Around 1920s, people began to discuss the problem of gear accuracy measurement. In 1922, Switzerland applied for the patent of the first industrial gear involute inspection instrument. The instrument adopts the method of measuring the involute tooth surface developed along the base circle, which is praised as ingenious conception; In 1923, the involute measuring instrument with fixed base disc structure was formally introduced into the industry, and it was a great success because of its simple and reliable structure. Since then, there have been mechanical and electronic gear measuring instruments with adjustable base circle structure; Nowadays, the high-performance coordinate CNC gear measuring center has become the leading instrument for gear accuracy detection (see Figure 1). In addition to the CMM with rectangular coordinate system, most of the involute profile measurement methods adopted by the four axis CNC special gear measuring instrument with rotary axis follow the measurement principle of involute profile formed by base circle generation (see Figure 2).
According to the current gear accuracy standard, the single gear accuracy evaluation index can be divided into two categories: Geometric single error and kinematic comprehensive error; In addition, there is the overall gear error which has not been recognized in the gear accuracy standard and was put forward by our country in the 1970s. It is the third kind of single gear accuracy evaluation index developed by Huang tongnian of Chengdu Tool Research Institute, a group of domestic scientific research scholars and engineering technicians in the field of, in the process of studying the internal relationship between gear single geometric error and gear motion comprehensive error. According to this index, a series of gear overall error measuring instruments have been successfully developed and mass produced, which have been widely used in China’s gear manufacturing industry and sold abroad (see Figure 3).
Based on the basic circle generating measurement principle of involute gear profile error, according to the concept and method of gear motion geometric error measurement, the internal relationship between the accuracy system and index of these three kinds of single gear is discussed from another angle.
As a geometric entity of a transmission element, the motion accuracy of a single gear is only determined by its own geometric accuracy when the accuracy quality of the gear is studied. Based on this fact, the kinematic geometry measurement of single gear error is carried out.
When measuring the tangential comprehensive error or the overall error of the gear, the gear to be measured is meshed with the measuring gear / worm / rack and other measuring elements whose geometric accuracy is much higher than that of the gear to be measured to form a gear measuring pair. The gear to be measured is driven by single-sided meshing in the form of rotation rotation or rotation linear movement, and the geometric accuracy of the gear to be measured is tested. By means of the rolling detection of the gear measuring pair, the motion error, such as the tangential comprehensive error of the gear or the overall error of the gear single section, is determined by the geometric accuracy of the gear entity. In particular, it is worth noting that the measurement results in the single point meshing area of the gear with overlap coefficient of 1 can correctly reflect and represent the tooth profile error of the detected tooth surface in the range of the single section error measurement without considering the influence of the tooth width, so as to realize the conversion of the tooth profile motion error to the tooth profile geometric error.
The overall gear error measurement technology studies the relationship between the gear tangential comprehensive error and the gear single geometric error, and develops a measuring element with special structure for measuring worm / measuring gear, so that the measuring element and the gear to be measured are in one-sided meshing motion, and the rolling measurement is within the full meshing range of the gear profile to be measured, It is ensured that only a certain point on the tooth surface of the gear to be measured is meshed with the special measuring element, so as to realize the point scanning measurement of meshing and rolling of the tooth profile geometric error along the determined trace on the tooth surface of the gear to be measured. In other words, in the whole process of rolling point scanning measurement, the meshing overlap coefficient of the gear to be measured and the measuring element (such as measuring worm or measuring gear) is 1, which can ensure and realize the accuracy measurement of the tooth profile (a trace) in the whole working range.
Scholars from Germany, Japan and the former Soviet Union also conducted similar research in the 1970s and 1980s, trying to construct the static comprehensive motion error or the static overall error of gear from the single geometric error of gear, and interpret the correlation between gear accuracy systems from the opposite direction. Figure 4 shows the intermittent motion error curve of the gear (single section) measured by the former Soviet Union scholars with the double probe involute measuring device.