Abstract: The planetary gears of RV reducers require that the internal spline teeth and external involute teeth be in phase. A precision-positioned internal spline tooth profile positioning tapered mandrel is used to eliminate the geometric eccentricity caused by the internal spline hole gear. Combined with hard-cut precision-broached internal spline teeth, and through effective and practical inspection techniques, the high precision and interchangeability of the planetary gears can be ensured, making them compatible and simplifying the machining process and reducing the defect rate.
Keywords: planetary gears, internal spline tooth profile locating tapered mandrel, geometric eccentricity, universal fit, interchangeability
The cycloidal pinwheel reducer was first proposed by the German Lorenz Brown as a low-tooth planetary transmission mechanism, also known as a cycloidal pinwheel planetary gear transmission. The RV transmission evolved from the traditional cycloidal planetary transmission and boasts advantages such as compact structure, long lifespan, light weight, large transmission ratio, small angular transmission error, low vibration, and small size. Industrial robots typically perform repetitive actions to complete identical processes; to ensure reliable task completion and process quality during operation, the positioning accuracy and repeatability of industrial robots are particularly high. The RV reducer meets the high-precision operation requirements of robots and is the most critical component among all core parts of industrial robots.
I. Technical Requirements for Planetary Gears in RV Reducers (Part Drawings, Crankshaft Assembly Images, Gear Transmission Images)
Figure 1 Planetary gear mechanism
Figure 2 Gear backlash
The RV reducer utilizes the differential planetary transmission principle. The first stage is an involute cylindrical gear planetary transmission mechanism, and the second stage is a cycloidal pinwheel planetary transmission mechanism. The crankshafts in the planetary gears and the second-stage transmission mechanism are connected by splines. As shown in Figure 1, the three planetary gears form a group and move in tandem. Therefore, the internal and external splines of the planetary gears require precise phase positioning, and the phase positions of the internal and external teeth of the three planetary gears must be consistent.
For example, the transmission loss of a cycloidal pinwheel precision transmission reducer is required to be less than 1 arcsecond. The design accuracy is taken as 1/2, that is, 0.5 arcseconds. Then, the first stage planetary gear transmission is allocated 1/3. Therefore, the transmission loss should be less than 10 arcseconds. Considering the influence of the first stage planetary gear transmission loss on the output end, it is 1/i2 of the second stage transmission, that is, Δθ1/i2.
Therefore, the maximum angular loss of the first-stage planetary gear transmission is Δθ1 = 10″xi2 (assuming i2 = 40°).
=400″(arc second)
=0.111° (angle)
Take the planetary gear pitch circle diameter d1 = 60mm
The allowable tooth thickness backlash is ΔWk = d1/2 * sinΔθ1 = 0.058 mm.
The concentricity of the input shaft should be less than 0.03mm, and the tooth thickness tolerance of the planetary gear and input gear should each be 0.02mm.
As shown in Figure 2, ΔWk = 0.058 ≈ 0.06 mm, and we take 0.06 ± 0.02.
Taking 190BX-121 as an example: R2=30, R1=7.25, then P1=1/4*ΔWk=0.015mm.
Phase angle α between the internal and external spline teeth of the planetary gear:
α = 0.015/R² = 0.0005 (radians) = 0.028° = 1.68′ (minutes)
Therefore, P2 = 1/4 * P1 = 0.00375 mm
Therefore, the tolerance of the common normal dimension of the internal spline needs to be controlled within 0.00375mm, which is almost an impossible goal to achieve.
II. Manufacturing Process of Planetary Gears
The phase angle between the internal spline teeth and external teeth of each planetary gear set is required to be less than 0.028°. The accuracy of the involute external teeth is grade 7 (GB/T10095-2008), and the common normal tolerance of the internal spline teeth is less than 0.00375mm. This poses a challenge to the machining of planetary gears, and conventional machining processes can no longer meet the requirements. It is necessary to adopt an economical tolerance grade 7 (IT7) to facilitate mass production. The two directions to consider are the use of internal spline teeth zero-backlash positioning and group machining. Therefore, the machining of planetary gears for reducers needs to solve the positioning problem of the internal spline teeth and the positioning problem of the phase consistency between the internal and external teeth.
Discussion on processing methods
The process is carried out in groups, that is, three planetary gears are processed in a group, and the internal splines are drawn, the external gears are roughed, carburized and quenched, and the external gears are precision rolled at the same time. The combination method is generally either an integral whole or a single piece group (Figure 3).
The method of using a single, integrated design involves machining the entire assembly, then dividing it into smaller pieces for further machining, and finally marking them. The method of using individual pieces in groups involves marking them after machining to distinguish them. Both methods solve the problem of ensuring the phase consistency of the internal and external teeth of each gear group.
Figure 3
When planetary gears are machined using a single-piece method, it is necessary to consider the consistency of the phase of the internal and external teeth and the tooling for zero-backlash centering of the internal spline teeth. The tooling requires good consistency in clamping, reliable positioning and centering, and is difficult to manufacture with high precision requirements.
Table 1 shows a comparison of the advantages and disadvantages of various processing methods.
Table 1 Comparison of various processing methods
B) Internal spline machining process
Planetary gears typically employ involute splines, and the gear material is low-carbon alloy steel, such as 20CrMo or 20CrMnTi. The internal splines are formed by broaching. After rough hobbing, the gears generally require carburizing and quenching. After heat treatment, the gears will deform. Taking the 190BX-121 planetary gear as an example, after carburizing and quenching, the deformation of the internal splines is approximately 0.02mm, with the inner hole, tooth profile, and tooth surface all deforming by about 0.02mm. Therefore, ensuring that the change in the common normal dimension of the internal spline teeth is within 0.00375mm is virtually impossible. The cumulative error from heat treatment deformation, broach wear, tooling errors, etc., far exceeds 0.00375mm, and is also greater than the IT7 tolerance.
The process of precision drawing internal splines after heat treatment is essential. After the planetary gears are carburized and quenched, the two planes are ground to a flatness within 0.01mm. A heat-hardened broach is used, with the broach material being powdered high-speed steel with a TiN coating. The broaching machine is a heat-hardened precision broaching machine from manufacturers such as Nachi and Sanyo. After heat treatment, the hardness of the planetary gears is controlled at HRC45-51. After precision drawing, the tolerance of the common normal dimension of the internal spline teeth can be controlled within ±0.01mm, which greatly improves the accuracy of the internal spline teeth, reaching IT7 grade or above, laying the foundation for subsequent precision machining of the external teeth.
Precision positioning internal spline tooth profile positioning tapered mandrel machining process
The group-based machining method and the internal spline precision broaching process mentioned above do not actually solve the problem of precision positioning and machining of the external teeth of planetary gears using internal splines. Since the common normal tolerance of internal splines cannot be guaranteed to be within 0.00375mm, it is generally controlled at IT7 grade. To ensure the accuracy of the planetary gears and the phase consistency of the internal and external teeth, specialized tooling design is an effective approach. Using a "precision positioning internal spline positioning tapered mandrel machining" is an effective method, as shown in Figure 4.
Figure 4
1) Tapered mandrels eliminate centering errors;
2) The spindle is precisely positioned to correspond to the gear markings, ensuring phase consistency;
3) Combine automated production, CNC machining, and precision guidance to improve production efficiency;
4) Planetary gears are interchangeable, reducing losses and lowering costs;
5) The planetary gear internal splines and the crankshaft spline tolerance are manufactured according to the economic tolerance grade IT7. The gear and crankshaft splines adopt a transition fit. The front end spline of the crankshaft is ground with a guide part to ensure a precise fit between the internal and external splines (Figure 5).
Figure 5 Crankshaft and planetary gear assembly
III. Planetary Gear Inspection Technology
The accuracy of planetary involute external gears includes tooth profile Fa, tooth direction Fβ, tooth runout Fr, cumulative pitch error Fp, fpt, etc. Planetary gears are installed in tapered mandrels and can be measured using a gear measuring center. The common normal length Wk is measured using a common normal micrometer.
The internal spline is formed by broaching. It is necessary to measure the common normal length Wk or the span M value of the internal spline teeth, as well as the phase position of the internal spline teeth and the external involute teeth. Because the internal spline teeth use a small module m≤1.5, the major diameter is generally less than φ30, which is difficult to measure using common measuring instruments.
Involute internal splines are usually inspected using spline go/no-go gauges, which only make a simple "Go" or "NoGo" judgment, but cannot determine the actual size of the spline teeth.
Based on the special requirements of planetary gears in RV reducers, Harbin Zhida Measurement & Control has developed a gear measurement center with a Z-series fully digital 3D probe and probe management system. Equipped with specialized measurement software, it can measure various elements of planetary gears in RV reducers, including the accuracy of external involute gears (Fp, Fα, Fβ, Fr, etc.), the M value of internal spline teeth, cumulative pitch deviation Fp, and the phase position of internal and external teeth, thus meeting the measurement requirements of planetary gears in RV reducers.
Conclusion:
The planetary gears of RV reducers are manufactured using a precision-positioned internal spline tooth profile tapered mandrel, which can eliminate centering errors, ensure phase consistency, improve production efficiency, reduce losses, and lower costs.
Single-piece processing can improve product interoperability and achieve higher processing accuracy.
After heat treatment, the internal spline is precision drawn and the external involute teeth are precision scraped, which can eliminate heat treatment deformation and improve product precision.
