A compensation method for the eccentricity and inclination errors of spiral bevel gear based on improved ICP algorithm

The coordinate system in the measurement of spiral bevel gear (SBG) by gear measuring center (GMC) is discussed and the misalignment between the actual coordinate system and the theoretical coordinate system of the SBG is analyzed. The misalignment will cause the measurement error and cannot be neglected in the SBG precision measurement. To calculate the misalignment and accurately establish the actual coordinate system, a novel re-fitting method by the measured positions of eight tooth surfaces is proposed. First, eight sets of gear axis direction vectors and original points can be obtained from the measurement of eight tooth surfaces, by the single tooth surface matching (SSM) method. Second, the actual axis vector and original point of the gear can be obtained, by re-fitting those eight sets of gear axis vectors and original points. Then, the actual coordinate system can be established by the actual gear axis direction vector and the original point. The least square method is used to calculate the original point, and a basis vector fitting method is proposed to solve the gear axis direction vector. Finally, two groups of preset coordinate system deviation tests are carried out to verify the accuracy and feasibility of the fitting algorithm. The results show that the fitting error of the original point is far less than 1×10^(-1) μm and the fitting error of the angle is far less than 1×10^(-7) degree, which are superior to the design accuracy of the GMC. Therefore, the proposed algorithm can be applied for improving the measurement accuracy of current GMC.

Section: Introductionmentioning

confidence: 99%

A method for determining the actual coordinate system of spiral bevel gears by the measured positions of eight tooth surfaces

Zhou,

Fang,

Liu

et al. 2024

“…After Besl and McKay proposed the iterative closest point (ICP) algorithm [12], surface matching is utilized to realize the fitting of two surfaces and the calculation of 6 degrees of freedom in space [13,14]. An improved ICP algorithm was proposed to solve the mismatch between the measured tooth surface and the theoretical tooth surface [15]. Based on the study of existing surface matching, the co-authors of this paper proposed a tooth surface matching method (noted as SSM) to compensate the alignment angle error [16], in which the measurement point matching problem was resolved and the ICP algorithm was improved.…”

Section: Introductionmentioning

confidence: 99%

Compensation method of the spiral bevel gear tooth surface error based on eight tooth-surface fitting

Zhou,

Fang,

Liu

et al. 2024

Self Cite

The misalignment error between the gear theoretical coordinate system and actual gear coordinate system is illustrated, as well as its influence on the measurement of tooth surface deviation is discussed. On the analysis of the tooth convex and concave surface error measurement process, the measured points in the theoretical coordinate system are transformed from the actual measured points in the actual coordinate system. Then, an eight tooth-surface fitting method is utilized to calculate the misalignment error and the compensation method is given. Finally, actual measurements of three different spiral bevel gears are analyzed, and the misalignment error are calculated. Using the proposed compensation method, both the eccentricity and tilt are compensated to some extent. And the machining suggestions of each spiral bevel gear are also given according to its compensated tooth surface error distribution.

“…Liu et al [4] designed an accurate matching method between theoretical surface and measured surface of a spiral bevel gear by using an iterative search method. Liu et al [5] pointed out that the deviation between the theoretical surface and the actual surface will affect the measurement results of the flank, and proposed a method to register the theoretical and actual surfaces. The method can compensate for the eccentricity and inclination errors.…”

Section: Introductionmentioning

confidence: 99%

A model construction and measurement method for tooth surface deviation of spiral bevel gear based on a one-dimensional probe

Dai¹,

Li²,

Zhang³

et al. 2023

The accurate measurement of tooth surface deviation is an important prerequisite for the quality monitoring of high-precision spiral bevel gear. A measurement method for tooth surface deviation of spiral bevel gear is proposed based on one-dimensional probe, which can accurately measure and evaluate tooth flank. According to the forming principle of spiral bevel gear tooth surface, the theoretical surface is constructed as the measurement reference flank. A series of measures and methods are adopted to ensure the accuracy and correctness of one-dimensional probe measurement. These effective methods include the construction of the precise positioning of the gear blank and its surface, the measurement planning of reduction dimension which the gear needs to rotate once the normal angle after each point is measured, and the compensation for the increasing dimension of the one-dimensional probe. In addition, the minimization of the normal deviation of the tooth flank is achieved by using the optimum matching technique of the theoretical and the actual surfaces. The deviation degree of the actual surface relative to the theoretical surface can be accurately calculated and evaluated by establishing deviation model, which ensures the correctness for the evaluation result of the deviation. Finally, the test of tooth surface deviation is carried out on JD45 + gear measuring center using one-dimensional probe and Gleason 650GMS gear measuring center using three-dimensional probe, respectively. The measurement results show that the evaluation results of one-dimensional probe are in good agreement with those of three-dimensional probe. The proposed theory and method not only expand the measurement range of gear measuring center using one-dimensional probe, but also have certain reference significance for the precision measurement of other complex surfaces.