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Research on deviation correction of curve-surface gear in solar alpha rotary joint processed by free form milling

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Abstract

Due to the characteristics of large bearing capacity, small sliding ratio, and error adaptability, curve-surface conjugate gear drives are utilized in the novel Solar Alpha Rotary Joint of China Space Station to ensure the posture of solar panels. However, conventional precision processing techniques face challenges in generating high-precision curve-surface gears due to the unique tooth surface geometry and non-envelope configuration principle. Fortunately, the advantages of free-form milling have made it possible to achieve precision manufacturing of curve-surface gears. Based on the geometric errors of machine tool and tool deformation, a novel deviation correction method is proposed for tooth surface reconstruction. Firstly, the design and construction methods for curve-surface conjugation are presented, along with the development of a mathematical model for curve-surface gear. The processing error model considering geometric errors of machine tool and tool deformation is established. Then, the mirror image method is introduced to derive the deviation correction model based on processing errors, and the simulated modification values are obtained. Finally, processing tests are conducted to verify the effectiveness of the proposed deviation correction method, resulting in an improvement in gear accuracy from quality class 8 to class 4.

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Abbreviations

Γ 1, Γ 2 :

Conjugate curves

Σ 1, Σ 2 :

Curve-surface conjugate surfaces

σ 0, σ p :

Fixed coordinate systems of gear drive

σ 1, σ 2 :

Movable coordinate systems

ω 1, ω 2 :

Angular velocities of gear pair

φ 1, φ 2 :

Rotation angles of gear pair

a :

Center distance of gear pair

u, v :

Surface parameters of involute surface

r b2 :

Base radius of internal gear

p 2 :

Lead of internal gear

n 2 :

Normal vector of internal gear

v 2 12 :

Relative velocity

M12 :

Coordinate transformation matrix from σ2 to σ1

Γ h :

Equidistant curve

Σ h :

Tubular surface of curve-surface gear

h i :

Equidistant distance

φ, α :

Surface parameters of tubular surface

σ M :

Fixed coordinate system of machine tool

σ T :

Fixed coordinate systems of tool

σ W :

Fixed coordinate systems of workpiece

T01 :

Ideal transformation matrix from machine bed to Z-axis

T’01 :

Actual transformation matrix from machine bed to Z-axis

T12 :

Ideal transformation matrix from Z-axis to C-axis

T’12 :

Actual transformation matrix from Z-axis to C-axis

T23 :

Ideal transformation matrix from C-axis to workpiece

T’23 :

Actual transformation matrix from C-axis to workpiece

T04 :

Ideal transformation matrix from machine bed to X-axis

T’04 :

Actual transformation matrix from machine bed to X-axis

T45 :

Ideal transformation matrix from X-axis to Y-axis

T’45 :

Actual transformation matrix from X-axis to Y-axis

T56 :

Ideal transformation matrix from Y-axis to B-axis

T’56 :

Actual transformation matrix from Y-axis to B-axis

T67 :

Ideal transformation matrix from B-axis to spindle

T’67 :

Actual transformation matrix from B-axis to spindle

T78 :

Ideal transformation matrix from spindle to tool

T’78 :

Actual transformation matrix from spindle to tool

V T, V W :

Orientation of tool and workpiece

T ideal :

Ideal transformation matrix from tool tip to workpiece

T actual :

Actual transformation matrix from tool tip to workpiece

∆ e, ∆v :

Position and orientation errors of tool tip

T E :

Simplified geometric errors matrix

F :

Milling force

σ f :

Coordinate system of milling force

f x, f y, f z :

Components of milling force in σf

δ 1 :

Deformation of tool arbor

δ h :

Deformation of tool bit

δ a :

Angle deformation of tool arbor

L :

Total length of tool

L h :

Length of tool bit

R :

Radius of tool

I 1, I 2 :

Moment of inertia of tool arbor and tool bit

δ xf, δ yf :

Components of tool deformation in σT

δ f :

Tool deformation in σW

P 0 :

Ideal data matrix of tooth surface

P 1 :

Actual data matrix of tooth surface

ΔE 1 :

Geometric error matrix of P1

δ 1 :

Tool deformation matrix of P1

Δε 1 :

Normal error matrix of P1

M 1 :

Mirror matrix of P1

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Funding

The research work in this article was supported by the Major Projects in Aviation Engines and Gas Turbines (J2019-IV-0001–0068) and the National Natural Science Foundation of China (Grant No. 52075053).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, 400030, People’s Republic of China

    Xinxin Ye, Luhe Zhang, Zhaoyang Li & Bingkui Chen

  2. Shanghai Aerospace System Engineering Research Institute, Shanghai, 201109, People’s Republic of China

    Jingming Jiang

  3. China Electronics Technology Group Corporation No.26 Research Institute, Chongqing, 400030, People’s Republic of China

    Rongrong Liu

Authors
  1. Xinxin Ye
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  2. Luhe Zhang
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  3. Jingming Jiang
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  4. Rongrong Liu
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  5. Zhaoyang Li
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  6. Bingkui Chen
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Contributions

Conceptualization: L. Z., B. C. Methodology: Z. L., B. C., R. L. Validation: X. Y., L. Z., J. J.

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Correspondence to Luhe Zhang.

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Ye, X., Zhang, L., Jiang, J. et al. Research on deviation correction of curve-surface gear in solar alpha rotary joint processed by free form milling. Int J Adv Manuf Technol 129, 4149–4164 (2023). https://doi.org/10.1007/s00170-023-12568-7

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  • DOI: https://doi.org/10.1007/s00170-023-12568-7

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