Based on the generating principle of base circle involute, the tooth profile measurement method of involute gear is proposed ° The imaginary measurement of the pressure angle is the tangential contact of the rack (see Fig. 1), and the virtual single-sided meshing linear motion point scanning tooth profile measurement is carried out along a meshing line tangent to the base circle (assuming that the rack motion is the linear motion of the involute unfolding point along the tangent line of the base circle); In the whole measuring process, the contact point between the rack and the tooth profile is a fixed point, that is, the contact point between the traditional generating method probe and the involute tooth profile. Involute error of gear profile under test Δ F causes the imaginary rack to produce the corresponding additional motion displacement Δ s. Among them Δ f = Δ s。 The additional displacement, that is, the tooth profile error, is detected by the displacement sensor connected with the hypothetical measuring rack, which is the detection result of the point probe.

And based on 0 ° The main differences of involute tooth profile generation measurement method are as follows: 1) because the probe tip (measuring ball) radius is smaller (mm level), the conjugate (or induced) curvature radius in measurement is obviously smaller than that in measurement of single-sided meshing motion point, The measurement results will be different due to the envelope difference; ② Due to the different mechanical and electrical performance of the measuring structure and displacement sensor, the measurement results obtained by using the probe to detect the additional displacement caused by the tooth profile error may be different from those obtained by using the thin plate to measure the rack; However, there is no essential difference between them in terms of measuring mechanism. They both move along the same tangent line tangent to the base circle — gear rack meshing pair or virtual gear point probe meshing action line. Under the condition of the measured gear rotating motion, the geometric error of the tooth profile is measured by point scanning in the normal direction of the tooth profile.

The above conditions also apply to the pressure angle α 15 °， twenty °， 22. 5 ° And other solid thin plates are used to measure the condition of the rack when scanning and measuring the tooth profile of the gear to be measured (see Fig. 2). At this time, the angle between the motion direction of the measuring rack and the tangent / meshing line of the base circle is the pressure angle of the rack α; When scanning the points of tooth profile geometric error, the contact measuring point on the measuring rack is no longer just a certain point, but a straight line segment composed of continuously moving and changing contact points on the linear tooth profile of the sheet rack; There is a pressure angle between the measured additional displacement and the normal error of the actual tooth profile α Cosine relationship.

In order to mesh with the involute tooth surface of the gear to be measured (see Fig. 3), the tooth profile error is measured by single-sided meshing rolling point scanning. Compared with the generating method of involute profile error based on the generating principle of base circle, the measuring mechanism of the two methods is similar to the single point meshing measurement of the measuring rack. At this time, the gear profile error is measured Δ F causes additional rotation angular displacement of the sheet measuring gear with the base circle radius of ro Δ If so, then Δ f = Ｒo × Δ  = Δ s。 The additional rotation angular displacement of the slice measuring gear caused by the tooth profile error will be detected by the angular displacement sensor connected with the measuring gear.

By comparing and analyzing the scanning measurement of the straight-line moving point probe of the base circle generating involute tooth profile, the scanning measurement of the straight-line moving point meshing of the slice rack meshing involute tooth profile and the scanning measurement of the rotary rolling point meshing of the slice gear meshing involute tooth profile, it can be seen that the measuring mechanism is the same: when the measured gear is rotating, The measuring point moves along a fixed tangent line of the base circle virtual or solid meshing line (at this time, the point probe / measuring rack makes a linear meshing movement, while the measuring gear / measuring worm makes a rotary meshing rotation); The geometric error of the solid gear tooth surface is measured by the displacement in the normal direction of the tooth profile or the linear or rotary displacement generated by the displacement, that is, the geometric error of the tooth profile is measured along the meshing line. It can be seen that the three measurement methods are essentially the same measurement principle, that is, the principle of gear motion geometry measurement.

In recent years, a new technology, which is different from the traditional (x, Φ) It is a new gear measuring instrument with two axis linkage and “tangential generating” involute measuring mode. Taking the CNC four axis (x, y, Z, z) of Tokyo Technology Instrument Co., Ltd, Φ) Taking the numerical control gear measuring instrument as an example (see FIG. 4A), when measuring the involute error of tooth profile, the (x, y, Φ) The movement mode of three-axis linkage enables the probe tip to move on the end plane along a tangent line (virtual meshing line) of the determined base circle at a certain angle with the vertical central axis y of the gear, and complete the point scanning measurement of the tooth profile according to the generating rules (see Fig. 4b). This kind of measurement form that the probe moves along the meshing line controlled by three-axis linkage is called NDG measurement method, namely “normal generating measurement method”. The instrument has some unique advantages and characteristics, such as reducing the structure size of the instrument in the x-coordinate direction and the range of motion during measurement, which will be conducive to the high-precision measurement and development of large gear, especially the large gear profile error, and the measurement of small module gear and internal gear profile error. The traditional TDG measurement method (tangential generating method) and NDG measurement method (normal generating method) belong to the category of motion geometry measurement method of gear error.

According to the gear overall error measurement technology, using special measuring worm or special measuring spur gear, the tooth profile error of gear end section can be measured quickly and accurately by scanning the meshing motion points under the condition of staggered axis or parallel axis meshing and rolling respectively. The CZ150 worm type gear overall error meter produced by Chengdu Tool Research Institute and the gear type rolling point scanning measuring meter produced by frenco of Germany have been recognized by the market (see Fig. 5 and Fig. 6).