, and the calculation formula for the full meshing cycle is as follows:
其中：n2为大轮转数，Z1为小轮齿数，X是大小轮齿数的最大公约数。Among them: n 2 is the number of revolutions of the large wheel, Z 1 is the number of teeth of the small wheel, and X is the greatest common divisor of the number of teeth of the large and small wheels.
第三步，测量得到齿轮副的传动误差后，首先进行单项误差的提取和计算，分别得到齿轮副的切向综合总偏差、齿轮副的一齿切向综合偏差、齿距累积总偏差、单个齿距偏差。这四项单项误差在传动误差曲线上的表示如图2所示，各项单项误差的提取算法如下：In the third step, after the transmission error of the gear pair is measured, the individual error is extracted and calculated first, and the tangential comprehensive deviation of the gear pair, the tangential comprehensive deviation of one tooth of the gear pair, the cumulative total deviation of the tooth pitch, and the single error are respectively obtained. Tooth pitch deviation. The representation of these four individual errors on the transmission error curve is shown in Figure 2, and the extraction algorithm of each individual error is as follows:
齿轮副的切向综合总偏差Fi’：F′i＝Max(φ[i])-Min(φ[i]),i＝1,…,N,(μm)The tangential comprehensive total deviation F i ' of the gear pair: F' i =Max(φ[i])-Min(φ[i]),i=1,…,N,(μm)
其中，N是采样点数，i是第i个采样采样点，是第i个采样点上传动误差值；Among them, N is the number of sampling points, i is the i-th sampling sampling point, is the transmission error value at the i-th sampling point;
齿轮副的一齿切向综合偏差 One-tooth tangential comprehensive deviation of gear pair
其中，是将划分为与被测齿轮齿数相同的Z个区间，为第k个齿距角内的圆周位移变动量，式中 in, will be Divided into Z intervals with the same number of gear teeth to be tested, is the circular displacement variation within the kth tooth pitch angle, where
齿距累积总偏差 Cumulative Total Deviation of Tooth Pitch
其中，是每个齿距角的中点误差值构成的数组；in, is an array composed of midpoint error values of each pitch angle;
单个齿距累积偏差 Cumulative deviation of single tooth pitch
其中，是将中相邻各点的差值组成的数组。in, will be An array composed of the difference values of adjacent points in .
第四步，建立公差数据库，在测量软件中查询公差数据库，将第三步中计算得到的各项偏差按照齿轮的分度圆直径和模数在公差数据库中依次进行查找，对各项偏差的精度等级做出评定；The fourth step is to establish a tolerance database, query the tolerance database in the measurement software, search the deviations calculated in the third step in the tolerance database in turn according to the pitch circle diameter and modulus of the gear, and check the tolerances of each deviation Accuracy grades are assessed;
第五步，对传动误差信号进行进一步的频谱分析和滤波分析等处理，得到以下几条曲线：传动误差幅频谱、旋转谐波曲线、齿距累积偏差曲线、平均齿廓误差曲线、长波分量曲线、短波分量曲线、角速度幅值谱、角速度平均误差曲线、角加速度幅值谱、角加速度平均误差曲线。其中旋转谐波曲线和齿距累积偏差曲线只有在基于齿轮副啮合整周期的测量方式下才能得到。各曲线的获得方式如下：The fifth step is to perform further spectrum analysis and filter analysis on the transmission error signal to obtain the following curves: transmission error amplitude spectrum, rotation harmonic curve, tooth pitch cumulative deviation curve, average tooth profile error curve, and long-wave component curve , Shortwave component curve, angular velocity amplitude spectrum, angular velocity average error curve, angular acceleration amplitude spectrum, angular acceleration average error curve. Among them, the rotation harmonic curve and tooth pitch cumulative deviation curve can only be obtained under the measurement method based on the full cycle of gear pair meshing. Each curve is obtained as follows:
传动误差幅频谱：将测定的传动误差数据进行FFT变换，并求出其幅值与频率的关系曲线，并将频率量化为齿频的倍数；Transmission error amplitude spectrum: perform FFT transformation on the measured transmission error data, and obtain the relationship curve between its amplitude and frequency, and quantify the frequency as a multiple of the tooth frequency;
旋转谐波曲线：齿轮副进行整周期啮合时，将传动误差幅频谱的前面齿频的0.8倍范围内的曲线放大显示得到旋转谐波曲线；Rotational harmonic curve: when the gear pair is engaged in the whole cycle, the curve within the range of 0.8 times the front tooth frequency of the transmission error amplitude spectrum is enlarged and displayed to obtain the rotational harmonic curve;
齿距累积偏差曲线：将旋转谐波的各次谐波对应点进行逆傅里叶变换就可以得到齿距累积偏差曲线，在进行逆傅里叶变换时要将大轮和小轮的各次谐波分别进行傅里叶变换，所以会得到两条曲线。两曲线中周期较长的为大轮的齿距累积误差，周期较短的为小轮的齿距累积偏差；Pitch accumulative deviation curve: The pitch accumulative deviation curve can be obtained by inverse Fourier transforming the corresponding points of each harmonic of the rotating harmonic. The harmonics are Fourier transformed separately, so you get two curves. Among the two curves, the one with the longer cycle is the cumulative error of the pitch of the large wheel, and the one with the shorter cycle is the cumulative error of the pitch of the small wheel;
平均齿廓偏差曲线：将传动误差幅频谱中各次谐波对应的点进行逆傅里叶变换，就可以得到平均齿廓偏差曲线。Average tooth profile deviation curve: The average tooth profile deviation curve can be obtained by inverse Fourier transforming the points corresponding to each harmonic in the transmission error amplitude spectrum.
长波分量曲线：将传动误差中的高频成分用低通滤波器去除掉，将信号的截止频率λc设置为齿频λz的0.2倍，即下式中的系数q等于0.2；Long-wave component curve: remove the high-frequency components in the transmission error with a low-pass filter, and set the cut-off frequency λc of the signal to 0.2 times the tooth frequency λz , that is, the coefficient q in the following formula is equal to 0.2;
λc＝q·λz(q<1)λ c =q·λ z (q<1)
短波分量曲线：用传动误差减去长波分量即得到短波分量曲线；Short-wave component curve: subtract the long-wave component from the transmission error to get the short-wave component curve;
角速度幅值谱：将传动误差幅值谱对时间进行的一次微分得到；Angular velocity amplitude spectrum: obtained by first differential of the transmission error amplitude spectrum with respect to time;
角速度平均误差曲线：将角速度幅值谱的各次谐波进行逆傅里叶变换得到；Angular velocity average error curve: obtained by inverse Fourier transform of each harmonic of the angular velocity amplitude spectrum;
角加速度幅值谱：将角速度幅值谱对时间进行的一次微分得到；Angular acceleration amplitude spectrum: obtained by first differentiation of the angular velocity amplitude spectrum with respect to time;
角加速度平均偏差差曲线：将角加速度频谱的各次谐波进行逆傅里叶变换得到。Angular acceleration average deviation difference curve: obtained by inverse Fourier transform of each harmonic of the angular acceleration spectrum.
通过上述实例分析总结出，本发明方法提供了一种在最佳安装距下对传动误差进行测量和分析的方法，最佳安装距的确定保证了测量的准确性，对齿轮副的传动误差也提供了更加精确和详细的分析方法，能够更全面的对齿轮副的传动质量进行分析和评价。上述对典型实例的说明并不用以限制本发明，在不背离本发明的情况下可以进行修改和改进等，其范围在权利要求书以及等同物中进行了限定。Through the above example analysis, it is concluded that the method of the present invention provides a method for measuring and analyzing the transmission error under the optimum installation distance, the determination of the optimum installation distance ensures the accuracy of the measurement, and the transmission error of the gear pair is also A more accurate and detailed analysis method is provided, which can analyze and evaluate the transmission quality of the gear pair more comprehensively. The above descriptions of typical examples are not intended to limit the present invention. Modifications and improvements can be made without departing from the present invention, and the scope thereof is defined in the claims and equivalents.
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| CN109500654B (en) * | 2018-12-14 | 2021-01-01 | 重庆大学 | Error compensation method and system for transmission chain of machine tool |
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