Interaction Mechanical Analysis between the Lunar Rover Wheel-Leg Foot and Lunar Soil

Transcription

1 Availale olie at Proedia Egieerig Iteratioal Worshop o Iformatio ad Eletrois Egieerig IWIEE Iteratio Mehaial Aalysis etwee the Luar over Wheel-Leg Foot ad Luar Soil Xiao-liu Yu a,lei Fag a,ji-fu Liu a a* a Departmet of Mehaial Egieerig,Ahui Uiversity of Tehology, Ma asha 43,Chia Astrat Taig the Wheel-leg Foot of the doule-half-revolutio mehaism of luar rover as the researh ojets ad osiderig the mehais harateristis of luar soil, the iteratio of mehaial ehavior etwee Wheelleg Foot ad luar soil is preseted. Based o the press-siage ad shear model of soil, estalished the fore alae equatio of the Foot ad the stress model. By settig the parameters of the foot mehaism ad the properties of luar soil, the stress model was simulated. The relatioship urves aout the siage, the struture parameters of foot, the mehaial performae, slip rate ad struture parameters of foot are give. Pulished y Elsevier Ltd. Seletio ad/or peer-review uder resposiility of Hari Uiversity of Siee ad Tehology. Ope aess uder CC BY-NC-ND liese. Keyword:luar rover;doule-half-revolutio mehaism;terramehais;stress distriutio model;simulatio. Itrodutio The struture of luar rover wheel ad the iteratio mehaial properties etwee wheel ad luar soil have a importat impat o the movemet performae of the rover; to uderstad the aove harateristis play a importat role i desig the rover [,]. Some researhes aout the iteratio mehaial properties have ee doe, oe of the asi theory of wheel-terrai whih is widely used was proposed y Beer [3], o that asis, a great umer of researhes have ee doe: MIT, Duowsy et al.[4] derived the losed aalyti expressio aout wheel luar rover o the level of soft groud; Tohou Uiversity, Ishigami et al.[5] studied ostale apaity of wheel luar rover o the soft luar surfae. At the same time, Chia sholars have proposed some differet wheel ofiguratio ad doe appropriate aalysis. HIT, Ji-heg Liu et al.[6] proposed a drum type wheel ad made the iteratio mehaial aalysis etwee the wheel ad loose sady soil; HIT, Jia-guo Tao et al.[7] proposed a ew wheel with differet diameters ad doe mehaial aalysis ad experimets of wheel-soil iteratio of rollig wheels with differet diameters o a luar rover. * Correspodig author. Tel.: ; fax: address: waxiyu@ahut.edu Pulished y Elsevier Ltd. doi:.6/j.proeg Ope aess uder CC BY-NC-ND liese.

2 Xiao-liu Yu et al. / Proedia Egieerig Wheel-terra mehais have ee deeply studied, while the iteratio mehaial properties etwee the foot of the wheel-legged luar rover ad soft luar soil are seldom researhed, eve few a refer to. With the Wheel-legged Foot of the doule-half-revolutio mehaism of luar rover as the researh ojets i this paper, the iteratio mehaial properties of the foot o the soft soil was aalyed whe luar rover i motio ad mehaial model of rigid foot i the soft soil movemet was estalished, ad the simulatio aalysis was made.. Itrodutio of sigle wheel-legged ad foot mehaism Fig.. a Sigle wheel-legged mehaism; Feet mehaism The sigle wheel-legged assemly mehaism of wheel-legged luar rover o the asis of doule-half-revolutio mehaism show i figure [8,9], it osists of sigle wheel-legged mehaism ad foot mehaism. The simplified model of sigle wheel-legged mehaism is show i Fig.a, it maily omposed of wheel-leg raet, suspesio sprig, steerig motor, drive motor ad doule-half-revolutio mehaism. Doule-half-revolutio mehaism omposed of first swivelig arm, seod swivelig arm ad stridig rods. The simplified model of foot mehaism is show i Fig., it omposed of steerig joit ad spherial row type s foot. The wheel-legged luar rover is further desiged o the asis of doule-half-revolutio mehaism luar rover, the foot mehaism of the wheel-leg overome the deeper siage prolem whih geerated y doulehalf-revolutio mehaism diretly as wal mehaism, while otat area with the soft luar surfae ad fritio are ireased, thus drive apaility ad moility of luar rover are ireased. 3. The siage ad ompatio resistae aalysis 3.. Iteratio mehaial aalysis etwee siale rigid foot ad luar soil I worig oditio, uder the oditios of the siage ad ompatio resistae oly are osidered, assumptios are preseted:. the luar soil deformatio uder rigid foot is ureoverale.. The press-siage of soil uder the atio of rigid wheel ad the stress-strai relatios of soil uder the atio of Beer pressure proe are exatly the same []. The most importat fator whih affets the siage of the feet of wheel-legged luar rover is ormal stress, therefore, the mehaial relatioship etwee the rigid foot ad luar soil is researhed, the ormal stress must e maily osidered, the the mehaial relatioship model etwee the foot ad luar soil is estalished, as show i fig.. V is the luar rover veloity, W is load of a wheel-leg, is radius of the spherial row type s foot, is the maximum siage, is a siage withi the sope of the maximum siage, r is radius of dimesios roud o the type of spherial row foot at the siage of, A, A ad A 3 are there positios respetively at the movemet of foot, OA, OA ad OA 3 are oudaries, i the right side of those oudaries is the iteratio area etwee foot ad soil.

3 6 Xiao-liu Yu et al. / Proedia Egieerig Fig..Aalysis siage ad ompatio resistae of foot 3.. Mehaial model of siage ad ompatio resistae Kow y the assumptio, iteratio area etwee luar soil ad rigid foot is the right side of those oudaries, equivalet to the right side of the iteratio area etwee statioary foot ad luar soil, so the effetive legth of the rollig foot is oly half of the statioary foot, the effetive legth a e got y geometri relatioship, as writte i. Where, r a e got y geometri relatioship from the fig., as writte i. r r Kow y the assumptio, aordig to the press-siage model whih is estalished y Beer [3], ormal stress σ satisfies the followig relatios, as desried i 3. p ϕ σ 3 Where, is the ohesive modulus of luar soil deformatio, φ is the fritioal modulus of luar soil; is the effetive legth ad equals the. Kow the ormal stress o the rigid foot uder the oditios of the luar rover is movig ad the siage is, whih is geerated y iteratio of rigid foot ad luar soil, as desried i 4. ϕ σ 4 Thus, i the vertial diretio, the supportig fore of the etire foot is N, as desried i 5. Kow that the umerial of supportig fore N of the rigid foot whih luar soil applied o equals the load W s whih the wheel-leg earig at the positio A from the fig.. d d N ϕ σ 5 I the horiotal diretio, the ompatio resistae of the rigid foot whih luar soil applied o is F r, as desried i 5. d d F r ϕ σ 6 4. Cotat stress aalysis the relatioship etwee the rigid foot ad luar soil i the level

4 Xiao-liu Yu et al. / Proedia Egieerig I worig oditio, uder the oditios of the iteratio otat stress is aalyed, assumptio is preseted: the maximum stress is t prepositive alog with the rigid wheel rollig over o the groud. The iteratio stress model etwee the rigid foot ad the luar soil is estalished, as show i fig.3. θ is the approah agle, whih is the orrespodig etral agle of the wheel from the vertial positio to the first touhdow positio; θ is the departure agle, whih is the orrespodig etral agle of the wheel from the vertial positio to the lift-off positio. Their iteratio regio etwee the foot ad soil a e divided ito two oes: [, θ ] ad [, θ ]. θ is a agle etwee the two oes. The aove assumptio is that the maximum ormal stress ad shear stress our at the same positio orrespodig to. σ, σ are the ormal stress of the two oes, τ, τ are the shear stress of the two oes, is siage at the positio of agle θ, is the maximum siage at the positio of [, θ ], is the maximum siage at the positio of [, θ ], V is the luar rover veloity, ω is rotatio agle veloity of wheel-leg ad foot, T is a torque, F DP is horiotal fore, that is drivig fore. Fig. 3. otat stress aalysis Based o the Beer press-siage model ad Jaosi shear model, the otat stress model of the foot a e estalished, ad writte i 7 ad 8. σ θ osθ os θ θ θ θ σ θ os θ os θ θ θ ϕ ϕ θ 7 [ θ θ s si θ si θ ] τ θ σ ta ϕ e 8 θ Where, is the ohesio of luar soil, is the shear deformatio modulus of luar soil, φ is the iteral fritio agle of luar soil, s is the slip ratio of feet., φ, ad osistet with the aove. Aordig to the fore equilirium relatioship, the dyamis equatios of the sigle rigid foot a e estalished, ad writte i 9, ad. W is the supportig fore. θ θ 9 W [ [ σ θ si θ osθ τ θ si θ ] dθ [ σ θ si θ osθ τ θ si θ ] dθ ] θ θ F [ [ τ θsiθ osθ- σ θsi θ] dθ [ τ θsiθ os θ σ θsi θ] dθ] DP θ T l τ θ si θ θ d θ Where, l is the legth of stridig rod. By simplified mehaial model, aordig to 7 -, the variales W, F DP ad T a e alulated. 5. Simulatio aalysis

5 6 Xiao-liu Yu et al. / Proedia Egieerig I order to aalye the mehaial properties of the foot of the doule-half-revolutio wheellegged luar rover, the mehaial parameters of the foot is simulated ad alulated y MATLAB programmig simulatio. Luar soil harateristi parameters are give i Tale, as i []. The weight of sigle wheel-leg is aout 5g. Tale. Luar soil parameters Aeleratio gm s - Siage oeffiiet Fritioal modulus φ N m - Cohesive modulus N m Shear deformatio modulusm Cohesio Pa Iteral fritio agle φ Feet siage aalysis Give the vertial load W ad differet radius suh as 4mm, 45mm, 5mm, the foot siage is determied aordig to -5, ad their relatioship urve is show i Fig.4.a. Simulatio shows: whe the luar rover veloity V is ertai, as the vertial load W ireasig, the siage is ireasig; whe the load is ertai, as the foot radius ireasig, the siage is dereasig. 5.. Aalysis of drivig fore Give the slip ratio s ad the vertial load W, the drivig fore F DP is determied aordig to 7-, ad their relatioship urve is show i Fig.4.. Simulatio shows: whe the luar rover veloity V is ertai, as the load W ireasig, the drivig fore F DP is ireasig; whe the load W is ertai, as the slip ratio s ireasig, the drivig fore F DP is dereasig. Give the slip ratio s ad the foot radius, the drivig fore F DP is determied aordig to 7-8 ad, ad their relatioship urve is show i Fig.4.. Simulatio shows: as the slip ratio s ireasig, the drivig fore F DP is ireasig; whe the slip ratio s is less tha., as the foot radius ireasig, the drivig fore F DP is dereasig, whe the slip ratio s is more tha or equal to., as the foot radius ireasig, the drivig fore F DP is ireasig Aalysis of the drivig torque Give the slip ratio s ad the foot radius, the drivig torque T is determied aordig to 7-8 ad, ad their relatioship urve is show i Fig.4.d. Simulatio shows: whe the luar rover veloity V ad the sigle wheel-leg load W is ertai, as the slip ratio s ireasig, the drivig torque T is ireasig; whe the slip ratio s is less tha., as the foot radius ireasig, the drivig torque T is dereasig, whe the slip ratio s is more tha or equal to., as the foot radius ireasig, the drivig fore F DP is ireasig. 6. Colusios Based o the traditioal theory of the terramehais, iteratio mehaial properties etwee the feet of wheel-legged luar rover are aalyed. The siage ad ompatio resistae mehaial model ad the iteratio mehaial model etwee the foot ad luar rover are estalished respetively, dyami formulas for alulatig mehaial parameters are derived. By give some relative parameters of the foot ad luar soil, mehaial parameters are alulatio ad aalyed. Simulatio shows: i ertai oditios, as the load ireasig, the foot siage is ireasig; as the load, the slip ratio ad the foot radius ireasig, drivig fore is ireasig; as the slip ratio ad the foot radius ireasig, the drivig torque is ireasig.

6 Xiao-liu Yu et al. / Proedia Egieerig Fig. 4. a elatioship urve of W, ad ; elatioship urve of W, S ad F DP ; elatioship urve of s, ad F DP ; d elatioship urve of s, ad T Aowledgemets This wor is supported y the Natioal Natural Siee Foudatio of Chia No.55, the fud of the ey iovatio projet grated y the Miistry of Eduatio of Chia No.7854 ad the ey projet of Ahui Eduatio Departmet i Chia No.KJA46. eferees [] Jiaguo Tao, Li Wag, Fegjiu Wu ad Zogqua Deg. Mehaial aalysis of wheel-soil iteratio of luar rover. Mahiery Desig & Maufature 6;: [] Meg Zou, Jiaqiao Li, Yiwu Li, Yag Jia, Wehe Ma. Iteratio preditio model etwee rigid wheel ad luar soil ad experimetal researh. Trasatio of the CSAE 7;3:9-3. [3] Beer G. Itrodutio to terrai-vehile systems. Mihiga: Uiversity of Mihiga Press; 969. [4] Shily H, Iagemma K, Duowsy S. A equivalet soil mehais formulatio for rigid wheels i deformale terrai with appliatio to plaetary exploratio rovers. Joural of Teramehais 5;4:-3. [5] Ishigami G, Miwa A, Nagatai K, et al. Terramehais-ased model for steerig maeuver of plaetary exploratio rovers o loose soil. Joural of Field ootis 7;4:33-5. [6] Jiheg Liu, Haio Gao, Zogqua Deg, Zhefa Bi, Yuhua Zhag. Mehaial aalysis of a drum type wheel rollig o loose sady soil. Joural of Hari Egieerig Uiversity, 9;3:9-34. [7] Jiaguo Tao, Qiqua Qua, Wede Zhao, ogqua Deg. Aalysis of wheel-soil iteratio of rollig wheels with differet diameters o a luar rover. Joural of Hari Egieerig Uiversity 7;8: [8] Xiaoliu Yu, Hui Luo, Wei Xia. A study o the displaemet system of luar rover ad its udulatio ased o semiturig mehaism. Joural of mahie desig 8;5:-3. [9] Xiaoliu Yu, Xiaoli Du, Yogmig Wag. Stati aalysis of the sigle-wheel-legged Mehaism of a Luar rover ased o a doule-half-revolutio mehaism. Mehaial Siee ad Tehology for Aerospae Egieerig ;3: [] Kejia Zhag. Vehile-Terramehais. Beijig: Natioal defese idustry press;. [] Natioal Aeroautis ad Spae Admiistratio. Nasa Spae Vehile Desig Criteria Eviromet: Luar Surfae Models[].Nasa:969.p.7-3.