Mathematical Modeling and Kinematics Analysis of Double Spherical Shell Rotary Docking Skirt

Transcription

1 MATEC Web of Conferences 114, 41 (217) DOI: 1.11/ matecconf/ MAE 217 Mathematical Modeling and Kinematics Analysis of Double Spherical Shell Rotary Docking Skirt Haixia Gong 1, Zhe Liu 1,a and Liquan Wang 1 1 School of Mechanical and Electrical, Harbin Engineering University, 11, China Abstract. In order to solve the problem of large trim and heel angles of the wrecked submarine, the double spherical shell rotating docking skirt is studied. According to the working principle of the rotating docking skirt, and the fixed skirt, the directional skirt, the angle skirt are simplified as the connecting rod. Therefore, the posture equation and kinematics model of the docking skirt are deduced, and according to the kinematics model, the angle of rotation of the directional skirt and the angle skirt is obtained when the wrecked submarine is in different trim and heel angles. Through the directional skirt and angle skirt with the matching rotation can make docking skirt interface in the ~2γ range within the rotation, to complete the docking skirt and the wrecked submarine docking. The MATLAB software is used to visualize the rotation angle of fixed skirt and directional skirt, which lays a good foundation for the development of the control of the double spherical shell rotating docking skirt in future. 1 Introduction At present, underwater space station docking, marine life-saving are widely used underwater docking technology [1]. Underwater rescue mainly relies on life-saving vehicle equipped with docking skirt active docking wrecked submarine. Docking skirt becomes bridge of connection life rescue vehicle and the wrecked submarine. Most of the initial life-saving vehicle take a fixed docking skirt [2-3]. In recent years, foreign countries has developed rotating docking skirt [4]. Based on the working principle of rotating docking skirt. In this paper, a mathematical model is established and a kinematic model is derived, and finally verifies the correctness of the theoretical analysis by MATLAB. 2 The working principle of rotating docking skirt Double spherical shell rotating skirt consists of three parts: fixed skirt, directional skirt and angle skirt [], as is shown in Figure 1. Fixed skirt and life-saving vehicle is fixed connection, play the role of connecting directional skirt and life-saving vehicle. The directional skirt and angle skirt are respectively the upper and lower part of the spherical shell, the angle between the rotation axis of the directional skirt and the rotation axis of the angle skirt is γ, in which the directional skirt can revolve around shaft, angle skirt can revolve around shaft. Through the directional skirt and angle skirt with the matching rotation can make docking skirt interface in the ~ 2γ range within the rotation, as shown in Figure 2. a Corresponding author : @qq.com The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4. (

2 MATEC Web of Conferences 114, 41 (217) DOI: 1.11/ matecconf/ MAE 217 Fixed skirt γ Directional Skirt Angle skirt 2γ Figure 1. Composition of rotary docking skirt Figure 2. Rotation condition of the rotary docking skirt 3 The establishment of the position matrix of the rotating docking skirt In order to facilitate deduction, this paper establishes a unified system. The midpoint of the contact plane of the fixed skirt and the directional skirt is O 1, Y 1 s forward direction is forward direction of the lifeboat, Z 1 s forward direction is vertical downward, X 1 s forward direction is perpendicular to the plane of the Y1Z1 and points to the inside. In order to facilitate the subsequent calculation, here making the global coordinate system OXYZ and coordinate system O 1 X 1 Y 1 Z 1 coincidence. The intersection of the axis Z 1 and the lower plane of the directional skirt is O 2, the intersection of the axis and the lower plane of angle skirt is O 3, the intersection of the axis and the axis is O 4, the intersection of the axis and the lower plane of the angle skirt is O, the center of docking skirt interface is O 6 ; We postulate the length of O 1 O 2 is D 1 and O 2 O 3 is D 2, and also postulate the length of O 3 O 4 is D 3 and O O 6 is D 4. The interface center of wrecked submarine is O n, as is shown in Figure 3. θ1 X1 O1 Y1 D1 Z1 γ 1 D2 γ 2 θ2 Docking interface of docking skirt O3 X Z2 X3 O2 Y3 Z3 γ 3 D3 Y2 X4 X2 O Y O4 Y4 Z D4 Z4 Docking interface of wrecked submarine On Xn Zn Yn Figure 3. Rotary docking skirt docking motion coordinate system 2

3 MATEC Web of Conferences 114, 41 (217) DOI: 1.11/ matecconf/ MAE 217 Here is the position transformation matrix of coordinate system O 1 X 1 Y 1 Z 1 to O 6 X 6 Y 6 Z 6 [6-8], the parameters are shown in Table 1. T Rot( Z, ) Trans( Z, D ) Rot( X, ) Trans( Z, D ) Rot( X, ) Trans( Z, D ) Rot( Z, ) Trans( Z, D ) Rot( X, ) Trans( Y, D ) nx ox ax px ny oy ay p y T T T T T T T nz oz az pz (1) (2) Table 1. Parameters in the coordinate system serial number of the link γ i /( ) θ i /( ) D i /mm 1 θ 1 D 1 2 -γ 1 D 2 3 γ 2 D 3 4 -γ 3 θ 2 D 4 D In equation: a ( cossin sin cos cos cos sinsin sin cos )sin x (sin cos sin sinsin cos )cos a ( sinsin cos cos cos cos cos sin sin cos )sin y ( cos cos sin cossin cos )cos (3) (4) a ( sin cos cos cos sin cos )sin (sin sin cos cos )cos () z p x p y [( cossin sin cos cos cos sin sin sin cos )cos sin cos sin sin sin sin cos sin )] D (sin cos sin sin sin cos ) D (sin1cos1sin2 sin1sin1cos 2) D3 sin1sin1d2 [( sinsin cos cos cos cos cos sin sin cos )cos ( cos cos sin cos sin cos )sin ] D ( cos cos sin cos sin cos ) D ( cos cos sin cos sin cos ) D cos1sin1d (6) (7) pz [( sin1cos2cos2cos3 cos1sin2cos2cos 3) (sin1sin2sin3 cos1cos2sin 3)] D (sin sin cos cos ) D (sin sin cos cos ) D cos D D (8) 4 Analysis on the Movement of Rotary Docking Skirt In this article, γ 2 =9. so a x, a y and a z can be simplified as: a cossin sin sinsin cos sin sincos cos (9) x

4 MATEC Web of Conferences 114, 41 (217) DOI: 1.11/ matecconf/ MAE 217 a sinsin sin cossin cos sin coscos cos (1) y a cos cos sin sin cos (11) z We postulate the docking interface center of wrecked submarine is coordinate system O n X n Y n Z n, the position matrix N of the wrecked submarine s docking interface center can be regarded as O 1 X 1 Y 1 Z 1 which is respectively moving X n along the axis X 1, moving Y n along the axis Y 1 and moving Z n along the axis Z 1, rotate β 2 around the axis Y 1, rotate the β 1 around the axis X 1. N Trans( X, X ) Trans( Y, Y ) Trans( Z, Z ) Rot( Y, ) Rot( X, ) n n n cos 2 sin 1sin 2 sin 2cos 1 X n cos 1 sin 1 Y = n sin 2 sin 1cos 2 cos 1cos 2 Z n (12) By the above formula, the direction cosine of the axis Z unit principal vector of the coordinate system O n X n Y n Z n relative to the coordinate system O 1 X 1 Y 1 Z 1 is: N sin cos sin cos cos (13) Z The direction cosine of the axis Z unit principal vector of the coordinate system O 6 X 6 Y 6 Z 6 relative to the coordinate system O 1 X 1 Y 1 Z 1 is: a a a a 6 x y z (14) In order to ensure docking skirt interface and wrecked submarine interface parallel docking, should make: a Z (1) 6 N We can obtain directional skirt angle θ 1 and angle skirt angle θ 2 from equation (1): sin cos cos sin cos sin sin sin cos sin sin cos sin sin cos sin sin cos cos cos 1cos 2 sin1cos3 cos2 cos sin 1 3 (16) (17) In order to ensure the docking skirt interface and the wrecked submarine interface coincidence, the life-saving vehicle needs to travel distance is: Lx Xn P, x L y Y n P y, L z Z n P z (18) The optimal distance is obtained, as shown in Figure 4: min n x n y n z L X P Y P Z P (19) 4

5 MATEC Web of Conferences 114, 41 (217) DOI: 1.11/ matecconf/ MAE 217 Z6 X6 Y6 Lmin Docking interface of docking skirt Ly Lx Zn Xn Lz Yn Docking interface of wrecked submarine Figure 4. The best route for a lifeboat Determination of the range of rotary docking operations Because of the position of the wrecked submarine is random in the seabed. Therefore, it is need to get the rotation angle of the directional skirt and angle skirt when the wrecked submarine is in different heel angle and trim angle. It is assumed that the range of the heel angle and trim angle of the wrecked submarine is all ~6, and the samples were sampled at intervals of 1. In this article, γ 1 =6, γ 2 =9 and γ 3 =3. Based on the range of angle cosine of the directional skirt and angle skirt in the kinematics model above, using Matlab to program can get the angle of directional skirt and angle skirt, as shown in Figure and Figure 6. The angle of directional skirt θ2/( ) The heel angle of the wrecked submarine β1/( ) The trim angle of the wrecked submarineβ2/( ) The angle of angle skirtθ1/( ) The heel angle of the wrecked submarine β1/( ) The trim angle of the wrecked submarineβ2/( ) Figure. The angle of rotation by angle skirt Figure 6. The angle of rotation by directional skirt 6 Conclusion Through the study of the double spherical shell rotating docking skirt. And the fixed skirt, the directional skirt, the angle skirt are simplified as the connecting rod. We get the pose equation and the kinematic model by analyzing the working principle of the rotating docking skirt. The angle of rotation of the directional skirt and the angle skirt is obtained when the wrecked submarine is in different trim and heel angles. Through the directional skirt and angle skirt with the matching rotation can make docking skirt interface in the ~2γ range within the rotation, to complete the docking skirt and the wrecked submarine docking. The MATLAB software is used to visualize the rotation angle of

6 MATEC Web of Conferences 114, 41 (217) DOI: 1.11/ matecconf/ MAE 217 fixed skirt and directional skirt, and the correctness of the theoretical analysis of the rotary skirt docking is proved, which lays a good foundation for the development of the control of the double spherical shell rotating docking skirt in future. References 1. L. Q. WANG, D. D. TANG, J. R. Wu, Z. L. Zhang, Research on Structure and Kinematics of a Novel Mating Skirt on the Underwater Vehicle [J]. China Mechanical Engineering, 19, (28) 2. X. Y. Meng, W. Tian. Comments on the nuclear submarine escape and rescue system development of foreign countries [J]. Ship Science and Technology, 34, (212) 3. B. G. Fu, Q. X. Meng, H. M. Liu, Current situation and development trend of deep submergence rescue vehicles [J]. The Ocean Engineering, 2, (27) 4. Owen F. Submarine rescue with an Australian twang, indepth rescue [J]. A Newsletter for Submarine Rescue Professionals, 1, 1-6 (24). D. D. TANG, L. Q. WANG, Q. X. Meng, J. R. Wu, Z. L. Zhang, Structure design and carrying capacity analysis of mating skirt on the DSRV [J], 31, 1-4 (29) 6. X. Zhang, Z. L. Zheng, Y. Qi, Parameter Identification and Calibration of D-H Model for 6-DOF Serial Robots [J]. Robot, 38, (216) 7. Y. Gan, J. L. Wang, F. J. Sun, Optimal Design of D-H Parameters of a 6R Robot for a Prescribed Workspace [J]. China Mechanical Engineering, 2, (214) 8. F. Y. Guo, T. Mei, J. H. Zhao, Problems and Improvement of D-H Method for Establishing Connecting Rod Coordinate System [J]. China Mechanical Engineering, 2, (214) 6